(0) Obligation:
Relative term rewrite system:
The relative TRS consists of the following R rules:
g(s(x), y) → g(f(x, y), y)
The relative TRS consists of the following S rules:
f(x, y) → f(x, s(y))
f(x, y) → x
(1) FlatCCProof (EQUIVALENT transformation)
We used flat context closure [ROOTLAB]
(2) Obligation:
Relative term rewrite system:
The relative TRS consists of the following R rules:
g(s(x), y) → g(f(x, y), y)
The relative TRS consists of the following S rules:
f(x, y) → f(x, s(y))
g(f(x, y), z1) → g(x, z1)
g(z0, f(x, y)) → g(z0, x)
s(f(x, y)) → s(x)
f(f(x, y), z1) → f(x, z1)
f(z0, f(x, y)) → f(z0, x)
(3) RootLabelingProof (EQUIVALENT transformation)
We used plain root labeling [ROOTLAB] with the following heuristic:
LabelAll: All function symbols get labeled
(4) Obligation:
Relative term rewrite system:
The relative TRS consists of the following R rules:
g_{s_1,g_2}(s_{g_2}(x), y) → g_{f_2,g_2}(f_{g_2,g_2}(x, y), y)
g_{s_1,s_1}(s_{g_2}(x), y) → g_{f_2,s_1}(f_{g_2,s_1}(x, y), y)
g_{s_1,f_2}(s_{g_2}(x), y) → g_{f_2,f_2}(f_{g_2,f_2}(x, y), y)
g_{s_1,g_2}(s_{s_1}(x), y) → g_{f_2,g_2}(f_{s_1,g_2}(x, y), y)
g_{s_1,s_1}(s_{s_1}(x), y) → g_{f_2,s_1}(f_{s_1,s_1}(x, y), y)
g_{s_1,f_2}(s_{s_1}(x), y) → g_{f_2,f_2}(f_{s_1,f_2}(x, y), y)
g_{s_1,g_2}(s_{f_2}(x), y) → g_{f_2,g_2}(f_{f_2,g_2}(x, y), y)
g_{s_1,s_1}(s_{f_2}(x), y) → g_{f_2,s_1}(f_{f_2,s_1}(x, y), y)
g_{s_1,f_2}(s_{f_2}(x), y) → g_{f_2,f_2}(f_{f_2,f_2}(x, y), y)
The relative TRS consists of the following S rules:
f_{g_2,g_2}(x, y) → f_{g_2,s_1}(x, s_{g_2}(y))
f_{g_2,s_1}(x, y) → f_{g_2,s_1}(x, s_{s_1}(y))
f_{g_2,f_2}(x, y) → f_{g_2,s_1}(x, s_{f_2}(y))
f_{s_1,g_2}(x, y) → f_{s_1,s_1}(x, s_{g_2}(y))
f_{s_1,s_1}(x, y) → f_{s_1,s_1}(x, s_{s_1}(y))
f_{s_1,f_2}(x, y) → f_{s_1,s_1}(x, s_{f_2}(y))
f_{f_2,g_2}(x, y) → f_{f_2,s_1}(x, s_{g_2}(y))
f_{f_2,s_1}(x, y) → f_{f_2,s_1}(x, s_{s_1}(y))
f_{f_2,f_2}(x, y) → f_{f_2,s_1}(x, s_{f_2}(y))
g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1) → g_{g_2,g_2}(x, z1)
g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1) → g_{g_2,s_1}(x, z1)
g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1) → g_{g_2,f_2}(x, z1)
g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1) → g_{g_2,g_2}(x, z1)
g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1) → g_{g_2,s_1}(x, z1)
g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1) → g_{g_2,f_2}(x, z1)
g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1) → g_{g_2,g_2}(x, z1)
g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1) → g_{g_2,s_1}(x, z1)
g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1) → g_{g_2,f_2}(x, z1)
g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1) → g_{s_1,g_2}(x, z1)
g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1) → g_{s_1,s_1}(x, z1)
g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1) → g_{s_1,f_2}(x, z1)
g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1) → g_{s_1,g_2}(x, z1)
g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1) → g_{s_1,s_1}(x, z1)
g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1) → g_{s_1,f_2}(x, z1)
g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1) → g_{s_1,g_2}(x, z1)
g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1) → g_{s_1,s_1}(x, z1)
g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1) → g_{s_1,f_2}(x, z1)
g_{f_2,g_2}(f_{f_2,g_2}(x, y), z1) → g_{f_2,g_2}(x, z1)
g_{f_2,s_1}(f_{f_2,g_2}(x, y), z1) → g_{f_2,s_1}(x, z1)
g_{f_2,f_2}(f_{f_2,g_2}(x, y), z1) → g_{f_2,f_2}(x, z1)
g_{f_2,g_2}(f_{f_2,s_1}(x, y), z1) → g_{f_2,g_2}(x, z1)
g_{f_2,s_1}(f_{f_2,s_1}(x, y), z1) → g_{f_2,s_1}(x, z1)
g_{f_2,f_2}(f_{f_2,s_1}(x, y), z1) → g_{f_2,f_2}(x, z1)
g_{f_2,g_2}(f_{f_2,f_2}(x, y), z1) → g_{f_2,g_2}(x, z1)
g_{f_2,s_1}(f_{f_2,f_2}(x, y), z1) → g_{f_2,s_1}(x, z1)
g_{f_2,f_2}(f_{f_2,f_2}(x, y), z1) → g_{f_2,f_2}(x, z1)
g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)) → g_{g_2,g_2}(z0, x)
g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)) → g_{g_2,g_2}(z0, x)
g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)) → g_{g_2,g_2}(z0, x)
g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)) → g_{g_2,s_1}(z0, x)
g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)) → g_{g_2,s_1}(z0, x)
g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)) → g_{g_2,s_1}(z0, x)
g_{g_2,f_2}(z0, f_{f_2,g_2}(x, y)) → g_{g_2,f_2}(z0, x)
g_{g_2,f_2}(z0, f_{f_2,s_1}(x, y)) → g_{g_2,f_2}(z0, x)
g_{g_2,f_2}(z0, f_{f_2,f_2}(x, y)) → g_{g_2,f_2}(z0, x)
g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)) → g_{s_1,g_2}(z0, x)
g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)) → g_{s_1,g_2}(z0, x)
g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)) → g_{s_1,g_2}(z0, x)
g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)) → g_{s_1,s_1}(z0, x)
g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)) → g_{s_1,s_1}(z0, x)
g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)) → g_{s_1,s_1}(z0, x)
g_{s_1,f_2}(z0, f_{f_2,g_2}(x, y)) → g_{s_1,f_2}(z0, x)
g_{s_1,f_2}(z0, f_{f_2,s_1}(x, y)) → g_{s_1,f_2}(z0, x)
g_{s_1,f_2}(z0, f_{f_2,f_2}(x, y)) → g_{s_1,f_2}(z0, x)
g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)) → g_{f_2,g_2}(z0, x)
g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)) → g_{f_2,g_2}(z0, x)
g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)) → g_{f_2,g_2}(z0, x)
g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)) → g_{f_2,s_1}(z0, x)
g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)) → g_{f_2,s_1}(z0, x)
g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)) → g_{f_2,s_1}(z0, x)
g_{f_2,f_2}(z0, f_{f_2,g_2}(x, y)) → g_{f_2,f_2}(z0, x)
g_{f_2,f_2}(z0, f_{f_2,s_1}(x, y)) → g_{f_2,f_2}(z0, x)
g_{f_2,f_2}(z0, f_{f_2,f_2}(x, y)) → g_{f_2,f_2}(z0, x)
s_{f_2}(f_{g_2,g_2}(x, y)) → s_{g_2}(x)
s_{f_2}(f_{g_2,s_1}(x, y)) → s_{g_2}(x)
s_{f_2}(f_{g_2,f_2}(x, y)) → s_{g_2}(x)
s_{f_2}(f_{s_1,g_2}(x, y)) → s_{s_1}(x)
s_{f_2}(f_{s_1,s_1}(x, y)) → s_{s_1}(x)
s_{f_2}(f_{s_1,f_2}(x, y)) → s_{s_1}(x)
s_{f_2}(f_{f_2,g_2}(x, y)) → s_{f_2}(x)
s_{f_2}(f_{f_2,s_1}(x, y)) → s_{f_2}(x)
s_{f_2}(f_{f_2,f_2}(x, y)) → s_{f_2}(x)
f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1) → f_{g_2,g_2}(x, z1)
f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1) → f_{g_2,s_1}(x, z1)
f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1) → f_{g_2,f_2}(x, z1)
f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1) → f_{g_2,g_2}(x, z1)
f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1) → f_{g_2,s_1}(x, z1)
f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1) → f_{g_2,f_2}(x, z1)
f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1) → f_{g_2,g_2}(x, z1)
f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1) → f_{g_2,s_1}(x, z1)
f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1) → f_{g_2,f_2}(x, z1)
f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1) → f_{s_1,g_2}(x, z1)
f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1) → f_{s_1,s_1}(x, z1)
f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1) → f_{s_1,f_2}(x, z1)
f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1) → f_{s_1,g_2}(x, z1)
f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1) → f_{s_1,s_1}(x, z1)
f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1) → f_{s_1,f_2}(x, z1)
f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1) → f_{s_1,g_2}(x, z1)
f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1) → f_{s_1,s_1}(x, z1)
f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1) → f_{s_1,f_2}(x, z1)
f_{f_2,g_2}(f_{f_2,g_2}(x, y), z1) → f_{f_2,g_2}(x, z1)
f_{f_2,s_1}(f_{f_2,g_2}(x, y), z1) → f_{f_2,s_1}(x, z1)
f_{f_2,f_2}(f_{f_2,g_2}(x, y), z1) → f_{f_2,f_2}(x, z1)
f_{f_2,g_2}(f_{f_2,s_1}(x, y), z1) → f_{f_2,g_2}(x, z1)
f_{f_2,s_1}(f_{f_2,s_1}(x, y), z1) → f_{f_2,s_1}(x, z1)
f_{f_2,f_2}(f_{f_2,s_1}(x, y), z1) → f_{f_2,f_2}(x, z1)
f_{f_2,g_2}(f_{f_2,f_2}(x, y), z1) → f_{f_2,g_2}(x, z1)
f_{f_2,s_1}(f_{f_2,f_2}(x, y), z1) → f_{f_2,s_1}(x, z1)
f_{f_2,f_2}(f_{f_2,f_2}(x, y), z1) → f_{f_2,f_2}(x, z1)
f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)) → f_{g_2,g_2}(z0, x)
f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)) → f_{g_2,g_2}(z0, x)
f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)) → f_{g_2,g_2}(z0, x)
f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)) → f_{g_2,s_1}(z0, x)
f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)) → f_{g_2,s_1}(z0, x)
f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)) → f_{g_2,s_1}(z0, x)
f_{g_2,f_2}(z0, f_{f_2,g_2}(x, y)) → f_{g_2,f_2}(z0, x)
f_{g_2,f_2}(z0, f_{f_2,s_1}(x, y)) → f_{g_2,f_2}(z0, x)
f_{g_2,f_2}(z0, f_{f_2,f_2}(x, y)) → f_{g_2,f_2}(z0, x)
f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)) → f_{s_1,g_2}(z0, x)
f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)) → f_{s_1,g_2}(z0, x)
f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)) → f_{s_1,g_2}(z0, x)
f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)) → f_{s_1,s_1}(z0, x)
f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)) → f_{s_1,s_1}(z0, x)
f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)) → f_{s_1,s_1}(z0, x)
f_{s_1,f_2}(z0, f_{f_2,g_2}(x, y)) → f_{s_1,f_2}(z0, x)
f_{s_1,f_2}(z0, f_{f_2,s_1}(x, y)) → f_{s_1,f_2}(z0, x)
f_{s_1,f_2}(z0, f_{f_2,f_2}(x, y)) → f_{s_1,f_2}(z0, x)
f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)) → f_{f_2,g_2}(z0, x)
f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)) → f_{f_2,g_2}(z0, x)
f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)) → f_{f_2,g_2}(z0, x)
f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)) → f_{f_2,s_1}(z0, x)
f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)) → f_{f_2,s_1}(z0, x)
f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)) → f_{f_2,s_1}(z0, x)
f_{f_2,f_2}(z0, f_{f_2,g_2}(x, y)) → f_{f_2,f_2}(z0, x)
f_{f_2,f_2}(z0, f_{f_2,s_1}(x, y)) → f_{f_2,f_2}(z0, x)
f_{f_2,f_2}(z0, f_{f_2,f_2}(x, y)) → f_{f_2,f_2}(z0, x)
(5) FlatCCProof (EQUIVALENT transformation)
We used flat context closure [ROOTLAB]
(6) Obligation:
Relative term rewrite system:
The relative TRS consists of the following R rules:
g_{s_1,g_2}(g_{s_1,g_2}(s_{g_2}(x), y), z10) → g_{s_1,g_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), y), z10)
g_{s_1,g_2}(z00, g_{s_1,g_2}(s_{g_2}(x), y)) → g_{s_1,g_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), y))
s_{g_2}(g_{s_1,g_2}(s_{g_2}(x), y)) → s_{g_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), y))
g_{f_2,g_2}(g_{s_1,g_2}(s_{g_2}(x), y), z10) → g_{f_2,g_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), y), z10)
g_{f_2,g_2}(z00, g_{s_1,g_2}(s_{g_2}(x), y)) → g_{f_2,g_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), y))
f_{g_2,g_2}(g_{s_1,g_2}(s_{g_2}(x), y), z10) → f_{g_2,g_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), y), z10)
f_{g_2,g_2}(z00, g_{s_1,g_2}(s_{g_2}(x), y)) → f_{g_2,g_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), y))
g_{s_1,s_1}(g_{s_1,g_2}(s_{g_2}(x), y), z10) → g_{s_1,s_1}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), y), z10)
g_{s_1,s_1}(z00, g_{s_1,g_2}(s_{g_2}(x), y)) → g_{s_1,s_1}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), y))
g_{f_2,s_1}(g_{s_1,g_2}(s_{g_2}(x), y), z10) → g_{f_2,s_1}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), y), z10)
g_{f_2,s_1}(z00, g_{s_1,g_2}(s_{g_2}(x), y)) → g_{f_2,s_1}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), y))
f_{g_2,s_1}(g_{s_1,g_2}(s_{g_2}(x), y), z10) → f_{g_2,s_1}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), y), z10)
f_{g_2,s_1}(z00, g_{s_1,g_2}(s_{g_2}(x), y)) → f_{g_2,s_1}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), y))
g_{s_1,f_2}(g_{s_1,g_2}(s_{g_2}(x), y), z10) → g_{s_1,f_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), y), z10)
g_{s_1,f_2}(z00, g_{s_1,g_2}(s_{g_2}(x), y)) → g_{s_1,f_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), y))
g_{f_2,f_2}(g_{s_1,g_2}(s_{g_2}(x), y), z10) → g_{f_2,f_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), y), z10)
g_{f_2,f_2}(z00, g_{s_1,g_2}(s_{g_2}(x), y)) → g_{f_2,f_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), y))
f_{g_2,f_2}(g_{s_1,g_2}(s_{g_2}(x), y), z10) → f_{g_2,f_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), y), z10)
f_{g_2,f_2}(z00, g_{s_1,g_2}(s_{g_2}(x), y)) → f_{g_2,f_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), y))
s_{s_1}(g_{s_1,g_2}(s_{g_2}(x), y)) → s_{s_1}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), y))
f_{s_1,g_2}(g_{s_1,g_2}(s_{g_2}(x), y), z10) → f_{s_1,g_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), y), z10)
f_{s_1,g_2}(z00, g_{s_1,g_2}(s_{g_2}(x), y)) → f_{s_1,g_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), y))
f_{s_1,s_1}(g_{s_1,g_2}(s_{g_2}(x), y), z10) → f_{s_1,s_1}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), y), z10)
f_{s_1,s_1}(z00, g_{s_1,g_2}(s_{g_2}(x), y)) → f_{s_1,s_1}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), y))
f_{s_1,f_2}(g_{s_1,g_2}(s_{g_2}(x), y), z10) → f_{s_1,f_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), y), z10)
f_{s_1,f_2}(z00, g_{s_1,g_2}(s_{g_2}(x), y)) → f_{s_1,f_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), y))
s_{f_2}(g_{s_1,g_2}(s_{g_2}(x), y)) → s_{f_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), y))
f_{f_2,g_2}(g_{s_1,g_2}(s_{g_2}(x), y), z10) → f_{f_2,g_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), y), z10)
f_{f_2,g_2}(z00, g_{s_1,g_2}(s_{g_2}(x), y)) → f_{f_2,g_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), y))
f_{f_2,s_1}(g_{s_1,g_2}(s_{g_2}(x), y), z10) → f_{f_2,s_1}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), y), z10)
f_{f_2,s_1}(z00, g_{s_1,g_2}(s_{g_2}(x), y)) → f_{f_2,s_1}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), y))
f_{f_2,f_2}(g_{s_1,g_2}(s_{g_2}(x), y), z10) → f_{f_2,f_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), y), z10)
f_{f_2,f_2}(z00, g_{s_1,g_2}(s_{g_2}(x), y)) → f_{f_2,f_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), y))
g_{g_2,g_2}(g_{s_1,g_2}(s_{g_2}(x), y), z10) → g_{g_2,g_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), y), z10)
g_{g_2,g_2}(z00, g_{s_1,g_2}(s_{g_2}(x), y)) → g_{g_2,g_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), y))
g_{g_2,s_1}(g_{s_1,g_2}(s_{g_2}(x), y), z10) → g_{g_2,s_1}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), y), z10)
g_{g_2,s_1}(z00, g_{s_1,g_2}(s_{g_2}(x), y)) → g_{g_2,s_1}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), y))
g_{g_2,f_2}(g_{s_1,g_2}(s_{g_2}(x), y), z10) → g_{g_2,f_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), y), z10)
g_{g_2,f_2}(z00, g_{s_1,g_2}(s_{g_2}(x), y)) → g_{g_2,f_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), y))
g_{s_1,g_2}(g_{s_1,s_1}(s_{g_2}(x), y), z10) → g_{s_1,g_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), y), z10)
g_{s_1,g_2}(z00, g_{s_1,s_1}(s_{g_2}(x), y)) → g_{s_1,g_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), y))
s_{g_2}(g_{s_1,s_1}(s_{g_2}(x), y)) → s_{g_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), y))
g_{f_2,g_2}(g_{s_1,s_1}(s_{g_2}(x), y), z10) → g_{f_2,g_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), y), z10)
g_{f_2,g_2}(z00, g_{s_1,s_1}(s_{g_2}(x), y)) → g_{f_2,g_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), y))
f_{g_2,g_2}(g_{s_1,s_1}(s_{g_2}(x), y), z10) → f_{g_2,g_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), y), z10)
f_{g_2,g_2}(z00, g_{s_1,s_1}(s_{g_2}(x), y)) → f_{g_2,g_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), y))
g_{s_1,s_1}(g_{s_1,s_1}(s_{g_2}(x), y), z10) → g_{s_1,s_1}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), y), z10)
g_{s_1,s_1}(z00, g_{s_1,s_1}(s_{g_2}(x), y)) → g_{s_1,s_1}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), y))
g_{f_2,s_1}(g_{s_1,s_1}(s_{g_2}(x), y), z10) → g_{f_2,s_1}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), y), z10)
g_{f_2,s_1}(z00, g_{s_1,s_1}(s_{g_2}(x), y)) → g_{f_2,s_1}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), y))
f_{g_2,s_1}(g_{s_1,s_1}(s_{g_2}(x), y), z10) → f_{g_2,s_1}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), y), z10)
f_{g_2,s_1}(z00, g_{s_1,s_1}(s_{g_2}(x), y)) → f_{g_2,s_1}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), y))
g_{s_1,f_2}(g_{s_1,s_1}(s_{g_2}(x), y), z10) → g_{s_1,f_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), y), z10)
g_{s_1,f_2}(z00, g_{s_1,s_1}(s_{g_2}(x), y)) → g_{s_1,f_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), y))
g_{f_2,f_2}(g_{s_1,s_1}(s_{g_2}(x), y), z10) → g_{f_2,f_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), y), z10)
g_{f_2,f_2}(z00, g_{s_1,s_1}(s_{g_2}(x), y)) → g_{f_2,f_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), y))
f_{g_2,f_2}(g_{s_1,s_1}(s_{g_2}(x), y), z10) → f_{g_2,f_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), y), z10)
f_{g_2,f_2}(z00, g_{s_1,s_1}(s_{g_2}(x), y)) → f_{g_2,f_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), y))
s_{s_1}(g_{s_1,s_1}(s_{g_2}(x), y)) → s_{s_1}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), y))
f_{s_1,g_2}(g_{s_1,s_1}(s_{g_2}(x), y), z10) → f_{s_1,g_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), y), z10)
f_{s_1,g_2}(z00, g_{s_1,s_1}(s_{g_2}(x), y)) → f_{s_1,g_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), y))
f_{s_1,s_1}(g_{s_1,s_1}(s_{g_2}(x), y), z10) → f_{s_1,s_1}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), y), z10)
f_{s_1,s_1}(z00, g_{s_1,s_1}(s_{g_2}(x), y)) → f_{s_1,s_1}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), y))
f_{s_1,f_2}(g_{s_1,s_1}(s_{g_2}(x), y), z10) → f_{s_1,f_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), y), z10)
f_{s_1,f_2}(z00, g_{s_1,s_1}(s_{g_2}(x), y)) → f_{s_1,f_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), y))
s_{f_2}(g_{s_1,s_1}(s_{g_2}(x), y)) → s_{f_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), y))
f_{f_2,g_2}(g_{s_1,s_1}(s_{g_2}(x), y), z10) → f_{f_2,g_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), y), z10)
f_{f_2,g_2}(z00, g_{s_1,s_1}(s_{g_2}(x), y)) → f_{f_2,g_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), y))
f_{f_2,s_1}(g_{s_1,s_1}(s_{g_2}(x), y), z10) → f_{f_2,s_1}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), y), z10)
f_{f_2,s_1}(z00, g_{s_1,s_1}(s_{g_2}(x), y)) → f_{f_2,s_1}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), y))
f_{f_2,f_2}(g_{s_1,s_1}(s_{g_2}(x), y), z10) → f_{f_2,f_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), y), z10)
f_{f_2,f_2}(z00, g_{s_1,s_1}(s_{g_2}(x), y)) → f_{f_2,f_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), y))
g_{g_2,g_2}(g_{s_1,s_1}(s_{g_2}(x), y), z10) → g_{g_2,g_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), y), z10)
g_{g_2,g_2}(z00, g_{s_1,s_1}(s_{g_2}(x), y)) → g_{g_2,g_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), y))
g_{g_2,s_1}(g_{s_1,s_1}(s_{g_2}(x), y), z10) → g_{g_2,s_1}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), y), z10)
g_{g_2,s_1}(z00, g_{s_1,s_1}(s_{g_2}(x), y)) → g_{g_2,s_1}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), y))
g_{g_2,f_2}(g_{s_1,s_1}(s_{g_2}(x), y), z10) → g_{g_2,f_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), y), z10)
g_{g_2,f_2}(z00, g_{s_1,s_1}(s_{g_2}(x), y)) → g_{g_2,f_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), y))
g_{s_1,g_2}(g_{s_1,f_2}(s_{g_2}(x), y), z10) → g_{s_1,g_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), y), z10)
g_{s_1,g_2}(z00, g_{s_1,f_2}(s_{g_2}(x), y)) → g_{s_1,g_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), y))
s_{g_2}(g_{s_1,f_2}(s_{g_2}(x), y)) → s_{g_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), y))
g_{f_2,g_2}(g_{s_1,f_2}(s_{g_2}(x), y), z10) → g_{f_2,g_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), y), z10)
g_{f_2,g_2}(z00, g_{s_1,f_2}(s_{g_2}(x), y)) → g_{f_2,g_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), y))
f_{g_2,g_2}(g_{s_1,f_2}(s_{g_2}(x), y), z10) → f_{g_2,g_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), y), z10)
f_{g_2,g_2}(z00, g_{s_1,f_2}(s_{g_2}(x), y)) → f_{g_2,g_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), y))
g_{s_1,s_1}(g_{s_1,f_2}(s_{g_2}(x), y), z10) → g_{s_1,s_1}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), y), z10)
g_{s_1,s_1}(z00, g_{s_1,f_2}(s_{g_2}(x), y)) → g_{s_1,s_1}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), y))
g_{f_2,s_1}(g_{s_1,f_2}(s_{g_2}(x), y), z10) → g_{f_2,s_1}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), y), z10)
g_{f_2,s_1}(z00, g_{s_1,f_2}(s_{g_2}(x), y)) → g_{f_2,s_1}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), y))
f_{g_2,s_1}(g_{s_1,f_2}(s_{g_2}(x), y), z10) → f_{g_2,s_1}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), y), z10)
f_{g_2,s_1}(z00, g_{s_1,f_2}(s_{g_2}(x), y)) → f_{g_2,s_1}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), y))
g_{s_1,f_2}(g_{s_1,f_2}(s_{g_2}(x), y), z10) → g_{s_1,f_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), y), z10)
g_{s_1,f_2}(z00, g_{s_1,f_2}(s_{g_2}(x), y)) → g_{s_1,f_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), y))
g_{f_2,f_2}(g_{s_1,f_2}(s_{g_2}(x), y), z10) → g_{f_2,f_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), y), z10)
g_{f_2,f_2}(z00, g_{s_1,f_2}(s_{g_2}(x), y)) → g_{f_2,f_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), y))
f_{g_2,f_2}(g_{s_1,f_2}(s_{g_2}(x), y), z10) → f_{g_2,f_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), y), z10)
f_{g_2,f_2}(z00, g_{s_1,f_2}(s_{g_2}(x), y)) → f_{g_2,f_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), y))
s_{s_1}(g_{s_1,f_2}(s_{g_2}(x), y)) → s_{s_1}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), y))
f_{s_1,g_2}(g_{s_1,f_2}(s_{g_2}(x), y), z10) → f_{s_1,g_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), y), z10)
f_{s_1,g_2}(z00, g_{s_1,f_2}(s_{g_2}(x), y)) → f_{s_1,g_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), y))
f_{s_1,s_1}(g_{s_1,f_2}(s_{g_2}(x), y), z10) → f_{s_1,s_1}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), y), z10)
f_{s_1,s_1}(z00, g_{s_1,f_2}(s_{g_2}(x), y)) → f_{s_1,s_1}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), y))
f_{s_1,f_2}(g_{s_1,f_2}(s_{g_2}(x), y), z10) → f_{s_1,f_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), y), z10)
f_{s_1,f_2}(z00, g_{s_1,f_2}(s_{g_2}(x), y)) → f_{s_1,f_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), y))
s_{f_2}(g_{s_1,f_2}(s_{g_2}(x), y)) → s_{f_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), y))
f_{f_2,g_2}(g_{s_1,f_2}(s_{g_2}(x), y), z10) → f_{f_2,g_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), y), z10)
f_{f_2,g_2}(z00, g_{s_1,f_2}(s_{g_2}(x), y)) → f_{f_2,g_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), y))
f_{f_2,s_1}(g_{s_1,f_2}(s_{g_2}(x), y), z10) → f_{f_2,s_1}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), y), z10)
f_{f_2,s_1}(z00, g_{s_1,f_2}(s_{g_2}(x), y)) → f_{f_2,s_1}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), y))
f_{f_2,f_2}(g_{s_1,f_2}(s_{g_2}(x), y), z10) → f_{f_2,f_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), y), z10)
f_{f_2,f_2}(z00, g_{s_1,f_2}(s_{g_2}(x), y)) → f_{f_2,f_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), y))
g_{g_2,g_2}(g_{s_1,f_2}(s_{g_2}(x), y), z10) → g_{g_2,g_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), y), z10)
g_{g_2,g_2}(z00, g_{s_1,f_2}(s_{g_2}(x), y)) → g_{g_2,g_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), y))
g_{g_2,s_1}(g_{s_1,f_2}(s_{g_2}(x), y), z10) → g_{g_2,s_1}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), y), z10)
g_{g_2,s_1}(z00, g_{s_1,f_2}(s_{g_2}(x), y)) → g_{g_2,s_1}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), y))
g_{g_2,f_2}(g_{s_1,f_2}(s_{g_2}(x), y), z10) → g_{g_2,f_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), y), z10)
g_{g_2,f_2}(z00, g_{s_1,f_2}(s_{g_2}(x), y)) → g_{g_2,f_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), y))
g_{s_1,g_2}(g_{s_1,g_2}(s_{s_1}(x), y), z10) → g_{s_1,g_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), y), z10)
g_{s_1,g_2}(z00, g_{s_1,g_2}(s_{s_1}(x), y)) → g_{s_1,g_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), y))
s_{g_2}(g_{s_1,g_2}(s_{s_1}(x), y)) → s_{g_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), y))
g_{f_2,g_2}(g_{s_1,g_2}(s_{s_1}(x), y), z10) → g_{f_2,g_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), y), z10)
g_{f_2,g_2}(z00, g_{s_1,g_2}(s_{s_1}(x), y)) → g_{f_2,g_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), y))
f_{g_2,g_2}(g_{s_1,g_2}(s_{s_1}(x), y), z10) → f_{g_2,g_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), y), z10)
f_{g_2,g_2}(z00, g_{s_1,g_2}(s_{s_1}(x), y)) → f_{g_2,g_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), y))
g_{s_1,s_1}(g_{s_1,g_2}(s_{s_1}(x), y), z10) → g_{s_1,s_1}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), y), z10)
g_{s_1,s_1}(z00, g_{s_1,g_2}(s_{s_1}(x), y)) → g_{s_1,s_1}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), y))
g_{f_2,s_1}(g_{s_1,g_2}(s_{s_1}(x), y), z10) → g_{f_2,s_1}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), y), z10)
g_{f_2,s_1}(z00, g_{s_1,g_2}(s_{s_1}(x), y)) → g_{f_2,s_1}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), y))
f_{g_2,s_1}(g_{s_1,g_2}(s_{s_1}(x), y), z10) → f_{g_2,s_1}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), y), z10)
f_{g_2,s_1}(z00, g_{s_1,g_2}(s_{s_1}(x), y)) → f_{g_2,s_1}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), y))
g_{s_1,f_2}(g_{s_1,g_2}(s_{s_1}(x), y), z10) → g_{s_1,f_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), y), z10)
g_{s_1,f_2}(z00, g_{s_1,g_2}(s_{s_1}(x), y)) → g_{s_1,f_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), y))
g_{f_2,f_2}(g_{s_1,g_2}(s_{s_1}(x), y), z10) → g_{f_2,f_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), y), z10)
g_{f_2,f_2}(z00, g_{s_1,g_2}(s_{s_1}(x), y)) → g_{f_2,f_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), y))
f_{g_2,f_2}(g_{s_1,g_2}(s_{s_1}(x), y), z10) → f_{g_2,f_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), y), z10)
f_{g_2,f_2}(z00, g_{s_1,g_2}(s_{s_1}(x), y)) → f_{g_2,f_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), y))
s_{s_1}(g_{s_1,g_2}(s_{s_1}(x), y)) → s_{s_1}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), y))
f_{s_1,g_2}(g_{s_1,g_2}(s_{s_1}(x), y), z10) → f_{s_1,g_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), y), z10)
f_{s_1,g_2}(z00, g_{s_1,g_2}(s_{s_1}(x), y)) → f_{s_1,g_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), y))
f_{s_1,s_1}(g_{s_1,g_2}(s_{s_1}(x), y), z10) → f_{s_1,s_1}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), y), z10)
f_{s_1,s_1}(z00, g_{s_1,g_2}(s_{s_1}(x), y)) → f_{s_1,s_1}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), y))
f_{s_1,f_2}(g_{s_1,g_2}(s_{s_1}(x), y), z10) → f_{s_1,f_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), y), z10)
f_{s_1,f_2}(z00, g_{s_1,g_2}(s_{s_1}(x), y)) → f_{s_1,f_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), y))
s_{f_2}(g_{s_1,g_2}(s_{s_1}(x), y)) → s_{f_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), y))
f_{f_2,g_2}(g_{s_1,g_2}(s_{s_1}(x), y), z10) → f_{f_2,g_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), y), z10)
f_{f_2,g_2}(z00, g_{s_1,g_2}(s_{s_1}(x), y)) → f_{f_2,g_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), y))
f_{f_2,s_1}(g_{s_1,g_2}(s_{s_1}(x), y), z10) → f_{f_2,s_1}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), y), z10)
f_{f_2,s_1}(z00, g_{s_1,g_2}(s_{s_1}(x), y)) → f_{f_2,s_1}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), y))
f_{f_2,f_2}(g_{s_1,g_2}(s_{s_1}(x), y), z10) → f_{f_2,f_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), y), z10)
f_{f_2,f_2}(z00, g_{s_1,g_2}(s_{s_1}(x), y)) → f_{f_2,f_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), y))
g_{g_2,g_2}(g_{s_1,g_2}(s_{s_1}(x), y), z10) → g_{g_2,g_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), y), z10)
g_{g_2,g_2}(z00, g_{s_1,g_2}(s_{s_1}(x), y)) → g_{g_2,g_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), y))
g_{g_2,s_1}(g_{s_1,g_2}(s_{s_1}(x), y), z10) → g_{g_2,s_1}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), y), z10)
g_{g_2,s_1}(z00, g_{s_1,g_2}(s_{s_1}(x), y)) → g_{g_2,s_1}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), y))
g_{g_2,f_2}(g_{s_1,g_2}(s_{s_1}(x), y), z10) → g_{g_2,f_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), y), z10)
g_{g_2,f_2}(z00, g_{s_1,g_2}(s_{s_1}(x), y)) → g_{g_2,f_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), y))
g_{s_1,g_2}(g_{s_1,s_1}(s_{s_1}(x), y), z10) → g_{s_1,g_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), y), z10)
g_{s_1,g_2}(z00, g_{s_1,s_1}(s_{s_1}(x), y)) → g_{s_1,g_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), y))
s_{g_2}(g_{s_1,s_1}(s_{s_1}(x), y)) → s_{g_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), y))
g_{f_2,g_2}(g_{s_1,s_1}(s_{s_1}(x), y), z10) → g_{f_2,g_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), y), z10)
g_{f_2,g_2}(z00, g_{s_1,s_1}(s_{s_1}(x), y)) → g_{f_2,g_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), y))
f_{g_2,g_2}(g_{s_1,s_1}(s_{s_1}(x), y), z10) → f_{g_2,g_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), y), z10)
f_{g_2,g_2}(z00, g_{s_1,s_1}(s_{s_1}(x), y)) → f_{g_2,g_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), y))
g_{s_1,s_1}(g_{s_1,s_1}(s_{s_1}(x), y), z10) → g_{s_1,s_1}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), y), z10)
g_{s_1,s_1}(z00, g_{s_1,s_1}(s_{s_1}(x), y)) → g_{s_1,s_1}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), y))
g_{f_2,s_1}(g_{s_1,s_1}(s_{s_1}(x), y), z10) → g_{f_2,s_1}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), y), z10)
g_{f_2,s_1}(z00, g_{s_1,s_1}(s_{s_1}(x), y)) → g_{f_2,s_1}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), y))
f_{g_2,s_1}(g_{s_1,s_1}(s_{s_1}(x), y), z10) → f_{g_2,s_1}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), y), z10)
f_{g_2,s_1}(z00, g_{s_1,s_1}(s_{s_1}(x), y)) → f_{g_2,s_1}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), y))
g_{s_1,f_2}(g_{s_1,s_1}(s_{s_1}(x), y), z10) → g_{s_1,f_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), y), z10)
g_{s_1,f_2}(z00, g_{s_1,s_1}(s_{s_1}(x), y)) → g_{s_1,f_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), y))
g_{f_2,f_2}(g_{s_1,s_1}(s_{s_1}(x), y), z10) → g_{f_2,f_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), y), z10)
g_{f_2,f_2}(z00, g_{s_1,s_1}(s_{s_1}(x), y)) → g_{f_2,f_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), y))
f_{g_2,f_2}(g_{s_1,s_1}(s_{s_1}(x), y), z10) → f_{g_2,f_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), y), z10)
f_{g_2,f_2}(z00, g_{s_1,s_1}(s_{s_1}(x), y)) → f_{g_2,f_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), y))
s_{s_1}(g_{s_1,s_1}(s_{s_1}(x), y)) → s_{s_1}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), y))
f_{s_1,g_2}(g_{s_1,s_1}(s_{s_1}(x), y), z10) → f_{s_1,g_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), y), z10)
f_{s_1,g_2}(z00, g_{s_1,s_1}(s_{s_1}(x), y)) → f_{s_1,g_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), y))
f_{s_1,s_1}(g_{s_1,s_1}(s_{s_1}(x), y), z10) → f_{s_1,s_1}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), y), z10)
f_{s_1,s_1}(z00, g_{s_1,s_1}(s_{s_1}(x), y)) → f_{s_1,s_1}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), y))
f_{s_1,f_2}(g_{s_1,s_1}(s_{s_1}(x), y), z10) → f_{s_1,f_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), y), z10)
f_{s_1,f_2}(z00, g_{s_1,s_1}(s_{s_1}(x), y)) → f_{s_1,f_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), y))
s_{f_2}(g_{s_1,s_1}(s_{s_1}(x), y)) → s_{f_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), y))
f_{f_2,g_2}(g_{s_1,s_1}(s_{s_1}(x), y), z10) → f_{f_2,g_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), y), z10)
f_{f_2,g_2}(z00, g_{s_1,s_1}(s_{s_1}(x), y)) → f_{f_2,g_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), y))
f_{f_2,s_1}(g_{s_1,s_1}(s_{s_1}(x), y), z10) → f_{f_2,s_1}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), y), z10)
f_{f_2,s_1}(z00, g_{s_1,s_1}(s_{s_1}(x), y)) → f_{f_2,s_1}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), y))
f_{f_2,f_2}(g_{s_1,s_1}(s_{s_1}(x), y), z10) → f_{f_2,f_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), y), z10)
f_{f_2,f_2}(z00, g_{s_1,s_1}(s_{s_1}(x), y)) → f_{f_2,f_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), y))
g_{g_2,g_2}(g_{s_1,s_1}(s_{s_1}(x), y), z10) → g_{g_2,g_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), y), z10)
g_{g_2,g_2}(z00, g_{s_1,s_1}(s_{s_1}(x), y)) → g_{g_2,g_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), y))
g_{g_2,s_1}(g_{s_1,s_1}(s_{s_1}(x), y), z10) → g_{g_2,s_1}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), y), z10)
g_{g_2,s_1}(z00, g_{s_1,s_1}(s_{s_1}(x), y)) → g_{g_2,s_1}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), y))
g_{g_2,f_2}(g_{s_1,s_1}(s_{s_1}(x), y), z10) → g_{g_2,f_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), y), z10)
g_{g_2,f_2}(z00, g_{s_1,s_1}(s_{s_1}(x), y)) → g_{g_2,f_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), y))
g_{s_1,g_2}(g_{s_1,f_2}(s_{s_1}(x), y), z10) → g_{s_1,g_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), y), z10)
g_{s_1,g_2}(z00, g_{s_1,f_2}(s_{s_1}(x), y)) → g_{s_1,g_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), y))
s_{g_2}(g_{s_1,f_2}(s_{s_1}(x), y)) → s_{g_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), y))
g_{f_2,g_2}(g_{s_1,f_2}(s_{s_1}(x), y), z10) → g_{f_2,g_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), y), z10)
g_{f_2,g_2}(z00, g_{s_1,f_2}(s_{s_1}(x), y)) → g_{f_2,g_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), y))
f_{g_2,g_2}(g_{s_1,f_2}(s_{s_1}(x), y), z10) → f_{g_2,g_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), y), z10)
f_{g_2,g_2}(z00, g_{s_1,f_2}(s_{s_1}(x), y)) → f_{g_2,g_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), y))
g_{s_1,s_1}(g_{s_1,f_2}(s_{s_1}(x), y), z10) → g_{s_1,s_1}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), y), z10)
g_{s_1,s_1}(z00, g_{s_1,f_2}(s_{s_1}(x), y)) → g_{s_1,s_1}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), y))
g_{f_2,s_1}(g_{s_1,f_2}(s_{s_1}(x), y), z10) → g_{f_2,s_1}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), y), z10)
g_{f_2,s_1}(z00, g_{s_1,f_2}(s_{s_1}(x), y)) → g_{f_2,s_1}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), y))
f_{g_2,s_1}(g_{s_1,f_2}(s_{s_1}(x), y), z10) → f_{g_2,s_1}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), y), z10)
f_{g_2,s_1}(z00, g_{s_1,f_2}(s_{s_1}(x), y)) → f_{g_2,s_1}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), y))
g_{s_1,f_2}(g_{s_1,f_2}(s_{s_1}(x), y), z10) → g_{s_1,f_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), y), z10)
g_{s_1,f_2}(z00, g_{s_1,f_2}(s_{s_1}(x), y)) → g_{s_1,f_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), y))
g_{f_2,f_2}(g_{s_1,f_2}(s_{s_1}(x), y), z10) → g_{f_2,f_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), y), z10)
g_{f_2,f_2}(z00, g_{s_1,f_2}(s_{s_1}(x), y)) → g_{f_2,f_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), y))
f_{g_2,f_2}(g_{s_1,f_2}(s_{s_1}(x), y), z10) → f_{g_2,f_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), y), z10)
f_{g_2,f_2}(z00, g_{s_1,f_2}(s_{s_1}(x), y)) → f_{g_2,f_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), y))
s_{s_1}(g_{s_1,f_2}(s_{s_1}(x), y)) → s_{s_1}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), y))
f_{s_1,g_2}(g_{s_1,f_2}(s_{s_1}(x), y), z10) → f_{s_1,g_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), y), z10)
f_{s_1,g_2}(z00, g_{s_1,f_2}(s_{s_1}(x), y)) → f_{s_1,g_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), y))
f_{s_1,s_1}(g_{s_1,f_2}(s_{s_1}(x), y), z10) → f_{s_1,s_1}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), y), z10)
f_{s_1,s_1}(z00, g_{s_1,f_2}(s_{s_1}(x), y)) → f_{s_1,s_1}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), y))
f_{s_1,f_2}(g_{s_1,f_2}(s_{s_1}(x), y), z10) → f_{s_1,f_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), y), z10)
f_{s_1,f_2}(z00, g_{s_1,f_2}(s_{s_1}(x), y)) → f_{s_1,f_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), y))
s_{f_2}(g_{s_1,f_2}(s_{s_1}(x), y)) → s_{f_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), y))
f_{f_2,g_2}(g_{s_1,f_2}(s_{s_1}(x), y), z10) → f_{f_2,g_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), y), z10)
f_{f_2,g_2}(z00, g_{s_1,f_2}(s_{s_1}(x), y)) → f_{f_2,g_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), y))
f_{f_2,s_1}(g_{s_1,f_2}(s_{s_1}(x), y), z10) → f_{f_2,s_1}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), y), z10)
f_{f_2,s_1}(z00, g_{s_1,f_2}(s_{s_1}(x), y)) → f_{f_2,s_1}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), y))
f_{f_2,f_2}(g_{s_1,f_2}(s_{s_1}(x), y), z10) → f_{f_2,f_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), y), z10)
f_{f_2,f_2}(z00, g_{s_1,f_2}(s_{s_1}(x), y)) → f_{f_2,f_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), y))
g_{g_2,g_2}(g_{s_1,f_2}(s_{s_1}(x), y), z10) → g_{g_2,g_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), y), z10)
g_{g_2,g_2}(z00, g_{s_1,f_2}(s_{s_1}(x), y)) → g_{g_2,g_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), y))
g_{g_2,s_1}(g_{s_1,f_2}(s_{s_1}(x), y), z10) → g_{g_2,s_1}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), y), z10)
g_{g_2,s_1}(z00, g_{s_1,f_2}(s_{s_1}(x), y)) → g_{g_2,s_1}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), y))
g_{g_2,f_2}(g_{s_1,f_2}(s_{s_1}(x), y), z10) → g_{g_2,f_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), y), z10)
g_{g_2,f_2}(z00, g_{s_1,f_2}(s_{s_1}(x), y)) → g_{g_2,f_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), y))
g_{s_1,g_2}(g_{s_1,g_2}(s_{f_2}(x), y), z10) → g_{s_1,g_2}(g_{f_2,g_2}(f_{f_2,g_2}(x, y), y), z10)
g_{s_1,g_2}(z00, g_{s_1,g_2}(s_{f_2}(x), y)) → g_{s_1,g_2}(z00, g_{f_2,g_2}(f_{f_2,g_2}(x, y), y))
s_{g_2}(g_{s_1,g_2}(s_{f_2}(x), y)) → s_{g_2}(g_{f_2,g_2}(f_{f_2,g_2}(x, y), y))
g_{f_2,g_2}(g_{s_1,g_2}(s_{f_2}(x), y), z10) → g_{f_2,g_2}(g_{f_2,g_2}(f_{f_2,g_2}(x, y), y), z10)
g_{f_2,g_2}(z00, g_{s_1,g_2}(s_{f_2}(x), y)) → g_{f_2,g_2}(z00, g_{f_2,g_2}(f_{f_2,g_2}(x, y), y))
f_{g_2,g_2}(g_{s_1,g_2}(s_{f_2}(x), y), z10) → f_{g_2,g_2}(g_{f_2,g_2}(f_{f_2,g_2}(x, y), y), z10)
f_{g_2,g_2}(z00, g_{s_1,g_2}(s_{f_2}(x), y)) → f_{g_2,g_2}(z00, g_{f_2,g_2}(f_{f_2,g_2}(x, y), y))
g_{s_1,s_1}(g_{s_1,g_2}(s_{f_2}(x), y), z10) → g_{s_1,s_1}(g_{f_2,g_2}(f_{f_2,g_2}(x, y), y), z10)
g_{s_1,s_1}(z00, g_{s_1,g_2}(s_{f_2}(x), y)) → g_{s_1,s_1}(z00, g_{f_2,g_2}(f_{f_2,g_2}(x, y), y))
g_{f_2,s_1}(g_{s_1,g_2}(s_{f_2}(x), y), z10) → g_{f_2,s_1}(g_{f_2,g_2}(f_{f_2,g_2}(x, y), y), z10)
g_{f_2,s_1}(z00, g_{s_1,g_2}(s_{f_2}(x), y)) → g_{f_2,s_1}(z00, g_{f_2,g_2}(f_{f_2,g_2}(x, y), y))
f_{g_2,s_1}(g_{s_1,g_2}(s_{f_2}(x), y), z10) → f_{g_2,s_1}(g_{f_2,g_2}(f_{f_2,g_2}(x, y), y), z10)
f_{g_2,s_1}(z00, g_{s_1,g_2}(s_{f_2}(x), y)) → f_{g_2,s_1}(z00, g_{f_2,g_2}(f_{f_2,g_2}(x, y), y))
g_{s_1,f_2}(g_{s_1,g_2}(s_{f_2}(x), y), z10) → g_{s_1,f_2}(g_{f_2,g_2}(f_{f_2,g_2}(x, y), y), z10)
g_{s_1,f_2}(z00, g_{s_1,g_2}(s_{f_2}(x), y)) → g_{s_1,f_2}(z00, g_{f_2,g_2}(f_{f_2,g_2}(x, y), y))
g_{f_2,f_2}(g_{s_1,g_2}(s_{f_2}(x), y), z10) → g_{f_2,f_2}(g_{f_2,g_2}(f_{f_2,g_2}(x, y), y), z10)
g_{f_2,f_2}(z00, g_{s_1,g_2}(s_{f_2}(x), y)) → g_{f_2,f_2}(z00, g_{f_2,g_2}(f_{f_2,g_2}(x, y), y))
f_{g_2,f_2}(g_{s_1,g_2}(s_{f_2}(x), y), z10) → f_{g_2,f_2}(g_{f_2,g_2}(f_{f_2,g_2}(x, y), y), z10)
f_{g_2,f_2}(z00, g_{s_1,g_2}(s_{f_2}(x), y)) → f_{g_2,f_2}(z00, g_{f_2,g_2}(f_{f_2,g_2}(x, y), y))
s_{s_1}(g_{s_1,g_2}(s_{f_2}(x), y)) → s_{s_1}(g_{f_2,g_2}(f_{f_2,g_2}(x, y), y))
f_{s_1,g_2}(g_{s_1,g_2}(s_{f_2}(x), y), z10) → f_{s_1,g_2}(g_{f_2,g_2}(f_{f_2,g_2}(x, y), y), z10)
f_{s_1,g_2}(z00, g_{s_1,g_2}(s_{f_2}(x), y)) → f_{s_1,g_2}(z00, g_{f_2,g_2}(f_{f_2,g_2}(x, y), y))
f_{s_1,s_1}(g_{s_1,g_2}(s_{f_2}(x), y), z10) → f_{s_1,s_1}(g_{f_2,g_2}(f_{f_2,g_2}(x, y), y), z10)
f_{s_1,s_1}(z00, g_{s_1,g_2}(s_{f_2}(x), y)) → f_{s_1,s_1}(z00, g_{f_2,g_2}(f_{f_2,g_2}(x, y), y))
f_{s_1,f_2}(g_{s_1,g_2}(s_{f_2}(x), y), z10) → f_{s_1,f_2}(g_{f_2,g_2}(f_{f_2,g_2}(x, y), y), z10)
f_{s_1,f_2}(z00, g_{s_1,g_2}(s_{f_2}(x), y)) → f_{s_1,f_2}(z00, g_{f_2,g_2}(f_{f_2,g_2}(x, y), y))
s_{f_2}(g_{s_1,g_2}(s_{f_2}(x), y)) → s_{f_2}(g_{f_2,g_2}(f_{f_2,g_2}(x, y), y))
f_{f_2,g_2}(g_{s_1,g_2}(s_{f_2}(x), y), z10) → f_{f_2,g_2}(g_{f_2,g_2}(f_{f_2,g_2}(x, y), y), z10)
f_{f_2,g_2}(z00, g_{s_1,g_2}(s_{f_2}(x), y)) → f_{f_2,g_2}(z00, g_{f_2,g_2}(f_{f_2,g_2}(x, y), y))
f_{f_2,s_1}(g_{s_1,g_2}(s_{f_2}(x), y), z10) → f_{f_2,s_1}(g_{f_2,g_2}(f_{f_2,g_2}(x, y), y), z10)
f_{f_2,s_1}(z00, g_{s_1,g_2}(s_{f_2}(x), y)) → f_{f_2,s_1}(z00, g_{f_2,g_2}(f_{f_2,g_2}(x, y), y))
f_{f_2,f_2}(g_{s_1,g_2}(s_{f_2}(x), y), z10) → f_{f_2,f_2}(g_{f_2,g_2}(f_{f_2,g_2}(x, y), y), z10)
f_{f_2,f_2}(z00, g_{s_1,g_2}(s_{f_2}(x), y)) → f_{f_2,f_2}(z00, g_{f_2,g_2}(f_{f_2,g_2}(x, y), y))
g_{g_2,g_2}(g_{s_1,g_2}(s_{f_2}(x), y), z10) → g_{g_2,g_2}(g_{f_2,g_2}(f_{f_2,g_2}(x, y), y), z10)
g_{g_2,g_2}(z00, g_{s_1,g_2}(s_{f_2}(x), y)) → g_{g_2,g_2}(z00, g_{f_2,g_2}(f_{f_2,g_2}(x, y), y))
g_{g_2,s_1}(g_{s_1,g_2}(s_{f_2}(x), y), z10) → g_{g_2,s_1}(g_{f_2,g_2}(f_{f_2,g_2}(x, y), y), z10)
g_{g_2,s_1}(z00, g_{s_1,g_2}(s_{f_2}(x), y)) → g_{g_2,s_1}(z00, g_{f_2,g_2}(f_{f_2,g_2}(x, y), y))
g_{g_2,f_2}(g_{s_1,g_2}(s_{f_2}(x), y), z10) → g_{g_2,f_2}(g_{f_2,g_2}(f_{f_2,g_2}(x, y), y), z10)
g_{g_2,f_2}(z00, g_{s_1,g_2}(s_{f_2}(x), y)) → g_{g_2,f_2}(z00, g_{f_2,g_2}(f_{f_2,g_2}(x, y), y))
g_{s_1,g_2}(g_{s_1,s_1}(s_{f_2}(x), y), z10) → g_{s_1,g_2}(g_{f_2,s_1}(f_{f_2,s_1}(x, y), y), z10)
g_{s_1,g_2}(z00, g_{s_1,s_1}(s_{f_2}(x), y)) → g_{s_1,g_2}(z00, g_{f_2,s_1}(f_{f_2,s_1}(x, y), y))
s_{g_2}(g_{s_1,s_1}(s_{f_2}(x), y)) → s_{g_2}(g_{f_2,s_1}(f_{f_2,s_1}(x, y), y))
g_{f_2,g_2}(g_{s_1,s_1}(s_{f_2}(x), y), z10) → g_{f_2,g_2}(g_{f_2,s_1}(f_{f_2,s_1}(x, y), y), z10)
g_{f_2,g_2}(z00, g_{s_1,s_1}(s_{f_2}(x), y)) → g_{f_2,g_2}(z00, g_{f_2,s_1}(f_{f_2,s_1}(x, y), y))
f_{g_2,g_2}(g_{s_1,s_1}(s_{f_2}(x), y), z10) → f_{g_2,g_2}(g_{f_2,s_1}(f_{f_2,s_1}(x, y), y), z10)
f_{g_2,g_2}(z00, g_{s_1,s_1}(s_{f_2}(x), y)) → f_{g_2,g_2}(z00, g_{f_2,s_1}(f_{f_2,s_1}(x, y), y))
g_{s_1,s_1}(g_{s_1,s_1}(s_{f_2}(x), y), z10) → g_{s_1,s_1}(g_{f_2,s_1}(f_{f_2,s_1}(x, y), y), z10)
g_{s_1,s_1}(z00, g_{s_1,s_1}(s_{f_2}(x), y)) → g_{s_1,s_1}(z00, g_{f_2,s_1}(f_{f_2,s_1}(x, y), y))
g_{f_2,s_1}(g_{s_1,s_1}(s_{f_2}(x), y), z10) → g_{f_2,s_1}(g_{f_2,s_1}(f_{f_2,s_1}(x, y), y), z10)
g_{f_2,s_1}(z00, g_{s_1,s_1}(s_{f_2}(x), y)) → g_{f_2,s_1}(z00, g_{f_2,s_1}(f_{f_2,s_1}(x, y), y))
f_{g_2,s_1}(g_{s_1,s_1}(s_{f_2}(x), y), z10) → f_{g_2,s_1}(g_{f_2,s_1}(f_{f_2,s_1}(x, y), y), z10)
f_{g_2,s_1}(z00, g_{s_1,s_1}(s_{f_2}(x), y)) → f_{g_2,s_1}(z00, g_{f_2,s_1}(f_{f_2,s_1}(x, y), y))
g_{s_1,f_2}(g_{s_1,s_1}(s_{f_2}(x), y), z10) → g_{s_1,f_2}(g_{f_2,s_1}(f_{f_2,s_1}(x, y), y), z10)
g_{s_1,f_2}(z00, g_{s_1,s_1}(s_{f_2}(x), y)) → g_{s_1,f_2}(z00, g_{f_2,s_1}(f_{f_2,s_1}(x, y), y))
g_{f_2,f_2}(g_{s_1,s_1}(s_{f_2}(x), y), z10) → g_{f_2,f_2}(g_{f_2,s_1}(f_{f_2,s_1}(x, y), y), z10)
g_{f_2,f_2}(z00, g_{s_1,s_1}(s_{f_2}(x), y)) → g_{f_2,f_2}(z00, g_{f_2,s_1}(f_{f_2,s_1}(x, y), y))
f_{g_2,f_2}(g_{s_1,s_1}(s_{f_2}(x), y), z10) → f_{g_2,f_2}(g_{f_2,s_1}(f_{f_2,s_1}(x, y), y), z10)
f_{g_2,f_2}(z00, g_{s_1,s_1}(s_{f_2}(x), y)) → f_{g_2,f_2}(z00, g_{f_2,s_1}(f_{f_2,s_1}(x, y), y))
s_{s_1}(g_{s_1,s_1}(s_{f_2}(x), y)) → s_{s_1}(g_{f_2,s_1}(f_{f_2,s_1}(x, y), y))
f_{s_1,g_2}(g_{s_1,s_1}(s_{f_2}(x), y), z10) → f_{s_1,g_2}(g_{f_2,s_1}(f_{f_2,s_1}(x, y), y), z10)
f_{s_1,g_2}(z00, g_{s_1,s_1}(s_{f_2}(x), y)) → f_{s_1,g_2}(z00, g_{f_2,s_1}(f_{f_2,s_1}(x, y), y))
f_{s_1,s_1}(g_{s_1,s_1}(s_{f_2}(x), y), z10) → f_{s_1,s_1}(g_{f_2,s_1}(f_{f_2,s_1}(x, y), y), z10)
f_{s_1,s_1}(z00, g_{s_1,s_1}(s_{f_2}(x), y)) → f_{s_1,s_1}(z00, g_{f_2,s_1}(f_{f_2,s_1}(x, y), y))
f_{s_1,f_2}(g_{s_1,s_1}(s_{f_2}(x), y), z10) → f_{s_1,f_2}(g_{f_2,s_1}(f_{f_2,s_1}(x, y), y), z10)
f_{s_1,f_2}(z00, g_{s_1,s_1}(s_{f_2}(x), y)) → f_{s_1,f_2}(z00, g_{f_2,s_1}(f_{f_2,s_1}(x, y), y))
s_{f_2}(g_{s_1,s_1}(s_{f_2}(x), y)) → s_{f_2}(g_{f_2,s_1}(f_{f_2,s_1}(x, y), y))
f_{f_2,g_2}(g_{s_1,s_1}(s_{f_2}(x), y), z10) → f_{f_2,g_2}(g_{f_2,s_1}(f_{f_2,s_1}(x, y), y), z10)
f_{f_2,g_2}(z00, g_{s_1,s_1}(s_{f_2}(x), y)) → f_{f_2,g_2}(z00, g_{f_2,s_1}(f_{f_2,s_1}(x, y), y))
f_{f_2,s_1}(g_{s_1,s_1}(s_{f_2}(x), y), z10) → f_{f_2,s_1}(g_{f_2,s_1}(f_{f_2,s_1}(x, y), y), z10)
f_{f_2,s_1}(z00, g_{s_1,s_1}(s_{f_2}(x), y)) → f_{f_2,s_1}(z00, g_{f_2,s_1}(f_{f_2,s_1}(x, y), y))
f_{f_2,f_2}(g_{s_1,s_1}(s_{f_2}(x), y), z10) → f_{f_2,f_2}(g_{f_2,s_1}(f_{f_2,s_1}(x, y), y), z10)
f_{f_2,f_2}(z00, g_{s_1,s_1}(s_{f_2}(x), y)) → f_{f_2,f_2}(z00, g_{f_2,s_1}(f_{f_2,s_1}(x, y), y))
g_{g_2,g_2}(g_{s_1,s_1}(s_{f_2}(x), y), z10) → g_{g_2,g_2}(g_{f_2,s_1}(f_{f_2,s_1}(x, y), y), z10)
g_{g_2,g_2}(z00, g_{s_1,s_1}(s_{f_2}(x), y)) → g_{g_2,g_2}(z00, g_{f_2,s_1}(f_{f_2,s_1}(x, y), y))
g_{g_2,s_1}(g_{s_1,s_1}(s_{f_2}(x), y), z10) → g_{g_2,s_1}(g_{f_2,s_1}(f_{f_2,s_1}(x, y), y), z10)
g_{g_2,s_1}(z00, g_{s_1,s_1}(s_{f_2}(x), y)) → g_{g_2,s_1}(z00, g_{f_2,s_1}(f_{f_2,s_1}(x, y), y))
g_{g_2,f_2}(g_{s_1,s_1}(s_{f_2}(x), y), z10) → g_{g_2,f_2}(g_{f_2,s_1}(f_{f_2,s_1}(x, y), y), z10)
g_{g_2,f_2}(z00, g_{s_1,s_1}(s_{f_2}(x), y)) → g_{g_2,f_2}(z00, g_{f_2,s_1}(f_{f_2,s_1}(x, y), y))
g_{s_1,g_2}(g_{s_1,f_2}(s_{f_2}(x), y), z10) → g_{s_1,g_2}(g_{f_2,f_2}(f_{f_2,f_2}(x, y), y), z10)
g_{s_1,g_2}(z00, g_{s_1,f_2}(s_{f_2}(x), y)) → g_{s_1,g_2}(z00, g_{f_2,f_2}(f_{f_2,f_2}(x, y), y))
s_{g_2}(g_{s_1,f_2}(s_{f_2}(x), y)) → s_{g_2}(g_{f_2,f_2}(f_{f_2,f_2}(x, y), y))
g_{f_2,g_2}(g_{s_1,f_2}(s_{f_2}(x), y), z10) → g_{f_2,g_2}(g_{f_2,f_2}(f_{f_2,f_2}(x, y), y), z10)
g_{f_2,g_2}(z00, g_{s_1,f_2}(s_{f_2}(x), y)) → g_{f_2,g_2}(z00, g_{f_2,f_2}(f_{f_2,f_2}(x, y), y))
f_{g_2,g_2}(g_{s_1,f_2}(s_{f_2}(x), y), z10) → f_{g_2,g_2}(g_{f_2,f_2}(f_{f_2,f_2}(x, y), y), z10)
f_{g_2,g_2}(z00, g_{s_1,f_2}(s_{f_2}(x), y)) → f_{g_2,g_2}(z00, g_{f_2,f_2}(f_{f_2,f_2}(x, y), y))
g_{s_1,s_1}(g_{s_1,f_2}(s_{f_2}(x), y), z10) → g_{s_1,s_1}(g_{f_2,f_2}(f_{f_2,f_2}(x, y), y), z10)
g_{s_1,s_1}(z00, g_{s_1,f_2}(s_{f_2}(x), y)) → g_{s_1,s_1}(z00, g_{f_2,f_2}(f_{f_2,f_2}(x, y), y))
g_{f_2,s_1}(g_{s_1,f_2}(s_{f_2}(x), y), z10) → g_{f_2,s_1}(g_{f_2,f_2}(f_{f_2,f_2}(x, y), y), z10)
g_{f_2,s_1}(z00, g_{s_1,f_2}(s_{f_2}(x), y)) → g_{f_2,s_1}(z00, g_{f_2,f_2}(f_{f_2,f_2}(x, y), y))
f_{g_2,s_1}(g_{s_1,f_2}(s_{f_2}(x), y), z10) → f_{g_2,s_1}(g_{f_2,f_2}(f_{f_2,f_2}(x, y), y), z10)
f_{g_2,s_1}(z00, g_{s_1,f_2}(s_{f_2}(x), y)) → f_{g_2,s_1}(z00, g_{f_2,f_2}(f_{f_2,f_2}(x, y), y))
g_{s_1,f_2}(g_{s_1,f_2}(s_{f_2}(x), y), z10) → g_{s_1,f_2}(g_{f_2,f_2}(f_{f_2,f_2}(x, y), y), z10)
g_{s_1,f_2}(z00, g_{s_1,f_2}(s_{f_2}(x), y)) → g_{s_1,f_2}(z00, g_{f_2,f_2}(f_{f_2,f_2}(x, y), y))
g_{f_2,f_2}(g_{s_1,f_2}(s_{f_2}(x), y), z10) → g_{f_2,f_2}(g_{f_2,f_2}(f_{f_2,f_2}(x, y), y), z10)
g_{f_2,f_2}(z00, g_{s_1,f_2}(s_{f_2}(x), y)) → g_{f_2,f_2}(z00, g_{f_2,f_2}(f_{f_2,f_2}(x, y), y))
f_{g_2,f_2}(g_{s_1,f_2}(s_{f_2}(x), y), z10) → f_{g_2,f_2}(g_{f_2,f_2}(f_{f_2,f_2}(x, y), y), z10)
f_{g_2,f_2}(z00, g_{s_1,f_2}(s_{f_2}(x), y)) → f_{g_2,f_2}(z00, g_{f_2,f_2}(f_{f_2,f_2}(x, y), y))
s_{s_1}(g_{s_1,f_2}(s_{f_2}(x), y)) → s_{s_1}(g_{f_2,f_2}(f_{f_2,f_2}(x, y), y))
f_{s_1,g_2}(g_{s_1,f_2}(s_{f_2}(x), y), z10) → f_{s_1,g_2}(g_{f_2,f_2}(f_{f_2,f_2}(x, y), y), z10)
f_{s_1,g_2}(z00, g_{s_1,f_2}(s_{f_2}(x), y)) → f_{s_1,g_2}(z00, g_{f_2,f_2}(f_{f_2,f_2}(x, y), y))
f_{s_1,s_1}(g_{s_1,f_2}(s_{f_2}(x), y), z10) → f_{s_1,s_1}(g_{f_2,f_2}(f_{f_2,f_2}(x, y), y), z10)
f_{s_1,s_1}(z00, g_{s_1,f_2}(s_{f_2}(x), y)) → f_{s_1,s_1}(z00, g_{f_2,f_2}(f_{f_2,f_2}(x, y), y))
f_{s_1,f_2}(g_{s_1,f_2}(s_{f_2}(x), y), z10) → f_{s_1,f_2}(g_{f_2,f_2}(f_{f_2,f_2}(x, y), y), z10)
f_{s_1,f_2}(z00, g_{s_1,f_2}(s_{f_2}(x), y)) → f_{s_1,f_2}(z00, g_{f_2,f_2}(f_{f_2,f_2}(x, y), y))
s_{f_2}(g_{s_1,f_2}(s_{f_2}(x), y)) → s_{f_2}(g_{f_2,f_2}(f_{f_2,f_2}(x, y), y))
f_{f_2,g_2}(g_{s_1,f_2}(s_{f_2}(x), y), z10) → f_{f_2,g_2}(g_{f_2,f_2}(f_{f_2,f_2}(x, y), y), z10)
f_{f_2,g_2}(z00, g_{s_1,f_2}(s_{f_2}(x), y)) → f_{f_2,g_2}(z00, g_{f_2,f_2}(f_{f_2,f_2}(x, y), y))
f_{f_2,s_1}(g_{s_1,f_2}(s_{f_2}(x), y), z10) → f_{f_2,s_1}(g_{f_2,f_2}(f_{f_2,f_2}(x, y), y), z10)
f_{f_2,s_1}(z00, g_{s_1,f_2}(s_{f_2}(x), y)) → f_{f_2,s_1}(z00, g_{f_2,f_2}(f_{f_2,f_2}(x, y), y))
f_{f_2,f_2}(g_{s_1,f_2}(s_{f_2}(x), y), z10) → f_{f_2,f_2}(g_{f_2,f_2}(f_{f_2,f_2}(x, y), y), z10)
f_{f_2,f_2}(z00, g_{s_1,f_2}(s_{f_2}(x), y)) → f_{f_2,f_2}(z00, g_{f_2,f_2}(f_{f_2,f_2}(x, y), y))
g_{g_2,g_2}(g_{s_1,f_2}(s_{f_2}(x), y), z10) → g_{g_2,g_2}(g_{f_2,f_2}(f_{f_2,f_2}(x, y), y), z10)
g_{g_2,g_2}(z00, g_{s_1,f_2}(s_{f_2}(x), y)) → g_{g_2,g_2}(z00, g_{f_2,f_2}(f_{f_2,f_2}(x, y), y))
g_{g_2,s_1}(g_{s_1,f_2}(s_{f_2}(x), y), z10) → g_{g_2,s_1}(g_{f_2,f_2}(f_{f_2,f_2}(x, y), y), z10)
g_{g_2,s_1}(z00, g_{s_1,f_2}(s_{f_2}(x), y)) → g_{g_2,s_1}(z00, g_{f_2,f_2}(f_{f_2,f_2}(x, y), y))
g_{g_2,f_2}(g_{s_1,f_2}(s_{f_2}(x), y), z10) → g_{g_2,f_2}(g_{f_2,f_2}(f_{f_2,f_2}(x, y), y), z10)
g_{g_2,f_2}(z00, g_{s_1,f_2}(s_{f_2}(x), y)) → g_{g_2,f_2}(z00, g_{f_2,f_2}(f_{f_2,f_2}(x, y), y))
The relative TRS consists of the following S rules:
f_{g_2,s_1}(x, y) → f_{g_2,s_1}(x, s_{s_1}(y))
f_{s_1,s_1}(x, y) → f_{s_1,s_1}(x, s_{s_1}(y))
f_{f_2,s_1}(x, y) → f_{f_2,s_1}(x, s_{s_1}(y))
g_{f_2,g_2}(f_{f_2,g_2}(x, y), z1) → g_{f_2,g_2}(x, z1)
g_{f_2,s_1}(f_{f_2,g_2}(x, y), z1) → g_{f_2,s_1}(x, z1)
g_{f_2,f_2}(f_{f_2,g_2}(x, y), z1) → g_{f_2,f_2}(x, z1)
g_{f_2,g_2}(f_{f_2,s_1}(x, y), z1) → g_{f_2,g_2}(x, z1)
g_{f_2,s_1}(f_{f_2,s_1}(x, y), z1) → g_{f_2,s_1}(x, z1)
g_{f_2,f_2}(f_{f_2,s_1}(x, y), z1) → g_{f_2,f_2}(x, z1)
g_{f_2,g_2}(f_{f_2,f_2}(x, y), z1) → g_{f_2,g_2}(x, z1)
g_{f_2,s_1}(f_{f_2,f_2}(x, y), z1) → g_{f_2,s_1}(x, z1)
g_{f_2,f_2}(f_{f_2,f_2}(x, y), z1) → g_{f_2,f_2}(x, z1)
g_{g_2,f_2}(z0, f_{f_2,g_2}(x, y)) → g_{g_2,f_2}(z0, x)
g_{g_2,f_2}(z0, f_{f_2,s_1}(x, y)) → g_{g_2,f_2}(z0, x)
g_{g_2,f_2}(z0, f_{f_2,f_2}(x, y)) → g_{g_2,f_2}(z0, x)
g_{s_1,f_2}(z0, f_{f_2,g_2}(x, y)) → g_{s_1,f_2}(z0, x)
g_{s_1,f_2}(z0, f_{f_2,s_1}(x, y)) → g_{s_1,f_2}(z0, x)
g_{s_1,f_2}(z0, f_{f_2,f_2}(x, y)) → g_{s_1,f_2}(z0, x)
g_{f_2,f_2}(z0, f_{f_2,g_2}(x, y)) → g_{f_2,f_2}(z0, x)
g_{f_2,f_2}(z0, f_{f_2,s_1}(x, y)) → g_{f_2,f_2}(z0, x)
g_{f_2,f_2}(z0, f_{f_2,f_2}(x, y)) → g_{f_2,f_2}(z0, x)
s_{f_2}(f_{f_2,g_2}(x, y)) → s_{f_2}(x)
s_{f_2}(f_{f_2,s_1}(x, y)) → s_{f_2}(x)
s_{f_2}(f_{f_2,f_2}(x, y)) → s_{f_2}(x)
f_{f_2,g_2}(f_{f_2,g_2}(x, y), z1) → f_{f_2,g_2}(x, z1)
f_{f_2,s_1}(f_{f_2,g_2}(x, y), z1) → f_{f_2,s_1}(x, z1)
f_{f_2,f_2}(f_{f_2,g_2}(x, y), z1) → f_{f_2,f_2}(x, z1)
f_{f_2,g_2}(f_{f_2,s_1}(x, y), z1) → f_{f_2,g_2}(x, z1)
f_{f_2,s_1}(f_{f_2,s_1}(x, y), z1) → f_{f_2,s_1}(x, z1)
f_{f_2,f_2}(f_{f_2,s_1}(x, y), z1) → f_{f_2,f_2}(x, z1)
f_{f_2,g_2}(f_{f_2,f_2}(x, y), z1) → f_{f_2,g_2}(x, z1)
f_{f_2,s_1}(f_{f_2,f_2}(x, y), z1) → f_{f_2,s_1}(x, z1)
f_{f_2,f_2}(f_{f_2,f_2}(x, y), z1) → f_{f_2,f_2}(x, z1)
f_{g_2,f_2}(z0, f_{f_2,g_2}(x, y)) → f_{g_2,f_2}(z0, x)
f_{g_2,f_2}(z0, f_{f_2,s_1}(x, y)) → f_{g_2,f_2}(z0, x)
f_{g_2,f_2}(z0, f_{f_2,f_2}(x, y)) → f_{g_2,f_2}(z0, x)
f_{s_1,f_2}(z0, f_{f_2,g_2}(x, y)) → f_{s_1,f_2}(z0, x)
f_{s_1,f_2}(z0, f_{f_2,s_1}(x, y)) → f_{s_1,f_2}(z0, x)
f_{s_1,f_2}(z0, f_{f_2,f_2}(x, y)) → f_{s_1,f_2}(z0, x)
f_{f_2,f_2}(z0, f_{f_2,g_2}(x, y)) → f_{f_2,f_2}(z0, x)
f_{f_2,f_2}(z0, f_{f_2,s_1}(x, y)) → f_{f_2,f_2}(z0, x)
f_{f_2,f_2}(z0, f_{f_2,f_2}(x, y)) → f_{f_2,f_2}(z0, x)
g_{s_1,g_2}(f_{g_2,g_2}(x, y), z10) → g_{s_1,g_2}(f_{g_2,s_1}(x, s_{g_2}(y)), z10)
g_{s_1,g_2}(z00, f_{g_2,g_2}(x, y)) → g_{s_1,g_2}(z00, f_{g_2,s_1}(x, s_{g_2}(y)))
s_{g_2}(f_{g_2,g_2}(x, y)) → s_{g_2}(f_{g_2,s_1}(x, s_{g_2}(y)))
g_{f_2,g_2}(f_{g_2,g_2}(x, y), z10) → g_{f_2,g_2}(f_{g_2,s_1}(x, s_{g_2}(y)), z10)
g_{f_2,g_2}(z00, f_{g_2,g_2}(x, y)) → g_{f_2,g_2}(z00, f_{g_2,s_1}(x, s_{g_2}(y)))
f_{g_2,g_2}(f_{g_2,g_2}(x, y), z10) → f_{g_2,g_2}(f_{g_2,s_1}(x, s_{g_2}(y)), z10)
f_{g_2,g_2}(z00, f_{g_2,g_2}(x, y)) → f_{g_2,g_2}(z00, f_{g_2,s_1}(x, s_{g_2}(y)))
g_{s_1,s_1}(f_{g_2,g_2}(x, y), z10) → g_{s_1,s_1}(f_{g_2,s_1}(x, s_{g_2}(y)), z10)
g_{s_1,s_1}(z00, f_{g_2,g_2}(x, y)) → g_{s_1,s_1}(z00, f_{g_2,s_1}(x, s_{g_2}(y)))
g_{f_2,s_1}(f_{g_2,g_2}(x, y), z10) → g_{f_2,s_1}(f_{g_2,s_1}(x, s_{g_2}(y)), z10)
g_{f_2,s_1}(z00, f_{g_2,g_2}(x, y)) → g_{f_2,s_1}(z00, f_{g_2,s_1}(x, s_{g_2}(y)))
f_{g_2,s_1}(f_{g_2,g_2}(x, y), z10) → f_{g_2,s_1}(f_{g_2,s_1}(x, s_{g_2}(y)), z10)
f_{g_2,s_1}(z00, f_{g_2,g_2}(x, y)) → f_{g_2,s_1}(z00, f_{g_2,s_1}(x, s_{g_2}(y)))
g_{s_1,f_2}(f_{g_2,g_2}(x, y), z10) → g_{s_1,f_2}(f_{g_2,s_1}(x, s_{g_2}(y)), z10)
g_{s_1,f_2}(z00, f_{g_2,g_2}(x, y)) → g_{s_1,f_2}(z00, f_{g_2,s_1}(x, s_{g_2}(y)))
g_{f_2,f_2}(f_{g_2,g_2}(x, y), z10) → g_{f_2,f_2}(f_{g_2,s_1}(x, s_{g_2}(y)), z10)
g_{f_2,f_2}(z00, f_{g_2,g_2}(x, y)) → g_{f_2,f_2}(z00, f_{g_2,s_1}(x, s_{g_2}(y)))
f_{g_2,f_2}(f_{g_2,g_2}(x, y), z10) → f_{g_2,f_2}(f_{g_2,s_1}(x, s_{g_2}(y)), z10)
f_{g_2,f_2}(z00, f_{g_2,g_2}(x, y)) → f_{g_2,f_2}(z00, f_{g_2,s_1}(x, s_{g_2}(y)))
s_{s_1}(f_{g_2,g_2}(x, y)) → s_{s_1}(f_{g_2,s_1}(x, s_{g_2}(y)))
f_{s_1,g_2}(f_{g_2,g_2}(x, y), z10) → f_{s_1,g_2}(f_{g_2,s_1}(x, s_{g_2}(y)), z10)
f_{s_1,g_2}(z00, f_{g_2,g_2}(x, y)) → f_{s_1,g_2}(z00, f_{g_2,s_1}(x, s_{g_2}(y)))
f_{s_1,s_1}(f_{g_2,g_2}(x, y), z10) → f_{s_1,s_1}(f_{g_2,s_1}(x, s_{g_2}(y)), z10)
f_{s_1,s_1}(z00, f_{g_2,g_2}(x, y)) → f_{s_1,s_1}(z00, f_{g_2,s_1}(x, s_{g_2}(y)))
f_{s_1,f_2}(f_{g_2,g_2}(x, y), z10) → f_{s_1,f_2}(f_{g_2,s_1}(x, s_{g_2}(y)), z10)
f_{s_1,f_2}(z00, f_{g_2,g_2}(x, y)) → f_{s_1,f_2}(z00, f_{g_2,s_1}(x, s_{g_2}(y)))
s_{f_2}(f_{g_2,g_2}(x, y)) → s_{f_2}(f_{g_2,s_1}(x, s_{g_2}(y)))
f_{f_2,g_2}(f_{g_2,g_2}(x, y), z10) → f_{f_2,g_2}(f_{g_2,s_1}(x, s_{g_2}(y)), z10)
f_{f_2,g_2}(z00, f_{g_2,g_2}(x, y)) → f_{f_2,g_2}(z00, f_{g_2,s_1}(x, s_{g_2}(y)))
f_{f_2,s_1}(f_{g_2,g_2}(x, y), z10) → f_{f_2,s_1}(f_{g_2,s_1}(x, s_{g_2}(y)), z10)
f_{f_2,s_1}(z00, f_{g_2,g_2}(x, y)) → f_{f_2,s_1}(z00, f_{g_2,s_1}(x, s_{g_2}(y)))
f_{f_2,f_2}(f_{g_2,g_2}(x, y), z10) → f_{f_2,f_2}(f_{g_2,s_1}(x, s_{g_2}(y)), z10)
f_{f_2,f_2}(z00, f_{g_2,g_2}(x, y)) → f_{f_2,f_2}(z00, f_{g_2,s_1}(x, s_{g_2}(y)))
g_{g_2,g_2}(f_{g_2,g_2}(x, y), z10) → g_{g_2,g_2}(f_{g_2,s_1}(x, s_{g_2}(y)), z10)
g_{g_2,g_2}(z00, f_{g_2,g_2}(x, y)) → g_{g_2,g_2}(z00, f_{g_2,s_1}(x, s_{g_2}(y)))
g_{g_2,s_1}(f_{g_2,g_2}(x, y), z10) → g_{g_2,s_1}(f_{g_2,s_1}(x, s_{g_2}(y)), z10)
g_{g_2,s_1}(z00, f_{g_2,g_2}(x, y)) → g_{g_2,s_1}(z00, f_{g_2,s_1}(x, s_{g_2}(y)))
g_{g_2,f_2}(f_{g_2,g_2}(x, y), z10) → g_{g_2,f_2}(f_{g_2,s_1}(x, s_{g_2}(y)), z10)
g_{g_2,f_2}(z00, f_{g_2,g_2}(x, y)) → g_{g_2,f_2}(z00, f_{g_2,s_1}(x, s_{g_2}(y)))
g_{s_1,g_2}(f_{g_2,f_2}(x, y), z10) → g_{s_1,g_2}(f_{g_2,s_1}(x, s_{f_2}(y)), z10)
g_{s_1,g_2}(z00, f_{g_2,f_2}(x, y)) → g_{s_1,g_2}(z00, f_{g_2,s_1}(x, s_{f_2}(y)))
s_{g_2}(f_{g_2,f_2}(x, y)) → s_{g_2}(f_{g_2,s_1}(x, s_{f_2}(y)))
g_{f_2,g_2}(f_{g_2,f_2}(x, y), z10) → g_{f_2,g_2}(f_{g_2,s_1}(x, s_{f_2}(y)), z10)
g_{f_2,g_2}(z00, f_{g_2,f_2}(x, y)) → g_{f_2,g_2}(z00, f_{g_2,s_1}(x, s_{f_2}(y)))
f_{g_2,g_2}(f_{g_2,f_2}(x, y), z10) → f_{g_2,g_2}(f_{g_2,s_1}(x, s_{f_2}(y)), z10)
f_{g_2,g_2}(z00, f_{g_2,f_2}(x, y)) → f_{g_2,g_2}(z00, f_{g_2,s_1}(x, s_{f_2}(y)))
g_{s_1,s_1}(f_{g_2,f_2}(x, y), z10) → g_{s_1,s_1}(f_{g_2,s_1}(x, s_{f_2}(y)), z10)
g_{s_1,s_1}(z00, f_{g_2,f_2}(x, y)) → g_{s_1,s_1}(z00, f_{g_2,s_1}(x, s_{f_2}(y)))
g_{f_2,s_1}(f_{g_2,f_2}(x, y), z10) → g_{f_2,s_1}(f_{g_2,s_1}(x, s_{f_2}(y)), z10)
g_{f_2,s_1}(z00, f_{g_2,f_2}(x, y)) → g_{f_2,s_1}(z00, f_{g_2,s_1}(x, s_{f_2}(y)))
f_{g_2,s_1}(f_{g_2,f_2}(x, y), z10) → f_{g_2,s_1}(f_{g_2,s_1}(x, s_{f_2}(y)), z10)
f_{g_2,s_1}(z00, f_{g_2,f_2}(x, y)) → f_{g_2,s_1}(z00, f_{g_2,s_1}(x, s_{f_2}(y)))
g_{s_1,f_2}(f_{g_2,f_2}(x, y), z10) → g_{s_1,f_2}(f_{g_2,s_1}(x, s_{f_2}(y)), z10)
g_{s_1,f_2}(z00, f_{g_2,f_2}(x, y)) → g_{s_1,f_2}(z00, f_{g_2,s_1}(x, s_{f_2}(y)))
g_{f_2,f_2}(f_{g_2,f_2}(x, y), z10) → g_{f_2,f_2}(f_{g_2,s_1}(x, s_{f_2}(y)), z10)
g_{f_2,f_2}(z00, f_{g_2,f_2}(x, y)) → g_{f_2,f_2}(z00, f_{g_2,s_1}(x, s_{f_2}(y)))
f_{g_2,f_2}(f_{g_2,f_2}(x, y), z10) → f_{g_2,f_2}(f_{g_2,s_1}(x, s_{f_2}(y)), z10)
f_{g_2,f_2}(z00, f_{g_2,f_2}(x, y)) → f_{g_2,f_2}(z00, f_{g_2,s_1}(x, s_{f_2}(y)))
s_{s_1}(f_{g_2,f_2}(x, y)) → s_{s_1}(f_{g_2,s_1}(x, s_{f_2}(y)))
f_{s_1,g_2}(f_{g_2,f_2}(x, y), z10) → f_{s_1,g_2}(f_{g_2,s_1}(x, s_{f_2}(y)), z10)
f_{s_1,g_2}(z00, f_{g_2,f_2}(x, y)) → f_{s_1,g_2}(z00, f_{g_2,s_1}(x, s_{f_2}(y)))
f_{s_1,s_1}(f_{g_2,f_2}(x, y), z10) → f_{s_1,s_1}(f_{g_2,s_1}(x, s_{f_2}(y)), z10)
f_{s_1,s_1}(z00, f_{g_2,f_2}(x, y)) → f_{s_1,s_1}(z00, f_{g_2,s_1}(x, s_{f_2}(y)))
f_{s_1,f_2}(f_{g_2,f_2}(x, y), z10) → f_{s_1,f_2}(f_{g_2,s_1}(x, s_{f_2}(y)), z10)
f_{s_1,f_2}(z00, f_{g_2,f_2}(x, y)) → f_{s_1,f_2}(z00, f_{g_2,s_1}(x, s_{f_2}(y)))
s_{f_2}(f_{g_2,f_2}(x, y)) → s_{f_2}(f_{g_2,s_1}(x, s_{f_2}(y)))
f_{f_2,g_2}(f_{g_2,f_2}(x, y), z10) → f_{f_2,g_2}(f_{g_2,s_1}(x, s_{f_2}(y)), z10)
f_{f_2,g_2}(z00, f_{g_2,f_2}(x, y)) → f_{f_2,g_2}(z00, f_{g_2,s_1}(x, s_{f_2}(y)))
f_{f_2,s_1}(f_{g_2,f_2}(x, y), z10) → f_{f_2,s_1}(f_{g_2,s_1}(x, s_{f_2}(y)), z10)
f_{f_2,s_1}(z00, f_{g_2,f_2}(x, y)) → f_{f_2,s_1}(z00, f_{g_2,s_1}(x, s_{f_2}(y)))
f_{f_2,f_2}(f_{g_2,f_2}(x, y), z10) → f_{f_2,f_2}(f_{g_2,s_1}(x, s_{f_2}(y)), z10)
f_{f_2,f_2}(z00, f_{g_2,f_2}(x, y)) → f_{f_2,f_2}(z00, f_{g_2,s_1}(x, s_{f_2}(y)))
g_{g_2,g_2}(f_{g_2,f_2}(x, y), z10) → g_{g_2,g_2}(f_{g_2,s_1}(x, s_{f_2}(y)), z10)
g_{g_2,g_2}(z00, f_{g_2,f_2}(x, y)) → g_{g_2,g_2}(z00, f_{g_2,s_1}(x, s_{f_2}(y)))
g_{g_2,s_1}(f_{g_2,f_2}(x, y), z10) → g_{g_2,s_1}(f_{g_2,s_1}(x, s_{f_2}(y)), z10)
g_{g_2,s_1}(z00, f_{g_2,f_2}(x, y)) → g_{g_2,s_1}(z00, f_{g_2,s_1}(x, s_{f_2}(y)))
g_{g_2,f_2}(f_{g_2,f_2}(x, y), z10) → g_{g_2,f_2}(f_{g_2,s_1}(x, s_{f_2}(y)), z10)
g_{g_2,f_2}(z00, f_{g_2,f_2}(x, y)) → g_{g_2,f_2}(z00, f_{g_2,s_1}(x, s_{f_2}(y)))
g_{s_1,g_2}(f_{s_1,g_2}(x, y), z10) → g_{s_1,g_2}(f_{s_1,s_1}(x, s_{g_2}(y)), z10)
g_{s_1,g_2}(z00, f_{s_1,g_2}(x, y)) → g_{s_1,g_2}(z00, f_{s_1,s_1}(x, s_{g_2}(y)))
s_{g_2}(f_{s_1,g_2}(x, y)) → s_{g_2}(f_{s_1,s_1}(x, s_{g_2}(y)))
g_{f_2,g_2}(f_{s_1,g_2}(x, y), z10) → g_{f_2,g_2}(f_{s_1,s_1}(x, s_{g_2}(y)), z10)
g_{f_2,g_2}(z00, f_{s_1,g_2}(x, y)) → g_{f_2,g_2}(z00, f_{s_1,s_1}(x, s_{g_2}(y)))
f_{g_2,g_2}(f_{s_1,g_2}(x, y), z10) → f_{g_2,g_2}(f_{s_1,s_1}(x, s_{g_2}(y)), z10)
f_{g_2,g_2}(z00, f_{s_1,g_2}(x, y)) → f_{g_2,g_2}(z00, f_{s_1,s_1}(x, s_{g_2}(y)))
g_{s_1,s_1}(f_{s_1,g_2}(x, y), z10) → g_{s_1,s_1}(f_{s_1,s_1}(x, s_{g_2}(y)), z10)
g_{s_1,s_1}(z00, f_{s_1,g_2}(x, y)) → g_{s_1,s_1}(z00, f_{s_1,s_1}(x, s_{g_2}(y)))
g_{f_2,s_1}(f_{s_1,g_2}(x, y), z10) → g_{f_2,s_1}(f_{s_1,s_1}(x, s_{g_2}(y)), z10)
g_{f_2,s_1}(z00, f_{s_1,g_2}(x, y)) → g_{f_2,s_1}(z00, f_{s_1,s_1}(x, s_{g_2}(y)))
f_{g_2,s_1}(f_{s_1,g_2}(x, y), z10) → f_{g_2,s_1}(f_{s_1,s_1}(x, s_{g_2}(y)), z10)
f_{g_2,s_1}(z00, f_{s_1,g_2}(x, y)) → f_{g_2,s_1}(z00, f_{s_1,s_1}(x, s_{g_2}(y)))
g_{s_1,f_2}(f_{s_1,g_2}(x, y), z10) → g_{s_1,f_2}(f_{s_1,s_1}(x, s_{g_2}(y)), z10)
g_{s_1,f_2}(z00, f_{s_1,g_2}(x, y)) → g_{s_1,f_2}(z00, f_{s_1,s_1}(x, s_{g_2}(y)))
g_{f_2,f_2}(f_{s_1,g_2}(x, y), z10) → g_{f_2,f_2}(f_{s_1,s_1}(x, s_{g_2}(y)), z10)
g_{f_2,f_2}(z00, f_{s_1,g_2}(x, y)) → g_{f_2,f_2}(z00, f_{s_1,s_1}(x, s_{g_2}(y)))
f_{g_2,f_2}(f_{s_1,g_2}(x, y), z10) → f_{g_2,f_2}(f_{s_1,s_1}(x, s_{g_2}(y)), z10)
f_{g_2,f_2}(z00, f_{s_1,g_2}(x, y)) → f_{g_2,f_2}(z00, f_{s_1,s_1}(x, s_{g_2}(y)))
s_{s_1}(f_{s_1,g_2}(x, y)) → s_{s_1}(f_{s_1,s_1}(x, s_{g_2}(y)))
f_{s_1,g_2}(f_{s_1,g_2}(x, y), z10) → f_{s_1,g_2}(f_{s_1,s_1}(x, s_{g_2}(y)), z10)
f_{s_1,g_2}(z00, f_{s_1,g_2}(x, y)) → f_{s_1,g_2}(z00, f_{s_1,s_1}(x, s_{g_2}(y)))
f_{s_1,s_1}(f_{s_1,g_2}(x, y), z10) → f_{s_1,s_1}(f_{s_1,s_1}(x, s_{g_2}(y)), z10)
f_{s_1,s_1}(z00, f_{s_1,g_2}(x, y)) → f_{s_1,s_1}(z00, f_{s_1,s_1}(x, s_{g_2}(y)))
f_{s_1,f_2}(f_{s_1,g_2}(x, y), z10) → f_{s_1,f_2}(f_{s_1,s_1}(x, s_{g_2}(y)), z10)
f_{s_1,f_2}(z00, f_{s_1,g_2}(x, y)) → f_{s_1,f_2}(z00, f_{s_1,s_1}(x, s_{g_2}(y)))
s_{f_2}(f_{s_1,g_2}(x, y)) → s_{f_2}(f_{s_1,s_1}(x, s_{g_2}(y)))
f_{f_2,g_2}(f_{s_1,g_2}(x, y), z10) → f_{f_2,g_2}(f_{s_1,s_1}(x, s_{g_2}(y)), z10)
f_{f_2,g_2}(z00, f_{s_1,g_2}(x, y)) → f_{f_2,g_2}(z00, f_{s_1,s_1}(x, s_{g_2}(y)))
f_{f_2,s_1}(f_{s_1,g_2}(x, y), z10) → f_{f_2,s_1}(f_{s_1,s_1}(x, s_{g_2}(y)), z10)
f_{f_2,s_1}(z00, f_{s_1,g_2}(x, y)) → f_{f_2,s_1}(z00, f_{s_1,s_1}(x, s_{g_2}(y)))
f_{f_2,f_2}(f_{s_1,g_2}(x, y), z10) → f_{f_2,f_2}(f_{s_1,s_1}(x, s_{g_2}(y)), z10)
f_{f_2,f_2}(z00, f_{s_1,g_2}(x, y)) → f_{f_2,f_2}(z00, f_{s_1,s_1}(x, s_{g_2}(y)))
g_{g_2,g_2}(f_{s_1,g_2}(x, y), z10) → g_{g_2,g_2}(f_{s_1,s_1}(x, s_{g_2}(y)), z10)
g_{g_2,g_2}(z00, f_{s_1,g_2}(x, y)) → g_{g_2,g_2}(z00, f_{s_1,s_1}(x, s_{g_2}(y)))
g_{g_2,s_1}(f_{s_1,g_2}(x, y), z10) → g_{g_2,s_1}(f_{s_1,s_1}(x, s_{g_2}(y)), z10)
g_{g_2,s_1}(z00, f_{s_1,g_2}(x, y)) → g_{g_2,s_1}(z00, f_{s_1,s_1}(x, s_{g_2}(y)))
g_{g_2,f_2}(f_{s_1,g_2}(x, y), z10) → g_{g_2,f_2}(f_{s_1,s_1}(x, s_{g_2}(y)), z10)
g_{g_2,f_2}(z00, f_{s_1,g_2}(x, y)) → g_{g_2,f_2}(z00, f_{s_1,s_1}(x, s_{g_2}(y)))
g_{s_1,g_2}(f_{s_1,f_2}(x, y), z10) → g_{s_1,g_2}(f_{s_1,s_1}(x, s_{f_2}(y)), z10)
g_{s_1,g_2}(z00, f_{s_1,f_2}(x, y)) → g_{s_1,g_2}(z00, f_{s_1,s_1}(x, s_{f_2}(y)))
s_{g_2}(f_{s_1,f_2}(x, y)) → s_{g_2}(f_{s_1,s_1}(x, s_{f_2}(y)))
g_{f_2,g_2}(f_{s_1,f_2}(x, y), z10) → g_{f_2,g_2}(f_{s_1,s_1}(x, s_{f_2}(y)), z10)
g_{f_2,g_2}(z00, f_{s_1,f_2}(x, y)) → g_{f_2,g_2}(z00, f_{s_1,s_1}(x, s_{f_2}(y)))
f_{g_2,g_2}(f_{s_1,f_2}(x, y), z10) → f_{g_2,g_2}(f_{s_1,s_1}(x, s_{f_2}(y)), z10)
f_{g_2,g_2}(z00, f_{s_1,f_2}(x, y)) → f_{g_2,g_2}(z00, f_{s_1,s_1}(x, s_{f_2}(y)))
g_{s_1,s_1}(f_{s_1,f_2}(x, y), z10) → g_{s_1,s_1}(f_{s_1,s_1}(x, s_{f_2}(y)), z10)
g_{s_1,s_1}(z00, f_{s_1,f_2}(x, y)) → g_{s_1,s_1}(z00, f_{s_1,s_1}(x, s_{f_2}(y)))
g_{f_2,s_1}(f_{s_1,f_2}(x, y), z10) → g_{f_2,s_1}(f_{s_1,s_1}(x, s_{f_2}(y)), z10)
g_{f_2,s_1}(z00, f_{s_1,f_2}(x, y)) → g_{f_2,s_1}(z00, f_{s_1,s_1}(x, s_{f_2}(y)))
f_{g_2,s_1}(f_{s_1,f_2}(x, y), z10) → f_{g_2,s_1}(f_{s_1,s_1}(x, s_{f_2}(y)), z10)
f_{g_2,s_1}(z00, f_{s_1,f_2}(x, y)) → f_{g_2,s_1}(z00, f_{s_1,s_1}(x, s_{f_2}(y)))
g_{s_1,f_2}(f_{s_1,f_2}(x, y), z10) → g_{s_1,f_2}(f_{s_1,s_1}(x, s_{f_2}(y)), z10)
g_{s_1,f_2}(z00, f_{s_1,f_2}(x, y)) → g_{s_1,f_2}(z00, f_{s_1,s_1}(x, s_{f_2}(y)))
g_{f_2,f_2}(f_{s_1,f_2}(x, y), z10) → g_{f_2,f_2}(f_{s_1,s_1}(x, s_{f_2}(y)), z10)
g_{f_2,f_2}(z00, f_{s_1,f_2}(x, y)) → g_{f_2,f_2}(z00, f_{s_1,s_1}(x, s_{f_2}(y)))
f_{g_2,f_2}(f_{s_1,f_2}(x, y), z10) → f_{g_2,f_2}(f_{s_1,s_1}(x, s_{f_2}(y)), z10)
f_{g_2,f_2}(z00, f_{s_1,f_2}(x, y)) → f_{g_2,f_2}(z00, f_{s_1,s_1}(x, s_{f_2}(y)))
s_{s_1}(f_{s_1,f_2}(x, y)) → s_{s_1}(f_{s_1,s_1}(x, s_{f_2}(y)))
f_{s_1,g_2}(f_{s_1,f_2}(x, y), z10) → f_{s_1,g_2}(f_{s_1,s_1}(x, s_{f_2}(y)), z10)
f_{s_1,g_2}(z00, f_{s_1,f_2}(x, y)) → f_{s_1,g_2}(z00, f_{s_1,s_1}(x, s_{f_2}(y)))
f_{s_1,s_1}(f_{s_1,f_2}(x, y), z10) → f_{s_1,s_1}(f_{s_1,s_1}(x, s_{f_2}(y)), z10)
f_{s_1,s_1}(z00, f_{s_1,f_2}(x, y)) → f_{s_1,s_1}(z00, f_{s_1,s_1}(x, s_{f_2}(y)))
f_{s_1,f_2}(f_{s_1,f_2}(x, y), z10) → f_{s_1,f_2}(f_{s_1,s_1}(x, s_{f_2}(y)), z10)
f_{s_1,f_2}(z00, f_{s_1,f_2}(x, y)) → f_{s_1,f_2}(z00, f_{s_1,s_1}(x, s_{f_2}(y)))
s_{f_2}(f_{s_1,f_2}(x, y)) → s_{f_2}(f_{s_1,s_1}(x, s_{f_2}(y)))
f_{f_2,g_2}(f_{s_1,f_2}(x, y), z10) → f_{f_2,g_2}(f_{s_1,s_1}(x, s_{f_2}(y)), z10)
f_{f_2,g_2}(z00, f_{s_1,f_2}(x, y)) → f_{f_2,g_2}(z00, f_{s_1,s_1}(x, s_{f_2}(y)))
f_{f_2,s_1}(f_{s_1,f_2}(x, y), z10) → f_{f_2,s_1}(f_{s_1,s_1}(x, s_{f_2}(y)), z10)
f_{f_2,s_1}(z00, f_{s_1,f_2}(x, y)) → f_{f_2,s_1}(z00, f_{s_1,s_1}(x, s_{f_2}(y)))
f_{f_2,f_2}(f_{s_1,f_2}(x, y), z10) → f_{f_2,f_2}(f_{s_1,s_1}(x, s_{f_2}(y)), z10)
f_{f_2,f_2}(z00, f_{s_1,f_2}(x, y)) → f_{f_2,f_2}(z00, f_{s_1,s_1}(x, s_{f_2}(y)))
g_{g_2,g_2}(f_{s_1,f_2}(x, y), z10) → g_{g_2,g_2}(f_{s_1,s_1}(x, s_{f_2}(y)), z10)
g_{g_2,g_2}(z00, f_{s_1,f_2}(x, y)) → g_{g_2,g_2}(z00, f_{s_1,s_1}(x, s_{f_2}(y)))
g_{g_2,s_1}(f_{s_1,f_2}(x, y), z10) → g_{g_2,s_1}(f_{s_1,s_1}(x, s_{f_2}(y)), z10)
g_{g_2,s_1}(z00, f_{s_1,f_2}(x, y)) → g_{g_2,s_1}(z00, f_{s_1,s_1}(x, s_{f_2}(y)))
g_{g_2,f_2}(f_{s_1,f_2}(x, y), z10) → g_{g_2,f_2}(f_{s_1,s_1}(x, s_{f_2}(y)), z10)
g_{g_2,f_2}(z00, f_{s_1,f_2}(x, y)) → g_{g_2,f_2}(z00, f_{s_1,s_1}(x, s_{f_2}(y)))
g_{s_1,g_2}(f_{f_2,g_2}(x, y), z10) → g_{s_1,g_2}(f_{f_2,s_1}(x, s_{g_2}(y)), z10)
g_{s_1,g_2}(z00, f_{f_2,g_2}(x, y)) → g_{s_1,g_2}(z00, f_{f_2,s_1}(x, s_{g_2}(y)))
s_{g_2}(f_{f_2,g_2}(x, y)) → s_{g_2}(f_{f_2,s_1}(x, s_{g_2}(y)))
g_{f_2,g_2}(f_{f_2,g_2}(x, y), z10) → g_{f_2,g_2}(f_{f_2,s_1}(x, s_{g_2}(y)), z10)
g_{f_2,g_2}(z00, f_{f_2,g_2}(x, y)) → g_{f_2,g_2}(z00, f_{f_2,s_1}(x, s_{g_2}(y)))
f_{g_2,g_2}(f_{f_2,g_2}(x, y), z10) → f_{g_2,g_2}(f_{f_2,s_1}(x, s_{g_2}(y)), z10)
f_{g_2,g_2}(z00, f_{f_2,g_2}(x, y)) → f_{g_2,g_2}(z00, f_{f_2,s_1}(x, s_{g_2}(y)))
g_{s_1,s_1}(f_{f_2,g_2}(x, y), z10) → g_{s_1,s_1}(f_{f_2,s_1}(x, s_{g_2}(y)), z10)
g_{s_1,s_1}(z00, f_{f_2,g_2}(x, y)) → g_{s_1,s_1}(z00, f_{f_2,s_1}(x, s_{g_2}(y)))
g_{f_2,s_1}(f_{f_2,g_2}(x, y), z10) → g_{f_2,s_1}(f_{f_2,s_1}(x, s_{g_2}(y)), z10)
g_{f_2,s_1}(z00, f_{f_2,g_2}(x, y)) → g_{f_2,s_1}(z00, f_{f_2,s_1}(x, s_{g_2}(y)))
f_{g_2,s_1}(f_{f_2,g_2}(x, y), z10) → f_{g_2,s_1}(f_{f_2,s_1}(x, s_{g_2}(y)), z10)
f_{g_2,s_1}(z00, f_{f_2,g_2}(x, y)) → f_{g_2,s_1}(z00, f_{f_2,s_1}(x, s_{g_2}(y)))
g_{s_1,f_2}(f_{f_2,g_2}(x, y), z10) → g_{s_1,f_2}(f_{f_2,s_1}(x, s_{g_2}(y)), z10)
g_{s_1,f_2}(z00, f_{f_2,g_2}(x, y)) → g_{s_1,f_2}(z00, f_{f_2,s_1}(x, s_{g_2}(y)))
g_{f_2,f_2}(f_{f_2,g_2}(x, y), z10) → g_{f_2,f_2}(f_{f_2,s_1}(x, s_{g_2}(y)), z10)
g_{f_2,f_2}(z00, f_{f_2,g_2}(x, y)) → g_{f_2,f_2}(z00, f_{f_2,s_1}(x, s_{g_2}(y)))
f_{g_2,f_2}(f_{f_2,g_2}(x, y), z10) → f_{g_2,f_2}(f_{f_2,s_1}(x, s_{g_2}(y)), z10)
f_{g_2,f_2}(z00, f_{f_2,g_2}(x, y)) → f_{g_2,f_2}(z00, f_{f_2,s_1}(x, s_{g_2}(y)))
s_{s_1}(f_{f_2,g_2}(x, y)) → s_{s_1}(f_{f_2,s_1}(x, s_{g_2}(y)))
f_{s_1,g_2}(f_{f_2,g_2}(x, y), z10) → f_{s_1,g_2}(f_{f_2,s_1}(x, s_{g_2}(y)), z10)
f_{s_1,g_2}(z00, f_{f_2,g_2}(x, y)) → f_{s_1,g_2}(z00, f_{f_2,s_1}(x, s_{g_2}(y)))
f_{s_1,s_1}(f_{f_2,g_2}(x, y), z10) → f_{s_1,s_1}(f_{f_2,s_1}(x, s_{g_2}(y)), z10)
f_{s_1,s_1}(z00, f_{f_2,g_2}(x, y)) → f_{s_1,s_1}(z00, f_{f_2,s_1}(x, s_{g_2}(y)))
f_{s_1,f_2}(f_{f_2,g_2}(x, y), z10) → f_{s_1,f_2}(f_{f_2,s_1}(x, s_{g_2}(y)), z10)
f_{s_1,f_2}(z00, f_{f_2,g_2}(x, y)) → f_{s_1,f_2}(z00, f_{f_2,s_1}(x, s_{g_2}(y)))
s_{f_2}(f_{f_2,g_2}(x, y)) → s_{f_2}(f_{f_2,s_1}(x, s_{g_2}(y)))
f_{f_2,g_2}(f_{f_2,g_2}(x, y), z10) → f_{f_2,g_2}(f_{f_2,s_1}(x, s_{g_2}(y)), z10)
f_{f_2,g_2}(z00, f_{f_2,g_2}(x, y)) → f_{f_2,g_2}(z00, f_{f_2,s_1}(x, s_{g_2}(y)))
f_{f_2,s_1}(f_{f_2,g_2}(x, y), z10) → f_{f_2,s_1}(f_{f_2,s_1}(x, s_{g_2}(y)), z10)
f_{f_2,s_1}(z00, f_{f_2,g_2}(x, y)) → f_{f_2,s_1}(z00, f_{f_2,s_1}(x, s_{g_2}(y)))
f_{f_2,f_2}(f_{f_2,g_2}(x, y), z10) → f_{f_2,f_2}(f_{f_2,s_1}(x, s_{g_2}(y)), z10)
f_{f_2,f_2}(z00, f_{f_2,g_2}(x, y)) → f_{f_2,f_2}(z00, f_{f_2,s_1}(x, s_{g_2}(y)))
g_{g_2,g_2}(f_{f_2,g_2}(x, y), z10) → g_{g_2,g_2}(f_{f_2,s_1}(x, s_{g_2}(y)), z10)
g_{g_2,g_2}(z00, f_{f_2,g_2}(x, y)) → g_{g_2,g_2}(z00, f_{f_2,s_1}(x, s_{g_2}(y)))
g_{g_2,s_1}(f_{f_2,g_2}(x, y), z10) → g_{g_2,s_1}(f_{f_2,s_1}(x, s_{g_2}(y)), z10)
g_{g_2,s_1}(z00, f_{f_2,g_2}(x, y)) → g_{g_2,s_1}(z00, f_{f_2,s_1}(x, s_{g_2}(y)))
g_{g_2,f_2}(f_{f_2,g_2}(x, y), z10) → g_{g_2,f_2}(f_{f_2,s_1}(x, s_{g_2}(y)), z10)
g_{g_2,f_2}(z00, f_{f_2,g_2}(x, y)) → g_{g_2,f_2}(z00, f_{f_2,s_1}(x, s_{g_2}(y)))
g_{s_1,g_2}(f_{f_2,f_2}(x, y), z10) → g_{s_1,g_2}(f_{f_2,s_1}(x, s_{f_2}(y)), z10)
g_{s_1,g_2}(z00, f_{f_2,f_2}(x, y)) → g_{s_1,g_2}(z00, f_{f_2,s_1}(x, s_{f_2}(y)))
s_{g_2}(f_{f_2,f_2}(x, y)) → s_{g_2}(f_{f_2,s_1}(x, s_{f_2}(y)))
g_{f_2,g_2}(f_{f_2,f_2}(x, y), z10) → g_{f_2,g_2}(f_{f_2,s_1}(x, s_{f_2}(y)), z10)
g_{f_2,g_2}(z00, f_{f_2,f_2}(x, y)) → g_{f_2,g_2}(z00, f_{f_2,s_1}(x, s_{f_2}(y)))
f_{g_2,g_2}(f_{f_2,f_2}(x, y), z10) → f_{g_2,g_2}(f_{f_2,s_1}(x, s_{f_2}(y)), z10)
f_{g_2,g_2}(z00, f_{f_2,f_2}(x, y)) → f_{g_2,g_2}(z00, f_{f_2,s_1}(x, s_{f_2}(y)))
g_{s_1,s_1}(f_{f_2,f_2}(x, y), z10) → g_{s_1,s_1}(f_{f_2,s_1}(x, s_{f_2}(y)), z10)
g_{s_1,s_1}(z00, f_{f_2,f_2}(x, y)) → g_{s_1,s_1}(z00, f_{f_2,s_1}(x, s_{f_2}(y)))
g_{f_2,s_1}(f_{f_2,f_2}(x, y), z10) → g_{f_2,s_1}(f_{f_2,s_1}(x, s_{f_2}(y)), z10)
g_{f_2,s_1}(z00, f_{f_2,f_2}(x, y)) → g_{f_2,s_1}(z00, f_{f_2,s_1}(x, s_{f_2}(y)))
f_{g_2,s_1}(f_{f_2,f_2}(x, y), z10) → f_{g_2,s_1}(f_{f_2,s_1}(x, s_{f_2}(y)), z10)
f_{g_2,s_1}(z00, f_{f_2,f_2}(x, y)) → f_{g_2,s_1}(z00, f_{f_2,s_1}(x, s_{f_2}(y)))
g_{s_1,f_2}(f_{f_2,f_2}(x, y), z10) → g_{s_1,f_2}(f_{f_2,s_1}(x, s_{f_2}(y)), z10)
g_{s_1,f_2}(z00, f_{f_2,f_2}(x, y)) → g_{s_1,f_2}(z00, f_{f_2,s_1}(x, s_{f_2}(y)))
g_{f_2,f_2}(f_{f_2,f_2}(x, y), z10) → g_{f_2,f_2}(f_{f_2,s_1}(x, s_{f_2}(y)), z10)
g_{f_2,f_2}(z00, f_{f_2,f_2}(x, y)) → g_{f_2,f_2}(z00, f_{f_2,s_1}(x, s_{f_2}(y)))
f_{g_2,f_2}(f_{f_2,f_2}(x, y), z10) → f_{g_2,f_2}(f_{f_2,s_1}(x, s_{f_2}(y)), z10)
f_{g_2,f_2}(z00, f_{f_2,f_2}(x, y)) → f_{g_2,f_2}(z00, f_{f_2,s_1}(x, s_{f_2}(y)))
s_{s_1}(f_{f_2,f_2}(x, y)) → s_{s_1}(f_{f_2,s_1}(x, s_{f_2}(y)))
f_{s_1,g_2}(f_{f_2,f_2}(x, y), z10) → f_{s_1,g_2}(f_{f_2,s_1}(x, s_{f_2}(y)), z10)
f_{s_1,g_2}(z00, f_{f_2,f_2}(x, y)) → f_{s_1,g_2}(z00, f_{f_2,s_1}(x, s_{f_2}(y)))
f_{s_1,s_1}(f_{f_2,f_2}(x, y), z10) → f_{s_1,s_1}(f_{f_2,s_1}(x, s_{f_2}(y)), z10)
f_{s_1,s_1}(z00, f_{f_2,f_2}(x, y)) → f_{s_1,s_1}(z00, f_{f_2,s_1}(x, s_{f_2}(y)))
f_{s_1,f_2}(f_{f_2,f_2}(x, y), z10) → f_{s_1,f_2}(f_{f_2,s_1}(x, s_{f_2}(y)), z10)
f_{s_1,f_2}(z00, f_{f_2,f_2}(x, y)) → f_{s_1,f_2}(z00, f_{f_2,s_1}(x, s_{f_2}(y)))
s_{f_2}(f_{f_2,f_2}(x, y)) → s_{f_2}(f_{f_2,s_1}(x, s_{f_2}(y)))
f_{f_2,g_2}(f_{f_2,f_2}(x, y), z10) → f_{f_2,g_2}(f_{f_2,s_1}(x, s_{f_2}(y)), z10)
f_{f_2,g_2}(z00, f_{f_2,f_2}(x, y)) → f_{f_2,g_2}(z00, f_{f_2,s_1}(x, s_{f_2}(y)))
f_{f_2,s_1}(f_{f_2,f_2}(x, y), z10) → f_{f_2,s_1}(f_{f_2,s_1}(x, s_{f_2}(y)), z10)
f_{f_2,s_1}(z00, f_{f_2,f_2}(x, y)) → f_{f_2,s_1}(z00, f_{f_2,s_1}(x, s_{f_2}(y)))
f_{f_2,f_2}(f_{f_2,f_2}(x, y), z10) → f_{f_2,f_2}(f_{f_2,s_1}(x, s_{f_2}(y)), z10)
f_{f_2,f_2}(z00, f_{f_2,f_2}(x, y)) → f_{f_2,f_2}(z00, f_{f_2,s_1}(x, s_{f_2}(y)))
g_{g_2,g_2}(f_{f_2,f_2}(x, y), z10) → g_{g_2,g_2}(f_{f_2,s_1}(x, s_{f_2}(y)), z10)
g_{g_2,g_2}(z00, f_{f_2,f_2}(x, y)) → g_{g_2,g_2}(z00, f_{f_2,s_1}(x, s_{f_2}(y)))
g_{g_2,s_1}(f_{f_2,f_2}(x, y), z10) → g_{g_2,s_1}(f_{f_2,s_1}(x, s_{f_2}(y)), z10)
g_{g_2,s_1}(z00, f_{f_2,f_2}(x, y)) → g_{g_2,s_1}(z00, f_{f_2,s_1}(x, s_{f_2}(y)))
g_{g_2,f_2}(f_{f_2,f_2}(x, y), z10) → g_{g_2,f_2}(f_{f_2,s_1}(x, s_{f_2}(y)), z10)
g_{g_2,f_2}(z00, f_{f_2,f_2}(x, y)) → g_{g_2,f_2}(z00, f_{f_2,s_1}(x, s_{f_2}(y)))
g_{s_1,g_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{s_1,g_2}(g_{g_2,g_2}(x, z1), z10)
g_{s_1,g_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → g_{s_1,g_2}(z00, g_{g_2,g_2}(x, z1))
s_{g_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → s_{g_2}(g_{g_2,g_2}(x, z1))
g_{f_2,g_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{f_2,g_2}(g_{g_2,g_2}(x, z1), z10)
g_{f_2,g_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → g_{f_2,g_2}(z00, g_{g_2,g_2}(x, z1))
f_{g_2,g_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{g_2,g_2}(g_{g_2,g_2}(x, z1), z10)
f_{g_2,g_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → f_{g_2,g_2}(z00, g_{g_2,g_2}(x, z1))
g_{s_1,s_1}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{s_1,s_1}(g_{g_2,g_2}(x, z1), z10)
g_{s_1,s_1}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → g_{s_1,s_1}(z00, g_{g_2,g_2}(x, z1))
g_{f_2,s_1}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{f_2,s_1}(g_{g_2,g_2}(x, z1), z10)
g_{f_2,s_1}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → g_{f_2,s_1}(z00, g_{g_2,g_2}(x, z1))
f_{g_2,s_1}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{g_2,s_1}(g_{g_2,g_2}(x, z1), z10)
f_{g_2,s_1}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → f_{g_2,s_1}(z00, g_{g_2,g_2}(x, z1))
g_{s_1,f_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{s_1,f_2}(g_{g_2,g_2}(x, z1), z10)
g_{s_1,f_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → g_{s_1,f_2}(z00, g_{g_2,g_2}(x, z1))
g_{f_2,f_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{f_2,f_2}(g_{g_2,g_2}(x, z1), z10)
g_{f_2,f_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → g_{f_2,f_2}(z00, g_{g_2,g_2}(x, z1))
f_{g_2,f_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{g_2,f_2}(g_{g_2,g_2}(x, z1), z10)
f_{g_2,f_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → f_{g_2,f_2}(z00, g_{g_2,g_2}(x, z1))
s_{s_1}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → s_{s_1}(g_{g_2,g_2}(x, z1))
f_{s_1,g_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{s_1,g_2}(g_{g_2,g_2}(x, z1), z10)
f_{s_1,g_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → f_{s_1,g_2}(z00, g_{g_2,g_2}(x, z1))
f_{s_1,s_1}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{s_1,s_1}(g_{g_2,g_2}(x, z1), z10)
f_{s_1,s_1}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → f_{s_1,s_1}(z00, g_{g_2,g_2}(x, z1))
f_{s_1,f_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{s_1,f_2}(g_{g_2,g_2}(x, z1), z10)
f_{s_1,f_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → f_{s_1,f_2}(z00, g_{g_2,g_2}(x, z1))
s_{f_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → s_{f_2}(g_{g_2,g_2}(x, z1))
f_{f_2,g_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{f_2,g_2}(g_{g_2,g_2}(x, z1), z10)
f_{f_2,g_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → f_{f_2,g_2}(z00, g_{g_2,g_2}(x, z1))
f_{f_2,s_1}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{f_2,s_1}(g_{g_2,g_2}(x, z1), z10)
f_{f_2,s_1}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → f_{f_2,s_1}(z00, g_{g_2,g_2}(x, z1))
f_{f_2,f_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{f_2,f_2}(g_{g_2,g_2}(x, z1), z10)
f_{f_2,f_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → f_{f_2,f_2}(z00, g_{g_2,g_2}(x, z1))
g_{g_2,g_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{g_2,g_2}(g_{g_2,g_2}(x, z1), z10)
g_{g_2,g_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → g_{g_2,g_2}(z00, g_{g_2,g_2}(x, z1))
g_{g_2,s_1}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{g_2,s_1}(g_{g_2,g_2}(x, z1), z10)
g_{g_2,s_1}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → g_{g_2,s_1}(z00, g_{g_2,g_2}(x, z1))
g_{g_2,f_2}(g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{g_2,f_2}(g_{g_2,g_2}(x, z1), z10)
g_{g_2,f_2}(z00, g_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → g_{g_2,f_2}(z00, g_{g_2,g_2}(x, z1))
g_{s_1,g_2}(g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → g_{s_1,g_2}(g_{g_2,s_1}(x, z1), z10)
g_{s_1,g_2}(z00, g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → g_{s_1,g_2}(z00, g_{g_2,s_1}(x, z1))
s_{g_2}(g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → s_{g_2}(g_{g_2,s_1}(x, z1))
g_{f_2,g_2}(g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → g_{f_2,g_2}(g_{g_2,s_1}(x, z1), z10)
g_{f_2,g_2}(z00, g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → g_{f_2,g_2}(z00, g_{g_2,s_1}(x, z1))
f_{g_2,g_2}(g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → f_{g_2,g_2}(g_{g_2,s_1}(x, z1), z10)
f_{g_2,g_2}(z00, g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → f_{g_2,g_2}(z00, g_{g_2,s_1}(x, z1))
g_{s_1,s_1}(g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → g_{s_1,s_1}(g_{g_2,s_1}(x, z1), z10)
g_{s_1,s_1}(z00, g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → g_{s_1,s_1}(z00, g_{g_2,s_1}(x, z1))
g_{f_2,s_1}(g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → g_{f_2,s_1}(g_{g_2,s_1}(x, z1), z10)
g_{f_2,s_1}(z00, g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → g_{f_2,s_1}(z00, g_{g_2,s_1}(x, z1))
f_{g_2,s_1}(g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → f_{g_2,s_1}(g_{g_2,s_1}(x, z1), z10)
f_{g_2,s_1}(z00, g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → f_{g_2,s_1}(z00, g_{g_2,s_1}(x, z1))
g_{s_1,f_2}(g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → g_{s_1,f_2}(g_{g_2,s_1}(x, z1), z10)
g_{s_1,f_2}(z00, g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → g_{s_1,f_2}(z00, g_{g_2,s_1}(x, z1))
g_{f_2,f_2}(g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → g_{f_2,f_2}(g_{g_2,s_1}(x, z1), z10)
g_{f_2,f_2}(z00, g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → g_{f_2,f_2}(z00, g_{g_2,s_1}(x, z1))
f_{g_2,f_2}(g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → f_{g_2,f_2}(g_{g_2,s_1}(x, z1), z10)
f_{g_2,f_2}(z00, g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → f_{g_2,f_2}(z00, g_{g_2,s_1}(x, z1))
s_{s_1}(g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → s_{s_1}(g_{g_2,s_1}(x, z1))
f_{s_1,g_2}(g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → f_{s_1,g_2}(g_{g_2,s_1}(x, z1), z10)
f_{s_1,g_2}(z00, g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → f_{s_1,g_2}(z00, g_{g_2,s_1}(x, z1))
f_{s_1,s_1}(g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → f_{s_1,s_1}(g_{g_2,s_1}(x, z1), z10)
f_{s_1,s_1}(z00, g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → f_{s_1,s_1}(z00, g_{g_2,s_1}(x, z1))
f_{s_1,f_2}(g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → f_{s_1,f_2}(g_{g_2,s_1}(x, z1), z10)
f_{s_1,f_2}(z00, g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → f_{s_1,f_2}(z00, g_{g_2,s_1}(x, z1))
s_{f_2}(g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → s_{f_2}(g_{g_2,s_1}(x, z1))
f_{f_2,g_2}(g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → f_{f_2,g_2}(g_{g_2,s_1}(x, z1), z10)
f_{f_2,g_2}(z00, g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → f_{f_2,g_2}(z00, g_{g_2,s_1}(x, z1))
f_{f_2,s_1}(g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → f_{f_2,s_1}(g_{g_2,s_1}(x, z1), z10)
f_{f_2,s_1}(z00, g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → f_{f_2,s_1}(z00, g_{g_2,s_1}(x, z1))
f_{f_2,f_2}(g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → f_{f_2,f_2}(g_{g_2,s_1}(x, z1), z10)
f_{f_2,f_2}(z00, g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → f_{f_2,f_2}(z00, g_{g_2,s_1}(x, z1))
g_{g_2,g_2}(g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → g_{g_2,g_2}(g_{g_2,s_1}(x, z1), z10)
g_{g_2,g_2}(z00, g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → g_{g_2,g_2}(z00, g_{g_2,s_1}(x, z1))
g_{g_2,s_1}(g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → g_{g_2,s_1}(g_{g_2,s_1}(x, z1), z10)
g_{g_2,s_1}(z00, g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → g_{g_2,s_1}(z00, g_{g_2,s_1}(x, z1))
g_{g_2,f_2}(g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → g_{g_2,f_2}(g_{g_2,s_1}(x, z1), z10)
g_{g_2,f_2}(z00, g_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → g_{g_2,f_2}(z00, g_{g_2,s_1}(x, z1))
g_{s_1,g_2}(g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{s_1,g_2}(g_{g_2,f_2}(x, z1), z10)
g_{s_1,g_2}(z00, g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → g_{s_1,g_2}(z00, g_{g_2,f_2}(x, z1))
s_{g_2}(g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → s_{g_2}(g_{g_2,f_2}(x, z1))
g_{f_2,g_2}(g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{f_2,g_2}(g_{g_2,f_2}(x, z1), z10)
g_{f_2,g_2}(z00, g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → g_{f_2,g_2}(z00, g_{g_2,f_2}(x, z1))
f_{g_2,g_2}(g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{g_2,g_2}(g_{g_2,f_2}(x, z1), z10)
f_{g_2,g_2}(z00, g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → f_{g_2,g_2}(z00, g_{g_2,f_2}(x, z1))
g_{s_1,s_1}(g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{s_1,s_1}(g_{g_2,f_2}(x, z1), z10)
g_{s_1,s_1}(z00, g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → g_{s_1,s_1}(z00, g_{g_2,f_2}(x, z1))
g_{f_2,s_1}(g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{f_2,s_1}(g_{g_2,f_2}(x, z1), z10)
g_{f_2,s_1}(z00, g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → g_{f_2,s_1}(z00, g_{g_2,f_2}(x, z1))
f_{g_2,s_1}(g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{g_2,s_1}(g_{g_2,f_2}(x, z1), z10)
f_{g_2,s_1}(z00, g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → f_{g_2,s_1}(z00, g_{g_2,f_2}(x, z1))
g_{s_1,f_2}(g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{s_1,f_2}(g_{g_2,f_2}(x, z1), z10)
g_{s_1,f_2}(z00, g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → g_{s_1,f_2}(z00, g_{g_2,f_2}(x, z1))
g_{f_2,f_2}(g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{f_2,f_2}(g_{g_2,f_2}(x, z1), z10)
g_{f_2,f_2}(z00, g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → g_{f_2,f_2}(z00, g_{g_2,f_2}(x, z1))
f_{g_2,f_2}(g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{g_2,f_2}(g_{g_2,f_2}(x, z1), z10)
f_{g_2,f_2}(z00, g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → f_{g_2,f_2}(z00, g_{g_2,f_2}(x, z1))
s_{s_1}(g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → s_{s_1}(g_{g_2,f_2}(x, z1))
f_{s_1,g_2}(g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{s_1,g_2}(g_{g_2,f_2}(x, z1), z10)
f_{s_1,g_2}(z00, g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → f_{s_1,g_2}(z00, g_{g_2,f_2}(x, z1))
f_{s_1,s_1}(g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{s_1,s_1}(g_{g_2,f_2}(x, z1), z10)
f_{s_1,s_1}(z00, g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → f_{s_1,s_1}(z00, g_{g_2,f_2}(x, z1))
f_{s_1,f_2}(g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{s_1,f_2}(g_{g_2,f_2}(x, z1), z10)
f_{s_1,f_2}(z00, g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → f_{s_1,f_2}(z00, g_{g_2,f_2}(x, z1))
s_{f_2}(g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → s_{f_2}(g_{g_2,f_2}(x, z1))
f_{f_2,g_2}(g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{f_2,g_2}(g_{g_2,f_2}(x, z1), z10)
f_{f_2,g_2}(z00, g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → f_{f_2,g_2}(z00, g_{g_2,f_2}(x, z1))
f_{f_2,s_1}(g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{f_2,s_1}(g_{g_2,f_2}(x, z1), z10)
f_{f_2,s_1}(z00, g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → f_{f_2,s_1}(z00, g_{g_2,f_2}(x, z1))
f_{f_2,f_2}(g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{f_2,f_2}(g_{g_2,f_2}(x, z1), z10)
f_{f_2,f_2}(z00, g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → f_{f_2,f_2}(z00, g_{g_2,f_2}(x, z1))
g_{g_2,g_2}(g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{g_2,g_2}(g_{g_2,f_2}(x, z1), z10)
g_{g_2,g_2}(z00, g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → g_{g_2,g_2}(z00, g_{g_2,f_2}(x, z1))
g_{g_2,s_1}(g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{g_2,s_1}(g_{g_2,f_2}(x, z1), z10)
g_{g_2,s_1}(z00, g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → g_{g_2,s_1}(z00, g_{g_2,f_2}(x, z1))
g_{g_2,f_2}(g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{g_2,f_2}(g_{g_2,f_2}(x, z1), z10)
g_{g_2,f_2}(z00, g_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → g_{g_2,f_2}(z00, g_{g_2,f_2}(x, z1))
g_{s_1,g_2}(g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{s_1,g_2}(g_{g_2,g_2}(x, z1), z10)
g_{s_1,g_2}(z00, g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → g_{s_1,g_2}(z00, g_{g_2,g_2}(x, z1))
s_{g_2}(g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → s_{g_2}(g_{g_2,g_2}(x, z1))
g_{f_2,g_2}(g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{f_2,g_2}(g_{g_2,g_2}(x, z1), z10)
g_{f_2,g_2}(z00, g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → g_{f_2,g_2}(z00, g_{g_2,g_2}(x, z1))
f_{g_2,g_2}(g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{g_2,g_2}(g_{g_2,g_2}(x, z1), z10)
f_{g_2,g_2}(z00, g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → f_{g_2,g_2}(z00, g_{g_2,g_2}(x, z1))
g_{s_1,s_1}(g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{s_1,s_1}(g_{g_2,g_2}(x, z1), z10)
g_{s_1,s_1}(z00, g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → g_{s_1,s_1}(z00, g_{g_2,g_2}(x, z1))
g_{f_2,s_1}(g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{f_2,s_1}(g_{g_2,g_2}(x, z1), z10)
g_{f_2,s_1}(z00, g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → g_{f_2,s_1}(z00, g_{g_2,g_2}(x, z1))
f_{g_2,s_1}(g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{g_2,s_1}(g_{g_2,g_2}(x, z1), z10)
f_{g_2,s_1}(z00, g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → f_{g_2,s_1}(z00, g_{g_2,g_2}(x, z1))
g_{s_1,f_2}(g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{s_1,f_2}(g_{g_2,g_2}(x, z1), z10)
g_{s_1,f_2}(z00, g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → g_{s_1,f_2}(z00, g_{g_2,g_2}(x, z1))
g_{f_2,f_2}(g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{f_2,f_2}(g_{g_2,g_2}(x, z1), z10)
g_{f_2,f_2}(z00, g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → g_{f_2,f_2}(z00, g_{g_2,g_2}(x, z1))
f_{g_2,f_2}(g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{g_2,f_2}(g_{g_2,g_2}(x, z1), z10)
f_{g_2,f_2}(z00, g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → f_{g_2,f_2}(z00, g_{g_2,g_2}(x, z1))
s_{s_1}(g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → s_{s_1}(g_{g_2,g_2}(x, z1))
f_{s_1,g_2}(g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{s_1,g_2}(g_{g_2,g_2}(x, z1), z10)
f_{s_1,g_2}(z00, g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → f_{s_1,g_2}(z00, g_{g_2,g_2}(x, z1))
f_{s_1,s_1}(g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{s_1,s_1}(g_{g_2,g_2}(x, z1), z10)
f_{s_1,s_1}(z00, g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → f_{s_1,s_1}(z00, g_{g_2,g_2}(x, z1))
f_{s_1,f_2}(g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{s_1,f_2}(g_{g_2,g_2}(x, z1), z10)
f_{s_1,f_2}(z00, g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → f_{s_1,f_2}(z00, g_{g_2,g_2}(x, z1))
s_{f_2}(g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → s_{f_2}(g_{g_2,g_2}(x, z1))
f_{f_2,g_2}(g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{f_2,g_2}(g_{g_2,g_2}(x, z1), z10)
f_{f_2,g_2}(z00, g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → f_{f_2,g_2}(z00, g_{g_2,g_2}(x, z1))
f_{f_2,s_1}(g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{f_2,s_1}(g_{g_2,g_2}(x, z1), z10)
f_{f_2,s_1}(z00, g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → f_{f_2,s_1}(z00, g_{g_2,g_2}(x, z1))
f_{f_2,f_2}(g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{f_2,f_2}(g_{g_2,g_2}(x, z1), z10)
f_{f_2,f_2}(z00, g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → f_{f_2,f_2}(z00, g_{g_2,g_2}(x, z1))
g_{g_2,g_2}(g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{g_2,g_2}(g_{g_2,g_2}(x, z1), z10)
g_{g_2,g_2}(z00, g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → g_{g_2,g_2}(z00, g_{g_2,g_2}(x, z1))
g_{g_2,s_1}(g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{g_2,s_1}(g_{g_2,g_2}(x, z1), z10)
g_{g_2,s_1}(z00, g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → g_{g_2,s_1}(z00, g_{g_2,g_2}(x, z1))
g_{g_2,f_2}(g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{g_2,f_2}(g_{g_2,g_2}(x, z1), z10)
g_{g_2,f_2}(z00, g_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → g_{g_2,f_2}(z00, g_{g_2,g_2}(x, z1))
g_{s_1,g_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → g_{s_1,g_2}(g_{g_2,s_1}(x, z1), z10)
g_{s_1,g_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → g_{s_1,g_2}(z00, g_{g_2,s_1}(x, z1))
s_{g_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → s_{g_2}(g_{g_2,s_1}(x, z1))
g_{f_2,g_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → g_{f_2,g_2}(g_{g_2,s_1}(x, z1), z10)
g_{f_2,g_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → g_{f_2,g_2}(z00, g_{g_2,s_1}(x, z1))
f_{g_2,g_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → f_{g_2,g_2}(g_{g_2,s_1}(x, z1), z10)
f_{g_2,g_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → f_{g_2,g_2}(z00, g_{g_2,s_1}(x, z1))
g_{s_1,s_1}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → g_{s_1,s_1}(g_{g_2,s_1}(x, z1), z10)
g_{s_1,s_1}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → g_{s_1,s_1}(z00, g_{g_2,s_1}(x, z1))
g_{f_2,s_1}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → g_{f_2,s_1}(g_{g_2,s_1}(x, z1), z10)
g_{f_2,s_1}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → g_{f_2,s_1}(z00, g_{g_2,s_1}(x, z1))
f_{g_2,s_1}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → f_{g_2,s_1}(g_{g_2,s_1}(x, z1), z10)
f_{g_2,s_1}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → f_{g_2,s_1}(z00, g_{g_2,s_1}(x, z1))
g_{s_1,f_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → g_{s_1,f_2}(g_{g_2,s_1}(x, z1), z10)
g_{s_1,f_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → g_{s_1,f_2}(z00, g_{g_2,s_1}(x, z1))
g_{f_2,f_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → g_{f_2,f_2}(g_{g_2,s_1}(x, z1), z10)
g_{f_2,f_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → g_{f_2,f_2}(z00, g_{g_2,s_1}(x, z1))
f_{g_2,f_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → f_{g_2,f_2}(g_{g_2,s_1}(x, z1), z10)
f_{g_2,f_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → f_{g_2,f_2}(z00, g_{g_2,s_1}(x, z1))
s_{s_1}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → s_{s_1}(g_{g_2,s_1}(x, z1))
f_{s_1,g_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → f_{s_1,g_2}(g_{g_2,s_1}(x, z1), z10)
f_{s_1,g_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → f_{s_1,g_2}(z00, g_{g_2,s_1}(x, z1))
f_{s_1,s_1}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → f_{s_1,s_1}(g_{g_2,s_1}(x, z1), z10)
f_{s_1,s_1}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → f_{s_1,s_1}(z00, g_{g_2,s_1}(x, z1))
f_{s_1,f_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → f_{s_1,f_2}(g_{g_2,s_1}(x, z1), z10)
f_{s_1,f_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → f_{s_1,f_2}(z00, g_{g_2,s_1}(x, z1))
s_{f_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → s_{f_2}(g_{g_2,s_1}(x, z1))
f_{f_2,g_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → f_{f_2,g_2}(g_{g_2,s_1}(x, z1), z10)
f_{f_2,g_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → f_{f_2,g_2}(z00, g_{g_2,s_1}(x, z1))
f_{f_2,s_1}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → f_{f_2,s_1}(g_{g_2,s_1}(x, z1), z10)
f_{f_2,s_1}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → f_{f_2,s_1}(z00, g_{g_2,s_1}(x, z1))
f_{f_2,f_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → f_{f_2,f_2}(g_{g_2,s_1}(x, z1), z10)
f_{f_2,f_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → f_{f_2,f_2}(z00, g_{g_2,s_1}(x, z1))
g_{g_2,g_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → g_{g_2,g_2}(g_{g_2,s_1}(x, z1), z10)
g_{g_2,g_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → g_{g_2,g_2}(z00, g_{g_2,s_1}(x, z1))
g_{g_2,s_1}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → g_{g_2,s_1}(g_{g_2,s_1}(x, z1), z10)
g_{g_2,s_1}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → g_{g_2,s_1}(z00, g_{g_2,s_1}(x, z1))
g_{g_2,f_2}(g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → g_{g_2,f_2}(g_{g_2,s_1}(x, z1), z10)
g_{g_2,f_2}(z00, g_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → g_{g_2,f_2}(z00, g_{g_2,s_1}(x, z1))
g_{s_1,g_2}(g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{s_1,g_2}(g_{g_2,f_2}(x, z1), z10)
g_{s_1,g_2}(z00, g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → g_{s_1,g_2}(z00, g_{g_2,f_2}(x, z1))
s_{g_2}(g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → s_{g_2}(g_{g_2,f_2}(x, z1))
g_{f_2,g_2}(g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{f_2,g_2}(g_{g_2,f_2}(x, z1), z10)
g_{f_2,g_2}(z00, g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → g_{f_2,g_2}(z00, g_{g_2,f_2}(x, z1))
f_{g_2,g_2}(g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{g_2,g_2}(g_{g_2,f_2}(x, z1), z10)
f_{g_2,g_2}(z00, g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → f_{g_2,g_2}(z00, g_{g_2,f_2}(x, z1))
g_{s_1,s_1}(g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{s_1,s_1}(g_{g_2,f_2}(x, z1), z10)
g_{s_1,s_1}(z00, g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → g_{s_1,s_1}(z00, g_{g_2,f_2}(x, z1))
g_{f_2,s_1}(g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{f_2,s_1}(g_{g_2,f_2}(x, z1), z10)
g_{f_2,s_1}(z00, g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → g_{f_2,s_1}(z00, g_{g_2,f_2}(x, z1))
f_{g_2,s_1}(g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{g_2,s_1}(g_{g_2,f_2}(x, z1), z10)
f_{g_2,s_1}(z00, g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → f_{g_2,s_1}(z00, g_{g_2,f_2}(x, z1))
g_{s_1,f_2}(g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{s_1,f_2}(g_{g_2,f_2}(x, z1), z10)
g_{s_1,f_2}(z00, g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → g_{s_1,f_2}(z00, g_{g_2,f_2}(x, z1))
g_{f_2,f_2}(g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{f_2,f_2}(g_{g_2,f_2}(x, z1), z10)
g_{f_2,f_2}(z00, g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → g_{f_2,f_2}(z00, g_{g_2,f_2}(x, z1))
f_{g_2,f_2}(g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{g_2,f_2}(g_{g_2,f_2}(x, z1), z10)
f_{g_2,f_2}(z00, g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → f_{g_2,f_2}(z00, g_{g_2,f_2}(x, z1))
s_{s_1}(g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → s_{s_1}(g_{g_2,f_2}(x, z1))
f_{s_1,g_2}(g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{s_1,g_2}(g_{g_2,f_2}(x, z1), z10)
f_{s_1,g_2}(z00, g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → f_{s_1,g_2}(z00, g_{g_2,f_2}(x, z1))
f_{s_1,s_1}(g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{s_1,s_1}(g_{g_2,f_2}(x, z1), z10)
f_{s_1,s_1}(z00, g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → f_{s_1,s_1}(z00, g_{g_2,f_2}(x, z1))
f_{s_1,f_2}(g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{s_1,f_2}(g_{g_2,f_2}(x, z1), z10)
f_{s_1,f_2}(z00, g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → f_{s_1,f_2}(z00, g_{g_2,f_2}(x, z1))
s_{f_2}(g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → s_{f_2}(g_{g_2,f_2}(x, z1))
f_{f_2,g_2}(g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{f_2,g_2}(g_{g_2,f_2}(x, z1), z10)
f_{f_2,g_2}(z00, g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → f_{f_2,g_2}(z00, g_{g_2,f_2}(x, z1))
f_{f_2,s_1}(g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{f_2,s_1}(g_{g_2,f_2}(x, z1), z10)
f_{f_2,s_1}(z00, g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → f_{f_2,s_1}(z00, g_{g_2,f_2}(x, z1))
f_{f_2,f_2}(g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{f_2,f_2}(g_{g_2,f_2}(x, z1), z10)
f_{f_2,f_2}(z00, g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → f_{f_2,f_2}(z00, g_{g_2,f_2}(x, z1))
g_{g_2,g_2}(g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{g_2,g_2}(g_{g_2,f_2}(x, z1), z10)
g_{g_2,g_2}(z00, g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → g_{g_2,g_2}(z00, g_{g_2,f_2}(x, z1))
g_{g_2,s_1}(g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{g_2,s_1}(g_{g_2,f_2}(x, z1), z10)
g_{g_2,s_1}(z00, g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → g_{g_2,s_1}(z00, g_{g_2,f_2}(x, z1))
g_{g_2,f_2}(g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{g_2,f_2}(g_{g_2,f_2}(x, z1), z10)
g_{g_2,f_2}(z00, g_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → g_{g_2,f_2}(z00, g_{g_2,f_2}(x, z1))
g_{s_1,g_2}(g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{s_1,g_2}(g_{g_2,g_2}(x, z1), z10)
g_{s_1,g_2}(z00, g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → g_{s_1,g_2}(z00, g_{g_2,g_2}(x, z1))
s_{g_2}(g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → s_{g_2}(g_{g_2,g_2}(x, z1))
g_{f_2,g_2}(g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{f_2,g_2}(g_{g_2,g_2}(x, z1), z10)
g_{f_2,g_2}(z00, g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → g_{f_2,g_2}(z00, g_{g_2,g_2}(x, z1))
f_{g_2,g_2}(g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{g_2,g_2}(g_{g_2,g_2}(x, z1), z10)
f_{g_2,g_2}(z00, g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → f_{g_2,g_2}(z00, g_{g_2,g_2}(x, z1))
g_{s_1,s_1}(g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{s_1,s_1}(g_{g_2,g_2}(x, z1), z10)
g_{s_1,s_1}(z00, g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → g_{s_1,s_1}(z00, g_{g_2,g_2}(x, z1))
g_{f_2,s_1}(g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{f_2,s_1}(g_{g_2,g_2}(x, z1), z10)
g_{f_2,s_1}(z00, g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → g_{f_2,s_1}(z00, g_{g_2,g_2}(x, z1))
f_{g_2,s_1}(g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{g_2,s_1}(g_{g_2,g_2}(x, z1), z10)
f_{g_2,s_1}(z00, g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → f_{g_2,s_1}(z00, g_{g_2,g_2}(x, z1))
g_{s_1,f_2}(g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{s_1,f_2}(g_{g_2,g_2}(x, z1), z10)
g_{s_1,f_2}(z00, g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → g_{s_1,f_2}(z00, g_{g_2,g_2}(x, z1))
g_{f_2,f_2}(g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{f_2,f_2}(g_{g_2,g_2}(x, z1), z10)
g_{f_2,f_2}(z00, g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → g_{f_2,f_2}(z00, g_{g_2,g_2}(x, z1))
f_{g_2,f_2}(g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{g_2,f_2}(g_{g_2,g_2}(x, z1), z10)
f_{g_2,f_2}(z00, g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → f_{g_2,f_2}(z00, g_{g_2,g_2}(x, z1))
s_{s_1}(g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → s_{s_1}(g_{g_2,g_2}(x, z1))
f_{s_1,g_2}(g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{s_1,g_2}(g_{g_2,g_2}(x, z1), z10)
f_{s_1,g_2}(z00, g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → f_{s_1,g_2}(z00, g_{g_2,g_2}(x, z1))
f_{s_1,s_1}(g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{s_1,s_1}(g_{g_2,g_2}(x, z1), z10)
f_{s_1,s_1}(z00, g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → f_{s_1,s_1}(z00, g_{g_2,g_2}(x, z1))
f_{s_1,f_2}(g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{s_1,f_2}(g_{g_2,g_2}(x, z1), z10)
f_{s_1,f_2}(z00, g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → f_{s_1,f_2}(z00, g_{g_2,g_2}(x, z1))
s_{f_2}(g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → s_{f_2}(g_{g_2,g_2}(x, z1))
f_{f_2,g_2}(g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{f_2,g_2}(g_{g_2,g_2}(x, z1), z10)
f_{f_2,g_2}(z00, g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → f_{f_2,g_2}(z00, g_{g_2,g_2}(x, z1))
f_{f_2,s_1}(g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{f_2,s_1}(g_{g_2,g_2}(x, z1), z10)
f_{f_2,s_1}(z00, g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → f_{f_2,s_1}(z00, g_{g_2,g_2}(x, z1))
f_{f_2,f_2}(g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{f_2,f_2}(g_{g_2,g_2}(x, z1), z10)
f_{f_2,f_2}(z00, g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → f_{f_2,f_2}(z00, g_{g_2,g_2}(x, z1))
g_{g_2,g_2}(g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{g_2,g_2}(g_{g_2,g_2}(x, z1), z10)
g_{g_2,g_2}(z00, g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → g_{g_2,g_2}(z00, g_{g_2,g_2}(x, z1))
g_{g_2,s_1}(g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{g_2,s_1}(g_{g_2,g_2}(x, z1), z10)
g_{g_2,s_1}(z00, g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → g_{g_2,s_1}(z00, g_{g_2,g_2}(x, z1))
g_{g_2,f_2}(g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{g_2,f_2}(g_{g_2,g_2}(x, z1), z10)
g_{g_2,f_2}(z00, g_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → g_{g_2,f_2}(z00, g_{g_2,g_2}(x, z1))
g_{s_1,g_2}(g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → g_{s_1,g_2}(g_{g_2,s_1}(x, z1), z10)
g_{s_1,g_2}(z00, g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → g_{s_1,g_2}(z00, g_{g_2,s_1}(x, z1))
s_{g_2}(g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → s_{g_2}(g_{g_2,s_1}(x, z1))
g_{f_2,g_2}(g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → g_{f_2,g_2}(g_{g_2,s_1}(x, z1), z10)
g_{f_2,g_2}(z00, g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → g_{f_2,g_2}(z00, g_{g_2,s_1}(x, z1))
f_{g_2,g_2}(g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → f_{g_2,g_2}(g_{g_2,s_1}(x, z1), z10)
f_{g_2,g_2}(z00, g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → f_{g_2,g_2}(z00, g_{g_2,s_1}(x, z1))
g_{s_1,s_1}(g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → g_{s_1,s_1}(g_{g_2,s_1}(x, z1), z10)
g_{s_1,s_1}(z00, g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → g_{s_1,s_1}(z00, g_{g_2,s_1}(x, z1))
g_{f_2,s_1}(g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → g_{f_2,s_1}(g_{g_2,s_1}(x, z1), z10)
g_{f_2,s_1}(z00, g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → g_{f_2,s_1}(z00, g_{g_2,s_1}(x, z1))
f_{g_2,s_1}(g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → f_{g_2,s_1}(g_{g_2,s_1}(x, z1), z10)
f_{g_2,s_1}(z00, g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → f_{g_2,s_1}(z00, g_{g_2,s_1}(x, z1))
g_{s_1,f_2}(g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → g_{s_1,f_2}(g_{g_2,s_1}(x, z1), z10)
g_{s_1,f_2}(z00, g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → g_{s_1,f_2}(z00, g_{g_2,s_1}(x, z1))
g_{f_2,f_2}(g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → g_{f_2,f_2}(g_{g_2,s_1}(x, z1), z10)
g_{f_2,f_2}(z00, g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → g_{f_2,f_2}(z00, g_{g_2,s_1}(x, z1))
f_{g_2,f_2}(g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → f_{g_2,f_2}(g_{g_2,s_1}(x, z1), z10)
f_{g_2,f_2}(z00, g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → f_{g_2,f_2}(z00, g_{g_2,s_1}(x, z1))
s_{s_1}(g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → s_{s_1}(g_{g_2,s_1}(x, z1))
f_{s_1,g_2}(g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → f_{s_1,g_2}(g_{g_2,s_1}(x, z1), z10)
f_{s_1,g_2}(z00, g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → f_{s_1,g_2}(z00, g_{g_2,s_1}(x, z1))
f_{s_1,s_1}(g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → f_{s_1,s_1}(g_{g_2,s_1}(x, z1), z10)
f_{s_1,s_1}(z00, g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → f_{s_1,s_1}(z00, g_{g_2,s_1}(x, z1))
f_{s_1,f_2}(g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → f_{s_1,f_2}(g_{g_2,s_1}(x, z1), z10)
f_{s_1,f_2}(z00, g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → f_{s_1,f_2}(z00, g_{g_2,s_1}(x, z1))
s_{f_2}(g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → s_{f_2}(g_{g_2,s_1}(x, z1))
f_{f_2,g_2}(g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → f_{f_2,g_2}(g_{g_2,s_1}(x, z1), z10)
f_{f_2,g_2}(z00, g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → f_{f_2,g_2}(z00, g_{g_2,s_1}(x, z1))
f_{f_2,s_1}(g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → f_{f_2,s_1}(g_{g_2,s_1}(x, z1), z10)
f_{f_2,s_1}(z00, g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → f_{f_2,s_1}(z00, g_{g_2,s_1}(x, z1))
f_{f_2,f_2}(g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → f_{f_2,f_2}(g_{g_2,s_1}(x, z1), z10)
f_{f_2,f_2}(z00, g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → f_{f_2,f_2}(z00, g_{g_2,s_1}(x, z1))
g_{g_2,g_2}(g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → g_{g_2,g_2}(g_{g_2,s_1}(x, z1), z10)
g_{g_2,g_2}(z00, g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → g_{g_2,g_2}(z00, g_{g_2,s_1}(x, z1))
g_{g_2,s_1}(g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → g_{g_2,s_1}(g_{g_2,s_1}(x, z1), z10)
g_{g_2,s_1}(z00, g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → g_{g_2,s_1}(z00, g_{g_2,s_1}(x, z1))
g_{g_2,f_2}(g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → g_{g_2,f_2}(g_{g_2,s_1}(x, z1), z10)
g_{g_2,f_2}(z00, g_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → g_{g_2,f_2}(z00, g_{g_2,s_1}(x, z1))
g_{s_1,g_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{s_1,g_2}(g_{g_2,f_2}(x, z1), z10)
g_{s_1,g_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → g_{s_1,g_2}(z00, g_{g_2,f_2}(x, z1))
s_{g_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → s_{g_2}(g_{g_2,f_2}(x, z1))
g_{f_2,g_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{f_2,g_2}(g_{g_2,f_2}(x, z1), z10)
g_{f_2,g_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → g_{f_2,g_2}(z00, g_{g_2,f_2}(x, z1))
f_{g_2,g_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{g_2,g_2}(g_{g_2,f_2}(x, z1), z10)
f_{g_2,g_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → f_{g_2,g_2}(z00, g_{g_2,f_2}(x, z1))
g_{s_1,s_1}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{s_1,s_1}(g_{g_2,f_2}(x, z1), z10)
g_{s_1,s_1}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → g_{s_1,s_1}(z00, g_{g_2,f_2}(x, z1))
g_{f_2,s_1}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{f_2,s_1}(g_{g_2,f_2}(x, z1), z10)
g_{f_2,s_1}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → g_{f_2,s_1}(z00, g_{g_2,f_2}(x, z1))
f_{g_2,s_1}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{g_2,s_1}(g_{g_2,f_2}(x, z1), z10)
f_{g_2,s_1}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → f_{g_2,s_1}(z00, g_{g_2,f_2}(x, z1))
g_{s_1,f_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{s_1,f_2}(g_{g_2,f_2}(x, z1), z10)
g_{s_1,f_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → g_{s_1,f_2}(z00, g_{g_2,f_2}(x, z1))
g_{f_2,f_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{f_2,f_2}(g_{g_2,f_2}(x, z1), z10)
g_{f_2,f_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → g_{f_2,f_2}(z00, g_{g_2,f_2}(x, z1))
f_{g_2,f_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{g_2,f_2}(g_{g_2,f_2}(x, z1), z10)
f_{g_2,f_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → f_{g_2,f_2}(z00, g_{g_2,f_2}(x, z1))
s_{s_1}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → s_{s_1}(g_{g_2,f_2}(x, z1))
f_{s_1,g_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{s_1,g_2}(g_{g_2,f_2}(x, z1), z10)
f_{s_1,g_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → f_{s_1,g_2}(z00, g_{g_2,f_2}(x, z1))
f_{s_1,s_1}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{s_1,s_1}(g_{g_2,f_2}(x, z1), z10)
f_{s_1,s_1}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → f_{s_1,s_1}(z00, g_{g_2,f_2}(x, z1))
f_{s_1,f_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{s_1,f_2}(g_{g_2,f_2}(x, z1), z10)
f_{s_1,f_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → f_{s_1,f_2}(z00, g_{g_2,f_2}(x, z1))
s_{f_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → s_{f_2}(g_{g_2,f_2}(x, z1))
f_{f_2,g_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{f_2,g_2}(g_{g_2,f_2}(x, z1), z10)
f_{f_2,g_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → f_{f_2,g_2}(z00, g_{g_2,f_2}(x, z1))
f_{f_2,s_1}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{f_2,s_1}(g_{g_2,f_2}(x, z1), z10)
f_{f_2,s_1}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → f_{f_2,s_1}(z00, g_{g_2,f_2}(x, z1))
f_{f_2,f_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{f_2,f_2}(g_{g_2,f_2}(x, z1), z10)
f_{f_2,f_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → f_{f_2,f_2}(z00, g_{g_2,f_2}(x, z1))
g_{g_2,g_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{g_2,g_2}(g_{g_2,f_2}(x, z1), z10)
g_{g_2,g_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → g_{g_2,g_2}(z00, g_{g_2,f_2}(x, z1))
g_{g_2,s_1}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{g_2,s_1}(g_{g_2,f_2}(x, z1), z10)
g_{g_2,s_1}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → g_{g_2,s_1}(z00, g_{g_2,f_2}(x, z1))
g_{g_2,f_2}(g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{g_2,f_2}(g_{g_2,f_2}(x, z1), z10)
g_{g_2,f_2}(z00, g_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → g_{g_2,f_2}(z00, g_{g_2,f_2}(x, z1))
g_{s_1,g_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{s_1,g_2}(g_{s_1,g_2}(x, z1), z10)
g_{s_1,g_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → g_{s_1,g_2}(z00, g_{s_1,g_2}(x, z1))
s_{g_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → s_{g_2}(g_{s_1,g_2}(x, z1))
g_{f_2,g_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{f_2,g_2}(g_{s_1,g_2}(x, z1), z10)
g_{f_2,g_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → g_{f_2,g_2}(z00, g_{s_1,g_2}(x, z1))
f_{g_2,g_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{g_2,g_2}(g_{s_1,g_2}(x, z1), z10)
f_{g_2,g_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → f_{g_2,g_2}(z00, g_{s_1,g_2}(x, z1))
g_{s_1,s_1}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{s_1,s_1}(g_{s_1,g_2}(x, z1), z10)
g_{s_1,s_1}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → g_{s_1,s_1}(z00, g_{s_1,g_2}(x, z1))
g_{f_2,s_1}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{f_2,s_1}(g_{s_1,g_2}(x, z1), z10)
g_{f_2,s_1}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → g_{f_2,s_1}(z00, g_{s_1,g_2}(x, z1))
f_{g_2,s_1}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{g_2,s_1}(g_{s_1,g_2}(x, z1), z10)
f_{g_2,s_1}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → f_{g_2,s_1}(z00, g_{s_1,g_2}(x, z1))
g_{s_1,f_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{s_1,f_2}(g_{s_1,g_2}(x, z1), z10)
g_{s_1,f_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → g_{s_1,f_2}(z00, g_{s_1,g_2}(x, z1))
g_{f_2,f_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{f_2,f_2}(g_{s_1,g_2}(x, z1), z10)
g_{f_2,f_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → g_{f_2,f_2}(z00, g_{s_1,g_2}(x, z1))
f_{g_2,f_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{g_2,f_2}(g_{s_1,g_2}(x, z1), z10)
f_{g_2,f_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → f_{g_2,f_2}(z00, g_{s_1,g_2}(x, z1))
s_{s_1}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → s_{s_1}(g_{s_1,g_2}(x, z1))
f_{s_1,g_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{s_1,g_2}(g_{s_1,g_2}(x, z1), z10)
f_{s_1,g_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → f_{s_1,g_2}(z00, g_{s_1,g_2}(x, z1))
f_{s_1,s_1}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{s_1,s_1}(g_{s_1,g_2}(x, z1), z10)
f_{s_1,s_1}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → f_{s_1,s_1}(z00, g_{s_1,g_2}(x, z1))
f_{s_1,f_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{s_1,f_2}(g_{s_1,g_2}(x, z1), z10)
f_{s_1,f_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → f_{s_1,f_2}(z00, g_{s_1,g_2}(x, z1))
s_{f_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → s_{f_2}(g_{s_1,g_2}(x, z1))
f_{f_2,g_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{f_2,g_2}(g_{s_1,g_2}(x, z1), z10)
f_{f_2,g_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → f_{f_2,g_2}(z00, g_{s_1,g_2}(x, z1))
f_{f_2,s_1}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{f_2,s_1}(g_{s_1,g_2}(x, z1), z10)
f_{f_2,s_1}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → f_{f_2,s_1}(z00, g_{s_1,g_2}(x, z1))
f_{f_2,f_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{f_2,f_2}(g_{s_1,g_2}(x, z1), z10)
f_{f_2,f_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → f_{f_2,f_2}(z00, g_{s_1,g_2}(x, z1))
g_{g_2,g_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{g_2,g_2}(g_{s_1,g_2}(x, z1), z10)
g_{g_2,g_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → g_{g_2,g_2}(z00, g_{s_1,g_2}(x, z1))
g_{g_2,s_1}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{g_2,s_1}(g_{s_1,g_2}(x, z1), z10)
g_{g_2,s_1}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → g_{g_2,s_1}(z00, g_{s_1,g_2}(x, z1))
g_{g_2,f_2}(g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{g_2,f_2}(g_{s_1,g_2}(x, z1), z10)
g_{g_2,f_2}(z00, g_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → g_{g_2,f_2}(z00, g_{s_1,g_2}(x, z1))
g_{s_1,g_2}(g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → g_{s_1,g_2}(g_{s_1,s_1}(x, z1), z10)
g_{s_1,g_2}(z00, g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → g_{s_1,g_2}(z00, g_{s_1,s_1}(x, z1))
s_{g_2}(g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → s_{g_2}(g_{s_1,s_1}(x, z1))
g_{f_2,g_2}(g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → g_{f_2,g_2}(g_{s_1,s_1}(x, z1), z10)
g_{f_2,g_2}(z00, g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → g_{f_2,g_2}(z00, g_{s_1,s_1}(x, z1))
f_{g_2,g_2}(g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → f_{g_2,g_2}(g_{s_1,s_1}(x, z1), z10)
f_{g_2,g_2}(z00, g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → f_{g_2,g_2}(z00, g_{s_1,s_1}(x, z1))
g_{s_1,s_1}(g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → g_{s_1,s_1}(g_{s_1,s_1}(x, z1), z10)
g_{s_1,s_1}(z00, g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → g_{s_1,s_1}(z00, g_{s_1,s_1}(x, z1))
g_{f_2,s_1}(g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → g_{f_2,s_1}(g_{s_1,s_1}(x, z1), z10)
g_{f_2,s_1}(z00, g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → g_{f_2,s_1}(z00, g_{s_1,s_1}(x, z1))
f_{g_2,s_1}(g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → f_{g_2,s_1}(g_{s_1,s_1}(x, z1), z10)
f_{g_2,s_1}(z00, g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → f_{g_2,s_1}(z00, g_{s_1,s_1}(x, z1))
g_{s_1,f_2}(g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → g_{s_1,f_2}(g_{s_1,s_1}(x, z1), z10)
g_{s_1,f_2}(z00, g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → g_{s_1,f_2}(z00, g_{s_1,s_1}(x, z1))
g_{f_2,f_2}(g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → g_{f_2,f_2}(g_{s_1,s_1}(x, z1), z10)
g_{f_2,f_2}(z00, g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → g_{f_2,f_2}(z00, g_{s_1,s_1}(x, z1))
f_{g_2,f_2}(g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → f_{g_2,f_2}(g_{s_1,s_1}(x, z1), z10)
f_{g_2,f_2}(z00, g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → f_{g_2,f_2}(z00, g_{s_1,s_1}(x, z1))
s_{s_1}(g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → s_{s_1}(g_{s_1,s_1}(x, z1))
f_{s_1,g_2}(g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → f_{s_1,g_2}(g_{s_1,s_1}(x, z1), z10)
f_{s_1,g_2}(z00, g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → f_{s_1,g_2}(z00, g_{s_1,s_1}(x, z1))
f_{s_1,s_1}(g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → f_{s_1,s_1}(g_{s_1,s_1}(x, z1), z10)
f_{s_1,s_1}(z00, g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → f_{s_1,s_1}(z00, g_{s_1,s_1}(x, z1))
f_{s_1,f_2}(g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → f_{s_1,f_2}(g_{s_1,s_1}(x, z1), z10)
f_{s_1,f_2}(z00, g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → f_{s_1,f_2}(z00, g_{s_1,s_1}(x, z1))
s_{f_2}(g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → s_{f_2}(g_{s_1,s_1}(x, z1))
f_{f_2,g_2}(g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → f_{f_2,g_2}(g_{s_1,s_1}(x, z1), z10)
f_{f_2,g_2}(z00, g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → f_{f_2,g_2}(z00, g_{s_1,s_1}(x, z1))
f_{f_2,s_1}(g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → f_{f_2,s_1}(g_{s_1,s_1}(x, z1), z10)
f_{f_2,s_1}(z00, g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → f_{f_2,s_1}(z00, g_{s_1,s_1}(x, z1))
f_{f_2,f_2}(g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → f_{f_2,f_2}(g_{s_1,s_1}(x, z1), z10)
f_{f_2,f_2}(z00, g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → f_{f_2,f_2}(z00, g_{s_1,s_1}(x, z1))
g_{g_2,g_2}(g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → g_{g_2,g_2}(g_{s_1,s_1}(x, z1), z10)
g_{g_2,g_2}(z00, g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → g_{g_2,g_2}(z00, g_{s_1,s_1}(x, z1))
g_{g_2,s_1}(g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → g_{g_2,s_1}(g_{s_1,s_1}(x, z1), z10)
g_{g_2,s_1}(z00, g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → g_{g_2,s_1}(z00, g_{s_1,s_1}(x, z1))
g_{g_2,f_2}(g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → g_{g_2,f_2}(g_{s_1,s_1}(x, z1), z10)
g_{g_2,f_2}(z00, g_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → g_{g_2,f_2}(z00, g_{s_1,s_1}(x, z1))
g_{s_1,g_2}(g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{s_1,g_2}(g_{s_1,f_2}(x, z1), z10)
g_{s_1,g_2}(z00, g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → g_{s_1,g_2}(z00, g_{s_1,f_2}(x, z1))
s_{g_2}(g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → s_{g_2}(g_{s_1,f_2}(x, z1))
g_{f_2,g_2}(g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{f_2,g_2}(g_{s_1,f_2}(x, z1), z10)
g_{f_2,g_2}(z00, g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → g_{f_2,g_2}(z00, g_{s_1,f_2}(x, z1))
f_{g_2,g_2}(g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{g_2,g_2}(g_{s_1,f_2}(x, z1), z10)
f_{g_2,g_2}(z00, g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → f_{g_2,g_2}(z00, g_{s_1,f_2}(x, z1))
g_{s_1,s_1}(g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{s_1,s_1}(g_{s_1,f_2}(x, z1), z10)
g_{s_1,s_1}(z00, g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → g_{s_1,s_1}(z00, g_{s_1,f_2}(x, z1))
g_{f_2,s_1}(g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{f_2,s_1}(g_{s_1,f_2}(x, z1), z10)
g_{f_2,s_1}(z00, g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → g_{f_2,s_1}(z00, g_{s_1,f_2}(x, z1))
f_{g_2,s_1}(g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{g_2,s_1}(g_{s_1,f_2}(x, z1), z10)
f_{g_2,s_1}(z00, g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → f_{g_2,s_1}(z00, g_{s_1,f_2}(x, z1))
g_{s_1,f_2}(g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{s_1,f_2}(g_{s_1,f_2}(x, z1), z10)
g_{s_1,f_2}(z00, g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → g_{s_1,f_2}(z00, g_{s_1,f_2}(x, z1))
g_{f_2,f_2}(g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{f_2,f_2}(g_{s_1,f_2}(x, z1), z10)
g_{f_2,f_2}(z00, g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → g_{f_2,f_2}(z00, g_{s_1,f_2}(x, z1))
f_{g_2,f_2}(g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{g_2,f_2}(g_{s_1,f_2}(x, z1), z10)
f_{g_2,f_2}(z00, g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → f_{g_2,f_2}(z00, g_{s_1,f_2}(x, z1))
s_{s_1}(g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → s_{s_1}(g_{s_1,f_2}(x, z1))
f_{s_1,g_2}(g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{s_1,g_2}(g_{s_1,f_2}(x, z1), z10)
f_{s_1,g_2}(z00, g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → f_{s_1,g_2}(z00, g_{s_1,f_2}(x, z1))
f_{s_1,s_1}(g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{s_1,s_1}(g_{s_1,f_2}(x, z1), z10)
f_{s_1,s_1}(z00, g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → f_{s_1,s_1}(z00, g_{s_1,f_2}(x, z1))
f_{s_1,f_2}(g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{s_1,f_2}(g_{s_1,f_2}(x, z1), z10)
f_{s_1,f_2}(z00, g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → f_{s_1,f_2}(z00, g_{s_1,f_2}(x, z1))
s_{f_2}(g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → s_{f_2}(g_{s_1,f_2}(x, z1))
f_{f_2,g_2}(g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{f_2,g_2}(g_{s_1,f_2}(x, z1), z10)
f_{f_2,g_2}(z00, g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → f_{f_2,g_2}(z00, g_{s_1,f_2}(x, z1))
f_{f_2,s_1}(g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{f_2,s_1}(g_{s_1,f_2}(x, z1), z10)
f_{f_2,s_1}(z00, g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → f_{f_2,s_1}(z00, g_{s_1,f_2}(x, z1))
f_{f_2,f_2}(g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{f_2,f_2}(g_{s_1,f_2}(x, z1), z10)
f_{f_2,f_2}(z00, g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → f_{f_2,f_2}(z00, g_{s_1,f_2}(x, z1))
g_{g_2,g_2}(g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{g_2,g_2}(g_{s_1,f_2}(x, z1), z10)
g_{g_2,g_2}(z00, g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → g_{g_2,g_2}(z00, g_{s_1,f_2}(x, z1))
g_{g_2,s_1}(g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{g_2,s_1}(g_{s_1,f_2}(x, z1), z10)
g_{g_2,s_1}(z00, g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → g_{g_2,s_1}(z00, g_{s_1,f_2}(x, z1))
g_{g_2,f_2}(g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{g_2,f_2}(g_{s_1,f_2}(x, z1), z10)
g_{g_2,f_2}(z00, g_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → g_{g_2,f_2}(z00, g_{s_1,f_2}(x, z1))
g_{s_1,g_2}(g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{s_1,g_2}(g_{s_1,g_2}(x, z1), z10)
g_{s_1,g_2}(z00, g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → g_{s_1,g_2}(z00, g_{s_1,g_2}(x, z1))
s_{g_2}(g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → s_{g_2}(g_{s_1,g_2}(x, z1))
g_{f_2,g_2}(g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{f_2,g_2}(g_{s_1,g_2}(x, z1), z10)
g_{f_2,g_2}(z00, g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → g_{f_2,g_2}(z00, g_{s_1,g_2}(x, z1))
f_{g_2,g_2}(g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{g_2,g_2}(g_{s_1,g_2}(x, z1), z10)
f_{g_2,g_2}(z00, g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → f_{g_2,g_2}(z00, g_{s_1,g_2}(x, z1))
g_{s_1,s_1}(g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{s_1,s_1}(g_{s_1,g_2}(x, z1), z10)
g_{s_1,s_1}(z00, g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → g_{s_1,s_1}(z00, g_{s_1,g_2}(x, z1))
g_{f_2,s_1}(g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{f_2,s_1}(g_{s_1,g_2}(x, z1), z10)
g_{f_2,s_1}(z00, g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → g_{f_2,s_1}(z00, g_{s_1,g_2}(x, z1))
f_{g_2,s_1}(g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{g_2,s_1}(g_{s_1,g_2}(x, z1), z10)
f_{g_2,s_1}(z00, g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → f_{g_2,s_1}(z00, g_{s_1,g_2}(x, z1))
g_{s_1,f_2}(g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{s_1,f_2}(g_{s_1,g_2}(x, z1), z10)
g_{s_1,f_2}(z00, g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → g_{s_1,f_2}(z00, g_{s_1,g_2}(x, z1))
g_{f_2,f_2}(g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{f_2,f_2}(g_{s_1,g_2}(x, z1), z10)
g_{f_2,f_2}(z00, g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → g_{f_2,f_2}(z00, g_{s_1,g_2}(x, z1))
f_{g_2,f_2}(g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{g_2,f_2}(g_{s_1,g_2}(x, z1), z10)
f_{g_2,f_2}(z00, g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → f_{g_2,f_2}(z00, g_{s_1,g_2}(x, z1))
s_{s_1}(g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → s_{s_1}(g_{s_1,g_2}(x, z1))
f_{s_1,g_2}(g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{s_1,g_2}(g_{s_1,g_2}(x, z1), z10)
f_{s_1,g_2}(z00, g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → f_{s_1,g_2}(z00, g_{s_1,g_2}(x, z1))
f_{s_1,s_1}(g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{s_1,s_1}(g_{s_1,g_2}(x, z1), z10)
f_{s_1,s_1}(z00, g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → f_{s_1,s_1}(z00, g_{s_1,g_2}(x, z1))
f_{s_1,f_2}(g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{s_1,f_2}(g_{s_1,g_2}(x, z1), z10)
f_{s_1,f_2}(z00, g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → f_{s_1,f_2}(z00, g_{s_1,g_2}(x, z1))
s_{f_2}(g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → s_{f_2}(g_{s_1,g_2}(x, z1))
f_{f_2,g_2}(g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{f_2,g_2}(g_{s_1,g_2}(x, z1), z10)
f_{f_2,g_2}(z00, g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → f_{f_2,g_2}(z00, g_{s_1,g_2}(x, z1))
f_{f_2,s_1}(g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{f_2,s_1}(g_{s_1,g_2}(x, z1), z10)
f_{f_2,s_1}(z00, g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → f_{f_2,s_1}(z00, g_{s_1,g_2}(x, z1))
f_{f_2,f_2}(g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{f_2,f_2}(g_{s_1,g_2}(x, z1), z10)
f_{f_2,f_2}(z00, g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → f_{f_2,f_2}(z00, g_{s_1,g_2}(x, z1))
g_{g_2,g_2}(g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{g_2,g_2}(g_{s_1,g_2}(x, z1), z10)
g_{g_2,g_2}(z00, g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → g_{g_2,g_2}(z00, g_{s_1,g_2}(x, z1))
g_{g_2,s_1}(g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{g_2,s_1}(g_{s_1,g_2}(x, z1), z10)
g_{g_2,s_1}(z00, g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → g_{g_2,s_1}(z00, g_{s_1,g_2}(x, z1))
g_{g_2,f_2}(g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{g_2,f_2}(g_{s_1,g_2}(x, z1), z10)
g_{g_2,f_2}(z00, g_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → g_{g_2,f_2}(z00, g_{s_1,g_2}(x, z1))
g_{s_1,g_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → g_{s_1,g_2}(g_{s_1,s_1}(x, z1), z10)
g_{s_1,g_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → g_{s_1,g_2}(z00, g_{s_1,s_1}(x, z1))
s_{g_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → s_{g_2}(g_{s_1,s_1}(x, z1))
g_{f_2,g_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → g_{f_2,g_2}(g_{s_1,s_1}(x, z1), z10)
g_{f_2,g_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → g_{f_2,g_2}(z00, g_{s_1,s_1}(x, z1))
f_{g_2,g_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → f_{g_2,g_2}(g_{s_1,s_1}(x, z1), z10)
f_{g_2,g_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → f_{g_2,g_2}(z00, g_{s_1,s_1}(x, z1))
g_{s_1,s_1}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → g_{s_1,s_1}(g_{s_1,s_1}(x, z1), z10)
g_{s_1,s_1}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → g_{s_1,s_1}(z00, g_{s_1,s_1}(x, z1))
g_{f_2,s_1}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → g_{f_2,s_1}(g_{s_1,s_1}(x, z1), z10)
g_{f_2,s_1}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → g_{f_2,s_1}(z00, g_{s_1,s_1}(x, z1))
f_{g_2,s_1}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → f_{g_2,s_1}(g_{s_1,s_1}(x, z1), z10)
f_{g_2,s_1}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → f_{g_2,s_1}(z00, g_{s_1,s_1}(x, z1))
g_{s_1,f_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → g_{s_1,f_2}(g_{s_1,s_1}(x, z1), z10)
g_{s_1,f_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → g_{s_1,f_2}(z00, g_{s_1,s_1}(x, z1))
g_{f_2,f_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → g_{f_2,f_2}(g_{s_1,s_1}(x, z1), z10)
g_{f_2,f_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → g_{f_2,f_2}(z00, g_{s_1,s_1}(x, z1))
f_{g_2,f_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → f_{g_2,f_2}(g_{s_1,s_1}(x, z1), z10)
f_{g_2,f_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → f_{g_2,f_2}(z00, g_{s_1,s_1}(x, z1))
s_{s_1}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → s_{s_1}(g_{s_1,s_1}(x, z1))
f_{s_1,g_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → f_{s_1,g_2}(g_{s_1,s_1}(x, z1), z10)
f_{s_1,g_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → f_{s_1,g_2}(z00, g_{s_1,s_1}(x, z1))
f_{s_1,s_1}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → f_{s_1,s_1}(g_{s_1,s_1}(x, z1), z10)
f_{s_1,s_1}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → f_{s_1,s_1}(z00, g_{s_1,s_1}(x, z1))
f_{s_1,f_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → f_{s_1,f_2}(g_{s_1,s_1}(x, z1), z10)
f_{s_1,f_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → f_{s_1,f_2}(z00, g_{s_1,s_1}(x, z1))
s_{f_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → s_{f_2}(g_{s_1,s_1}(x, z1))
f_{f_2,g_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → f_{f_2,g_2}(g_{s_1,s_1}(x, z1), z10)
f_{f_2,g_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → f_{f_2,g_2}(z00, g_{s_1,s_1}(x, z1))
f_{f_2,s_1}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → f_{f_2,s_1}(g_{s_1,s_1}(x, z1), z10)
f_{f_2,s_1}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → f_{f_2,s_1}(z00, g_{s_1,s_1}(x, z1))
f_{f_2,f_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → f_{f_2,f_2}(g_{s_1,s_1}(x, z1), z10)
f_{f_2,f_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → f_{f_2,f_2}(z00, g_{s_1,s_1}(x, z1))
g_{g_2,g_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → g_{g_2,g_2}(g_{s_1,s_1}(x, z1), z10)
g_{g_2,g_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → g_{g_2,g_2}(z00, g_{s_1,s_1}(x, z1))
g_{g_2,s_1}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → g_{g_2,s_1}(g_{s_1,s_1}(x, z1), z10)
g_{g_2,s_1}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → g_{g_2,s_1}(z00, g_{s_1,s_1}(x, z1))
g_{g_2,f_2}(g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → g_{g_2,f_2}(g_{s_1,s_1}(x, z1), z10)
g_{g_2,f_2}(z00, g_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → g_{g_2,f_2}(z00, g_{s_1,s_1}(x, z1))
g_{s_1,g_2}(g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{s_1,g_2}(g_{s_1,f_2}(x, z1), z10)
g_{s_1,g_2}(z00, g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → g_{s_1,g_2}(z00, g_{s_1,f_2}(x, z1))
s_{g_2}(g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → s_{g_2}(g_{s_1,f_2}(x, z1))
g_{f_2,g_2}(g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{f_2,g_2}(g_{s_1,f_2}(x, z1), z10)
g_{f_2,g_2}(z00, g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → g_{f_2,g_2}(z00, g_{s_1,f_2}(x, z1))
f_{g_2,g_2}(g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{g_2,g_2}(g_{s_1,f_2}(x, z1), z10)
f_{g_2,g_2}(z00, g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → f_{g_2,g_2}(z00, g_{s_1,f_2}(x, z1))
g_{s_1,s_1}(g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{s_1,s_1}(g_{s_1,f_2}(x, z1), z10)
g_{s_1,s_1}(z00, g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → g_{s_1,s_1}(z00, g_{s_1,f_2}(x, z1))
g_{f_2,s_1}(g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{f_2,s_1}(g_{s_1,f_2}(x, z1), z10)
g_{f_2,s_1}(z00, g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → g_{f_2,s_1}(z00, g_{s_1,f_2}(x, z1))
f_{g_2,s_1}(g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{g_2,s_1}(g_{s_1,f_2}(x, z1), z10)
f_{g_2,s_1}(z00, g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → f_{g_2,s_1}(z00, g_{s_1,f_2}(x, z1))
g_{s_1,f_2}(g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{s_1,f_2}(g_{s_1,f_2}(x, z1), z10)
g_{s_1,f_2}(z00, g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → g_{s_1,f_2}(z00, g_{s_1,f_2}(x, z1))
g_{f_2,f_2}(g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{f_2,f_2}(g_{s_1,f_2}(x, z1), z10)
g_{f_2,f_2}(z00, g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → g_{f_2,f_2}(z00, g_{s_1,f_2}(x, z1))
f_{g_2,f_2}(g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{g_2,f_2}(g_{s_1,f_2}(x, z1), z10)
f_{g_2,f_2}(z00, g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → f_{g_2,f_2}(z00, g_{s_1,f_2}(x, z1))
s_{s_1}(g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → s_{s_1}(g_{s_1,f_2}(x, z1))
f_{s_1,g_2}(g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{s_1,g_2}(g_{s_1,f_2}(x, z1), z10)
f_{s_1,g_2}(z00, g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → f_{s_1,g_2}(z00, g_{s_1,f_2}(x, z1))
f_{s_1,s_1}(g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{s_1,s_1}(g_{s_1,f_2}(x, z1), z10)
f_{s_1,s_1}(z00, g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → f_{s_1,s_1}(z00, g_{s_1,f_2}(x, z1))
f_{s_1,f_2}(g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{s_1,f_2}(g_{s_1,f_2}(x, z1), z10)
f_{s_1,f_2}(z00, g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → f_{s_1,f_2}(z00, g_{s_1,f_2}(x, z1))
s_{f_2}(g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → s_{f_2}(g_{s_1,f_2}(x, z1))
f_{f_2,g_2}(g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{f_2,g_2}(g_{s_1,f_2}(x, z1), z10)
f_{f_2,g_2}(z00, g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → f_{f_2,g_2}(z00, g_{s_1,f_2}(x, z1))
f_{f_2,s_1}(g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{f_2,s_1}(g_{s_1,f_2}(x, z1), z10)
f_{f_2,s_1}(z00, g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → f_{f_2,s_1}(z00, g_{s_1,f_2}(x, z1))
f_{f_2,f_2}(g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{f_2,f_2}(g_{s_1,f_2}(x, z1), z10)
f_{f_2,f_2}(z00, g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → f_{f_2,f_2}(z00, g_{s_1,f_2}(x, z1))
g_{g_2,g_2}(g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{g_2,g_2}(g_{s_1,f_2}(x, z1), z10)
g_{g_2,g_2}(z00, g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → g_{g_2,g_2}(z00, g_{s_1,f_2}(x, z1))
g_{g_2,s_1}(g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{g_2,s_1}(g_{s_1,f_2}(x, z1), z10)
g_{g_2,s_1}(z00, g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → g_{g_2,s_1}(z00, g_{s_1,f_2}(x, z1))
g_{g_2,f_2}(g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{g_2,f_2}(g_{s_1,f_2}(x, z1), z10)
g_{g_2,f_2}(z00, g_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → g_{g_2,f_2}(z00, g_{s_1,f_2}(x, z1))
g_{s_1,g_2}(g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{s_1,g_2}(g_{s_1,g_2}(x, z1), z10)
g_{s_1,g_2}(z00, g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → g_{s_1,g_2}(z00, g_{s_1,g_2}(x, z1))
s_{g_2}(g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → s_{g_2}(g_{s_1,g_2}(x, z1))
g_{f_2,g_2}(g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{f_2,g_2}(g_{s_1,g_2}(x, z1), z10)
g_{f_2,g_2}(z00, g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → g_{f_2,g_2}(z00, g_{s_1,g_2}(x, z1))
f_{g_2,g_2}(g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{g_2,g_2}(g_{s_1,g_2}(x, z1), z10)
f_{g_2,g_2}(z00, g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → f_{g_2,g_2}(z00, g_{s_1,g_2}(x, z1))
g_{s_1,s_1}(g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{s_1,s_1}(g_{s_1,g_2}(x, z1), z10)
g_{s_1,s_1}(z00, g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → g_{s_1,s_1}(z00, g_{s_1,g_2}(x, z1))
g_{f_2,s_1}(g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{f_2,s_1}(g_{s_1,g_2}(x, z1), z10)
g_{f_2,s_1}(z00, g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → g_{f_2,s_1}(z00, g_{s_1,g_2}(x, z1))
f_{g_2,s_1}(g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{g_2,s_1}(g_{s_1,g_2}(x, z1), z10)
f_{g_2,s_1}(z00, g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → f_{g_2,s_1}(z00, g_{s_1,g_2}(x, z1))
g_{s_1,f_2}(g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{s_1,f_2}(g_{s_1,g_2}(x, z1), z10)
g_{s_1,f_2}(z00, g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → g_{s_1,f_2}(z00, g_{s_1,g_2}(x, z1))
g_{f_2,f_2}(g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{f_2,f_2}(g_{s_1,g_2}(x, z1), z10)
g_{f_2,f_2}(z00, g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → g_{f_2,f_2}(z00, g_{s_1,g_2}(x, z1))
f_{g_2,f_2}(g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{g_2,f_2}(g_{s_1,g_2}(x, z1), z10)
f_{g_2,f_2}(z00, g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → f_{g_2,f_2}(z00, g_{s_1,g_2}(x, z1))
s_{s_1}(g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → s_{s_1}(g_{s_1,g_2}(x, z1))
f_{s_1,g_2}(g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{s_1,g_2}(g_{s_1,g_2}(x, z1), z10)
f_{s_1,g_2}(z00, g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → f_{s_1,g_2}(z00, g_{s_1,g_2}(x, z1))
f_{s_1,s_1}(g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{s_1,s_1}(g_{s_1,g_2}(x, z1), z10)
f_{s_1,s_1}(z00, g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → f_{s_1,s_1}(z00, g_{s_1,g_2}(x, z1))
f_{s_1,f_2}(g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{s_1,f_2}(g_{s_1,g_2}(x, z1), z10)
f_{s_1,f_2}(z00, g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → f_{s_1,f_2}(z00, g_{s_1,g_2}(x, z1))
s_{f_2}(g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → s_{f_2}(g_{s_1,g_2}(x, z1))
f_{f_2,g_2}(g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{f_2,g_2}(g_{s_1,g_2}(x, z1), z10)
f_{f_2,g_2}(z00, g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → f_{f_2,g_2}(z00, g_{s_1,g_2}(x, z1))
f_{f_2,s_1}(g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{f_2,s_1}(g_{s_1,g_2}(x, z1), z10)
f_{f_2,s_1}(z00, g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → f_{f_2,s_1}(z00, g_{s_1,g_2}(x, z1))
f_{f_2,f_2}(g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{f_2,f_2}(g_{s_1,g_2}(x, z1), z10)
f_{f_2,f_2}(z00, g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → f_{f_2,f_2}(z00, g_{s_1,g_2}(x, z1))
g_{g_2,g_2}(g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{g_2,g_2}(g_{s_1,g_2}(x, z1), z10)
g_{g_2,g_2}(z00, g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → g_{g_2,g_2}(z00, g_{s_1,g_2}(x, z1))
g_{g_2,s_1}(g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{g_2,s_1}(g_{s_1,g_2}(x, z1), z10)
g_{g_2,s_1}(z00, g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → g_{g_2,s_1}(z00, g_{s_1,g_2}(x, z1))
g_{g_2,f_2}(g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{g_2,f_2}(g_{s_1,g_2}(x, z1), z10)
g_{g_2,f_2}(z00, g_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → g_{g_2,f_2}(z00, g_{s_1,g_2}(x, z1))
g_{s_1,g_2}(g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → g_{s_1,g_2}(g_{s_1,s_1}(x, z1), z10)
g_{s_1,g_2}(z00, g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → g_{s_1,g_2}(z00, g_{s_1,s_1}(x, z1))
s_{g_2}(g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → s_{g_2}(g_{s_1,s_1}(x, z1))
g_{f_2,g_2}(g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → g_{f_2,g_2}(g_{s_1,s_1}(x, z1), z10)
g_{f_2,g_2}(z00, g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → g_{f_2,g_2}(z00, g_{s_1,s_1}(x, z1))
f_{g_2,g_2}(g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → f_{g_2,g_2}(g_{s_1,s_1}(x, z1), z10)
f_{g_2,g_2}(z00, g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → f_{g_2,g_2}(z00, g_{s_1,s_1}(x, z1))
g_{s_1,s_1}(g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → g_{s_1,s_1}(g_{s_1,s_1}(x, z1), z10)
g_{s_1,s_1}(z00, g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → g_{s_1,s_1}(z00, g_{s_1,s_1}(x, z1))
g_{f_2,s_1}(g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → g_{f_2,s_1}(g_{s_1,s_1}(x, z1), z10)
g_{f_2,s_1}(z00, g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → g_{f_2,s_1}(z00, g_{s_1,s_1}(x, z1))
f_{g_2,s_1}(g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → f_{g_2,s_1}(g_{s_1,s_1}(x, z1), z10)
f_{g_2,s_1}(z00, g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → f_{g_2,s_1}(z00, g_{s_1,s_1}(x, z1))
g_{s_1,f_2}(g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → g_{s_1,f_2}(g_{s_1,s_1}(x, z1), z10)
g_{s_1,f_2}(z00, g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → g_{s_1,f_2}(z00, g_{s_1,s_1}(x, z1))
g_{f_2,f_2}(g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → g_{f_2,f_2}(g_{s_1,s_1}(x, z1), z10)
g_{f_2,f_2}(z00, g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → g_{f_2,f_2}(z00, g_{s_1,s_1}(x, z1))
f_{g_2,f_2}(g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → f_{g_2,f_2}(g_{s_1,s_1}(x, z1), z10)
f_{g_2,f_2}(z00, g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → f_{g_2,f_2}(z00, g_{s_1,s_1}(x, z1))
s_{s_1}(g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → s_{s_1}(g_{s_1,s_1}(x, z1))
f_{s_1,g_2}(g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → f_{s_1,g_2}(g_{s_1,s_1}(x, z1), z10)
f_{s_1,g_2}(z00, g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → f_{s_1,g_2}(z00, g_{s_1,s_1}(x, z1))
f_{s_1,s_1}(g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → f_{s_1,s_1}(g_{s_1,s_1}(x, z1), z10)
f_{s_1,s_1}(z00, g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → f_{s_1,s_1}(z00, g_{s_1,s_1}(x, z1))
f_{s_1,f_2}(g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → f_{s_1,f_2}(g_{s_1,s_1}(x, z1), z10)
f_{s_1,f_2}(z00, g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → f_{s_1,f_2}(z00, g_{s_1,s_1}(x, z1))
s_{f_2}(g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → s_{f_2}(g_{s_1,s_1}(x, z1))
f_{f_2,g_2}(g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → f_{f_2,g_2}(g_{s_1,s_1}(x, z1), z10)
f_{f_2,g_2}(z00, g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → f_{f_2,g_2}(z00, g_{s_1,s_1}(x, z1))
f_{f_2,s_1}(g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → f_{f_2,s_1}(g_{s_1,s_1}(x, z1), z10)
f_{f_2,s_1}(z00, g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → f_{f_2,s_1}(z00, g_{s_1,s_1}(x, z1))
f_{f_2,f_2}(g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → f_{f_2,f_2}(g_{s_1,s_1}(x, z1), z10)
f_{f_2,f_2}(z00, g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → f_{f_2,f_2}(z00, g_{s_1,s_1}(x, z1))
g_{g_2,g_2}(g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → g_{g_2,g_2}(g_{s_1,s_1}(x, z1), z10)
g_{g_2,g_2}(z00, g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → g_{g_2,g_2}(z00, g_{s_1,s_1}(x, z1))
g_{g_2,s_1}(g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → g_{g_2,s_1}(g_{s_1,s_1}(x, z1), z10)
g_{g_2,s_1}(z00, g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → g_{g_2,s_1}(z00, g_{s_1,s_1}(x, z1))
g_{g_2,f_2}(g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → g_{g_2,f_2}(g_{s_1,s_1}(x, z1), z10)
g_{g_2,f_2}(z00, g_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → g_{g_2,f_2}(z00, g_{s_1,s_1}(x, z1))
g_{s_1,g_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{s_1,g_2}(g_{s_1,f_2}(x, z1), z10)
g_{s_1,g_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → g_{s_1,g_2}(z00, g_{s_1,f_2}(x, z1))
s_{g_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → s_{g_2}(g_{s_1,f_2}(x, z1))
g_{f_2,g_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{f_2,g_2}(g_{s_1,f_2}(x, z1), z10)
g_{f_2,g_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → g_{f_2,g_2}(z00, g_{s_1,f_2}(x, z1))
f_{g_2,g_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{g_2,g_2}(g_{s_1,f_2}(x, z1), z10)
f_{g_2,g_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → f_{g_2,g_2}(z00, g_{s_1,f_2}(x, z1))
g_{s_1,s_1}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{s_1,s_1}(g_{s_1,f_2}(x, z1), z10)
g_{s_1,s_1}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → g_{s_1,s_1}(z00, g_{s_1,f_2}(x, z1))
g_{f_2,s_1}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{f_2,s_1}(g_{s_1,f_2}(x, z1), z10)
g_{f_2,s_1}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → g_{f_2,s_1}(z00, g_{s_1,f_2}(x, z1))
f_{g_2,s_1}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{g_2,s_1}(g_{s_1,f_2}(x, z1), z10)
f_{g_2,s_1}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → f_{g_2,s_1}(z00, g_{s_1,f_2}(x, z1))
g_{s_1,f_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{s_1,f_2}(g_{s_1,f_2}(x, z1), z10)
g_{s_1,f_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → g_{s_1,f_2}(z00, g_{s_1,f_2}(x, z1))
g_{f_2,f_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{f_2,f_2}(g_{s_1,f_2}(x, z1), z10)
g_{f_2,f_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → g_{f_2,f_2}(z00, g_{s_1,f_2}(x, z1))
f_{g_2,f_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{g_2,f_2}(g_{s_1,f_2}(x, z1), z10)
f_{g_2,f_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → f_{g_2,f_2}(z00, g_{s_1,f_2}(x, z1))
s_{s_1}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → s_{s_1}(g_{s_1,f_2}(x, z1))
f_{s_1,g_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{s_1,g_2}(g_{s_1,f_2}(x, z1), z10)
f_{s_1,g_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → f_{s_1,g_2}(z00, g_{s_1,f_2}(x, z1))
f_{s_1,s_1}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{s_1,s_1}(g_{s_1,f_2}(x, z1), z10)
f_{s_1,s_1}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → f_{s_1,s_1}(z00, g_{s_1,f_2}(x, z1))
f_{s_1,f_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{s_1,f_2}(g_{s_1,f_2}(x, z1), z10)
f_{s_1,f_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → f_{s_1,f_2}(z00, g_{s_1,f_2}(x, z1))
s_{f_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → s_{f_2}(g_{s_1,f_2}(x, z1))
f_{f_2,g_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{f_2,g_2}(g_{s_1,f_2}(x, z1), z10)
f_{f_2,g_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → f_{f_2,g_2}(z00, g_{s_1,f_2}(x, z1))
f_{f_2,s_1}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{f_2,s_1}(g_{s_1,f_2}(x, z1), z10)
f_{f_2,s_1}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → f_{f_2,s_1}(z00, g_{s_1,f_2}(x, z1))
f_{f_2,f_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{f_2,f_2}(g_{s_1,f_2}(x, z1), z10)
f_{f_2,f_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → f_{f_2,f_2}(z00, g_{s_1,f_2}(x, z1))
g_{g_2,g_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{g_2,g_2}(g_{s_1,f_2}(x, z1), z10)
g_{g_2,g_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → g_{g_2,g_2}(z00, g_{s_1,f_2}(x, z1))
g_{g_2,s_1}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{g_2,s_1}(g_{s_1,f_2}(x, z1), z10)
g_{g_2,s_1}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → g_{g_2,s_1}(z00, g_{s_1,f_2}(x, z1))
g_{g_2,f_2}(g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{g_2,f_2}(g_{s_1,f_2}(x, z1), z10)
g_{g_2,f_2}(z00, g_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → g_{g_2,f_2}(z00, g_{s_1,f_2}(x, z1))
g_{s_1,g_2}(g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{s_1,g_2}(g_{g_2,g_2}(z0, x), z10)
g_{s_1,g_2}(z00, g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{s_1,g_2}(z00, g_{g_2,g_2}(z0, x))
s_{g_2}(g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → s_{g_2}(g_{g_2,g_2}(z0, x))
g_{f_2,g_2}(g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{f_2,g_2}(g_{g_2,g_2}(z0, x), z10)
g_{f_2,g_2}(z00, g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{f_2,g_2}(z00, g_{g_2,g_2}(z0, x))
f_{g_2,g_2}(g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{g_2,g_2}(g_{g_2,g_2}(z0, x), z10)
f_{g_2,g_2}(z00, g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{g_2,g_2}(z00, g_{g_2,g_2}(z0, x))
g_{s_1,s_1}(g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{s_1,s_1}(g_{g_2,g_2}(z0, x), z10)
g_{s_1,s_1}(z00, g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{s_1,s_1}(z00, g_{g_2,g_2}(z0, x))
g_{f_2,s_1}(g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{f_2,s_1}(g_{g_2,g_2}(z0, x), z10)
g_{f_2,s_1}(z00, g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{f_2,s_1}(z00, g_{g_2,g_2}(z0, x))
f_{g_2,s_1}(g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{g_2,s_1}(g_{g_2,g_2}(z0, x), z10)
f_{g_2,s_1}(z00, g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{g_2,s_1}(z00, g_{g_2,g_2}(z0, x))
g_{s_1,f_2}(g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{s_1,f_2}(g_{g_2,g_2}(z0, x), z10)
g_{s_1,f_2}(z00, g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{s_1,f_2}(z00, g_{g_2,g_2}(z0, x))
g_{f_2,f_2}(g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{f_2,f_2}(g_{g_2,g_2}(z0, x), z10)
g_{f_2,f_2}(z00, g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{f_2,f_2}(z00, g_{g_2,g_2}(z0, x))
f_{g_2,f_2}(g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{g_2,f_2}(g_{g_2,g_2}(z0, x), z10)
f_{g_2,f_2}(z00, g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{g_2,f_2}(z00, g_{g_2,g_2}(z0, x))
s_{s_1}(g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → s_{s_1}(g_{g_2,g_2}(z0, x))
f_{s_1,g_2}(g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{s_1,g_2}(g_{g_2,g_2}(z0, x), z10)
f_{s_1,g_2}(z00, g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{s_1,g_2}(z00, g_{g_2,g_2}(z0, x))
f_{s_1,s_1}(g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{s_1,s_1}(g_{g_2,g_2}(z0, x), z10)
f_{s_1,s_1}(z00, g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{s_1,s_1}(z00, g_{g_2,g_2}(z0, x))
f_{s_1,f_2}(g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{s_1,f_2}(g_{g_2,g_2}(z0, x), z10)
f_{s_1,f_2}(z00, g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{s_1,f_2}(z00, g_{g_2,g_2}(z0, x))
s_{f_2}(g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → s_{f_2}(g_{g_2,g_2}(z0, x))
f_{f_2,g_2}(g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{f_2,g_2}(g_{g_2,g_2}(z0, x), z10)
f_{f_2,g_2}(z00, g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{f_2,g_2}(z00, g_{g_2,g_2}(z0, x))
f_{f_2,s_1}(g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{f_2,s_1}(g_{g_2,g_2}(z0, x), z10)
f_{f_2,s_1}(z00, g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{f_2,s_1}(z00, g_{g_2,g_2}(z0, x))
f_{f_2,f_2}(g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{f_2,f_2}(g_{g_2,g_2}(z0, x), z10)
f_{f_2,f_2}(z00, g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{f_2,f_2}(z00, g_{g_2,g_2}(z0, x))
g_{g_2,g_2}(g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{g_2,g_2}(g_{g_2,g_2}(z0, x), z10)
g_{g_2,g_2}(z00, g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{g_2,g_2}(z00, g_{g_2,g_2}(z0, x))
g_{g_2,s_1}(g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{g_2,s_1}(g_{g_2,g_2}(z0, x), z10)
g_{g_2,s_1}(z00, g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{g_2,s_1}(z00, g_{g_2,g_2}(z0, x))
g_{g_2,f_2}(g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{g_2,f_2}(g_{g_2,g_2}(z0, x), z10)
g_{g_2,f_2}(z00, g_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{g_2,f_2}(z00, g_{g_2,g_2}(z0, x))
g_{s_1,g_2}(g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{s_1,g_2}(g_{g_2,g_2}(z0, x), z10)
g_{s_1,g_2}(z00, g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{s_1,g_2}(z00, g_{g_2,g_2}(z0, x))
s_{g_2}(g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → s_{g_2}(g_{g_2,g_2}(z0, x))
g_{f_2,g_2}(g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{f_2,g_2}(g_{g_2,g_2}(z0, x), z10)
g_{f_2,g_2}(z00, g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{f_2,g_2}(z00, g_{g_2,g_2}(z0, x))
f_{g_2,g_2}(g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{g_2,g_2}(g_{g_2,g_2}(z0, x), z10)
f_{g_2,g_2}(z00, g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{g_2,g_2}(z00, g_{g_2,g_2}(z0, x))
g_{s_1,s_1}(g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{s_1,s_1}(g_{g_2,g_2}(z0, x), z10)
g_{s_1,s_1}(z00, g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{s_1,s_1}(z00, g_{g_2,g_2}(z0, x))
g_{f_2,s_1}(g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{f_2,s_1}(g_{g_2,g_2}(z0, x), z10)
g_{f_2,s_1}(z00, g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{f_2,s_1}(z00, g_{g_2,g_2}(z0, x))
f_{g_2,s_1}(g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{g_2,s_1}(g_{g_2,g_2}(z0, x), z10)
f_{g_2,s_1}(z00, g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{g_2,s_1}(z00, g_{g_2,g_2}(z0, x))
g_{s_1,f_2}(g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{s_1,f_2}(g_{g_2,g_2}(z0, x), z10)
g_{s_1,f_2}(z00, g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{s_1,f_2}(z00, g_{g_2,g_2}(z0, x))
g_{f_2,f_2}(g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{f_2,f_2}(g_{g_2,g_2}(z0, x), z10)
g_{f_2,f_2}(z00, g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{f_2,f_2}(z00, g_{g_2,g_2}(z0, x))
f_{g_2,f_2}(g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{g_2,f_2}(g_{g_2,g_2}(z0, x), z10)
f_{g_2,f_2}(z00, g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{g_2,f_2}(z00, g_{g_2,g_2}(z0, x))
s_{s_1}(g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → s_{s_1}(g_{g_2,g_2}(z0, x))
f_{s_1,g_2}(g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{s_1,g_2}(g_{g_2,g_2}(z0, x), z10)
f_{s_1,g_2}(z00, g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{s_1,g_2}(z00, g_{g_2,g_2}(z0, x))
f_{s_1,s_1}(g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{s_1,s_1}(g_{g_2,g_2}(z0, x), z10)
f_{s_1,s_1}(z00, g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{s_1,s_1}(z00, g_{g_2,g_2}(z0, x))
f_{s_1,f_2}(g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{s_1,f_2}(g_{g_2,g_2}(z0, x), z10)
f_{s_1,f_2}(z00, g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{s_1,f_2}(z00, g_{g_2,g_2}(z0, x))
s_{f_2}(g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → s_{f_2}(g_{g_2,g_2}(z0, x))
f_{f_2,g_2}(g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{f_2,g_2}(g_{g_2,g_2}(z0, x), z10)
f_{f_2,g_2}(z00, g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{f_2,g_2}(z00, g_{g_2,g_2}(z0, x))
f_{f_2,s_1}(g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{f_2,s_1}(g_{g_2,g_2}(z0, x), z10)
f_{f_2,s_1}(z00, g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{f_2,s_1}(z00, g_{g_2,g_2}(z0, x))
f_{f_2,f_2}(g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{f_2,f_2}(g_{g_2,g_2}(z0, x), z10)
f_{f_2,f_2}(z00, g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{f_2,f_2}(z00, g_{g_2,g_2}(z0, x))
g_{g_2,g_2}(g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{g_2,g_2}(g_{g_2,g_2}(z0, x), z10)
g_{g_2,g_2}(z00, g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{g_2,g_2}(z00, g_{g_2,g_2}(z0, x))
g_{g_2,s_1}(g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{g_2,s_1}(g_{g_2,g_2}(z0, x), z10)
g_{g_2,s_1}(z00, g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{g_2,s_1}(z00, g_{g_2,g_2}(z0, x))
g_{g_2,f_2}(g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{g_2,f_2}(g_{g_2,g_2}(z0, x), z10)
g_{g_2,f_2}(z00, g_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{g_2,f_2}(z00, g_{g_2,g_2}(z0, x))
g_{s_1,g_2}(g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{s_1,g_2}(g_{g_2,g_2}(z0, x), z10)
g_{s_1,g_2}(z00, g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{s_1,g_2}(z00, g_{g_2,g_2}(z0, x))
s_{g_2}(g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → s_{g_2}(g_{g_2,g_2}(z0, x))
g_{f_2,g_2}(g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{f_2,g_2}(g_{g_2,g_2}(z0, x), z10)
g_{f_2,g_2}(z00, g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{f_2,g_2}(z00, g_{g_2,g_2}(z0, x))
f_{g_2,g_2}(g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{g_2,g_2}(g_{g_2,g_2}(z0, x), z10)
f_{g_2,g_2}(z00, g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{g_2,g_2}(z00, g_{g_2,g_2}(z0, x))
g_{s_1,s_1}(g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{s_1,s_1}(g_{g_2,g_2}(z0, x), z10)
g_{s_1,s_1}(z00, g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{s_1,s_1}(z00, g_{g_2,g_2}(z0, x))
g_{f_2,s_1}(g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{f_2,s_1}(g_{g_2,g_2}(z0, x), z10)
g_{f_2,s_1}(z00, g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{f_2,s_1}(z00, g_{g_2,g_2}(z0, x))
f_{g_2,s_1}(g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{g_2,s_1}(g_{g_2,g_2}(z0, x), z10)
f_{g_2,s_1}(z00, g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{g_2,s_1}(z00, g_{g_2,g_2}(z0, x))
g_{s_1,f_2}(g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{s_1,f_2}(g_{g_2,g_2}(z0, x), z10)
g_{s_1,f_2}(z00, g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{s_1,f_2}(z00, g_{g_2,g_2}(z0, x))
g_{f_2,f_2}(g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{f_2,f_2}(g_{g_2,g_2}(z0, x), z10)
g_{f_2,f_2}(z00, g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{f_2,f_2}(z00, g_{g_2,g_2}(z0, x))
f_{g_2,f_2}(g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{g_2,f_2}(g_{g_2,g_2}(z0, x), z10)
f_{g_2,f_2}(z00, g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{g_2,f_2}(z00, g_{g_2,g_2}(z0, x))
s_{s_1}(g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → s_{s_1}(g_{g_2,g_2}(z0, x))
f_{s_1,g_2}(g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{s_1,g_2}(g_{g_2,g_2}(z0, x), z10)
f_{s_1,g_2}(z00, g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{s_1,g_2}(z00, g_{g_2,g_2}(z0, x))
f_{s_1,s_1}(g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{s_1,s_1}(g_{g_2,g_2}(z0, x), z10)
f_{s_1,s_1}(z00, g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{s_1,s_1}(z00, g_{g_2,g_2}(z0, x))
f_{s_1,f_2}(g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{s_1,f_2}(g_{g_2,g_2}(z0, x), z10)
f_{s_1,f_2}(z00, g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{s_1,f_2}(z00, g_{g_2,g_2}(z0, x))
s_{f_2}(g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → s_{f_2}(g_{g_2,g_2}(z0, x))
f_{f_2,g_2}(g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{f_2,g_2}(g_{g_2,g_2}(z0, x), z10)
f_{f_2,g_2}(z00, g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{f_2,g_2}(z00, g_{g_2,g_2}(z0, x))
f_{f_2,s_1}(g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{f_2,s_1}(g_{g_2,g_2}(z0, x), z10)
f_{f_2,s_1}(z00, g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{f_2,s_1}(z00, g_{g_2,g_2}(z0, x))
f_{f_2,f_2}(g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{f_2,f_2}(g_{g_2,g_2}(z0, x), z10)
f_{f_2,f_2}(z00, g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{f_2,f_2}(z00, g_{g_2,g_2}(z0, x))
g_{g_2,g_2}(g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{g_2,g_2}(g_{g_2,g_2}(z0, x), z10)
g_{g_2,g_2}(z00, g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{g_2,g_2}(z00, g_{g_2,g_2}(z0, x))
g_{g_2,s_1}(g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{g_2,s_1}(g_{g_2,g_2}(z0, x), z10)
g_{g_2,s_1}(z00, g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{g_2,s_1}(z00, g_{g_2,g_2}(z0, x))
g_{g_2,f_2}(g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{g_2,f_2}(g_{g_2,g_2}(z0, x), z10)
g_{g_2,f_2}(z00, g_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{g_2,f_2}(z00, g_{g_2,g_2}(z0, x))
g_{s_1,g_2}(g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{s_1,g_2}(g_{g_2,s_1}(z0, x), z10)
g_{s_1,g_2}(z00, g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{s_1,g_2}(z00, g_{g_2,s_1}(z0, x))
s_{g_2}(g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → s_{g_2}(g_{g_2,s_1}(z0, x))
g_{f_2,g_2}(g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{f_2,g_2}(g_{g_2,s_1}(z0, x), z10)
g_{f_2,g_2}(z00, g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{f_2,g_2}(z00, g_{g_2,s_1}(z0, x))
f_{g_2,g_2}(g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{g_2,g_2}(g_{g_2,s_1}(z0, x), z10)
f_{g_2,g_2}(z00, g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{g_2,g_2}(z00, g_{g_2,s_1}(z0, x))
g_{s_1,s_1}(g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{s_1,s_1}(g_{g_2,s_1}(z0, x), z10)
g_{s_1,s_1}(z00, g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{s_1,s_1}(z00, g_{g_2,s_1}(z0, x))
g_{f_2,s_1}(g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{f_2,s_1}(g_{g_2,s_1}(z0, x), z10)
g_{f_2,s_1}(z00, g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{f_2,s_1}(z00, g_{g_2,s_1}(z0, x))
f_{g_2,s_1}(g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{g_2,s_1}(g_{g_2,s_1}(z0, x), z10)
f_{g_2,s_1}(z00, g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{g_2,s_1}(z00, g_{g_2,s_1}(z0, x))
g_{s_1,f_2}(g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{s_1,f_2}(g_{g_2,s_1}(z0, x), z10)
g_{s_1,f_2}(z00, g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{s_1,f_2}(z00, g_{g_2,s_1}(z0, x))
g_{f_2,f_2}(g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{f_2,f_2}(g_{g_2,s_1}(z0, x), z10)
g_{f_2,f_2}(z00, g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{f_2,f_2}(z00, g_{g_2,s_1}(z0, x))
f_{g_2,f_2}(g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{g_2,f_2}(g_{g_2,s_1}(z0, x), z10)
f_{g_2,f_2}(z00, g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{g_2,f_2}(z00, g_{g_2,s_1}(z0, x))
s_{s_1}(g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → s_{s_1}(g_{g_2,s_1}(z0, x))
f_{s_1,g_2}(g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{s_1,g_2}(g_{g_2,s_1}(z0, x), z10)
f_{s_1,g_2}(z00, g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{s_1,g_2}(z00, g_{g_2,s_1}(z0, x))
f_{s_1,s_1}(g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{s_1,s_1}(g_{g_2,s_1}(z0, x), z10)
f_{s_1,s_1}(z00, g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{s_1,s_1}(z00, g_{g_2,s_1}(z0, x))
f_{s_1,f_2}(g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{s_1,f_2}(g_{g_2,s_1}(z0, x), z10)
f_{s_1,f_2}(z00, g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{s_1,f_2}(z00, g_{g_2,s_1}(z0, x))
s_{f_2}(g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → s_{f_2}(g_{g_2,s_1}(z0, x))
f_{f_2,g_2}(g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{f_2,g_2}(g_{g_2,s_1}(z0, x), z10)
f_{f_2,g_2}(z00, g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{f_2,g_2}(z00, g_{g_2,s_1}(z0, x))
f_{f_2,s_1}(g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{f_2,s_1}(g_{g_2,s_1}(z0, x), z10)
f_{f_2,s_1}(z00, g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{f_2,s_1}(z00, g_{g_2,s_1}(z0, x))
f_{f_2,f_2}(g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{f_2,f_2}(g_{g_2,s_1}(z0, x), z10)
f_{f_2,f_2}(z00, g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{f_2,f_2}(z00, g_{g_2,s_1}(z0, x))
g_{g_2,g_2}(g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{g_2,g_2}(g_{g_2,s_1}(z0, x), z10)
g_{g_2,g_2}(z00, g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{g_2,g_2}(z00, g_{g_2,s_1}(z0, x))
g_{g_2,s_1}(g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{g_2,s_1}(g_{g_2,s_1}(z0, x), z10)
g_{g_2,s_1}(z00, g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{g_2,s_1}(z00, g_{g_2,s_1}(z0, x))
g_{g_2,f_2}(g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{g_2,f_2}(g_{g_2,s_1}(z0, x), z10)
g_{g_2,f_2}(z00, g_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{g_2,f_2}(z00, g_{g_2,s_1}(z0, x))
g_{s_1,g_2}(g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{s_1,g_2}(g_{g_2,s_1}(z0, x), z10)
g_{s_1,g_2}(z00, g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{s_1,g_2}(z00, g_{g_2,s_1}(z0, x))
s_{g_2}(g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → s_{g_2}(g_{g_2,s_1}(z0, x))
g_{f_2,g_2}(g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{f_2,g_2}(g_{g_2,s_1}(z0, x), z10)
g_{f_2,g_2}(z00, g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{f_2,g_2}(z00, g_{g_2,s_1}(z0, x))
f_{g_2,g_2}(g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{g_2,g_2}(g_{g_2,s_1}(z0, x), z10)
f_{g_2,g_2}(z00, g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{g_2,g_2}(z00, g_{g_2,s_1}(z0, x))
g_{s_1,s_1}(g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{s_1,s_1}(g_{g_2,s_1}(z0, x), z10)
g_{s_1,s_1}(z00, g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{s_1,s_1}(z00, g_{g_2,s_1}(z0, x))
g_{f_2,s_1}(g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{f_2,s_1}(g_{g_2,s_1}(z0, x), z10)
g_{f_2,s_1}(z00, g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{f_2,s_1}(z00, g_{g_2,s_1}(z0, x))
f_{g_2,s_1}(g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{g_2,s_1}(g_{g_2,s_1}(z0, x), z10)
f_{g_2,s_1}(z00, g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{g_2,s_1}(z00, g_{g_2,s_1}(z0, x))
g_{s_1,f_2}(g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{s_1,f_2}(g_{g_2,s_1}(z0, x), z10)
g_{s_1,f_2}(z00, g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{s_1,f_2}(z00, g_{g_2,s_1}(z0, x))
g_{f_2,f_2}(g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{f_2,f_2}(g_{g_2,s_1}(z0, x), z10)
g_{f_2,f_2}(z00, g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{f_2,f_2}(z00, g_{g_2,s_1}(z0, x))
f_{g_2,f_2}(g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{g_2,f_2}(g_{g_2,s_1}(z0, x), z10)
f_{g_2,f_2}(z00, g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{g_2,f_2}(z00, g_{g_2,s_1}(z0, x))
s_{s_1}(g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → s_{s_1}(g_{g_2,s_1}(z0, x))
f_{s_1,g_2}(g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{s_1,g_2}(g_{g_2,s_1}(z0, x), z10)
f_{s_1,g_2}(z00, g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{s_1,g_2}(z00, g_{g_2,s_1}(z0, x))
f_{s_1,s_1}(g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{s_1,s_1}(g_{g_2,s_1}(z0, x), z10)
f_{s_1,s_1}(z00, g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{s_1,s_1}(z00, g_{g_2,s_1}(z0, x))
f_{s_1,f_2}(g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{s_1,f_2}(g_{g_2,s_1}(z0, x), z10)
f_{s_1,f_2}(z00, g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{s_1,f_2}(z00, g_{g_2,s_1}(z0, x))
s_{f_2}(g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → s_{f_2}(g_{g_2,s_1}(z0, x))
f_{f_2,g_2}(g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{f_2,g_2}(g_{g_2,s_1}(z0, x), z10)
f_{f_2,g_2}(z00, g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{f_2,g_2}(z00, g_{g_2,s_1}(z0, x))
f_{f_2,s_1}(g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{f_2,s_1}(g_{g_2,s_1}(z0, x), z10)
f_{f_2,s_1}(z00, g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{f_2,s_1}(z00, g_{g_2,s_1}(z0, x))
f_{f_2,f_2}(g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{f_2,f_2}(g_{g_2,s_1}(z0, x), z10)
f_{f_2,f_2}(z00, g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{f_2,f_2}(z00, g_{g_2,s_1}(z0, x))
g_{g_2,g_2}(g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{g_2,g_2}(g_{g_2,s_1}(z0, x), z10)
g_{g_2,g_2}(z00, g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{g_2,g_2}(z00, g_{g_2,s_1}(z0, x))
g_{g_2,s_1}(g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{g_2,s_1}(g_{g_2,s_1}(z0, x), z10)
g_{g_2,s_1}(z00, g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{g_2,s_1}(z00, g_{g_2,s_1}(z0, x))
g_{g_2,f_2}(g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{g_2,f_2}(g_{g_2,s_1}(z0, x), z10)
g_{g_2,f_2}(z00, g_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{g_2,f_2}(z00, g_{g_2,s_1}(z0, x))
g_{s_1,g_2}(g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{s_1,g_2}(g_{g_2,s_1}(z0, x), z10)
g_{s_1,g_2}(z00, g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{s_1,g_2}(z00, g_{g_2,s_1}(z0, x))
s_{g_2}(g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → s_{g_2}(g_{g_2,s_1}(z0, x))
g_{f_2,g_2}(g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{f_2,g_2}(g_{g_2,s_1}(z0, x), z10)
g_{f_2,g_2}(z00, g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{f_2,g_2}(z00, g_{g_2,s_1}(z0, x))
f_{g_2,g_2}(g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{g_2,g_2}(g_{g_2,s_1}(z0, x), z10)
f_{g_2,g_2}(z00, g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{g_2,g_2}(z00, g_{g_2,s_1}(z0, x))
g_{s_1,s_1}(g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{s_1,s_1}(g_{g_2,s_1}(z0, x), z10)
g_{s_1,s_1}(z00, g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{s_1,s_1}(z00, g_{g_2,s_1}(z0, x))
g_{f_2,s_1}(g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{f_2,s_1}(g_{g_2,s_1}(z0, x), z10)
g_{f_2,s_1}(z00, g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{f_2,s_1}(z00, g_{g_2,s_1}(z0, x))
f_{g_2,s_1}(g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{g_2,s_1}(g_{g_2,s_1}(z0, x), z10)
f_{g_2,s_1}(z00, g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{g_2,s_1}(z00, g_{g_2,s_1}(z0, x))
g_{s_1,f_2}(g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{s_1,f_2}(g_{g_2,s_1}(z0, x), z10)
g_{s_1,f_2}(z00, g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{s_1,f_2}(z00, g_{g_2,s_1}(z0, x))
g_{f_2,f_2}(g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{f_2,f_2}(g_{g_2,s_1}(z0, x), z10)
g_{f_2,f_2}(z00, g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{f_2,f_2}(z00, g_{g_2,s_1}(z0, x))
f_{g_2,f_2}(g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{g_2,f_2}(g_{g_2,s_1}(z0, x), z10)
f_{g_2,f_2}(z00, g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{g_2,f_2}(z00, g_{g_2,s_1}(z0, x))
s_{s_1}(g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → s_{s_1}(g_{g_2,s_1}(z0, x))
f_{s_1,g_2}(g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{s_1,g_2}(g_{g_2,s_1}(z0, x), z10)
f_{s_1,g_2}(z00, g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{s_1,g_2}(z00, g_{g_2,s_1}(z0, x))
f_{s_1,s_1}(g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{s_1,s_1}(g_{g_2,s_1}(z0, x), z10)
f_{s_1,s_1}(z00, g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{s_1,s_1}(z00, g_{g_2,s_1}(z0, x))
f_{s_1,f_2}(g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{s_1,f_2}(g_{g_2,s_1}(z0, x), z10)
f_{s_1,f_2}(z00, g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{s_1,f_2}(z00, g_{g_2,s_1}(z0, x))
s_{f_2}(g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → s_{f_2}(g_{g_2,s_1}(z0, x))
f_{f_2,g_2}(g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{f_2,g_2}(g_{g_2,s_1}(z0, x), z10)
f_{f_2,g_2}(z00, g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{f_2,g_2}(z00, g_{g_2,s_1}(z0, x))
f_{f_2,s_1}(g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{f_2,s_1}(g_{g_2,s_1}(z0, x), z10)
f_{f_2,s_1}(z00, g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{f_2,s_1}(z00, g_{g_2,s_1}(z0, x))
f_{f_2,f_2}(g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{f_2,f_2}(g_{g_2,s_1}(z0, x), z10)
f_{f_2,f_2}(z00, g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{f_2,f_2}(z00, g_{g_2,s_1}(z0, x))
g_{g_2,g_2}(g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{g_2,g_2}(g_{g_2,s_1}(z0, x), z10)
g_{g_2,g_2}(z00, g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{g_2,g_2}(z00, g_{g_2,s_1}(z0, x))
g_{g_2,s_1}(g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{g_2,s_1}(g_{g_2,s_1}(z0, x), z10)
g_{g_2,s_1}(z00, g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{g_2,s_1}(z00, g_{g_2,s_1}(z0, x))
g_{g_2,f_2}(g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{g_2,f_2}(g_{g_2,s_1}(z0, x), z10)
g_{g_2,f_2}(z00, g_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{g_2,f_2}(z00, g_{g_2,s_1}(z0, x))
g_{s_1,g_2}(g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{s_1,g_2}(g_{s_1,g_2}(z0, x), z10)
g_{s_1,g_2}(z00, g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{s_1,g_2}(z00, g_{s_1,g_2}(z0, x))
s_{g_2}(g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → s_{g_2}(g_{s_1,g_2}(z0, x))
g_{f_2,g_2}(g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{f_2,g_2}(g_{s_1,g_2}(z0, x), z10)
g_{f_2,g_2}(z00, g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{f_2,g_2}(z00, g_{s_1,g_2}(z0, x))
f_{g_2,g_2}(g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{g_2,g_2}(g_{s_1,g_2}(z0, x), z10)
f_{g_2,g_2}(z00, g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{g_2,g_2}(z00, g_{s_1,g_2}(z0, x))
g_{s_1,s_1}(g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{s_1,s_1}(g_{s_1,g_2}(z0, x), z10)
g_{s_1,s_1}(z00, g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{s_1,s_1}(z00, g_{s_1,g_2}(z0, x))
g_{f_2,s_1}(g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{f_2,s_1}(g_{s_1,g_2}(z0, x), z10)
g_{f_2,s_1}(z00, g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{f_2,s_1}(z00, g_{s_1,g_2}(z0, x))
f_{g_2,s_1}(g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{g_2,s_1}(g_{s_1,g_2}(z0, x), z10)
f_{g_2,s_1}(z00, g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{g_2,s_1}(z00, g_{s_1,g_2}(z0, x))
g_{s_1,f_2}(g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{s_1,f_2}(g_{s_1,g_2}(z0, x), z10)
g_{s_1,f_2}(z00, g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{s_1,f_2}(z00, g_{s_1,g_2}(z0, x))
g_{f_2,f_2}(g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{f_2,f_2}(g_{s_1,g_2}(z0, x), z10)
g_{f_2,f_2}(z00, g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{f_2,f_2}(z00, g_{s_1,g_2}(z0, x))
f_{g_2,f_2}(g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{g_2,f_2}(g_{s_1,g_2}(z0, x), z10)
f_{g_2,f_2}(z00, g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{g_2,f_2}(z00, g_{s_1,g_2}(z0, x))
s_{s_1}(g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → s_{s_1}(g_{s_1,g_2}(z0, x))
f_{s_1,g_2}(g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{s_1,g_2}(g_{s_1,g_2}(z0, x), z10)
f_{s_1,g_2}(z00, g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{s_1,g_2}(z00, g_{s_1,g_2}(z0, x))
f_{s_1,s_1}(g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{s_1,s_1}(g_{s_1,g_2}(z0, x), z10)
f_{s_1,s_1}(z00, g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{s_1,s_1}(z00, g_{s_1,g_2}(z0, x))
f_{s_1,f_2}(g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{s_1,f_2}(g_{s_1,g_2}(z0, x), z10)
f_{s_1,f_2}(z00, g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{s_1,f_2}(z00, g_{s_1,g_2}(z0, x))
s_{f_2}(g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → s_{f_2}(g_{s_1,g_2}(z0, x))
f_{f_2,g_2}(g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{f_2,g_2}(g_{s_1,g_2}(z0, x), z10)
f_{f_2,g_2}(z00, g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{f_2,g_2}(z00, g_{s_1,g_2}(z0, x))
f_{f_2,s_1}(g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{f_2,s_1}(g_{s_1,g_2}(z0, x), z10)
f_{f_2,s_1}(z00, g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{f_2,s_1}(z00, g_{s_1,g_2}(z0, x))
f_{f_2,f_2}(g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{f_2,f_2}(g_{s_1,g_2}(z0, x), z10)
f_{f_2,f_2}(z00, g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{f_2,f_2}(z00, g_{s_1,g_2}(z0, x))
g_{g_2,g_2}(g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{g_2,g_2}(g_{s_1,g_2}(z0, x), z10)
g_{g_2,g_2}(z00, g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{g_2,g_2}(z00, g_{s_1,g_2}(z0, x))
g_{g_2,s_1}(g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{g_2,s_1}(g_{s_1,g_2}(z0, x), z10)
g_{g_2,s_1}(z00, g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{g_2,s_1}(z00, g_{s_1,g_2}(z0, x))
g_{g_2,f_2}(g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{g_2,f_2}(g_{s_1,g_2}(z0, x), z10)
g_{g_2,f_2}(z00, g_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{g_2,f_2}(z00, g_{s_1,g_2}(z0, x))
g_{s_1,g_2}(g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{s_1,g_2}(g_{s_1,g_2}(z0, x), z10)
g_{s_1,g_2}(z00, g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{s_1,g_2}(z00, g_{s_1,g_2}(z0, x))
s_{g_2}(g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → s_{g_2}(g_{s_1,g_2}(z0, x))
g_{f_2,g_2}(g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{f_2,g_2}(g_{s_1,g_2}(z0, x), z10)
g_{f_2,g_2}(z00, g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{f_2,g_2}(z00, g_{s_1,g_2}(z0, x))
f_{g_2,g_2}(g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{g_2,g_2}(g_{s_1,g_2}(z0, x), z10)
f_{g_2,g_2}(z00, g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{g_2,g_2}(z00, g_{s_1,g_2}(z0, x))
g_{s_1,s_1}(g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{s_1,s_1}(g_{s_1,g_2}(z0, x), z10)
g_{s_1,s_1}(z00, g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{s_1,s_1}(z00, g_{s_1,g_2}(z0, x))
g_{f_2,s_1}(g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{f_2,s_1}(g_{s_1,g_2}(z0, x), z10)
g_{f_2,s_1}(z00, g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{f_2,s_1}(z00, g_{s_1,g_2}(z0, x))
f_{g_2,s_1}(g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{g_2,s_1}(g_{s_1,g_2}(z0, x), z10)
f_{g_2,s_1}(z00, g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{g_2,s_1}(z00, g_{s_1,g_2}(z0, x))
g_{s_1,f_2}(g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{s_1,f_2}(g_{s_1,g_2}(z0, x), z10)
g_{s_1,f_2}(z00, g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{s_1,f_2}(z00, g_{s_1,g_2}(z0, x))
g_{f_2,f_2}(g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{f_2,f_2}(g_{s_1,g_2}(z0, x), z10)
g_{f_2,f_2}(z00, g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{f_2,f_2}(z00, g_{s_1,g_2}(z0, x))
f_{g_2,f_2}(g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{g_2,f_2}(g_{s_1,g_2}(z0, x), z10)
f_{g_2,f_2}(z00, g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{g_2,f_2}(z00, g_{s_1,g_2}(z0, x))
s_{s_1}(g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → s_{s_1}(g_{s_1,g_2}(z0, x))
f_{s_1,g_2}(g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{s_1,g_2}(g_{s_1,g_2}(z0, x), z10)
f_{s_1,g_2}(z00, g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{s_1,g_2}(z00, g_{s_1,g_2}(z0, x))
f_{s_1,s_1}(g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{s_1,s_1}(g_{s_1,g_2}(z0, x), z10)
f_{s_1,s_1}(z00, g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{s_1,s_1}(z00, g_{s_1,g_2}(z0, x))
f_{s_1,f_2}(g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{s_1,f_2}(g_{s_1,g_2}(z0, x), z10)
f_{s_1,f_2}(z00, g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{s_1,f_2}(z00, g_{s_1,g_2}(z0, x))
s_{f_2}(g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → s_{f_2}(g_{s_1,g_2}(z0, x))
f_{f_2,g_2}(g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{f_2,g_2}(g_{s_1,g_2}(z0, x), z10)
f_{f_2,g_2}(z00, g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{f_2,g_2}(z00, g_{s_1,g_2}(z0, x))
f_{f_2,s_1}(g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{f_2,s_1}(g_{s_1,g_2}(z0, x), z10)
f_{f_2,s_1}(z00, g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{f_2,s_1}(z00, g_{s_1,g_2}(z0, x))
f_{f_2,f_2}(g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{f_2,f_2}(g_{s_1,g_2}(z0, x), z10)
f_{f_2,f_2}(z00, g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{f_2,f_2}(z00, g_{s_1,g_2}(z0, x))
g_{g_2,g_2}(g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{g_2,g_2}(g_{s_1,g_2}(z0, x), z10)
g_{g_2,g_2}(z00, g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{g_2,g_2}(z00, g_{s_1,g_2}(z0, x))
g_{g_2,s_1}(g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{g_2,s_1}(g_{s_1,g_2}(z0, x), z10)
g_{g_2,s_1}(z00, g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{g_2,s_1}(z00, g_{s_1,g_2}(z0, x))
g_{g_2,f_2}(g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{g_2,f_2}(g_{s_1,g_2}(z0, x), z10)
g_{g_2,f_2}(z00, g_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{g_2,f_2}(z00, g_{s_1,g_2}(z0, x))
g_{s_1,g_2}(g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{s_1,g_2}(g_{s_1,g_2}(z0, x), z10)
g_{s_1,g_2}(z00, g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{s_1,g_2}(z00, g_{s_1,g_2}(z0, x))
s_{g_2}(g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → s_{g_2}(g_{s_1,g_2}(z0, x))
g_{f_2,g_2}(g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{f_2,g_2}(g_{s_1,g_2}(z0, x), z10)
g_{f_2,g_2}(z00, g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{f_2,g_2}(z00, g_{s_1,g_2}(z0, x))
f_{g_2,g_2}(g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{g_2,g_2}(g_{s_1,g_2}(z0, x), z10)
f_{g_2,g_2}(z00, g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{g_2,g_2}(z00, g_{s_1,g_2}(z0, x))
g_{s_1,s_1}(g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{s_1,s_1}(g_{s_1,g_2}(z0, x), z10)
g_{s_1,s_1}(z00, g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{s_1,s_1}(z00, g_{s_1,g_2}(z0, x))
g_{f_2,s_1}(g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{f_2,s_1}(g_{s_1,g_2}(z0, x), z10)
g_{f_2,s_1}(z00, g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{f_2,s_1}(z00, g_{s_1,g_2}(z0, x))
f_{g_2,s_1}(g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{g_2,s_1}(g_{s_1,g_2}(z0, x), z10)
f_{g_2,s_1}(z00, g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{g_2,s_1}(z00, g_{s_1,g_2}(z0, x))
g_{s_1,f_2}(g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{s_1,f_2}(g_{s_1,g_2}(z0, x), z10)
g_{s_1,f_2}(z00, g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{s_1,f_2}(z00, g_{s_1,g_2}(z0, x))
g_{f_2,f_2}(g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{f_2,f_2}(g_{s_1,g_2}(z0, x), z10)
g_{f_2,f_2}(z00, g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{f_2,f_2}(z00, g_{s_1,g_2}(z0, x))
f_{g_2,f_2}(g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{g_2,f_2}(g_{s_1,g_2}(z0, x), z10)
f_{g_2,f_2}(z00, g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{g_2,f_2}(z00, g_{s_1,g_2}(z0, x))
s_{s_1}(g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → s_{s_1}(g_{s_1,g_2}(z0, x))
f_{s_1,g_2}(g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{s_1,g_2}(g_{s_1,g_2}(z0, x), z10)
f_{s_1,g_2}(z00, g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{s_1,g_2}(z00, g_{s_1,g_2}(z0, x))
f_{s_1,s_1}(g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{s_1,s_1}(g_{s_1,g_2}(z0, x), z10)
f_{s_1,s_1}(z00, g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{s_1,s_1}(z00, g_{s_1,g_2}(z0, x))
f_{s_1,f_2}(g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{s_1,f_2}(g_{s_1,g_2}(z0, x), z10)
f_{s_1,f_2}(z00, g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{s_1,f_2}(z00, g_{s_1,g_2}(z0, x))
s_{f_2}(g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → s_{f_2}(g_{s_1,g_2}(z0, x))
f_{f_2,g_2}(g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{f_2,g_2}(g_{s_1,g_2}(z0, x), z10)
f_{f_2,g_2}(z00, g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{f_2,g_2}(z00, g_{s_1,g_2}(z0, x))
f_{f_2,s_1}(g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{f_2,s_1}(g_{s_1,g_2}(z0, x), z10)
f_{f_2,s_1}(z00, g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{f_2,s_1}(z00, g_{s_1,g_2}(z0, x))
f_{f_2,f_2}(g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{f_2,f_2}(g_{s_1,g_2}(z0, x), z10)
f_{f_2,f_2}(z00, g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{f_2,f_2}(z00, g_{s_1,g_2}(z0, x))
g_{g_2,g_2}(g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{g_2,g_2}(g_{s_1,g_2}(z0, x), z10)
g_{g_2,g_2}(z00, g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{g_2,g_2}(z00, g_{s_1,g_2}(z0, x))
g_{g_2,s_1}(g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{g_2,s_1}(g_{s_1,g_2}(z0, x), z10)
g_{g_2,s_1}(z00, g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{g_2,s_1}(z00, g_{s_1,g_2}(z0, x))
g_{g_2,f_2}(g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{g_2,f_2}(g_{s_1,g_2}(z0, x), z10)
g_{g_2,f_2}(z00, g_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{g_2,f_2}(z00, g_{s_1,g_2}(z0, x))
g_{s_1,g_2}(g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{s_1,g_2}(g_{s_1,s_1}(z0, x), z10)
g_{s_1,g_2}(z00, g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{s_1,g_2}(z00, g_{s_1,s_1}(z0, x))
s_{g_2}(g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → s_{g_2}(g_{s_1,s_1}(z0, x))
g_{f_2,g_2}(g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{f_2,g_2}(g_{s_1,s_1}(z0, x), z10)
g_{f_2,g_2}(z00, g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{f_2,g_2}(z00, g_{s_1,s_1}(z0, x))
f_{g_2,g_2}(g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{g_2,g_2}(g_{s_1,s_1}(z0, x), z10)
f_{g_2,g_2}(z00, g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{g_2,g_2}(z00, g_{s_1,s_1}(z0, x))
g_{s_1,s_1}(g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{s_1,s_1}(g_{s_1,s_1}(z0, x), z10)
g_{s_1,s_1}(z00, g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{s_1,s_1}(z00, g_{s_1,s_1}(z0, x))
g_{f_2,s_1}(g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{f_2,s_1}(g_{s_1,s_1}(z0, x), z10)
g_{f_2,s_1}(z00, g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{f_2,s_1}(z00, g_{s_1,s_1}(z0, x))
f_{g_2,s_1}(g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{g_2,s_1}(g_{s_1,s_1}(z0, x), z10)
f_{g_2,s_1}(z00, g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{g_2,s_1}(z00, g_{s_1,s_1}(z0, x))
g_{s_1,f_2}(g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{s_1,f_2}(g_{s_1,s_1}(z0, x), z10)
g_{s_1,f_2}(z00, g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{s_1,f_2}(z00, g_{s_1,s_1}(z0, x))
g_{f_2,f_2}(g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{f_2,f_2}(g_{s_1,s_1}(z0, x), z10)
g_{f_2,f_2}(z00, g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{f_2,f_2}(z00, g_{s_1,s_1}(z0, x))
f_{g_2,f_2}(g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{g_2,f_2}(g_{s_1,s_1}(z0, x), z10)
f_{g_2,f_2}(z00, g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{g_2,f_2}(z00, g_{s_1,s_1}(z0, x))
s_{s_1}(g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → s_{s_1}(g_{s_1,s_1}(z0, x))
f_{s_1,g_2}(g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{s_1,g_2}(g_{s_1,s_1}(z0, x), z10)
f_{s_1,g_2}(z00, g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{s_1,g_2}(z00, g_{s_1,s_1}(z0, x))
f_{s_1,s_1}(g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{s_1,s_1}(g_{s_1,s_1}(z0, x), z10)
f_{s_1,s_1}(z00, g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{s_1,s_1}(z00, g_{s_1,s_1}(z0, x))
f_{s_1,f_2}(g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{s_1,f_2}(g_{s_1,s_1}(z0, x), z10)
f_{s_1,f_2}(z00, g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{s_1,f_2}(z00, g_{s_1,s_1}(z0, x))
s_{f_2}(g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → s_{f_2}(g_{s_1,s_1}(z0, x))
f_{f_2,g_2}(g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{f_2,g_2}(g_{s_1,s_1}(z0, x), z10)
f_{f_2,g_2}(z00, g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{f_2,g_2}(z00, g_{s_1,s_1}(z0, x))
f_{f_2,s_1}(g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{f_2,s_1}(g_{s_1,s_1}(z0, x), z10)
f_{f_2,s_1}(z00, g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{f_2,s_1}(z00, g_{s_1,s_1}(z0, x))
f_{f_2,f_2}(g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{f_2,f_2}(g_{s_1,s_1}(z0, x), z10)
f_{f_2,f_2}(z00, g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{f_2,f_2}(z00, g_{s_1,s_1}(z0, x))
g_{g_2,g_2}(g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{g_2,g_2}(g_{s_1,s_1}(z0, x), z10)
g_{g_2,g_2}(z00, g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{g_2,g_2}(z00, g_{s_1,s_1}(z0, x))
g_{g_2,s_1}(g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{g_2,s_1}(g_{s_1,s_1}(z0, x), z10)
g_{g_2,s_1}(z00, g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{g_2,s_1}(z00, g_{s_1,s_1}(z0, x))
g_{g_2,f_2}(g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{g_2,f_2}(g_{s_1,s_1}(z0, x), z10)
g_{g_2,f_2}(z00, g_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{g_2,f_2}(z00, g_{s_1,s_1}(z0, x))
g_{s_1,g_2}(g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{s_1,g_2}(g_{s_1,s_1}(z0, x), z10)
g_{s_1,g_2}(z00, g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{s_1,g_2}(z00, g_{s_1,s_1}(z0, x))
s_{g_2}(g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → s_{g_2}(g_{s_1,s_1}(z0, x))
g_{f_2,g_2}(g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{f_2,g_2}(g_{s_1,s_1}(z0, x), z10)
g_{f_2,g_2}(z00, g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{f_2,g_2}(z00, g_{s_1,s_1}(z0, x))
f_{g_2,g_2}(g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{g_2,g_2}(g_{s_1,s_1}(z0, x), z10)
f_{g_2,g_2}(z00, g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{g_2,g_2}(z00, g_{s_1,s_1}(z0, x))
g_{s_1,s_1}(g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{s_1,s_1}(g_{s_1,s_1}(z0, x), z10)
g_{s_1,s_1}(z00, g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{s_1,s_1}(z00, g_{s_1,s_1}(z0, x))
g_{f_2,s_1}(g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{f_2,s_1}(g_{s_1,s_1}(z0, x), z10)
g_{f_2,s_1}(z00, g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{f_2,s_1}(z00, g_{s_1,s_1}(z0, x))
f_{g_2,s_1}(g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{g_2,s_1}(g_{s_1,s_1}(z0, x), z10)
f_{g_2,s_1}(z00, g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{g_2,s_1}(z00, g_{s_1,s_1}(z0, x))
g_{s_1,f_2}(g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{s_1,f_2}(g_{s_1,s_1}(z0, x), z10)
g_{s_1,f_2}(z00, g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{s_1,f_2}(z00, g_{s_1,s_1}(z0, x))
g_{f_2,f_2}(g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{f_2,f_2}(g_{s_1,s_1}(z0, x), z10)
g_{f_2,f_2}(z00, g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{f_2,f_2}(z00, g_{s_1,s_1}(z0, x))
f_{g_2,f_2}(g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{g_2,f_2}(g_{s_1,s_1}(z0, x), z10)
f_{g_2,f_2}(z00, g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{g_2,f_2}(z00, g_{s_1,s_1}(z0, x))
s_{s_1}(g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → s_{s_1}(g_{s_1,s_1}(z0, x))
f_{s_1,g_2}(g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{s_1,g_2}(g_{s_1,s_1}(z0, x), z10)
f_{s_1,g_2}(z00, g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{s_1,g_2}(z00, g_{s_1,s_1}(z0, x))
f_{s_1,s_1}(g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{s_1,s_1}(g_{s_1,s_1}(z0, x), z10)
f_{s_1,s_1}(z00, g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{s_1,s_1}(z00, g_{s_1,s_1}(z0, x))
f_{s_1,f_2}(g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{s_1,f_2}(g_{s_1,s_1}(z0, x), z10)
f_{s_1,f_2}(z00, g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{s_1,f_2}(z00, g_{s_1,s_1}(z0, x))
s_{f_2}(g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → s_{f_2}(g_{s_1,s_1}(z0, x))
f_{f_2,g_2}(g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{f_2,g_2}(g_{s_1,s_1}(z0, x), z10)
f_{f_2,g_2}(z00, g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{f_2,g_2}(z00, g_{s_1,s_1}(z0, x))
f_{f_2,s_1}(g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{f_2,s_1}(g_{s_1,s_1}(z0, x), z10)
f_{f_2,s_1}(z00, g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{f_2,s_1}(z00, g_{s_1,s_1}(z0, x))
f_{f_2,f_2}(g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{f_2,f_2}(g_{s_1,s_1}(z0, x), z10)
f_{f_2,f_2}(z00, g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{f_2,f_2}(z00, g_{s_1,s_1}(z0, x))
g_{g_2,g_2}(g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{g_2,g_2}(g_{s_1,s_1}(z0, x), z10)
g_{g_2,g_2}(z00, g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{g_2,g_2}(z00, g_{s_1,s_1}(z0, x))
g_{g_2,s_1}(g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{g_2,s_1}(g_{s_1,s_1}(z0, x), z10)
g_{g_2,s_1}(z00, g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{g_2,s_1}(z00, g_{s_1,s_1}(z0, x))
g_{g_2,f_2}(g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{g_2,f_2}(g_{s_1,s_1}(z0, x), z10)
g_{g_2,f_2}(z00, g_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{g_2,f_2}(z00, g_{s_1,s_1}(z0, x))
g_{s_1,g_2}(g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{s_1,g_2}(g_{s_1,s_1}(z0, x), z10)
g_{s_1,g_2}(z00, g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{s_1,g_2}(z00, g_{s_1,s_1}(z0, x))
s_{g_2}(g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → s_{g_2}(g_{s_1,s_1}(z0, x))
g_{f_2,g_2}(g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{f_2,g_2}(g_{s_1,s_1}(z0, x), z10)
g_{f_2,g_2}(z00, g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{f_2,g_2}(z00, g_{s_1,s_1}(z0, x))
f_{g_2,g_2}(g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{g_2,g_2}(g_{s_1,s_1}(z0, x), z10)
f_{g_2,g_2}(z00, g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{g_2,g_2}(z00, g_{s_1,s_1}(z0, x))
g_{s_1,s_1}(g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{s_1,s_1}(g_{s_1,s_1}(z0, x), z10)
g_{s_1,s_1}(z00, g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{s_1,s_1}(z00, g_{s_1,s_1}(z0, x))
g_{f_2,s_1}(g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{f_2,s_1}(g_{s_1,s_1}(z0, x), z10)
g_{f_2,s_1}(z00, g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{f_2,s_1}(z00, g_{s_1,s_1}(z0, x))
f_{g_2,s_1}(g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{g_2,s_1}(g_{s_1,s_1}(z0, x), z10)
f_{g_2,s_1}(z00, g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{g_2,s_1}(z00, g_{s_1,s_1}(z0, x))
g_{s_1,f_2}(g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{s_1,f_2}(g_{s_1,s_1}(z0, x), z10)
g_{s_1,f_2}(z00, g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{s_1,f_2}(z00, g_{s_1,s_1}(z0, x))
g_{f_2,f_2}(g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{f_2,f_2}(g_{s_1,s_1}(z0, x), z10)
g_{f_2,f_2}(z00, g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{f_2,f_2}(z00, g_{s_1,s_1}(z0, x))
f_{g_2,f_2}(g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{g_2,f_2}(g_{s_1,s_1}(z0, x), z10)
f_{g_2,f_2}(z00, g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{g_2,f_2}(z00, g_{s_1,s_1}(z0, x))
s_{s_1}(g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → s_{s_1}(g_{s_1,s_1}(z0, x))
f_{s_1,g_2}(g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{s_1,g_2}(g_{s_1,s_1}(z0, x), z10)
f_{s_1,g_2}(z00, g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{s_1,g_2}(z00, g_{s_1,s_1}(z0, x))
f_{s_1,s_1}(g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{s_1,s_1}(g_{s_1,s_1}(z0, x), z10)
f_{s_1,s_1}(z00, g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{s_1,s_1}(z00, g_{s_1,s_1}(z0, x))
f_{s_1,f_2}(g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{s_1,f_2}(g_{s_1,s_1}(z0, x), z10)
f_{s_1,f_2}(z00, g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{s_1,f_2}(z00, g_{s_1,s_1}(z0, x))
s_{f_2}(g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → s_{f_2}(g_{s_1,s_1}(z0, x))
f_{f_2,g_2}(g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{f_2,g_2}(g_{s_1,s_1}(z0, x), z10)
f_{f_2,g_2}(z00, g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{f_2,g_2}(z00, g_{s_1,s_1}(z0, x))
f_{f_2,s_1}(g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{f_2,s_1}(g_{s_1,s_1}(z0, x), z10)
f_{f_2,s_1}(z00, g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{f_2,s_1}(z00, g_{s_1,s_1}(z0, x))
f_{f_2,f_2}(g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{f_2,f_2}(g_{s_1,s_1}(z0, x), z10)
f_{f_2,f_2}(z00, g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{f_2,f_2}(z00, g_{s_1,s_1}(z0, x))
g_{g_2,g_2}(g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{g_2,g_2}(g_{s_1,s_1}(z0, x), z10)
g_{g_2,g_2}(z00, g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{g_2,g_2}(z00, g_{s_1,s_1}(z0, x))
g_{g_2,s_1}(g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{g_2,s_1}(g_{s_1,s_1}(z0, x), z10)
g_{g_2,s_1}(z00, g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{g_2,s_1}(z00, g_{s_1,s_1}(z0, x))
g_{g_2,f_2}(g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{g_2,f_2}(g_{s_1,s_1}(z0, x), z10)
g_{g_2,f_2}(z00, g_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{g_2,f_2}(z00, g_{s_1,s_1}(z0, x))
g_{s_1,g_2}(g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{s_1,g_2}(g_{f_2,g_2}(z0, x), z10)
g_{s_1,g_2}(z00, g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{s_1,g_2}(z00, g_{f_2,g_2}(z0, x))
s_{g_2}(g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → s_{g_2}(g_{f_2,g_2}(z0, x))
g_{f_2,g_2}(g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{f_2,g_2}(g_{f_2,g_2}(z0, x), z10)
g_{f_2,g_2}(z00, g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{f_2,g_2}(z00, g_{f_2,g_2}(z0, x))
f_{g_2,g_2}(g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{g_2,g_2}(g_{f_2,g_2}(z0, x), z10)
f_{g_2,g_2}(z00, g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{g_2,g_2}(z00, g_{f_2,g_2}(z0, x))
g_{s_1,s_1}(g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{s_1,s_1}(g_{f_2,g_2}(z0, x), z10)
g_{s_1,s_1}(z00, g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{s_1,s_1}(z00, g_{f_2,g_2}(z0, x))
g_{f_2,s_1}(g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{f_2,s_1}(g_{f_2,g_2}(z0, x), z10)
g_{f_2,s_1}(z00, g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{f_2,s_1}(z00, g_{f_2,g_2}(z0, x))
f_{g_2,s_1}(g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{g_2,s_1}(g_{f_2,g_2}(z0, x), z10)
f_{g_2,s_1}(z00, g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{g_2,s_1}(z00, g_{f_2,g_2}(z0, x))
g_{s_1,f_2}(g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{s_1,f_2}(g_{f_2,g_2}(z0, x), z10)
g_{s_1,f_2}(z00, g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{s_1,f_2}(z00, g_{f_2,g_2}(z0, x))
g_{f_2,f_2}(g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{f_2,f_2}(g_{f_2,g_2}(z0, x), z10)
g_{f_2,f_2}(z00, g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{f_2,f_2}(z00, g_{f_2,g_2}(z0, x))
f_{g_2,f_2}(g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{g_2,f_2}(g_{f_2,g_2}(z0, x), z10)
f_{g_2,f_2}(z00, g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{g_2,f_2}(z00, g_{f_2,g_2}(z0, x))
s_{s_1}(g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → s_{s_1}(g_{f_2,g_2}(z0, x))
f_{s_1,g_2}(g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{s_1,g_2}(g_{f_2,g_2}(z0, x), z10)
f_{s_1,g_2}(z00, g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{s_1,g_2}(z00, g_{f_2,g_2}(z0, x))
f_{s_1,s_1}(g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{s_1,s_1}(g_{f_2,g_2}(z0, x), z10)
f_{s_1,s_1}(z00, g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{s_1,s_1}(z00, g_{f_2,g_2}(z0, x))
f_{s_1,f_2}(g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{s_1,f_2}(g_{f_2,g_2}(z0, x), z10)
f_{s_1,f_2}(z00, g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{s_1,f_2}(z00, g_{f_2,g_2}(z0, x))
s_{f_2}(g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → s_{f_2}(g_{f_2,g_2}(z0, x))
f_{f_2,g_2}(g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{f_2,g_2}(g_{f_2,g_2}(z0, x), z10)
f_{f_2,g_2}(z00, g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{f_2,g_2}(z00, g_{f_2,g_2}(z0, x))
f_{f_2,s_1}(g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{f_2,s_1}(g_{f_2,g_2}(z0, x), z10)
f_{f_2,s_1}(z00, g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{f_2,s_1}(z00, g_{f_2,g_2}(z0, x))
f_{f_2,f_2}(g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{f_2,f_2}(g_{f_2,g_2}(z0, x), z10)
f_{f_2,f_2}(z00, g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{f_2,f_2}(z00, g_{f_2,g_2}(z0, x))
g_{g_2,g_2}(g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{g_2,g_2}(g_{f_2,g_2}(z0, x), z10)
g_{g_2,g_2}(z00, g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{g_2,g_2}(z00, g_{f_2,g_2}(z0, x))
g_{g_2,s_1}(g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{g_2,s_1}(g_{f_2,g_2}(z0, x), z10)
g_{g_2,s_1}(z00, g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{g_2,s_1}(z00, g_{f_2,g_2}(z0, x))
g_{g_2,f_2}(g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{g_2,f_2}(g_{f_2,g_2}(z0, x), z10)
g_{g_2,f_2}(z00, g_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{g_2,f_2}(z00, g_{f_2,g_2}(z0, x))
g_{s_1,g_2}(g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{s_1,g_2}(g_{f_2,g_2}(z0, x), z10)
g_{s_1,g_2}(z00, g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{s_1,g_2}(z00, g_{f_2,g_2}(z0, x))
s_{g_2}(g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → s_{g_2}(g_{f_2,g_2}(z0, x))
g_{f_2,g_2}(g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{f_2,g_2}(g_{f_2,g_2}(z0, x), z10)
g_{f_2,g_2}(z00, g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{f_2,g_2}(z00, g_{f_2,g_2}(z0, x))
f_{g_2,g_2}(g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{g_2,g_2}(g_{f_2,g_2}(z0, x), z10)
f_{g_2,g_2}(z00, g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{g_2,g_2}(z00, g_{f_2,g_2}(z0, x))
g_{s_1,s_1}(g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{s_1,s_1}(g_{f_2,g_2}(z0, x), z10)
g_{s_1,s_1}(z00, g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{s_1,s_1}(z00, g_{f_2,g_2}(z0, x))
g_{f_2,s_1}(g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{f_2,s_1}(g_{f_2,g_2}(z0, x), z10)
g_{f_2,s_1}(z00, g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{f_2,s_1}(z00, g_{f_2,g_2}(z0, x))
f_{g_2,s_1}(g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{g_2,s_1}(g_{f_2,g_2}(z0, x), z10)
f_{g_2,s_1}(z00, g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{g_2,s_1}(z00, g_{f_2,g_2}(z0, x))
g_{s_1,f_2}(g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{s_1,f_2}(g_{f_2,g_2}(z0, x), z10)
g_{s_1,f_2}(z00, g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{s_1,f_2}(z00, g_{f_2,g_2}(z0, x))
g_{f_2,f_2}(g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{f_2,f_2}(g_{f_2,g_2}(z0, x), z10)
g_{f_2,f_2}(z00, g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{f_2,f_2}(z00, g_{f_2,g_2}(z0, x))
f_{g_2,f_2}(g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{g_2,f_2}(g_{f_2,g_2}(z0, x), z10)
f_{g_2,f_2}(z00, g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{g_2,f_2}(z00, g_{f_2,g_2}(z0, x))
s_{s_1}(g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → s_{s_1}(g_{f_2,g_2}(z0, x))
f_{s_1,g_2}(g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{s_1,g_2}(g_{f_2,g_2}(z0, x), z10)
f_{s_1,g_2}(z00, g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{s_1,g_2}(z00, g_{f_2,g_2}(z0, x))
f_{s_1,s_1}(g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{s_1,s_1}(g_{f_2,g_2}(z0, x), z10)
f_{s_1,s_1}(z00, g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{s_1,s_1}(z00, g_{f_2,g_2}(z0, x))
f_{s_1,f_2}(g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{s_1,f_2}(g_{f_2,g_2}(z0, x), z10)
f_{s_1,f_2}(z00, g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{s_1,f_2}(z00, g_{f_2,g_2}(z0, x))
s_{f_2}(g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → s_{f_2}(g_{f_2,g_2}(z0, x))
f_{f_2,g_2}(g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{f_2,g_2}(g_{f_2,g_2}(z0, x), z10)
f_{f_2,g_2}(z00, g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{f_2,g_2}(z00, g_{f_2,g_2}(z0, x))
f_{f_2,s_1}(g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{f_2,s_1}(g_{f_2,g_2}(z0, x), z10)
f_{f_2,s_1}(z00, g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{f_2,s_1}(z00, g_{f_2,g_2}(z0, x))
f_{f_2,f_2}(g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{f_2,f_2}(g_{f_2,g_2}(z0, x), z10)
f_{f_2,f_2}(z00, g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{f_2,f_2}(z00, g_{f_2,g_2}(z0, x))
g_{g_2,g_2}(g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{g_2,g_2}(g_{f_2,g_2}(z0, x), z10)
g_{g_2,g_2}(z00, g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{g_2,g_2}(z00, g_{f_2,g_2}(z0, x))
g_{g_2,s_1}(g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{g_2,s_1}(g_{f_2,g_2}(z0, x), z10)
g_{g_2,s_1}(z00, g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{g_2,s_1}(z00, g_{f_2,g_2}(z0, x))
g_{g_2,f_2}(g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{g_2,f_2}(g_{f_2,g_2}(z0, x), z10)
g_{g_2,f_2}(z00, g_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{g_2,f_2}(z00, g_{f_2,g_2}(z0, x))
g_{s_1,g_2}(g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{s_1,g_2}(g_{f_2,g_2}(z0, x), z10)
g_{s_1,g_2}(z00, g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{s_1,g_2}(z00, g_{f_2,g_2}(z0, x))
s_{g_2}(g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → s_{g_2}(g_{f_2,g_2}(z0, x))
g_{f_2,g_2}(g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{f_2,g_2}(g_{f_2,g_2}(z0, x), z10)
g_{f_2,g_2}(z00, g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{f_2,g_2}(z00, g_{f_2,g_2}(z0, x))
f_{g_2,g_2}(g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{g_2,g_2}(g_{f_2,g_2}(z0, x), z10)
f_{g_2,g_2}(z00, g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{g_2,g_2}(z00, g_{f_2,g_2}(z0, x))
g_{s_1,s_1}(g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{s_1,s_1}(g_{f_2,g_2}(z0, x), z10)
g_{s_1,s_1}(z00, g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{s_1,s_1}(z00, g_{f_2,g_2}(z0, x))
g_{f_2,s_1}(g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{f_2,s_1}(g_{f_2,g_2}(z0, x), z10)
g_{f_2,s_1}(z00, g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{f_2,s_1}(z00, g_{f_2,g_2}(z0, x))
f_{g_2,s_1}(g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{g_2,s_1}(g_{f_2,g_2}(z0, x), z10)
f_{g_2,s_1}(z00, g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{g_2,s_1}(z00, g_{f_2,g_2}(z0, x))
g_{s_1,f_2}(g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{s_1,f_2}(g_{f_2,g_2}(z0, x), z10)
g_{s_1,f_2}(z00, g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{s_1,f_2}(z00, g_{f_2,g_2}(z0, x))
g_{f_2,f_2}(g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{f_2,f_2}(g_{f_2,g_2}(z0, x), z10)
g_{f_2,f_2}(z00, g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{f_2,f_2}(z00, g_{f_2,g_2}(z0, x))
f_{g_2,f_2}(g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{g_2,f_2}(g_{f_2,g_2}(z0, x), z10)
f_{g_2,f_2}(z00, g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{g_2,f_2}(z00, g_{f_2,g_2}(z0, x))
s_{s_1}(g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → s_{s_1}(g_{f_2,g_2}(z0, x))
f_{s_1,g_2}(g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{s_1,g_2}(g_{f_2,g_2}(z0, x), z10)
f_{s_1,g_2}(z00, g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{s_1,g_2}(z00, g_{f_2,g_2}(z0, x))
f_{s_1,s_1}(g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{s_1,s_1}(g_{f_2,g_2}(z0, x), z10)
f_{s_1,s_1}(z00, g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{s_1,s_1}(z00, g_{f_2,g_2}(z0, x))
f_{s_1,f_2}(g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{s_1,f_2}(g_{f_2,g_2}(z0, x), z10)
f_{s_1,f_2}(z00, g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{s_1,f_2}(z00, g_{f_2,g_2}(z0, x))
s_{f_2}(g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → s_{f_2}(g_{f_2,g_2}(z0, x))
f_{f_2,g_2}(g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{f_2,g_2}(g_{f_2,g_2}(z0, x), z10)
f_{f_2,g_2}(z00, g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{f_2,g_2}(z00, g_{f_2,g_2}(z0, x))
f_{f_2,s_1}(g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{f_2,s_1}(g_{f_2,g_2}(z0, x), z10)
f_{f_2,s_1}(z00, g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{f_2,s_1}(z00, g_{f_2,g_2}(z0, x))
f_{f_2,f_2}(g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{f_2,f_2}(g_{f_2,g_2}(z0, x), z10)
f_{f_2,f_2}(z00, g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{f_2,f_2}(z00, g_{f_2,g_2}(z0, x))
g_{g_2,g_2}(g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{g_2,g_2}(g_{f_2,g_2}(z0, x), z10)
g_{g_2,g_2}(z00, g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{g_2,g_2}(z00, g_{f_2,g_2}(z0, x))
g_{g_2,s_1}(g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{g_2,s_1}(g_{f_2,g_2}(z0, x), z10)
g_{g_2,s_1}(z00, g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{g_2,s_1}(z00, g_{f_2,g_2}(z0, x))
g_{g_2,f_2}(g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{g_2,f_2}(g_{f_2,g_2}(z0, x), z10)
g_{g_2,f_2}(z00, g_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{g_2,f_2}(z00, g_{f_2,g_2}(z0, x))
g_{s_1,g_2}(g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{s_1,g_2}(g_{f_2,s_1}(z0, x), z10)
g_{s_1,g_2}(z00, g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{s_1,g_2}(z00, g_{f_2,s_1}(z0, x))
s_{g_2}(g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → s_{g_2}(g_{f_2,s_1}(z0, x))
g_{f_2,g_2}(g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{f_2,g_2}(g_{f_2,s_1}(z0, x), z10)
g_{f_2,g_2}(z00, g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{f_2,g_2}(z00, g_{f_2,s_1}(z0, x))
f_{g_2,g_2}(g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{g_2,g_2}(g_{f_2,s_1}(z0, x), z10)
f_{g_2,g_2}(z00, g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{g_2,g_2}(z00, g_{f_2,s_1}(z0, x))
g_{s_1,s_1}(g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{s_1,s_1}(g_{f_2,s_1}(z0, x), z10)
g_{s_1,s_1}(z00, g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{s_1,s_1}(z00, g_{f_2,s_1}(z0, x))
g_{f_2,s_1}(g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{f_2,s_1}(g_{f_2,s_1}(z0, x), z10)
g_{f_2,s_1}(z00, g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{f_2,s_1}(z00, g_{f_2,s_1}(z0, x))
f_{g_2,s_1}(g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{g_2,s_1}(g_{f_2,s_1}(z0, x), z10)
f_{g_2,s_1}(z00, g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{g_2,s_1}(z00, g_{f_2,s_1}(z0, x))
g_{s_1,f_2}(g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{s_1,f_2}(g_{f_2,s_1}(z0, x), z10)
g_{s_1,f_2}(z00, g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{s_1,f_2}(z00, g_{f_2,s_1}(z0, x))
g_{f_2,f_2}(g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{f_2,f_2}(g_{f_2,s_1}(z0, x), z10)
g_{f_2,f_2}(z00, g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{f_2,f_2}(z00, g_{f_2,s_1}(z0, x))
f_{g_2,f_2}(g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{g_2,f_2}(g_{f_2,s_1}(z0, x), z10)
f_{g_2,f_2}(z00, g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{g_2,f_2}(z00, g_{f_2,s_1}(z0, x))
s_{s_1}(g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → s_{s_1}(g_{f_2,s_1}(z0, x))
f_{s_1,g_2}(g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{s_1,g_2}(g_{f_2,s_1}(z0, x), z10)
f_{s_1,g_2}(z00, g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{s_1,g_2}(z00, g_{f_2,s_1}(z0, x))
f_{s_1,s_1}(g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{s_1,s_1}(g_{f_2,s_1}(z0, x), z10)
f_{s_1,s_1}(z00, g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{s_1,s_1}(z00, g_{f_2,s_1}(z0, x))
f_{s_1,f_2}(g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{s_1,f_2}(g_{f_2,s_1}(z0, x), z10)
f_{s_1,f_2}(z00, g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{s_1,f_2}(z00, g_{f_2,s_1}(z0, x))
s_{f_2}(g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → s_{f_2}(g_{f_2,s_1}(z0, x))
f_{f_2,g_2}(g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{f_2,g_2}(g_{f_2,s_1}(z0, x), z10)
f_{f_2,g_2}(z00, g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{f_2,g_2}(z00, g_{f_2,s_1}(z0, x))
f_{f_2,s_1}(g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{f_2,s_1}(g_{f_2,s_1}(z0, x), z10)
f_{f_2,s_1}(z00, g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{f_2,s_1}(z00, g_{f_2,s_1}(z0, x))
f_{f_2,f_2}(g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{f_2,f_2}(g_{f_2,s_1}(z0, x), z10)
f_{f_2,f_2}(z00, g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{f_2,f_2}(z00, g_{f_2,s_1}(z0, x))
g_{g_2,g_2}(g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{g_2,g_2}(g_{f_2,s_1}(z0, x), z10)
g_{g_2,g_2}(z00, g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{g_2,g_2}(z00, g_{f_2,s_1}(z0, x))
g_{g_2,s_1}(g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{g_2,s_1}(g_{f_2,s_1}(z0, x), z10)
g_{g_2,s_1}(z00, g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{g_2,s_1}(z00, g_{f_2,s_1}(z0, x))
g_{g_2,f_2}(g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{g_2,f_2}(g_{f_2,s_1}(z0, x), z10)
g_{g_2,f_2}(z00, g_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{g_2,f_2}(z00, g_{f_2,s_1}(z0, x))
g_{s_1,g_2}(g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{s_1,g_2}(g_{f_2,s_1}(z0, x), z10)
g_{s_1,g_2}(z00, g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{s_1,g_2}(z00, g_{f_2,s_1}(z0, x))
s_{g_2}(g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → s_{g_2}(g_{f_2,s_1}(z0, x))
g_{f_2,g_2}(g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{f_2,g_2}(g_{f_2,s_1}(z0, x), z10)
g_{f_2,g_2}(z00, g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{f_2,g_2}(z00, g_{f_2,s_1}(z0, x))
f_{g_2,g_2}(g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{g_2,g_2}(g_{f_2,s_1}(z0, x), z10)
f_{g_2,g_2}(z00, g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{g_2,g_2}(z00, g_{f_2,s_1}(z0, x))
g_{s_1,s_1}(g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{s_1,s_1}(g_{f_2,s_1}(z0, x), z10)
g_{s_1,s_1}(z00, g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{s_1,s_1}(z00, g_{f_2,s_1}(z0, x))
g_{f_2,s_1}(g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{f_2,s_1}(g_{f_2,s_1}(z0, x), z10)
g_{f_2,s_1}(z00, g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{f_2,s_1}(z00, g_{f_2,s_1}(z0, x))
f_{g_2,s_1}(g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{g_2,s_1}(g_{f_2,s_1}(z0, x), z10)
f_{g_2,s_1}(z00, g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{g_2,s_1}(z00, g_{f_2,s_1}(z0, x))
g_{s_1,f_2}(g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{s_1,f_2}(g_{f_2,s_1}(z0, x), z10)
g_{s_1,f_2}(z00, g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{s_1,f_2}(z00, g_{f_2,s_1}(z0, x))
g_{f_2,f_2}(g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{f_2,f_2}(g_{f_2,s_1}(z0, x), z10)
g_{f_2,f_2}(z00, g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{f_2,f_2}(z00, g_{f_2,s_1}(z0, x))
f_{g_2,f_2}(g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{g_2,f_2}(g_{f_2,s_1}(z0, x), z10)
f_{g_2,f_2}(z00, g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{g_2,f_2}(z00, g_{f_2,s_1}(z0, x))
s_{s_1}(g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → s_{s_1}(g_{f_2,s_1}(z0, x))
f_{s_1,g_2}(g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{s_1,g_2}(g_{f_2,s_1}(z0, x), z10)
f_{s_1,g_2}(z00, g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{s_1,g_2}(z00, g_{f_2,s_1}(z0, x))
f_{s_1,s_1}(g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{s_1,s_1}(g_{f_2,s_1}(z0, x), z10)
f_{s_1,s_1}(z00, g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{s_1,s_1}(z00, g_{f_2,s_1}(z0, x))
f_{s_1,f_2}(g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{s_1,f_2}(g_{f_2,s_1}(z0, x), z10)
f_{s_1,f_2}(z00, g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{s_1,f_2}(z00, g_{f_2,s_1}(z0, x))
s_{f_2}(g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → s_{f_2}(g_{f_2,s_1}(z0, x))
f_{f_2,g_2}(g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{f_2,g_2}(g_{f_2,s_1}(z0, x), z10)
f_{f_2,g_2}(z00, g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{f_2,g_2}(z00, g_{f_2,s_1}(z0, x))
f_{f_2,s_1}(g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{f_2,s_1}(g_{f_2,s_1}(z0, x), z10)
f_{f_2,s_1}(z00, g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{f_2,s_1}(z00, g_{f_2,s_1}(z0, x))
f_{f_2,f_2}(g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{f_2,f_2}(g_{f_2,s_1}(z0, x), z10)
f_{f_2,f_2}(z00, g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{f_2,f_2}(z00, g_{f_2,s_1}(z0, x))
g_{g_2,g_2}(g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{g_2,g_2}(g_{f_2,s_1}(z0, x), z10)
g_{g_2,g_2}(z00, g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{g_2,g_2}(z00, g_{f_2,s_1}(z0, x))
g_{g_2,s_1}(g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{g_2,s_1}(g_{f_2,s_1}(z0, x), z10)
g_{g_2,s_1}(z00, g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{g_2,s_1}(z00, g_{f_2,s_1}(z0, x))
g_{g_2,f_2}(g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{g_2,f_2}(g_{f_2,s_1}(z0, x), z10)
g_{g_2,f_2}(z00, g_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{g_2,f_2}(z00, g_{f_2,s_1}(z0, x))
g_{s_1,g_2}(g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{s_1,g_2}(g_{f_2,s_1}(z0, x), z10)
g_{s_1,g_2}(z00, g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{s_1,g_2}(z00, g_{f_2,s_1}(z0, x))
s_{g_2}(g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → s_{g_2}(g_{f_2,s_1}(z0, x))
g_{f_2,g_2}(g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{f_2,g_2}(g_{f_2,s_1}(z0, x), z10)
g_{f_2,g_2}(z00, g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{f_2,g_2}(z00, g_{f_2,s_1}(z0, x))
f_{g_2,g_2}(g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{g_2,g_2}(g_{f_2,s_1}(z0, x), z10)
f_{g_2,g_2}(z00, g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{g_2,g_2}(z00, g_{f_2,s_1}(z0, x))
g_{s_1,s_1}(g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{s_1,s_1}(g_{f_2,s_1}(z0, x), z10)
g_{s_1,s_1}(z00, g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{s_1,s_1}(z00, g_{f_2,s_1}(z0, x))
g_{f_2,s_1}(g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{f_2,s_1}(g_{f_2,s_1}(z0, x), z10)
g_{f_2,s_1}(z00, g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{f_2,s_1}(z00, g_{f_2,s_1}(z0, x))
f_{g_2,s_1}(g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{g_2,s_1}(g_{f_2,s_1}(z0, x), z10)
f_{g_2,s_1}(z00, g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{g_2,s_1}(z00, g_{f_2,s_1}(z0, x))
g_{s_1,f_2}(g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{s_1,f_2}(g_{f_2,s_1}(z0, x), z10)
g_{s_1,f_2}(z00, g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{s_1,f_2}(z00, g_{f_2,s_1}(z0, x))
g_{f_2,f_2}(g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{f_2,f_2}(g_{f_2,s_1}(z0, x), z10)
g_{f_2,f_2}(z00, g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{f_2,f_2}(z00, g_{f_2,s_1}(z0, x))
f_{g_2,f_2}(g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{g_2,f_2}(g_{f_2,s_1}(z0, x), z10)
f_{g_2,f_2}(z00, g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{g_2,f_2}(z00, g_{f_2,s_1}(z0, x))
s_{s_1}(g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → s_{s_1}(g_{f_2,s_1}(z0, x))
f_{s_1,g_2}(g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{s_1,g_2}(g_{f_2,s_1}(z0, x), z10)
f_{s_1,g_2}(z00, g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{s_1,g_2}(z00, g_{f_2,s_1}(z0, x))
f_{s_1,s_1}(g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{s_1,s_1}(g_{f_2,s_1}(z0, x), z10)
f_{s_1,s_1}(z00, g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{s_1,s_1}(z00, g_{f_2,s_1}(z0, x))
f_{s_1,f_2}(g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{s_1,f_2}(g_{f_2,s_1}(z0, x), z10)
f_{s_1,f_2}(z00, g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{s_1,f_2}(z00, g_{f_2,s_1}(z0, x))
s_{f_2}(g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → s_{f_2}(g_{f_2,s_1}(z0, x))
f_{f_2,g_2}(g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{f_2,g_2}(g_{f_2,s_1}(z0, x), z10)
f_{f_2,g_2}(z00, g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{f_2,g_2}(z00, g_{f_2,s_1}(z0, x))
f_{f_2,s_1}(g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{f_2,s_1}(g_{f_2,s_1}(z0, x), z10)
f_{f_2,s_1}(z00, g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{f_2,s_1}(z00, g_{f_2,s_1}(z0, x))
f_{f_2,f_2}(g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{f_2,f_2}(g_{f_2,s_1}(z0, x), z10)
f_{f_2,f_2}(z00, g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{f_2,f_2}(z00, g_{f_2,s_1}(z0, x))
g_{g_2,g_2}(g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{g_2,g_2}(g_{f_2,s_1}(z0, x), z10)
g_{g_2,g_2}(z00, g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{g_2,g_2}(z00, g_{f_2,s_1}(z0, x))
g_{g_2,s_1}(g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{g_2,s_1}(g_{f_2,s_1}(z0, x), z10)
g_{g_2,s_1}(z00, g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{g_2,s_1}(z00, g_{f_2,s_1}(z0, x))
g_{g_2,f_2}(g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{g_2,f_2}(g_{f_2,s_1}(z0, x), z10)
g_{g_2,f_2}(z00, g_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{g_2,f_2}(z00, g_{f_2,s_1}(z0, x))
g_{s_1,g_2}(s_{f_2}(f_{g_2,g_2}(x, y)), z10) → g_{s_1,g_2}(s_{g_2}(x), z10)
g_{s_1,g_2}(z00, s_{f_2}(f_{g_2,g_2}(x, y))) → g_{s_1,g_2}(z00, s_{g_2}(x))
s_{g_2}(s_{f_2}(f_{g_2,g_2}(x, y))) → s_{g_2}(s_{g_2}(x))
g_{f_2,g_2}(s_{f_2}(f_{g_2,g_2}(x, y)), z10) → g_{f_2,g_2}(s_{g_2}(x), z10)
g_{f_2,g_2}(z00, s_{f_2}(f_{g_2,g_2}(x, y))) → g_{f_2,g_2}(z00, s_{g_2}(x))
f_{g_2,g_2}(s_{f_2}(f_{g_2,g_2}(x, y)), z10) → f_{g_2,g_2}(s_{g_2}(x), z10)
f_{g_2,g_2}(z00, s_{f_2}(f_{g_2,g_2}(x, y))) → f_{g_2,g_2}(z00, s_{g_2}(x))
g_{s_1,s_1}(s_{f_2}(f_{g_2,g_2}(x, y)), z10) → g_{s_1,s_1}(s_{g_2}(x), z10)
g_{s_1,s_1}(z00, s_{f_2}(f_{g_2,g_2}(x, y))) → g_{s_1,s_1}(z00, s_{g_2}(x))
g_{f_2,s_1}(s_{f_2}(f_{g_2,g_2}(x, y)), z10) → g_{f_2,s_1}(s_{g_2}(x), z10)
g_{f_2,s_1}(z00, s_{f_2}(f_{g_2,g_2}(x, y))) → g_{f_2,s_1}(z00, s_{g_2}(x))
f_{g_2,s_1}(s_{f_2}(f_{g_2,g_2}(x, y)), z10) → f_{g_2,s_1}(s_{g_2}(x), z10)
f_{g_2,s_1}(z00, s_{f_2}(f_{g_2,g_2}(x, y))) → f_{g_2,s_1}(z00, s_{g_2}(x))
g_{s_1,f_2}(s_{f_2}(f_{g_2,g_2}(x, y)), z10) → g_{s_1,f_2}(s_{g_2}(x), z10)
g_{s_1,f_2}(z00, s_{f_2}(f_{g_2,g_2}(x, y))) → g_{s_1,f_2}(z00, s_{g_2}(x))
g_{f_2,f_2}(s_{f_2}(f_{g_2,g_2}(x, y)), z10) → g_{f_2,f_2}(s_{g_2}(x), z10)
g_{f_2,f_2}(z00, s_{f_2}(f_{g_2,g_2}(x, y))) → g_{f_2,f_2}(z00, s_{g_2}(x))
f_{g_2,f_2}(s_{f_2}(f_{g_2,g_2}(x, y)), z10) → f_{g_2,f_2}(s_{g_2}(x), z10)
f_{g_2,f_2}(z00, s_{f_2}(f_{g_2,g_2}(x, y))) → f_{g_2,f_2}(z00, s_{g_2}(x))
s_{s_1}(s_{f_2}(f_{g_2,g_2}(x, y))) → s_{s_1}(s_{g_2}(x))
f_{s_1,g_2}(s_{f_2}(f_{g_2,g_2}(x, y)), z10) → f_{s_1,g_2}(s_{g_2}(x), z10)
f_{s_1,g_2}(z00, s_{f_2}(f_{g_2,g_2}(x, y))) → f_{s_1,g_2}(z00, s_{g_2}(x))
f_{s_1,s_1}(s_{f_2}(f_{g_2,g_2}(x, y)), z10) → f_{s_1,s_1}(s_{g_2}(x), z10)
f_{s_1,s_1}(z00, s_{f_2}(f_{g_2,g_2}(x, y))) → f_{s_1,s_1}(z00, s_{g_2}(x))
f_{s_1,f_2}(s_{f_2}(f_{g_2,g_2}(x, y)), z10) → f_{s_1,f_2}(s_{g_2}(x), z10)
f_{s_1,f_2}(z00, s_{f_2}(f_{g_2,g_2}(x, y))) → f_{s_1,f_2}(z00, s_{g_2}(x))
s_{f_2}(s_{f_2}(f_{g_2,g_2}(x, y))) → s_{f_2}(s_{g_2}(x))
f_{f_2,g_2}(s_{f_2}(f_{g_2,g_2}(x, y)), z10) → f_{f_2,g_2}(s_{g_2}(x), z10)
f_{f_2,g_2}(z00, s_{f_2}(f_{g_2,g_2}(x, y))) → f_{f_2,g_2}(z00, s_{g_2}(x))
f_{f_2,s_1}(s_{f_2}(f_{g_2,g_2}(x, y)), z10) → f_{f_2,s_1}(s_{g_2}(x), z10)
f_{f_2,s_1}(z00, s_{f_2}(f_{g_2,g_2}(x, y))) → f_{f_2,s_1}(z00, s_{g_2}(x))
f_{f_2,f_2}(s_{f_2}(f_{g_2,g_2}(x, y)), z10) → f_{f_2,f_2}(s_{g_2}(x), z10)
f_{f_2,f_2}(z00, s_{f_2}(f_{g_2,g_2}(x, y))) → f_{f_2,f_2}(z00, s_{g_2}(x))
g_{g_2,g_2}(s_{f_2}(f_{g_2,g_2}(x, y)), z10) → g_{g_2,g_2}(s_{g_2}(x), z10)
g_{g_2,g_2}(z00, s_{f_2}(f_{g_2,g_2}(x, y))) → g_{g_2,g_2}(z00, s_{g_2}(x))
g_{g_2,s_1}(s_{f_2}(f_{g_2,g_2}(x, y)), z10) → g_{g_2,s_1}(s_{g_2}(x), z10)
g_{g_2,s_1}(z00, s_{f_2}(f_{g_2,g_2}(x, y))) → g_{g_2,s_1}(z00, s_{g_2}(x))
g_{g_2,f_2}(s_{f_2}(f_{g_2,g_2}(x, y)), z10) → g_{g_2,f_2}(s_{g_2}(x), z10)
g_{g_2,f_2}(z00, s_{f_2}(f_{g_2,g_2}(x, y))) → g_{g_2,f_2}(z00, s_{g_2}(x))
g_{s_1,g_2}(s_{f_2}(f_{g_2,s_1}(x, y)), z10) → g_{s_1,g_2}(s_{g_2}(x), z10)
g_{s_1,g_2}(z00, s_{f_2}(f_{g_2,s_1}(x, y))) → g_{s_1,g_2}(z00, s_{g_2}(x))
s_{g_2}(s_{f_2}(f_{g_2,s_1}(x, y))) → s_{g_2}(s_{g_2}(x))
g_{f_2,g_2}(s_{f_2}(f_{g_2,s_1}(x, y)), z10) → g_{f_2,g_2}(s_{g_2}(x), z10)
g_{f_2,g_2}(z00, s_{f_2}(f_{g_2,s_1}(x, y))) → g_{f_2,g_2}(z00, s_{g_2}(x))
f_{g_2,g_2}(s_{f_2}(f_{g_2,s_1}(x, y)), z10) → f_{g_2,g_2}(s_{g_2}(x), z10)
f_{g_2,g_2}(z00, s_{f_2}(f_{g_2,s_1}(x, y))) → f_{g_2,g_2}(z00, s_{g_2}(x))
g_{s_1,s_1}(s_{f_2}(f_{g_2,s_1}(x, y)), z10) → g_{s_1,s_1}(s_{g_2}(x), z10)
g_{s_1,s_1}(z00, s_{f_2}(f_{g_2,s_1}(x, y))) → g_{s_1,s_1}(z00, s_{g_2}(x))
g_{f_2,s_1}(s_{f_2}(f_{g_2,s_1}(x, y)), z10) → g_{f_2,s_1}(s_{g_2}(x), z10)
g_{f_2,s_1}(z00, s_{f_2}(f_{g_2,s_1}(x, y))) → g_{f_2,s_1}(z00, s_{g_2}(x))
f_{g_2,s_1}(s_{f_2}(f_{g_2,s_1}(x, y)), z10) → f_{g_2,s_1}(s_{g_2}(x), z10)
f_{g_2,s_1}(z00, s_{f_2}(f_{g_2,s_1}(x, y))) → f_{g_2,s_1}(z00, s_{g_2}(x))
g_{s_1,f_2}(s_{f_2}(f_{g_2,s_1}(x, y)), z10) → g_{s_1,f_2}(s_{g_2}(x), z10)
g_{s_1,f_2}(z00, s_{f_2}(f_{g_2,s_1}(x, y))) → g_{s_1,f_2}(z00, s_{g_2}(x))
g_{f_2,f_2}(s_{f_2}(f_{g_2,s_1}(x, y)), z10) → g_{f_2,f_2}(s_{g_2}(x), z10)
g_{f_2,f_2}(z00, s_{f_2}(f_{g_2,s_1}(x, y))) → g_{f_2,f_2}(z00, s_{g_2}(x))
f_{g_2,f_2}(s_{f_2}(f_{g_2,s_1}(x, y)), z10) → f_{g_2,f_2}(s_{g_2}(x), z10)
f_{g_2,f_2}(z00, s_{f_2}(f_{g_2,s_1}(x, y))) → f_{g_2,f_2}(z00, s_{g_2}(x))
s_{s_1}(s_{f_2}(f_{g_2,s_1}(x, y))) → s_{s_1}(s_{g_2}(x))
f_{s_1,g_2}(s_{f_2}(f_{g_2,s_1}(x, y)), z10) → f_{s_1,g_2}(s_{g_2}(x), z10)
f_{s_1,g_2}(z00, s_{f_2}(f_{g_2,s_1}(x, y))) → f_{s_1,g_2}(z00, s_{g_2}(x))
f_{s_1,s_1}(s_{f_2}(f_{g_2,s_1}(x, y)), z10) → f_{s_1,s_1}(s_{g_2}(x), z10)
f_{s_1,s_1}(z00, s_{f_2}(f_{g_2,s_1}(x, y))) → f_{s_1,s_1}(z00, s_{g_2}(x))
f_{s_1,f_2}(s_{f_2}(f_{g_2,s_1}(x, y)), z10) → f_{s_1,f_2}(s_{g_2}(x), z10)
f_{s_1,f_2}(z00, s_{f_2}(f_{g_2,s_1}(x, y))) → f_{s_1,f_2}(z00, s_{g_2}(x))
s_{f_2}(s_{f_2}(f_{g_2,s_1}(x, y))) → s_{f_2}(s_{g_2}(x))
f_{f_2,g_2}(s_{f_2}(f_{g_2,s_1}(x, y)), z10) → f_{f_2,g_2}(s_{g_2}(x), z10)
f_{f_2,g_2}(z00, s_{f_2}(f_{g_2,s_1}(x, y))) → f_{f_2,g_2}(z00, s_{g_2}(x))
f_{f_2,s_1}(s_{f_2}(f_{g_2,s_1}(x, y)), z10) → f_{f_2,s_1}(s_{g_2}(x), z10)
f_{f_2,s_1}(z00, s_{f_2}(f_{g_2,s_1}(x, y))) → f_{f_2,s_1}(z00, s_{g_2}(x))
f_{f_2,f_2}(s_{f_2}(f_{g_2,s_1}(x, y)), z10) → f_{f_2,f_2}(s_{g_2}(x), z10)
f_{f_2,f_2}(z00, s_{f_2}(f_{g_2,s_1}(x, y))) → f_{f_2,f_2}(z00, s_{g_2}(x))
g_{g_2,g_2}(s_{f_2}(f_{g_2,s_1}(x, y)), z10) → g_{g_2,g_2}(s_{g_2}(x), z10)
g_{g_2,g_2}(z00, s_{f_2}(f_{g_2,s_1}(x, y))) → g_{g_2,g_2}(z00, s_{g_2}(x))
g_{g_2,s_1}(s_{f_2}(f_{g_2,s_1}(x, y)), z10) → g_{g_2,s_1}(s_{g_2}(x), z10)
g_{g_2,s_1}(z00, s_{f_2}(f_{g_2,s_1}(x, y))) → g_{g_2,s_1}(z00, s_{g_2}(x))
g_{g_2,f_2}(s_{f_2}(f_{g_2,s_1}(x, y)), z10) → g_{g_2,f_2}(s_{g_2}(x), z10)
g_{g_2,f_2}(z00, s_{f_2}(f_{g_2,s_1}(x, y))) → g_{g_2,f_2}(z00, s_{g_2}(x))
g_{s_1,g_2}(s_{f_2}(f_{g_2,f_2}(x, y)), z10) → g_{s_1,g_2}(s_{g_2}(x), z10)
g_{s_1,g_2}(z00, s_{f_2}(f_{g_2,f_2}(x, y))) → g_{s_1,g_2}(z00, s_{g_2}(x))
s_{g_2}(s_{f_2}(f_{g_2,f_2}(x, y))) → s_{g_2}(s_{g_2}(x))
g_{f_2,g_2}(s_{f_2}(f_{g_2,f_2}(x, y)), z10) → g_{f_2,g_2}(s_{g_2}(x), z10)
g_{f_2,g_2}(z00, s_{f_2}(f_{g_2,f_2}(x, y))) → g_{f_2,g_2}(z00, s_{g_2}(x))
f_{g_2,g_2}(s_{f_2}(f_{g_2,f_2}(x, y)), z10) → f_{g_2,g_2}(s_{g_2}(x), z10)
f_{g_2,g_2}(z00, s_{f_2}(f_{g_2,f_2}(x, y))) → f_{g_2,g_2}(z00, s_{g_2}(x))
g_{s_1,s_1}(s_{f_2}(f_{g_2,f_2}(x, y)), z10) → g_{s_1,s_1}(s_{g_2}(x), z10)
g_{s_1,s_1}(z00, s_{f_2}(f_{g_2,f_2}(x, y))) → g_{s_1,s_1}(z00, s_{g_2}(x))
g_{f_2,s_1}(s_{f_2}(f_{g_2,f_2}(x, y)), z10) → g_{f_2,s_1}(s_{g_2}(x), z10)
g_{f_2,s_1}(z00, s_{f_2}(f_{g_2,f_2}(x, y))) → g_{f_2,s_1}(z00, s_{g_2}(x))
f_{g_2,s_1}(s_{f_2}(f_{g_2,f_2}(x, y)), z10) → f_{g_2,s_1}(s_{g_2}(x), z10)
f_{g_2,s_1}(z00, s_{f_2}(f_{g_2,f_2}(x, y))) → f_{g_2,s_1}(z00, s_{g_2}(x))
g_{s_1,f_2}(s_{f_2}(f_{g_2,f_2}(x, y)), z10) → g_{s_1,f_2}(s_{g_2}(x), z10)
g_{s_1,f_2}(z00, s_{f_2}(f_{g_2,f_2}(x, y))) → g_{s_1,f_2}(z00, s_{g_2}(x))
g_{f_2,f_2}(s_{f_2}(f_{g_2,f_2}(x, y)), z10) → g_{f_2,f_2}(s_{g_2}(x), z10)
g_{f_2,f_2}(z00, s_{f_2}(f_{g_2,f_2}(x, y))) → g_{f_2,f_2}(z00, s_{g_2}(x))
f_{g_2,f_2}(s_{f_2}(f_{g_2,f_2}(x, y)), z10) → f_{g_2,f_2}(s_{g_2}(x), z10)
f_{g_2,f_2}(z00, s_{f_2}(f_{g_2,f_2}(x, y))) → f_{g_2,f_2}(z00, s_{g_2}(x))
s_{s_1}(s_{f_2}(f_{g_2,f_2}(x, y))) → s_{s_1}(s_{g_2}(x))
f_{s_1,g_2}(s_{f_2}(f_{g_2,f_2}(x, y)), z10) → f_{s_1,g_2}(s_{g_2}(x), z10)
f_{s_1,g_2}(z00, s_{f_2}(f_{g_2,f_2}(x, y))) → f_{s_1,g_2}(z00, s_{g_2}(x))
f_{s_1,s_1}(s_{f_2}(f_{g_2,f_2}(x, y)), z10) → f_{s_1,s_1}(s_{g_2}(x), z10)
f_{s_1,s_1}(z00, s_{f_2}(f_{g_2,f_2}(x, y))) → f_{s_1,s_1}(z00, s_{g_2}(x))
f_{s_1,f_2}(s_{f_2}(f_{g_2,f_2}(x, y)), z10) → f_{s_1,f_2}(s_{g_2}(x), z10)
f_{s_1,f_2}(z00, s_{f_2}(f_{g_2,f_2}(x, y))) → f_{s_1,f_2}(z00, s_{g_2}(x))
s_{f_2}(s_{f_2}(f_{g_2,f_2}(x, y))) → s_{f_2}(s_{g_2}(x))
f_{f_2,g_2}(s_{f_2}(f_{g_2,f_2}(x, y)), z10) → f_{f_2,g_2}(s_{g_2}(x), z10)
f_{f_2,g_2}(z00, s_{f_2}(f_{g_2,f_2}(x, y))) → f_{f_2,g_2}(z00, s_{g_2}(x))
f_{f_2,s_1}(s_{f_2}(f_{g_2,f_2}(x, y)), z10) → f_{f_2,s_1}(s_{g_2}(x), z10)
f_{f_2,s_1}(z00, s_{f_2}(f_{g_2,f_2}(x, y))) → f_{f_2,s_1}(z00, s_{g_2}(x))
f_{f_2,f_2}(s_{f_2}(f_{g_2,f_2}(x, y)), z10) → f_{f_2,f_2}(s_{g_2}(x), z10)
f_{f_2,f_2}(z00, s_{f_2}(f_{g_2,f_2}(x, y))) → f_{f_2,f_2}(z00, s_{g_2}(x))
g_{g_2,g_2}(s_{f_2}(f_{g_2,f_2}(x, y)), z10) → g_{g_2,g_2}(s_{g_2}(x), z10)
g_{g_2,g_2}(z00, s_{f_2}(f_{g_2,f_2}(x, y))) → g_{g_2,g_2}(z00, s_{g_2}(x))
g_{g_2,s_1}(s_{f_2}(f_{g_2,f_2}(x, y)), z10) → g_{g_2,s_1}(s_{g_2}(x), z10)
g_{g_2,s_1}(z00, s_{f_2}(f_{g_2,f_2}(x, y))) → g_{g_2,s_1}(z00, s_{g_2}(x))
g_{g_2,f_2}(s_{f_2}(f_{g_2,f_2}(x, y)), z10) → g_{g_2,f_2}(s_{g_2}(x), z10)
g_{g_2,f_2}(z00, s_{f_2}(f_{g_2,f_2}(x, y))) → g_{g_2,f_2}(z00, s_{g_2}(x))
g_{s_1,g_2}(s_{f_2}(f_{s_1,g_2}(x, y)), z10) → g_{s_1,g_2}(s_{s_1}(x), z10)
g_{s_1,g_2}(z00, s_{f_2}(f_{s_1,g_2}(x, y))) → g_{s_1,g_2}(z00, s_{s_1}(x))
s_{g_2}(s_{f_2}(f_{s_1,g_2}(x, y))) → s_{g_2}(s_{s_1}(x))
g_{f_2,g_2}(s_{f_2}(f_{s_1,g_2}(x, y)), z10) → g_{f_2,g_2}(s_{s_1}(x), z10)
g_{f_2,g_2}(z00, s_{f_2}(f_{s_1,g_2}(x, y))) → g_{f_2,g_2}(z00, s_{s_1}(x))
f_{g_2,g_2}(s_{f_2}(f_{s_1,g_2}(x, y)), z10) → f_{g_2,g_2}(s_{s_1}(x), z10)
f_{g_2,g_2}(z00, s_{f_2}(f_{s_1,g_2}(x, y))) → f_{g_2,g_2}(z00, s_{s_1}(x))
g_{s_1,s_1}(s_{f_2}(f_{s_1,g_2}(x, y)), z10) → g_{s_1,s_1}(s_{s_1}(x), z10)
g_{s_1,s_1}(z00, s_{f_2}(f_{s_1,g_2}(x, y))) → g_{s_1,s_1}(z00, s_{s_1}(x))
g_{f_2,s_1}(s_{f_2}(f_{s_1,g_2}(x, y)), z10) → g_{f_2,s_1}(s_{s_1}(x), z10)
g_{f_2,s_1}(z00, s_{f_2}(f_{s_1,g_2}(x, y))) → g_{f_2,s_1}(z00, s_{s_1}(x))
f_{g_2,s_1}(s_{f_2}(f_{s_1,g_2}(x, y)), z10) → f_{g_2,s_1}(s_{s_1}(x), z10)
f_{g_2,s_1}(z00, s_{f_2}(f_{s_1,g_2}(x, y))) → f_{g_2,s_1}(z00, s_{s_1}(x))
g_{s_1,f_2}(s_{f_2}(f_{s_1,g_2}(x, y)), z10) → g_{s_1,f_2}(s_{s_1}(x), z10)
g_{s_1,f_2}(z00, s_{f_2}(f_{s_1,g_2}(x, y))) → g_{s_1,f_2}(z00, s_{s_1}(x))
g_{f_2,f_2}(s_{f_2}(f_{s_1,g_2}(x, y)), z10) → g_{f_2,f_2}(s_{s_1}(x), z10)
g_{f_2,f_2}(z00, s_{f_2}(f_{s_1,g_2}(x, y))) → g_{f_2,f_2}(z00, s_{s_1}(x))
f_{g_2,f_2}(s_{f_2}(f_{s_1,g_2}(x, y)), z10) → f_{g_2,f_2}(s_{s_1}(x), z10)
f_{g_2,f_2}(z00, s_{f_2}(f_{s_1,g_2}(x, y))) → f_{g_2,f_2}(z00, s_{s_1}(x))
s_{s_1}(s_{f_2}(f_{s_1,g_2}(x, y))) → s_{s_1}(s_{s_1}(x))
f_{s_1,g_2}(s_{f_2}(f_{s_1,g_2}(x, y)), z10) → f_{s_1,g_2}(s_{s_1}(x), z10)
f_{s_1,g_2}(z00, s_{f_2}(f_{s_1,g_2}(x, y))) → f_{s_1,g_2}(z00, s_{s_1}(x))
f_{s_1,s_1}(s_{f_2}(f_{s_1,g_2}(x, y)), z10) → f_{s_1,s_1}(s_{s_1}(x), z10)
f_{s_1,s_1}(z00, s_{f_2}(f_{s_1,g_2}(x, y))) → f_{s_1,s_1}(z00, s_{s_1}(x))
f_{s_1,f_2}(s_{f_2}(f_{s_1,g_2}(x, y)), z10) → f_{s_1,f_2}(s_{s_1}(x), z10)
f_{s_1,f_2}(z00, s_{f_2}(f_{s_1,g_2}(x, y))) → f_{s_1,f_2}(z00, s_{s_1}(x))
s_{f_2}(s_{f_2}(f_{s_1,g_2}(x, y))) → s_{f_2}(s_{s_1}(x))
f_{f_2,g_2}(s_{f_2}(f_{s_1,g_2}(x, y)), z10) → f_{f_2,g_2}(s_{s_1}(x), z10)
f_{f_2,g_2}(z00, s_{f_2}(f_{s_1,g_2}(x, y))) → f_{f_2,g_2}(z00, s_{s_1}(x))
f_{f_2,s_1}(s_{f_2}(f_{s_1,g_2}(x, y)), z10) → f_{f_2,s_1}(s_{s_1}(x), z10)
f_{f_2,s_1}(z00, s_{f_2}(f_{s_1,g_2}(x, y))) → f_{f_2,s_1}(z00, s_{s_1}(x))
f_{f_2,f_2}(s_{f_2}(f_{s_1,g_2}(x, y)), z10) → f_{f_2,f_2}(s_{s_1}(x), z10)
f_{f_2,f_2}(z00, s_{f_2}(f_{s_1,g_2}(x, y))) → f_{f_2,f_2}(z00, s_{s_1}(x))
g_{g_2,g_2}(s_{f_2}(f_{s_1,g_2}(x, y)), z10) → g_{g_2,g_2}(s_{s_1}(x), z10)
g_{g_2,g_2}(z00, s_{f_2}(f_{s_1,g_2}(x, y))) → g_{g_2,g_2}(z00, s_{s_1}(x))
g_{g_2,s_1}(s_{f_2}(f_{s_1,g_2}(x, y)), z10) → g_{g_2,s_1}(s_{s_1}(x), z10)
g_{g_2,s_1}(z00, s_{f_2}(f_{s_1,g_2}(x, y))) → g_{g_2,s_1}(z00, s_{s_1}(x))
g_{g_2,f_2}(s_{f_2}(f_{s_1,g_2}(x, y)), z10) → g_{g_2,f_2}(s_{s_1}(x), z10)
g_{g_2,f_2}(z00, s_{f_2}(f_{s_1,g_2}(x, y))) → g_{g_2,f_2}(z00, s_{s_1}(x))
g_{s_1,g_2}(s_{f_2}(f_{s_1,s_1}(x, y)), z10) → g_{s_1,g_2}(s_{s_1}(x), z10)
g_{s_1,g_2}(z00, s_{f_2}(f_{s_1,s_1}(x, y))) → g_{s_1,g_2}(z00, s_{s_1}(x))
s_{g_2}(s_{f_2}(f_{s_1,s_1}(x, y))) → s_{g_2}(s_{s_1}(x))
g_{f_2,g_2}(s_{f_2}(f_{s_1,s_1}(x, y)), z10) → g_{f_2,g_2}(s_{s_1}(x), z10)
g_{f_2,g_2}(z00, s_{f_2}(f_{s_1,s_1}(x, y))) → g_{f_2,g_2}(z00, s_{s_1}(x))
f_{g_2,g_2}(s_{f_2}(f_{s_1,s_1}(x, y)), z10) → f_{g_2,g_2}(s_{s_1}(x), z10)
f_{g_2,g_2}(z00, s_{f_2}(f_{s_1,s_1}(x, y))) → f_{g_2,g_2}(z00, s_{s_1}(x))
g_{s_1,s_1}(s_{f_2}(f_{s_1,s_1}(x, y)), z10) → g_{s_1,s_1}(s_{s_1}(x), z10)
g_{s_1,s_1}(z00, s_{f_2}(f_{s_1,s_1}(x, y))) → g_{s_1,s_1}(z00, s_{s_1}(x))
g_{f_2,s_1}(s_{f_2}(f_{s_1,s_1}(x, y)), z10) → g_{f_2,s_1}(s_{s_1}(x), z10)
g_{f_2,s_1}(z00, s_{f_2}(f_{s_1,s_1}(x, y))) → g_{f_2,s_1}(z00, s_{s_1}(x))
f_{g_2,s_1}(s_{f_2}(f_{s_1,s_1}(x, y)), z10) → f_{g_2,s_1}(s_{s_1}(x), z10)
f_{g_2,s_1}(z00, s_{f_2}(f_{s_1,s_1}(x, y))) → f_{g_2,s_1}(z00, s_{s_1}(x))
g_{s_1,f_2}(s_{f_2}(f_{s_1,s_1}(x, y)), z10) → g_{s_1,f_2}(s_{s_1}(x), z10)
g_{s_1,f_2}(z00, s_{f_2}(f_{s_1,s_1}(x, y))) → g_{s_1,f_2}(z00, s_{s_1}(x))
g_{f_2,f_2}(s_{f_2}(f_{s_1,s_1}(x, y)), z10) → g_{f_2,f_2}(s_{s_1}(x), z10)
g_{f_2,f_2}(z00, s_{f_2}(f_{s_1,s_1}(x, y))) → g_{f_2,f_2}(z00, s_{s_1}(x))
f_{g_2,f_2}(s_{f_2}(f_{s_1,s_1}(x, y)), z10) → f_{g_2,f_2}(s_{s_1}(x), z10)
f_{g_2,f_2}(z00, s_{f_2}(f_{s_1,s_1}(x, y))) → f_{g_2,f_2}(z00, s_{s_1}(x))
s_{s_1}(s_{f_2}(f_{s_1,s_1}(x, y))) → s_{s_1}(s_{s_1}(x))
f_{s_1,g_2}(s_{f_2}(f_{s_1,s_1}(x, y)), z10) → f_{s_1,g_2}(s_{s_1}(x), z10)
f_{s_1,g_2}(z00, s_{f_2}(f_{s_1,s_1}(x, y))) → f_{s_1,g_2}(z00, s_{s_1}(x))
f_{s_1,s_1}(s_{f_2}(f_{s_1,s_1}(x, y)), z10) → f_{s_1,s_1}(s_{s_1}(x), z10)
f_{s_1,s_1}(z00, s_{f_2}(f_{s_1,s_1}(x, y))) → f_{s_1,s_1}(z00, s_{s_1}(x))
f_{s_1,f_2}(s_{f_2}(f_{s_1,s_1}(x, y)), z10) → f_{s_1,f_2}(s_{s_1}(x), z10)
f_{s_1,f_2}(z00, s_{f_2}(f_{s_1,s_1}(x, y))) → f_{s_1,f_2}(z00, s_{s_1}(x))
s_{f_2}(s_{f_2}(f_{s_1,s_1}(x, y))) → s_{f_2}(s_{s_1}(x))
f_{f_2,g_2}(s_{f_2}(f_{s_1,s_1}(x, y)), z10) → f_{f_2,g_2}(s_{s_1}(x), z10)
f_{f_2,g_2}(z00, s_{f_2}(f_{s_1,s_1}(x, y))) → f_{f_2,g_2}(z00, s_{s_1}(x))
f_{f_2,s_1}(s_{f_2}(f_{s_1,s_1}(x, y)), z10) → f_{f_2,s_1}(s_{s_1}(x), z10)
f_{f_2,s_1}(z00, s_{f_2}(f_{s_1,s_1}(x, y))) → f_{f_2,s_1}(z00, s_{s_1}(x))
f_{f_2,f_2}(s_{f_2}(f_{s_1,s_1}(x, y)), z10) → f_{f_2,f_2}(s_{s_1}(x), z10)
f_{f_2,f_2}(z00, s_{f_2}(f_{s_1,s_1}(x, y))) → f_{f_2,f_2}(z00, s_{s_1}(x))
g_{g_2,g_2}(s_{f_2}(f_{s_1,s_1}(x, y)), z10) → g_{g_2,g_2}(s_{s_1}(x), z10)
g_{g_2,g_2}(z00, s_{f_2}(f_{s_1,s_1}(x, y))) → g_{g_2,g_2}(z00, s_{s_1}(x))
g_{g_2,s_1}(s_{f_2}(f_{s_1,s_1}(x, y)), z10) → g_{g_2,s_1}(s_{s_1}(x), z10)
g_{g_2,s_1}(z00, s_{f_2}(f_{s_1,s_1}(x, y))) → g_{g_2,s_1}(z00, s_{s_1}(x))
g_{g_2,f_2}(s_{f_2}(f_{s_1,s_1}(x, y)), z10) → g_{g_2,f_2}(s_{s_1}(x), z10)
g_{g_2,f_2}(z00, s_{f_2}(f_{s_1,s_1}(x, y))) → g_{g_2,f_2}(z00, s_{s_1}(x))
g_{s_1,g_2}(s_{f_2}(f_{s_1,f_2}(x, y)), z10) → g_{s_1,g_2}(s_{s_1}(x), z10)
g_{s_1,g_2}(z00, s_{f_2}(f_{s_1,f_2}(x, y))) → g_{s_1,g_2}(z00, s_{s_1}(x))
s_{g_2}(s_{f_2}(f_{s_1,f_2}(x, y))) → s_{g_2}(s_{s_1}(x))
g_{f_2,g_2}(s_{f_2}(f_{s_1,f_2}(x, y)), z10) → g_{f_2,g_2}(s_{s_1}(x), z10)
g_{f_2,g_2}(z00, s_{f_2}(f_{s_1,f_2}(x, y))) → g_{f_2,g_2}(z00, s_{s_1}(x))
f_{g_2,g_2}(s_{f_2}(f_{s_1,f_2}(x, y)), z10) → f_{g_2,g_2}(s_{s_1}(x), z10)
f_{g_2,g_2}(z00, s_{f_2}(f_{s_1,f_2}(x, y))) → f_{g_2,g_2}(z00, s_{s_1}(x))
g_{s_1,s_1}(s_{f_2}(f_{s_1,f_2}(x, y)), z10) → g_{s_1,s_1}(s_{s_1}(x), z10)
g_{s_1,s_1}(z00, s_{f_2}(f_{s_1,f_2}(x, y))) → g_{s_1,s_1}(z00, s_{s_1}(x))
g_{f_2,s_1}(s_{f_2}(f_{s_1,f_2}(x, y)), z10) → g_{f_2,s_1}(s_{s_1}(x), z10)
g_{f_2,s_1}(z00, s_{f_2}(f_{s_1,f_2}(x, y))) → g_{f_2,s_1}(z00, s_{s_1}(x))
f_{g_2,s_1}(s_{f_2}(f_{s_1,f_2}(x, y)), z10) → f_{g_2,s_1}(s_{s_1}(x), z10)
f_{g_2,s_1}(z00, s_{f_2}(f_{s_1,f_2}(x, y))) → f_{g_2,s_1}(z00, s_{s_1}(x))
g_{s_1,f_2}(s_{f_2}(f_{s_1,f_2}(x, y)), z10) → g_{s_1,f_2}(s_{s_1}(x), z10)
g_{s_1,f_2}(z00, s_{f_2}(f_{s_1,f_2}(x, y))) → g_{s_1,f_2}(z00, s_{s_1}(x))
g_{f_2,f_2}(s_{f_2}(f_{s_1,f_2}(x, y)), z10) → g_{f_2,f_2}(s_{s_1}(x), z10)
g_{f_2,f_2}(z00, s_{f_2}(f_{s_1,f_2}(x, y))) → g_{f_2,f_2}(z00, s_{s_1}(x))
f_{g_2,f_2}(s_{f_2}(f_{s_1,f_2}(x, y)), z10) → f_{g_2,f_2}(s_{s_1}(x), z10)
f_{g_2,f_2}(z00, s_{f_2}(f_{s_1,f_2}(x, y))) → f_{g_2,f_2}(z00, s_{s_1}(x))
s_{s_1}(s_{f_2}(f_{s_1,f_2}(x, y))) → s_{s_1}(s_{s_1}(x))
f_{s_1,g_2}(s_{f_2}(f_{s_1,f_2}(x, y)), z10) → f_{s_1,g_2}(s_{s_1}(x), z10)
f_{s_1,g_2}(z00, s_{f_2}(f_{s_1,f_2}(x, y))) → f_{s_1,g_2}(z00, s_{s_1}(x))
f_{s_1,s_1}(s_{f_2}(f_{s_1,f_2}(x, y)), z10) → f_{s_1,s_1}(s_{s_1}(x), z10)
f_{s_1,s_1}(z00, s_{f_2}(f_{s_1,f_2}(x, y))) → f_{s_1,s_1}(z00, s_{s_1}(x))
f_{s_1,f_2}(s_{f_2}(f_{s_1,f_2}(x, y)), z10) → f_{s_1,f_2}(s_{s_1}(x), z10)
f_{s_1,f_2}(z00, s_{f_2}(f_{s_1,f_2}(x, y))) → f_{s_1,f_2}(z00, s_{s_1}(x))
s_{f_2}(s_{f_2}(f_{s_1,f_2}(x, y))) → s_{f_2}(s_{s_1}(x))
f_{f_2,g_2}(s_{f_2}(f_{s_1,f_2}(x, y)), z10) → f_{f_2,g_2}(s_{s_1}(x), z10)
f_{f_2,g_2}(z00, s_{f_2}(f_{s_1,f_2}(x, y))) → f_{f_2,g_2}(z00, s_{s_1}(x))
f_{f_2,s_1}(s_{f_2}(f_{s_1,f_2}(x, y)), z10) → f_{f_2,s_1}(s_{s_1}(x), z10)
f_{f_2,s_1}(z00, s_{f_2}(f_{s_1,f_2}(x, y))) → f_{f_2,s_1}(z00, s_{s_1}(x))
f_{f_2,f_2}(s_{f_2}(f_{s_1,f_2}(x, y)), z10) → f_{f_2,f_2}(s_{s_1}(x), z10)
f_{f_2,f_2}(z00, s_{f_2}(f_{s_1,f_2}(x, y))) → f_{f_2,f_2}(z00, s_{s_1}(x))
g_{g_2,g_2}(s_{f_2}(f_{s_1,f_2}(x, y)), z10) → g_{g_2,g_2}(s_{s_1}(x), z10)
g_{g_2,g_2}(z00, s_{f_2}(f_{s_1,f_2}(x, y))) → g_{g_2,g_2}(z00, s_{s_1}(x))
g_{g_2,s_1}(s_{f_2}(f_{s_1,f_2}(x, y)), z10) → g_{g_2,s_1}(s_{s_1}(x), z10)
g_{g_2,s_1}(z00, s_{f_2}(f_{s_1,f_2}(x, y))) → g_{g_2,s_1}(z00, s_{s_1}(x))
g_{g_2,f_2}(s_{f_2}(f_{s_1,f_2}(x, y)), z10) → g_{g_2,f_2}(s_{s_1}(x), z10)
g_{g_2,f_2}(z00, s_{f_2}(f_{s_1,f_2}(x, y))) → g_{g_2,f_2}(z00, s_{s_1}(x))
g_{s_1,g_2}(f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{s_1,g_2}(f_{g_2,g_2}(x, z1), z10)
g_{s_1,g_2}(z00, f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → g_{s_1,g_2}(z00, f_{g_2,g_2}(x, z1))
s_{g_2}(f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → s_{g_2}(f_{g_2,g_2}(x, z1))
g_{f_2,g_2}(f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{f_2,g_2}(f_{g_2,g_2}(x, z1), z10)
g_{f_2,g_2}(z00, f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → g_{f_2,g_2}(z00, f_{g_2,g_2}(x, z1))
f_{g_2,g_2}(f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{g_2,g_2}(f_{g_2,g_2}(x, z1), z10)
f_{g_2,g_2}(z00, f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → f_{g_2,g_2}(z00, f_{g_2,g_2}(x, z1))
g_{s_1,s_1}(f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{s_1,s_1}(f_{g_2,g_2}(x, z1), z10)
g_{s_1,s_1}(z00, f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → g_{s_1,s_1}(z00, f_{g_2,g_2}(x, z1))
g_{f_2,s_1}(f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{f_2,s_1}(f_{g_2,g_2}(x, z1), z10)
g_{f_2,s_1}(z00, f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → g_{f_2,s_1}(z00, f_{g_2,g_2}(x, z1))
f_{g_2,s_1}(f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{g_2,s_1}(f_{g_2,g_2}(x, z1), z10)
f_{g_2,s_1}(z00, f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → f_{g_2,s_1}(z00, f_{g_2,g_2}(x, z1))
g_{s_1,f_2}(f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{s_1,f_2}(f_{g_2,g_2}(x, z1), z10)
g_{s_1,f_2}(z00, f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → g_{s_1,f_2}(z00, f_{g_2,g_2}(x, z1))
g_{f_2,f_2}(f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{f_2,f_2}(f_{g_2,g_2}(x, z1), z10)
g_{f_2,f_2}(z00, f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → g_{f_2,f_2}(z00, f_{g_2,g_2}(x, z1))
f_{g_2,f_2}(f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{g_2,f_2}(f_{g_2,g_2}(x, z1), z10)
f_{g_2,f_2}(z00, f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → f_{g_2,f_2}(z00, f_{g_2,g_2}(x, z1))
s_{s_1}(f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → s_{s_1}(f_{g_2,g_2}(x, z1))
f_{s_1,g_2}(f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{s_1,g_2}(f_{g_2,g_2}(x, z1), z10)
f_{s_1,g_2}(z00, f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → f_{s_1,g_2}(z00, f_{g_2,g_2}(x, z1))
f_{s_1,s_1}(f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{s_1,s_1}(f_{g_2,g_2}(x, z1), z10)
f_{s_1,s_1}(z00, f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → f_{s_1,s_1}(z00, f_{g_2,g_2}(x, z1))
f_{s_1,f_2}(f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{s_1,f_2}(f_{g_2,g_2}(x, z1), z10)
f_{s_1,f_2}(z00, f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → f_{s_1,f_2}(z00, f_{g_2,g_2}(x, z1))
s_{f_2}(f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → s_{f_2}(f_{g_2,g_2}(x, z1))
f_{f_2,g_2}(f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{f_2,g_2}(f_{g_2,g_2}(x, z1), z10)
f_{f_2,g_2}(z00, f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → f_{f_2,g_2}(z00, f_{g_2,g_2}(x, z1))
f_{f_2,s_1}(f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{f_2,s_1}(f_{g_2,g_2}(x, z1), z10)
f_{f_2,s_1}(z00, f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → f_{f_2,s_1}(z00, f_{g_2,g_2}(x, z1))
f_{f_2,f_2}(f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{f_2,f_2}(f_{g_2,g_2}(x, z1), z10)
f_{f_2,f_2}(z00, f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → f_{f_2,f_2}(z00, f_{g_2,g_2}(x, z1))
g_{g_2,g_2}(f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{g_2,g_2}(f_{g_2,g_2}(x, z1), z10)
g_{g_2,g_2}(z00, f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → g_{g_2,g_2}(z00, f_{g_2,g_2}(x, z1))
g_{g_2,s_1}(f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{g_2,s_1}(f_{g_2,g_2}(x, z1), z10)
g_{g_2,s_1}(z00, f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → g_{g_2,s_1}(z00, f_{g_2,g_2}(x, z1))
g_{g_2,f_2}(f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{g_2,f_2}(f_{g_2,g_2}(x, z1), z10)
g_{g_2,f_2}(z00, f_{f_2,g_2}(f_{g_2,g_2}(x, y), z1)) → g_{g_2,f_2}(z00, f_{g_2,g_2}(x, z1))
g_{s_1,g_2}(f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → g_{s_1,g_2}(f_{g_2,s_1}(x, z1), z10)
g_{s_1,g_2}(z00, f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → g_{s_1,g_2}(z00, f_{g_2,s_1}(x, z1))
s_{g_2}(f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → s_{g_2}(f_{g_2,s_1}(x, z1))
g_{f_2,g_2}(f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → g_{f_2,g_2}(f_{g_2,s_1}(x, z1), z10)
g_{f_2,g_2}(z00, f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → g_{f_2,g_2}(z00, f_{g_2,s_1}(x, z1))
f_{g_2,g_2}(f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → f_{g_2,g_2}(f_{g_2,s_1}(x, z1), z10)
f_{g_2,g_2}(z00, f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → f_{g_2,g_2}(z00, f_{g_2,s_1}(x, z1))
g_{s_1,s_1}(f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → g_{s_1,s_1}(f_{g_2,s_1}(x, z1), z10)
g_{s_1,s_1}(z00, f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → g_{s_1,s_1}(z00, f_{g_2,s_1}(x, z1))
g_{f_2,s_1}(f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → g_{f_2,s_1}(f_{g_2,s_1}(x, z1), z10)
g_{f_2,s_1}(z00, f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → g_{f_2,s_1}(z00, f_{g_2,s_1}(x, z1))
f_{g_2,s_1}(f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → f_{g_2,s_1}(f_{g_2,s_1}(x, z1), z10)
f_{g_2,s_1}(z00, f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → f_{g_2,s_1}(z00, f_{g_2,s_1}(x, z1))
g_{s_1,f_2}(f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → g_{s_1,f_2}(f_{g_2,s_1}(x, z1), z10)
g_{s_1,f_2}(z00, f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → g_{s_1,f_2}(z00, f_{g_2,s_1}(x, z1))
g_{f_2,f_2}(f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → g_{f_2,f_2}(f_{g_2,s_1}(x, z1), z10)
g_{f_2,f_2}(z00, f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → g_{f_2,f_2}(z00, f_{g_2,s_1}(x, z1))
f_{g_2,f_2}(f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → f_{g_2,f_2}(f_{g_2,s_1}(x, z1), z10)
f_{g_2,f_2}(z00, f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → f_{g_2,f_2}(z00, f_{g_2,s_1}(x, z1))
s_{s_1}(f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → s_{s_1}(f_{g_2,s_1}(x, z1))
f_{s_1,g_2}(f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → f_{s_1,g_2}(f_{g_2,s_1}(x, z1), z10)
f_{s_1,g_2}(z00, f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → f_{s_1,g_2}(z00, f_{g_2,s_1}(x, z1))
f_{s_1,s_1}(f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → f_{s_1,s_1}(f_{g_2,s_1}(x, z1), z10)
f_{s_1,s_1}(z00, f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → f_{s_1,s_1}(z00, f_{g_2,s_1}(x, z1))
f_{s_1,f_2}(f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → f_{s_1,f_2}(f_{g_2,s_1}(x, z1), z10)
f_{s_1,f_2}(z00, f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → f_{s_1,f_2}(z00, f_{g_2,s_1}(x, z1))
s_{f_2}(f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → s_{f_2}(f_{g_2,s_1}(x, z1))
f_{f_2,g_2}(f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → f_{f_2,g_2}(f_{g_2,s_1}(x, z1), z10)
f_{f_2,g_2}(z00, f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → f_{f_2,g_2}(z00, f_{g_2,s_1}(x, z1))
f_{f_2,s_1}(f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → f_{f_2,s_1}(f_{g_2,s_1}(x, z1), z10)
f_{f_2,s_1}(z00, f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → f_{f_2,s_1}(z00, f_{g_2,s_1}(x, z1))
f_{f_2,f_2}(f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → f_{f_2,f_2}(f_{g_2,s_1}(x, z1), z10)
f_{f_2,f_2}(z00, f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → f_{f_2,f_2}(z00, f_{g_2,s_1}(x, z1))
g_{g_2,g_2}(f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → g_{g_2,g_2}(f_{g_2,s_1}(x, z1), z10)
g_{g_2,g_2}(z00, f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → g_{g_2,g_2}(z00, f_{g_2,s_1}(x, z1))
g_{g_2,s_1}(f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → g_{g_2,s_1}(f_{g_2,s_1}(x, z1), z10)
g_{g_2,s_1}(z00, f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → g_{g_2,s_1}(z00, f_{g_2,s_1}(x, z1))
g_{g_2,f_2}(f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1), z10) → g_{g_2,f_2}(f_{g_2,s_1}(x, z1), z10)
g_{g_2,f_2}(z00, f_{f_2,s_1}(f_{g_2,g_2}(x, y), z1)) → g_{g_2,f_2}(z00, f_{g_2,s_1}(x, z1))
g_{s_1,g_2}(f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{s_1,g_2}(f_{g_2,f_2}(x, z1), z10)
g_{s_1,g_2}(z00, f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → g_{s_1,g_2}(z00, f_{g_2,f_2}(x, z1))
s_{g_2}(f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → s_{g_2}(f_{g_2,f_2}(x, z1))
g_{f_2,g_2}(f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{f_2,g_2}(f_{g_2,f_2}(x, z1), z10)
g_{f_2,g_2}(z00, f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → g_{f_2,g_2}(z00, f_{g_2,f_2}(x, z1))
f_{g_2,g_2}(f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{g_2,g_2}(f_{g_2,f_2}(x, z1), z10)
f_{g_2,g_2}(z00, f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → f_{g_2,g_2}(z00, f_{g_2,f_2}(x, z1))
g_{s_1,s_1}(f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{s_1,s_1}(f_{g_2,f_2}(x, z1), z10)
g_{s_1,s_1}(z00, f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → g_{s_1,s_1}(z00, f_{g_2,f_2}(x, z1))
g_{f_2,s_1}(f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{f_2,s_1}(f_{g_2,f_2}(x, z1), z10)
g_{f_2,s_1}(z00, f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → g_{f_2,s_1}(z00, f_{g_2,f_2}(x, z1))
f_{g_2,s_1}(f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{g_2,s_1}(f_{g_2,f_2}(x, z1), z10)
f_{g_2,s_1}(z00, f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → f_{g_2,s_1}(z00, f_{g_2,f_2}(x, z1))
g_{s_1,f_2}(f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{s_1,f_2}(f_{g_2,f_2}(x, z1), z10)
g_{s_1,f_2}(z00, f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → g_{s_1,f_2}(z00, f_{g_2,f_2}(x, z1))
g_{f_2,f_2}(f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{f_2,f_2}(f_{g_2,f_2}(x, z1), z10)
g_{f_2,f_2}(z00, f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → g_{f_2,f_2}(z00, f_{g_2,f_2}(x, z1))
f_{g_2,f_2}(f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{g_2,f_2}(f_{g_2,f_2}(x, z1), z10)
f_{g_2,f_2}(z00, f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → f_{g_2,f_2}(z00, f_{g_2,f_2}(x, z1))
s_{s_1}(f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → s_{s_1}(f_{g_2,f_2}(x, z1))
f_{s_1,g_2}(f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{s_1,g_2}(f_{g_2,f_2}(x, z1), z10)
f_{s_1,g_2}(z00, f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → f_{s_1,g_2}(z00, f_{g_2,f_2}(x, z1))
f_{s_1,s_1}(f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{s_1,s_1}(f_{g_2,f_2}(x, z1), z10)
f_{s_1,s_1}(z00, f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → f_{s_1,s_1}(z00, f_{g_2,f_2}(x, z1))
f_{s_1,f_2}(f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{s_1,f_2}(f_{g_2,f_2}(x, z1), z10)
f_{s_1,f_2}(z00, f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → f_{s_1,f_2}(z00, f_{g_2,f_2}(x, z1))
s_{f_2}(f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → s_{f_2}(f_{g_2,f_2}(x, z1))
f_{f_2,g_2}(f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{f_2,g_2}(f_{g_2,f_2}(x, z1), z10)
f_{f_2,g_2}(z00, f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → f_{f_2,g_2}(z00, f_{g_2,f_2}(x, z1))
f_{f_2,s_1}(f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{f_2,s_1}(f_{g_2,f_2}(x, z1), z10)
f_{f_2,s_1}(z00, f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → f_{f_2,s_1}(z00, f_{g_2,f_2}(x, z1))
f_{f_2,f_2}(f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → f_{f_2,f_2}(f_{g_2,f_2}(x, z1), z10)
f_{f_2,f_2}(z00, f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → f_{f_2,f_2}(z00, f_{g_2,f_2}(x, z1))
g_{g_2,g_2}(f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{g_2,g_2}(f_{g_2,f_2}(x, z1), z10)
g_{g_2,g_2}(z00, f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → g_{g_2,g_2}(z00, f_{g_2,f_2}(x, z1))
g_{g_2,s_1}(f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{g_2,s_1}(f_{g_2,f_2}(x, z1), z10)
g_{g_2,s_1}(z00, f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → g_{g_2,s_1}(z00, f_{g_2,f_2}(x, z1))
g_{g_2,f_2}(f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1), z10) → g_{g_2,f_2}(f_{g_2,f_2}(x, z1), z10)
g_{g_2,f_2}(z00, f_{f_2,f_2}(f_{g_2,g_2}(x, y), z1)) → g_{g_2,f_2}(z00, f_{g_2,f_2}(x, z1))
g_{s_1,g_2}(f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{s_1,g_2}(f_{g_2,g_2}(x, z1), z10)
g_{s_1,g_2}(z00, f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → g_{s_1,g_2}(z00, f_{g_2,g_2}(x, z1))
s_{g_2}(f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → s_{g_2}(f_{g_2,g_2}(x, z1))
g_{f_2,g_2}(f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{f_2,g_2}(f_{g_2,g_2}(x, z1), z10)
g_{f_2,g_2}(z00, f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → g_{f_2,g_2}(z00, f_{g_2,g_2}(x, z1))
f_{g_2,g_2}(f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{g_2,g_2}(f_{g_2,g_2}(x, z1), z10)
f_{g_2,g_2}(z00, f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → f_{g_2,g_2}(z00, f_{g_2,g_2}(x, z1))
g_{s_1,s_1}(f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{s_1,s_1}(f_{g_2,g_2}(x, z1), z10)
g_{s_1,s_1}(z00, f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → g_{s_1,s_1}(z00, f_{g_2,g_2}(x, z1))
g_{f_2,s_1}(f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{f_2,s_1}(f_{g_2,g_2}(x, z1), z10)
g_{f_2,s_1}(z00, f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → g_{f_2,s_1}(z00, f_{g_2,g_2}(x, z1))
f_{g_2,s_1}(f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{g_2,s_1}(f_{g_2,g_2}(x, z1), z10)
f_{g_2,s_1}(z00, f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → f_{g_2,s_1}(z00, f_{g_2,g_2}(x, z1))
g_{s_1,f_2}(f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{s_1,f_2}(f_{g_2,g_2}(x, z1), z10)
g_{s_1,f_2}(z00, f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → g_{s_1,f_2}(z00, f_{g_2,g_2}(x, z1))
g_{f_2,f_2}(f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{f_2,f_2}(f_{g_2,g_2}(x, z1), z10)
g_{f_2,f_2}(z00, f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → g_{f_2,f_2}(z00, f_{g_2,g_2}(x, z1))
f_{g_2,f_2}(f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{g_2,f_2}(f_{g_2,g_2}(x, z1), z10)
f_{g_2,f_2}(z00, f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → f_{g_2,f_2}(z00, f_{g_2,g_2}(x, z1))
s_{s_1}(f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → s_{s_1}(f_{g_2,g_2}(x, z1))
f_{s_1,g_2}(f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{s_1,g_2}(f_{g_2,g_2}(x, z1), z10)
f_{s_1,g_2}(z00, f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → f_{s_1,g_2}(z00, f_{g_2,g_2}(x, z1))
f_{s_1,s_1}(f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{s_1,s_1}(f_{g_2,g_2}(x, z1), z10)
f_{s_1,s_1}(z00, f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → f_{s_1,s_1}(z00, f_{g_2,g_2}(x, z1))
f_{s_1,f_2}(f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{s_1,f_2}(f_{g_2,g_2}(x, z1), z10)
f_{s_1,f_2}(z00, f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → f_{s_1,f_2}(z00, f_{g_2,g_2}(x, z1))
s_{f_2}(f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → s_{f_2}(f_{g_2,g_2}(x, z1))
f_{f_2,g_2}(f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{f_2,g_2}(f_{g_2,g_2}(x, z1), z10)
f_{f_2,g_2}(z00, f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → f_{f_2,g_2}(z00, f_{g_2,g_2}(x, z1))
f_{f_2,s_1}(f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{f_2,s_1}(f_{g_2,g_2}(x, z1), z10)
f_{f_2,s_1}(z00, f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → f_{f_2,s_1}(z00, f_{g_2,g_2}(x, z1))
f_{f_2,f_2}(f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{f_2,f_2}(f_{g_2,g_2}(x, z1), z10)
f_{f_2,f_2}(z00, f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → f_{f_2,f_2}(z00, f_{g_2,g_2}(x, z1))
g_{g_2,g_2}(f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{g_2,g_2}(f_{g_2,g_2}(x, z1), z10)
g_{g_2,g_2}(z00, f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → g_{g_2,g_2}(z00, f_{g_2,g_2}(x, z1))
g_{g_2,s_1}(f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{g_2,s_1}(f_{g_2,g_2}(x, z1), z10)
g_{g_2,s_1}(z00, f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → g_{g_2,s_1}(z00, f_{g_2,g_2}(x, z1))
g_{g_2,f_2}(f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{g_2,f_2}(f_{g_2,g_2}(x, z1), z10)
g_{g_2,f_2}(z00, f_{f_2,g_2}(f_{g_2,s_1}(x, y), z1)) → g_{g_2,f_2}(z00, f_{g_2,g_2}(x, z1))
g_{s_1,g_2}(f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → g_{s_1,g_2}(f_{g_2,s_1}(x, z1), z10)
g_{s_1,g_2}(z00, f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → g_{s_1,g_2}(z00, f_{g_2,s_1}(x, z1))
s_{g_2}(f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → s_{g_2}(f_{g_2,s_1}(x, z1))
g_{f_2,g_2}(f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → g_{f_2,g_2}(f_{g_2,s_1}(x, z1), z10)
g_{f_2,g_2}(z00, f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → g_{f_2,g_2}(z00, f_{g_2,s_1}(x, z1))
f_{g_2,g_2}(f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → f_{g_2,g_2}(f_{g_2,s_1}(x, z1), z10)
f_{g_2,g_2}(z00, f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → f_{g_2,g_2}(z00, f_{g_2,s_1}(x, z1))
g_{s_1,s_1}(f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → g_{s_1,s_1}(f_{g_2,s_1}(x, z1), z10)
g_{s_1,s_1}(z00, f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → g_{s_1,s_1}(z00, f_{g_2,s_1}(x, z1))
g_{f_2,s_1}(f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → g_{f_2,s_1}(f_{g_2,s_1}(x, z1), z10)
g_{f_2,s_1}(z00, f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → g_{f_2,s_1}(z00, f_{g_2,s_1}(x, z1))
f_{g_2,s_1}(f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → f_{g_2,s_1}(f_{g_2,s_1}(x, z1), z10)
f_{g_2,s_1}(z00, f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → f_{g_2,s_1}(z00, f_{g_2,s_1}(x, z1))
g_{s_1,f_2}(f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → g_{s_1,f_2}(f_{g_2,s_1}(x, z1), z10)
g_{s_1,f_2}(z00, f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → g_{s_1,f_2}(z00, f_{g_2,s_1}(x, z1))
g_{f_2,f_2}(f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → g_{f_2,f_2}(f_{g_2,s_1}(x, z1), z10)
g_{f_2,f_2}(z00, f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → g_{f_2,f_2}(z00, f_{g_2,s_1}(x, z1))
f_{g_2,f_2}(f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → f_{g_2,f_2}(f_{g_2,s_1}(x, z1), z10)
f_{g_2,f_2}(z00, f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → f_{g_2,f_2}(z00, f_{g_2,s_1}(x, z1))
s_{s_1}(f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → s_{s_1}(f_{g_2,s_1}(x, z1))
f_{s_1,g_2}(f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → f_{s_1,g_2}(f_{g_2,s_1}(x, z1), z10)
f_{s_1,g_2}(z00, f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → f_{s_1,g_2}(z00, f_{g_2,s_1}(x, z1))
f_{s_1,s_1}(f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → f_{s_1,s_1}(f_{g_2,s_1}(x, z1), z10)
f_{s_1,s_1}(z00, f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → f_{s_1,s_1}(z00, f_{g_2,s_1}(x, z1))
f_{s_1,f_2}(f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → f_{s_1,f_2}(f_{g_2,s_1}(x, z1), z10)
f_{s_1,f_2}(z00, f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → f_{s_1,f_2}(z00, f_{g_2,s_1}(x, z1))
s_{f_2}(f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → s_{f_2}(f_{g_2,s_1}(x, z1))
f_{f_2,g_2}(f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → f_{f_2,g_2}(f_{g_2,s_1}(x, z1), z10)
f_{f_2,g_2}(z00, f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → f_{f_2,g_2}(z00, f_{g_2,s_1}(x, z1))
f_{f_2,s_1}(f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → f_{f_2,s_1}(f_{g_2,s_1}(x, z1), z10)
f_{f_2,s_1}(z00, f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → f_{f_2,s_1}(z00, f_{g_2,s_1}(x, z1))
f_{f_2,f_2}(f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → f_{f_2,f_2}(f_{g_2,s_1}(x, z1), z10)
f_{f_2,f_2}(z00, f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → f_{f_2,f_2}(z00, f_{g_2,s_1}(x, z1))
g_{g_2,g_2}(f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → g_{g_2,g_2}(f_{g_2,s_1}(x, z1), z10)
g_{g_2,g_2}(z00, f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → g_{g_2,g_2}(z00, f_{g_2,s_1}(x, z1))
g_{g_2,s_1}(f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → g_{g_2,s_1}(f_{g_2,s_1}(x, z1), z10)
g_{g_2,s_1}(z00, f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → g_{g_2,s_1}(z00, f_{g_2,s_1}(x, z1))
g_{g_2,f_2}(f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1), z10) → g_{g_2,f_2}(f_{g_2,s_1}(x, z1), z10)
g_{g_2,f_2}(z00, f_{f_2,s_1}(f_{g_2,s_1}(x, y), z1)) → g_{g_2,f_2}(z00, f_{g_2,s_1}(x, z1))
g_{s_1,g_2}(f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{s_1,g_2}(f_{g_2,f_2}(x, z1), z10)
g_{s_1,g_2}(z00, f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → g_{s_1,g_2}(z00, f_{g_2,f_2}(x, z1))
s_{g_2}(f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → s_{g_2}(f_{g_2,f_2}(x, z1))
g_{f_2,g_2}(f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{f_2,g_2}(f_{g_2,f_2}(x, z1), z10)
g_{f_2,g_2}(z00, f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → g_{f_2,g_2}(z00, f_{g_2,f_2}(x, z1))
f_{g_2,g_2}(f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{g_2,g_2}(f_{g_2,f_2}(x, z1), z10)
f_{g_2,g_2}(z00, f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → f_{g_2,g_2}(z00, f_{g_2,f_2}(x, z1))
g_{s_1,s_1}(f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{s_1,s_1}(f_{g_2,f_2}(x, z1), z10)
g_{s_1,s_1}(z00, f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → g_{s_1,s_1}(z00, f_{g_2,f_2}(x, z1))
g_{f_2,s_1}(f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{f_2,s_1}(f_{g_2,f_2}(x, z1), z10)
g_{f_2,s_1}(z00, f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → g_{f_2,s_1}(z00, f_{g_2,f_2}(x, z1))
f_{g_2,s_1}(f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{g_2,s_1}(f_{g_2,f_2}(x, z1), z10)
f_{g_2,s_1}(z00, f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → f_{g_2,s_1}(z00, f_{g_2,f_2}(x, z1))
g_{s_1,f_2}(f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{s_1,f_2}(f_{g_2,f_2}(x, z1), z10)
g_{s_1,f_2}(z00, f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → g_{s_1,f_2}(z00, f_{g_2,f_2}(x, z1))
g_{f_2,f_2}(f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{f_2,f_2}(f_{g_2,f_2}(x, z1), z10)
g_{f_2,f_2}(z00, f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → g_{f_2,f_2}(z00, f_{g_2,f_2}(x, z1))
f_{g_2,f_2}(f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{g_2,f_2}(f_{g_2,f_2}(x, z1), z10)
f_{g_2,f_2}(z00, f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → f_{g_2,f_2}(z00, f_{g_2,f_2}(x, z1))
s_{s_1}(f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → s_{s_1}(f_{g_2,f_2}(x, z1))
f_{s_1,g_2}(f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{s_1,g_2}(f_{g_2,f_2}(x, z1), z10)
f_{s_1,g_2}(z00, f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → f_{s_1,g_2}(z00, f_{g_2,f_2}(x, z1))
f_{s_1,s_1}(f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{s_1,s_1}(f_{g_2,f_2}(x, z1), z10)
f_{s_1,s_1}(z00, f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → f_{s_1,s_1}(z00, f_{g_2,f_2}(x, z1))
f_{s_1,f_2}(f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{s_1,f_2}(f_{g_2,f_2}(x, z1), z10)
f_{s_1,f_2}(z00, f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → f_{s_1,f_2}(z00, f_{g_2,f_2}(x, z1))
s_{f_2}(f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → s_{f_2}(f_{g_2,f_2}(x, z1))
f_{f_2,g_2}(f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{f_2,g_2}(f_{g_2,f_2}(x, z1), z10)
f_{f_2,g_2}(z00, f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → f_{f_2,g_2}(z00, f_{g_2,f_2}(x, z1))
f_{f_2,s_1}(f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{f_2,s_1}(f_{g_2,f_2}(x, z1), z10)
f_{f_2,s_1}(z00, f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → f_{f_2,s_1}(z00, f_{g_2,f_2}(x, z1))
f_{f_2,f_2}(f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → f_{f_2,f_2}(f_{g_2,f_2}(x, z1), z10)
f_{f_2,f_2}(z00, f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → f_{f_2,f_2}(z00, f_{g_2,f_2}(x, z1))
g_{g_2,g_2}(f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{g_2,g_2}(f_{g_2,f_2}(x, z1), z10)
g_{g_2,g_2}(z00, f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → g_{g_2,g_2}(z00, f_{g_2,f_2}(x, z1))
g_{g_2,s_1}(f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{g_2,s_1}(f_{g_2,f_2}(x, z1), z10)
g_{g_2,s_1}(z00, f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → g_{g_2,s_1}(z00, f_{g_2,f_2}(x, z1))
g_{g_2,f_2}(f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1), z10) → g_{g_2,f_2}(f_{g_2,f_2}(x, z1), z10)
g_{g_2,f_2}(z00, f_{f_2,f_2}(f_{g_2,s_1}(x, y), z1)) → g_{g_2,f_2}(z00, f_{g_2,f_2}(x, z1))
g_{s_1,g_2}(f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{s_1,g_2}(f_{g_2,g_2}(x, z1), z10)
g_{s_1,g_2}(z00, f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → g_{s_1,g_2}(z00, f_{g_2,g_2}(x, z1))
s_{g_2}(f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → s_{g_2}(f_{g_2,g_2}(x, z1))
g_{f_2,g_2}(f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{f_2,g_2}(f_{g_2,g_2}(x, z1), z10)
g_{f_2,g_2}(z00, f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → g_{f_2,g_2}(z00, f_{g_2,g_2}(x, z1))
f_{g_2,g_2}(f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{g_2,g_2}(f_{g_2,g_2}(x, z1), z10)
f_{g_2,g_2}(z00, f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → f_{g_2,g_2}(z00, f_{g_2,g_2}(x, z1))
g_{s_1,s_1}(f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{s_1,s_1}(f_{g_2,g_2}(x, z1), z10)
g_{s_1,s_1}(z00, f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → g_{s_1,s_1}(z00, f_{g_2,g_2}(x, z1))
g_{f_2,s_1}(f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{f_2,s_1}(f_{g_2,g_2}(x, z1), z10)
g_{f_2,s_1}(z00, f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → g_{f_2,s_1}(z00, f_{g_2,g_2}(x, z1))
f_{g_2,s_1}(f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{g_2,s_1}(f_{g_2,g_2}(x, z1), z10)
f_{g_2,s_1}(z00, f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → f_{g_2,s_1}(z00, f_{g_2,g_2}(x, z1))
g_{s_1,f_2}(f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{s_1,f_2}(f_{g_2,g_2}(x, z1), z10)
g_{s_1,f_2}(z00, f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → g_{s_1,f_2}(z00, f_{g_2,g_2}(x, z1))
g_{f_2,f_2}(f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{f_2,f_2}(f_{g_2,g_2}(x, z1), z10)
g_{f_2,f_2}(z00, f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → g_{f_2,f_2}(z00, f_{g_2,g_2}(x, z1))
f_{g_2,f_2}(f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{g_2,f_2}(f_{g_2,g_2}(x, z1), z10)
f_{g_2,f_2}(z00, f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → f_{g_2,f_2}(z00, f_{g_2,g_2}(x, z1))
s_{s_1}(f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → s_{s_1}(f_{g_2,g_2}(x, z1))
f_{s_1,g_2}(f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{s_1,g_2}(f_{g_2,g_2}(x, z1), z10)
f_{s_1,g_2}(z00, f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → f_{s_1,g_2}(z00, f_{g_2,g_2}(x, z1))
f_{s_1,s_1}(f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{s_1,s_1}(f_{g_2,g_2}(x, z1), z10)
f_{s_1,s_1}(z00, f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → f_{s_1,s_1}(z00, f_{g_2,g_2}(x, z1))
f_{s_1,f_2}(f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{s_1,f_2}(f_{g_2,g_2}(x, z1), z10)
f_{s_1,f_2}(z00, f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → f_{s_1,f_2}(z00, f_{g_2,g_2}(x, z1))
s_{f_2}(f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → s_{f_2}(f_{g_2,g_2}(x, z1))
f_{f_2,g_2}(f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{f_2,g_2}(f_{g_2,g_2}(x, z1), z10)
f_{f_2,g_2}(z00, f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → f_{f_2,g_2}(z00, f_{g_2,g_2}(x, z1))
f_{f_2,s_1}(f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{f_2,s_1}(f_{g_2,g_2}(x, z1), z10)
f_{f_2,s_1}(z00, f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → f_{f_2,s_1}(z00, f_{g_2,g_2}(x, z1))
f_{f_2,f_2}(f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{f_2,f_2}(f_{g_2,g_2}(x, z1), z10)
f_{f_2,f_2}(z00, f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → f_{f_2,f_2}(z00, f_{g_2,g_2}(x, z1))
g_{g_2,g_2}(f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{g_2,g_2}(f_{g_2,g_2}(x, z1), z10)
g_{g_2,g_2}(z00, f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → g_{g_2,g_2}(z00, f_{g_2,g_2}(x, z1))
g_{g_2,s_1}(f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{g_2,s_1}(f_{g_2,g_2}(x, z1), z10)
g_{g_2,s_1}(z00, f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → g_{g_2,s_1}(z00, f_{g_2,g_2}(x, z1))
g_{g_2,f_2}(f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{g_2,f_2}(f_{g_2,g_2}(x, z1), z10)
g_{g_2,f_2}(z00, f_{f_2,g_2}(f_{g_2,f_2}(x, y), z1)) → g_{g_2,f_2}(z00, f_{g_2,g_2}(x, z1))
g_{s_1,g_2}(f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → g_{s_1,g_2}(f_{g_2,s_1}(x, z1), z10)
g_{s_1,g_2}(z00, f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → g_{s_1,g_2}(z00, f_{g_2,s_1}(x, z1))
s_{g_2}(f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → s_{g_2}(f_{g_2,s_1}(x, z1))
g_{f_2,g_2}(f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → g_{f_2,g_2}(f_{g_2,s_1}(x, z1), z10)
g_{f_2,g_2}(z00, f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → g_{f_2,g_2}(z00, f_{g_2,s_1}(x, z1))
f_{g_2,g_2}(f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → f_{g_2,g_2}(f_{g_2,s_1}(x, z1), z10)
f_{g_2,g_2}(z00, f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → f_{g_2,g_2}(z00, f_{g_2,s_1}(x, z1))
g_{s_1,s_1}(f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → g_{s_1,s_1}(f_{g_2,s_1}(x, z1), z10)
g_{s_1,s_1}(z00, f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → g_{s_1,s_1}(z00, f_{g_2,s_1}(x, z1))
g_{f_2,s_1}(f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → g_{f_2,s_1}(f_{g_2,s_1}(x, z1), z10)
g_{f_2,s_1}(z00, f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → g_{f_2,s_1}(z00, f_{g_2,s_1}(x, z1))
f_{g_2,s_1}(f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → f_{g_2,s_1}(f_{g_2,s_1}(x, z1), z10)
f_{g_2,s_1}(z00, f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → f_{g_2,s_1}(z00, f_{g_2,s_1}(x, z1))
g_{s_1,f_2}(f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → g_{s_1,f_2}(f_{g_2,s_1}(x, z1), z10)
g_{s_1,f_2}(z00, f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → g_{s_1,f_2}(z00, f_{g_2,s_1}(x, z1))
g_{f_2,f_2}(f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → g_{f_2,f_2}(f_{g_2,s_1}(x, z1), z10)
g_{f_2,f_2}(z00, f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → g_{f_2,f_2}(z00, f_{g_2,s_1}(x, z1))
f_{g_2,f_2}(f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → f_{g_2,f_2}(f_{g_2,s_1}(x, z1), z10)
f_{g_2,f_2}(z00, f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → f_{g_2,f_2}(z00, f_{g_2,s_1}(x, z1))
s_{s_1}(f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → s_{s_1}(f_{g_2,s_1}(x, z1))
f_{s_1,g_2}(f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → f_{s_1,g_2}(f_{g_2,s_1}(x, z1), z10)
f_{s_1,g_2}(z00, f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → f_{s_1,g_2}(z00, f_{g_2,s_1}(x, z1))
f_{s_1,s_1}(f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → f_{s_1,s_1}(f_{g_2,s_1}(x, z1), z10)
f_{s_1,s_1}(z00, f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → f_{s_1,s_1}(z00, f_{g_2,s_1}(x, z1))
f_{s_1,f_2}(f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → f_{s_1,f_2}(f_{g_2,s_1}(x, z1), z10)
f_{s_1,f_2}(z00, f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → f_{s_1,f_2}(z00, f_{g_2,s_1}(x, z1))
s_{f_2}(f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → s_{f_2}(f_{g_2,s_1}(x, z1))
f_{f_2,g_2}(f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → f_{f_2,g_2}(f_{g_2,s_1}(x, z1), z10)
f_{f_2,g_2}(z00, f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → f_{f_2,g_2}(z00, f_{g_2,s_1}(x, z1))
f_{f_2,s_1}(f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → f_{f_2,s_1}(f_{g_2,s_1}(x, z1), z10)
f_{f_2,s_1}(z00, f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → f_{f_2,s_1}(z00, f_{g_2,s_1}(x, z1))
f_{f_2,f_2}(f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → f_{f_2,f_2}(f_{g_2,s_1}(x, z1), z10)
f_{f_2,f_2}(z00, f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → f_{f_2,f_2}(z00, f_{g_2,s_1}(x, z1))
g_{g_2,g_2}(f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → g_{g_2,g_2}(f_{g_2,s_1}(x, z1), z10)
g_{g_2,g_2}(z00, f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → g_{g_2,g_2}(z00, f_{g_2,s_1}(x, z1))
g_{g_2,s_1}(f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → g_{g_2,s_1}(f_{g_2,s_1}(x, z1), z10)
g_{g_2,s_1}(z00, f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → g_{g_2,s_1}(z00, f_{g_2,s_1}(x, z1))
g_{g_2,f_2}(f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1), z10) → g_{g_2,f_2}(f_{g_2,s_1}(x, z1), z10)
g_{g_2,f_2}(z00, f_{f_2,s_1}(f_{g_2,f_2}(x, y), z1)) → g_{g_2,f_2}(z00, f_{g_2,s_1}(x, z1))
g_{s_1,g_2}(f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{s_1,g_2}(f_{g_2,f_2}(x, z1), z10)
g_{s_1,g_2}(z00, f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → g_{s_1,g_2}(z00, f_{g_2,f_2}(x, z1))
s_{g_2}(f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → s_{g_2}(f_{g_2,f_2}(x, z1))
g_{f_2,g_2}(f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{f_2,g_2}(f_{g_2,f_2}(x, z1), z10)
g_{f_2,g_2}(z00, f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → g_{f_2,g_2}(z00, f_{g_2,f_2}(x, z1))
f_{g_2,g_2}(f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{g_2,g_2}(f_{g_2,f_2}(x, z1), z10)
f_{g_2,g_2}(z00, f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → f_{g_2,g_2}(z00, f_{g_2,f_2}(x, z1))
g_{s_1,s_1}(f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{s_1,s_1}(f_{g_2,f_2}(x, z1), z10)
g_{s_1,s_1}(z00, f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → g_{s_1,s_1}(z00, f_{g_2,f_2}(x, z1))
g_{f_2,s_1}(f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{f_2,s_1}(f_{g_2,f_2}(x, z1), z10)
g_{f_2,s_1}(z00, f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → g_{f_2,s_1}(z00, f_{g_2,f_2}(x, z1))
f_{g_2,s_1}(f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{g_2,s_1}(f_{g_2,f_2}(x, z1), z10)
f_{g_2,s_1}(z00, f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → f_{g_2,s_1}(z00, f_{g_2,f_2}(x, z1))
g_{s_1,f_2}(f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{s_1,f_2}(f_{g_2,f_2}(x, z1), z10)
g_{s_1,f_2}(z00, f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → g_{s_1,f_2}(z00, f_{g_2,f_2}(x, z1))
g_{f_2,f_2}(f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{f_2,f_2}(f_{g_2,f_2}(x, z1), z10)
g_{f_2,f_2}(z00, f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → g_{f_2,f_2}(z00, f_{g_2,f_2}(x, z1))
f_{g_2,f_2}(f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{g_2,f_2}(f_{g_2,f_2}(x, z1), z10)
f_{g_2,f_2}(z00, f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → f_{g_2,f_2}(z00, f_{g_2,f_2}(x, z1))
s_{s_1}(f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → s_{s_1}(f_{g_2,f_2}(x, z1))
f_{s_1,g_2}(f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{s_1,g_2}(f_{g_2,f_2}(x, z1), z10)
f_{s_1,g_2}(z00, f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → f_{s_1,g_2}(z00, f_{g_2,f_2}(x, z1))
f_{s_1,s_1}(f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{s_1,s_1}(f_{g_2,f_2}(x, z1), z10)
f_{s_1,s_1}(z00, f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → f_{s_1,s_1}(z00, f_{g_2,f_2}(x, z1))
f_{s_1,f_2}(f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{s_1,f_2}(f_{g_2,f_2}(x, z1), z10)
f_{s_1,f_2}(z00, f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → f_{s_1,f_2}(z00, f_{g_2,f_2}(x, z1))
s_{f_2}(f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → s_{f_2}(f_{g_2,f_2}(x, z1))
f_{f_2,g_2}(f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{f_2,g_2}(f_{g_2,f_2}(x, z1), z10)
f_{f_2,g_2}(z00, f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → f_{f_2,g_2}(z00, f_{g_2,f_2}(x, z1))
f_{f_2,s_1}(f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{f_2,s_1}(f_{g_2,f_2}(x, z1), z10)
f_{f_2,s_1}(z00, f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → f_{f_2,s_1}(z00, f_{g_2,f_2}(x, z1))
f_{f_2,f_2}(f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → f_{f_2,f_2}(f_{g_2,f_2}(x, z1), z10)
f_{f_2,f_2}(z00, f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → f_{f_2,f_2}(z00, f_{g_2,f_2}(x, z1))
g_{g_2,g_2}(f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{g_2,g_2}(f_{g_2,f_2}(x, z1), z10)
g_{g_2,g_2}(z00, f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → g_{g_2,g_2}(z00, f_{g_2,f_2}(x, z1))
g_{g_2,s_1}(f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{g_2,s_1}(f_{g_2,f_2}(x, z1), z10)
g_{g_2,s_1}(z00, f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → g_{g_2,s_1}(z00, f_{g_2,f_2}(x, z1))
g_{g_2,f_2}(f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1), z10) → g_{g_2,f_2}(f_{g_2,f_2}(x, z1), z10)
g_{g_2,f_2}(z00, f_{f_2,f_2}(f_{g_2,f_2}(x, y), z1)) → g_{g_2,f_2}(z00, f_{g_2,f_2}(x, z1))
g_{s_1,g_2}(f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{s_1,g_2}(f_{s_1,g_2}(x, z1), z10)
g_{s_1,g_2}(z00, f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → g_{s_1,g_2}(z00, f_{s_1,g_2}(x, z1))
s_{g_2}(f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → s_{g_2}(f_{s_1,g_2}(x, z1))
g_{f_2,g_2}(f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{f_2,g_2}(f_{s_1,g_2}(x, z1), z10)
g_{f_2,g_2}(z00, f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → g_{f_2,g_2}(z00, f_{s_1,g_2}(x, z1))
f_{g_2,g_2}(f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{g_2,g_2}(f_{s_1,g_2}(x, z1), z10)
f_{g_2,g_2}(z00, f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → f_{g_2,g_2}(z00, f_{s_1,g_2}(x, z1))
g_{s_1,s_1}(f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{s_1,s_1}(f_{s_1,g_2}(x, z1), z10)
g_{s_1,s_1}(z00, f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → g_{s_1,s_1}(z00, f_{s_1,g_2}(x, z1))
g_{f_2,s_1}(f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{f_2,s_1}(f_{s_1,g_2}(x, z1), z10)
g_{f_2,s_1}(z00, f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → g_{f_2,s_1}(z00, f_{s_1,g_2}(x, z1))
f_{g_2,s_1}(f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{g_2,s_1}(f_{s_1,g_2}(x, z1), z10)
f_{g_2,s_1}(z00, f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → f_{g_2,s_1}(z00, f_{s_1,g_2}(x, z1))
g_{s_1,f_2}(f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{s_1,f_2}(f_{s_1,g_2}(x, z1), z10)
g_{s_1,f_2}(z00, f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → g_{s_1,f_2}(z00, f_{s_1,g_2}(x, z1))
g_{f_2,f_2}(f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{f_2,f_2}(f_{s_1,g_2}(x, z1), z10)
g_{f_2,f_2}(z00, f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → g_{f_2,f_2}(z00, f_{s_1,g_2}(x, z1))
f_{g_2,f_2}(f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{g_2,f_2}(f_{s_1,g_2}(x, z1), z10)
f_{g_2,f_2}(z00, f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → f_{g_2,f_2}(z00, f_{s_1,g_2}(x, z1))
s_{s_1}(f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → s_{s_1}(f_{s_1,g_2}(x, z1))
f_{s_1,g_2}(f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{s_1,g_2}(f_{s_1,g_2}(x, z1), z10)
f_{s_1,g_2}(z00, f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → f_{s_1,g_2}(z00, f_{s_1,g_2}(x, z1))
f_{s_1,s_1}(f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{s_1,s_1}(f_{s_1,g_2}(x, z1), z10)
f_{s_1,s_1}(z00, f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → f_{s_1,s_1}(z00, f_{s_1,g_2}(x, z1))
f_{s_1,f_2}(f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{s_1,f_2}(f_{s_1,g_2}(x, z1), z10)
f_{s_1,f_2}(z00, f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → f_{s_1,f_2}(z00, f_{s_1,g_2}(x, z1))
s_{f_2}(f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → s_{f_2}(f_{s_1,g_2}(x, z1))
f_{f_2,g_2}(f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{f_2,g_2}(f_{s_1,g_2}(x, z1), z10)
f_{f_2,g_2}(z00, f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → f_{f_2,g_2}(z00, f_{s_1,g_2}(x, z1))
f_{f_2,s_1}(f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{f_2,s_1}(f_{s_1,g_2}(x, z1), z10)
f_{f_2,s_1}(z00, f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → f_{f_2,s_1}(z00, f_{s_1,g_2}(x, z1))
f_{f_2,f_2}(f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{f_2,f_2}(f_{s_1,g_2}(x, z1), z10)
f_{f_2,f_2}(z00, f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → f_{f_2,f_2}(z00, f_{s_1,g_2}(x, z1))
g_{g_2,g_2}(f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{g_2,g_2}(f_{s_1,g_2}(x, z1), z10)
g_{g_2,g_2}(z00, f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → g_{g_2,g_2}(z00, f_{s_1,g_2}(x, z1))
g_{g_2,s_1}(f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{g_2,s_1}(f_{s_1,g_2}(x, z1), z10)
g_{g_2,s_1}(z00, f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → g_{g_2,s_1}(z00, f_{s_1,g_2}(x, z1))
g_{g_2,f_2}(f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{g_2,f_2}(f_{s_1,g_2}(x, z1), z10)
g_{g_2,f_2}(z00, f_{f_2,g_2}(f_{s_1,g_2}(x, y), z1)) → g_{g_2,f_2}(z00, f_{s_1,g_2}(x, z1))
g_{s_1,g_2}(f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → g_{s_1,g_2}(f_{s_1,s_1}(x, z1), z10)
g_{s_1,g_2}(z00, f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → g_{s_1,g_2}(z00, f_{s_1,s_1}(x, z1))
s_{g_2}(f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → s_{g_2}(f_{s_1,s_1}(x, z1))
g_{f_2,g_2}(f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → g_{f_2,g_2}(f_{s_1,s_1}(x, z1), z10)
g_{f_2,g_2}(z00, f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → g_{f_2,g_2}(z00, f_{s_1,s_1}(x, z1))
f_{g_2,g_2}(f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → f_{g_2,g_2}(f_{s_1,s_1}(x, z1), z10)
f_{g_2,g_2}(z00, f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → f_{g_2,g_2}(z00, f_{s_1,s_1}(x, z1))
g_{s_1,s_1}(f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → g_{s_1,s_1}(f_{s_1,s_1}(x, z1), z10)
g_{s_1,s_1}(z00, f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → g_{s_1,s_1}(z00, f_{s_1,s_1}(x, z1))
g_{f_2,s_1}(f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → g_{f_2,s_1}(f_{s_1,s_1}(x, z1), z10)
g_{f_2,s_1}(z00, f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → g_{f_2,s_1}(z00, f_{s_1,s_1}(x, z1))
f_{g_2,s_1}(f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → f_{g_2,s_1}(f_{s_1,s_1}(x, z1), z10)
f_{g_2,s_1}(z00, f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → f_{g_2,s_1}(z00, f_{s_1,s_1}(x, z1))
g_{s_1,f_2}(f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → g_{s_1,f_2}(f_{s_1,s_1}(x, z1), z10)
g_{s_1,f_2}(z00, f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → g_{s_1,f_2}(z00, f_{s_1,s_1}(x, z1))
g_{f_2,f_2}(f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → g_{f_2,f_2}(f_{s_1,s_1}(x, z1), z10)
g_{f_2,f_2}(z00, f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → g_{f_2,f_2}(z00, f_{s_1,s_1}(x, z1))
f_{g_2,f_2}(f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → f_{g_2,f_2}(f_{s_1,s_1}(x, z1), z10)
f_{g_2,f_2}(z00, f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → f_{g_2,f_2}(z00, f_{s_1,s_1}(x, z1))
s_{s_1}(f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → s_{s_1}(f_{s_1,s_1}(x, z1))
f_{s_1,g_2}(f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → f_{s_1,g_2}(f_{s_1,s_1}(x, z1), z10)
f_{s_1,g_2}(z00, f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → f_{s_1,g_2}(z00, f_{s_1,s_1}(x, z1))
f_{s_1,s_1}(f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → f_{s_1,s_1}(f_{s_1,s_1}(x, z1), z10)
f_{s_1,s_1}(z00, f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → f_{s_1,s_1}(z00, f_{s_1,s_1}(x, z1))
f_{s_1,f_2}(f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → f_{s_1,f_2}(f_{s_1,s_1}(x, z1), z10)
f_{s_1,f_2}(z00, f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → f_{s_1,f_2}(z00, f_{s_1,s_1}(x, z1))
s_{f_2}(f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → s_{f_2}(f_{s_1,s_1}(x, z1))
f_{f_2,g_2}(f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → f_{f_2,g_2}(f_{s_1,s_1}(x, z1), z10)
f_{f_2,g_2}(z00, f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → f_{f_2,g_2}(z00, f_{s_1,s_1}(x, z1))
f_{f_2,s_1}(f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → f_{f_2,s_1}(f_{s_1,s_1}(x, z1), z10)
f_{f_2,s_1}(z00, f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → f_{f_2,s_1}(z00, f_{s_1,s_1}(x, z1))
f_{f_2,f_2}(f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → f_{f_2,f_2}(f_{s_1,s_1}(x, z1), z10)
f_{f_2,f_2}(z00, f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → f_{f_2,f_2}(z00, f_{s_1,s_1}(x, z1))
g_{g_2,g_2}(f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → g_{g_2,g_2}(f_{s_1,s_1}(x, z1), z10)
g_{g_2,g_2}(z00, f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → g_{g_2,g_2}(z00, f_{s_1,s_1}(x, z1))
g_{g_2,s_1}(f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → g_{g_2,s_1}(f_{s_1,s_1}(x, z1), z10)
g_{g_2,s_1}(z00, f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → g_{g_2,s_1}(z00, f_{s_1,s_1}(x, z1))
g_{g_2,f_2}(f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1), z10) → g_{g_2,f_2}(f_{s_1,s_1}(x, z1), z10)
g_{g_2,f_2}(z00, f_{f_2,s_1}(f_{s_1,g_2}(x, y), z1)) → g_{g_2,f_2}(z00, f_{s_1,s_1}(x, z1))
g_{s_1,g_2}(f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{s_1,g_2}(f_{s_1,f_2}(x, z1), z10)
g_{s_1,g_2}(z00, f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → g_{s_1,g_2}(z00, f_{s_1,f_2}(x, z1))
s_{g_2}(f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → s_{g_2}(f_{s_1,f_2}(x, z1))
g_{f_2,g_2}(f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{f_2,g_2}(f_{s_1,f_2}(x, z1), z10)
g_{f_2,g_2}(z00, f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → g_{f_2,g_2}(z00, f_{s_1,f_2}(x, z1))
f_{g_2,g_2}(f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{g_2,g_2}(f_{s_1,f_2}(x, z1), z10)
f_{g_2,g_2}(z00, f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → f_{g_2,g_2}(z00, f_{s_1,f_2}(x, z1))
g_{s_1,s_1}(f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{s_1,s_1}(f_{s_1,f_2}(x, z1), z10)
g_{s_1,s_1}(z00, f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → g_{s_1,s_1}(z00, f_{s_1,f_2}(x, z1))
g_{f_2,s_1}(f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{f_2,s_1}(f_{s_1,f_2}(x, z1), z10)
g_{f_2,s_1}(z00, f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → g_{f_2,s_1}(z00, f_{s_1,f_2}(x, z1))
f_{g_2,s_1}(f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{g_2,s_1}(f_{s_1,f_2}(x, z1), z10)
f_{g_2,s_1}(z00, f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → f_{g_2,s_1}(z00, f_{s_1,f_2}(x, z1))
g_{s_1,f_2}(f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{s_1,f_2}(f_{s_1,f_2}(x, z1), z10)
g_{s_1,f_2}(z00, f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → g_{s_1,f_2}(z00, f_{s_1,f_2}(x, z1))
g_{f_2,f_2}(f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{f_2,f_2}(f_{s_1,f_2}(x, z1), z10)
g_{f_2,f_2}(z00, f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → g_{f_2,f_2}(z00, f_{s_1,f_2}(x, z1))
f_{g_2,f_2}(f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{g_2,f_2}(f_{s_1,f_2}(x, z1), z10)
f_{g_2,f_2}(z00, f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → f_{g_2,f_2}(z00, f_{s_1,f_2}(x, z1))
s_{s_1}(f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → s_{s_1}(f_{s_1,f_2}(x, z1))
f_{s_1,g_2}(f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{s_1,g_2}(f_{s_1,f_2}(x, z1), z10)
f_{s_1,g_2}(z00, f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → f_{s_1,g_2}(z00, f_{s_1,f_2}(x, z1))
f_{s_1,s_1}(f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{s_1,s_1}(f_{s_1,f_2}(x, z1), z10)
f_{s_1,s_1}(z00, f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → f_{s_1,s_1}(z00, f_{s_1,f_2}(x, z1))
f_{s_1,f_2}(f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{s_1,f_2}(f_{s_1,f_2}(x, z1), z10)
f_{s_1,f_2}(z00, f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → f_{s_1,f_2}(z00, f_{s_1,f_2}(x, z1))
s_{f_2}(f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → s_{f_2}(f_{s_1,f_2}(x, z1))
f_{f_2,g_2}(f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{f_2,g_2}(f_{s_1,f_2}(x, z1), z10)
f_{f_2,g_2}(z00, f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → f_{f_2,g_2}(z00, f_{s_1,f_2}(x, z1))
f_{f_2,s_1}(f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{f_2,s_1}(f_{s_1,f_2}(x, z1), z10)
f_{f_2,s_1}(z00, f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → f_{f_2,s_1}(z00, f_{s_1,f_2}(x, z1))
f_{f_2,f_2}(f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → f_{f_2,f_2}(f_{s_1,f_2}(x, z1), z10)
f_{f_2,f_2}(z00, f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → f_{f_2,f_2}(z00, f_{s_1,f_2}(x, z1))
g_{g_2,g_2}(f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{g_2,g_2}(f_{s_1,f_2}(x, z1), z10)
g_{g_2,g_2}(z00, f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → g_{g_2,g_2}(z00, f_{s_1,f_2}(x, z1))
g_{g_2,s_1}(f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{g_2,s_1}(f_{s_1,f_2}(x, z1), z10)
g_{g_2,s_1}(z00, f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → g_{g_2,s_1}(z00, f_{s_1,f_2}(x, z1))
g_{g_2,f_2}(f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1), z10) → g_{g_2,f_2}(f_{s_1,f_2}(x, z1), z10)
g_{g_2,f_2}(z00, f_{f_2,f_2}(f_{s_1,g_2}(x, y), z1)) → g_{g_2,f_2}(z00, f_{s_1,f_2}(x, z1))
g_{s_1,g_2}(f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{s_1,g_2}(f_{s_1,g_2}(x, z1), z10)
g_{s_1,g_2}(z00, f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → g_{s_1,g_2}(z00, f_{s_1,g_2}(x, z1))
s_{g_2}(f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → s_{g_2}(f_{s_1,g_2}(x, z1))
g_{f_2,g_2}(f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{f_2,g_2}(f_{s_1,g_2}(x, z1), z10)
g_{f_2,g_2}(z00, f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → g_{f_2,g_2}(z00, f_{s_1,g_2}(x, z1))
f_{g_2,g_2}(f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{g_2,g_2}(f_{s_1,g_2}(x, z1), z10)
f_{g_2,g_2}(z00, f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → f_{g_2,g_2}(z00, f_{s_1,g_2}(x, z1))
g_{s_1,s_1}(f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{s_1,s_1}(f_{s_1,g_2}(x, z1), z10)
g_{s_1,s_1}(z00, f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → g_{s_1,s_1}(z00, f_{s_1,g_2}(x, z1))
g_{f_2,s_1}(f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{f_2,s_1}(f_{s_1,g_2}(x, z1), z10)
g_{f_2,s_1}(z00, f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → g_{f_2,s_1}(z00, f_{s_1,g_2}(x, z1))
f_{g_2,s_1}(f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{g_2,s_1}(f_{s_1,g_2}(x, z1), z10)
f_{g_2,s_1}(z00, f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → f_{g_2,s_1}(z00, f_{s_1,g_2}(x, z1))
g_{s_1,f_2}(f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{s_1,f_2}(f_{s_1,g_2}(x, z1), z10)
g_{s_1,f_2}(z00, f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → g_{s_1,f_2}(z00, f_{s_1,g_2}(x, z1))
g_{f_2,f_2}(f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{f_2,f_2}(f_{s_1,g_2}(x, z1), z10)
g_{f_2,f_2}(z00, f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → g_{f_2,f_2}(z00, f_{s_1,g_2}(x, z1))
f_{g_2,f_2}(f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{g_2,f_2}(f_{s_1,g_2}(x, z1), z10)
f_{g_2,f_2}(z00, f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → f_{g_2,f_2}(z00, f_{s_1,g_2}(x, z1))
s_{s_1}(f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → s_{s_1}(f_{s_1,g_2}(x, z1))
f_{s_1,g_2}(f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{s_1,g_2}(f_{s_1,g_2}(x, z1), z10)
f_{s_1,g_2}(z00, f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → f_{s_1,g_2}(z00, f_{s_1,g_2}(x, z1))
f_{s_1,s_1}(f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{s_1,s_1}(f_{s_1,g_2}(x, z1), z10)
f_{s_1,s_1}(z00, f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → f_{s_1,s_1}(z00, f_{s_1,g_2}(x, z1))
f_{s_1,f_2}(f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{s_1,f_2}(f_{s_1,g_2}(x, z1), z10)
f_{s_1,f_2}(z00, f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → f_{s_1,f_2}(z00, f_{s_1,g_2}(x, z1))
s_{f_2}(f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → s_{f_2}(f_{s_1,g_2}(x, z1))
f_{f_2,g_2}(f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{f_2,g_2}(f_{s_1,g_2}(x, z1), z10)
f_{f_2,g_2}(z00, f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → f_{f_2,g_2}(z00, f_{s_1,g_2}(x, z1))
f_{f_2,s_1}(f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{f_2,s_1}(f_{s_1,g_2}(x, z1), z10)
f_{f_2,s_1}(z00, f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → f_{f_2,s_1}(z00, f_{s_1,g_2}(x, z1))
f_{f_2,f_2}(f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{f_2,f_2}(f_{s_1,g_2}(x, z1), z10)
f_{f_2,f_2}(z00, f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → f_{f_2,f_2}(z00, f_{s_1,g_2}(x, z1))
g_{g_2,g_2}(f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{g_2,g_2}(f_{s_1,g_2}(x, z1), z10)
g_{g_2,g_2}(z00, f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → g_{g_2,g_2}(z00, f_{s_1,g_2}(x, z1))
g_{g_2,s_1}(f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{g_2,s_1}(f_{s_1,g_2}(x, z1), z10)
g_{g_2,s_1}(z00, f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → g_{g_2,s_1}(z00, f_{s_1,g_2}(x, z1))
g_{g_2,f_2}(f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{g_2,f_2}(f_{s_1,g_2}(x, z1), z10)
g_{g_2,f_2}(z00, f_{f_2,g_2}(f_{s_1,s_1}(x, y), z1)) → g_{g_2,f_2}(z00, f_{s_1,g_2}(x, z1))
g_{s_1,g_2}(f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → g_{s_1,g_2}(f_{s_1,s_1}(x, z1), z10)
g_{s_1,g_2}(z00, f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → g_{s_1,g_2}(z00, f_{s_1,s_1}(x, z1))
s_{g_2}(f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → s_{g_2}(f_{s_1,s_1}(x, z1))
g_{f_2,g_2}(f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → g_{f_2,g_2}(f_{s_1,s_1}(x, z1), z10)
g_{f_2,g_2}(z00, f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → g_{f_2,g_2}(z00, f_{s_1,s_1}(x, z1))
f_{g_2,g_2}(f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → f_{g_2,g_2}(f_{s_1,s_1}(x, z1), z10)
f_{g_2,g_2}(z00, f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → f_{g_2,g_2}(z00, f_{s_1,s_1}(x, z1))
g_{s_1,s_1}(f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → g_{s_1,s_1}(f_{s_1,s_1}(x, z1), z10)
g_{s_1,s_1}(z00, f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → g_{s_1,s_1}(z00, f_{s_1,s_1}(x, z1))
g_{f_2,s_1}(f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → g_{f_2,s_1}(f_{s_1,s_1}(x, z1), z10)
g_{f_2,s_1}(z00, f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → g_{f_2,s_1}(z00, f_{s_1,s_1}(x, z1))
f_{g_2,s_1}(f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → f_{g_2,s_1}(f_{s_1,s_1}(x, z1), z10)
f_{g_2,s_1}(z00, f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → f_{g_2,s_1}(z00, f_{s_1,s_1}(x, z1))
g_{s_1,f_2}(f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → g_{s_1,f_2}(f_{s_1,s_1}(x, z1), z10)
g_{s_1,f_2}(z00, f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → g_{s_1,f_2}(z00, f_{s_1,s_1}(x, z1))
g_{f_2,f_2}(f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → g_{f_2,f_2}(f_{s_1,s_1}(x, z1), z10)
g_{f_2,f_2}(z00, f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → g_{f_2,f_2}(z00, f_{s_1,s_1}(x, z1))
f_{g_2,f_2}(f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → f_{g_2,f_2}(f_{s_1,s_1}(x, z1), z10)
f_{g_2,f_2}(z00, f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → f_{g_2,f_2}(z00, f_{s_1,s_1}(x, z1))
s_{s_1}(f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → s_{s_1}(f_{s_1,s_1}(x, z1))
f_{s_1,g_2}(f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → f_{s_1,g_2}(f_{s_1,s_1}(x, z1), z10)
f_{s_1,g_2}(z00, f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → f_{s_1,g_2}(z00, f_{s_1,s_1}(x, z1))
f_{s_1,s_1}(f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → f_{s_1,s_1}(f_{s_1,s_1}(x, z1), z10)
f_{s_1,s_1}(z00, f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → f_{s_1,s_1}(z00, f_{s_1,s_1}(x, z1))
f_{s_1,f_2}(f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → f_{s_1,f_2}(f_{s_1,s_1}(x, z1), z10)
f_{s_1,f_2}(z00, f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → f_{s_1,f_2}(z00, f_{s_1,s_1}(x, z1))
s_{f_2}(f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → s_{f_2}(f_{s_1,s_1}(x, z1))
f_{f_2,g_2}(f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → f_{f_2,g_2}(f_{s_1,s_1}(x, z1), z10)
f_{f_2,g_2}(z00, f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → f_{f_2,g_2}(z00, f_{s_1,s_1}(x, z1))
f_{f_2,s_1}(f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → f_{f_2,s_1}(f_{s_1,s_1}(x, z1), z10)
f_{f_2,s_1}(z00, f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → f_{f_2,s_1}(z00, f_{s_1,s_1}(x, z1))
f_{f_2,f_2}(f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → f_{f_2,f_2}(f_{s_1,s_1}(x, z1), z10)
f_{f_2,f_2}(z00, f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → f_{f_2,f_2}(z00, f_{s_1,s_1}(x, z1))
g_{g_2,g_2}(f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → g_{g_2,g_2}(f_{s_1,s_1}(x, z1), z10)
g_{g_2,g_2}(z00, f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → g_{g_2,g_2}(z00, f_{s_1,s_1}(x, z1))
g_{g_2,s_1}(f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → g_{g_2,s_1}(f_{s_1,s_1}(x, z1), z10)
g_{g_2,s_1}(z00, f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → g_{g_2,s_1}(z00, f_{s_1,s_1}(x, z1))
g_{g_2,f_2}(f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1), z10) → g_{g_2,f_2}(f_{s_1,s_1}(x, z1), z10)
g_{g_2,f_2}(z00, f_{f_2,s_1}(f_{s_1,s_1}(x, y), z1)) → g_{g_2,f_2}(z00, f_{s_1,s_1}(x, z1))
g_{s_1,g_2}(f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{s_1,g_2}(f_{s_1,f_2}(x, z1), z10)
g_{s_1,g_2}(z00, f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → g_{s_1,g_2}(z00, f_{s_1,f_2}(x, z1))
s_{g_2}(f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → s_{g_2}(f_{s_1,f_2}(x, z1))
g_{f_2,g_2}(f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{f_2,g_2}(f_{s_1,f_2}(x, z1), z10)
g_{f_2,g_2}(z00, f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → g_{f_2,g_2}(z00, f_{s_1,f_2}(x, z1))
f_{g_2,g_2}(f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{g_2,g_2}(f_{s_1,f_2}(x, z1), z10)
f_{g_2,g_2}(z00, f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → f_{g_2,g_2}(z00, f_{s_1,f_2}(x, z1))
g_{s_1,s_1}(f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{s_1,s_1}(f_{s_1,f_2}(x, z1), z10)
g_{s_1,s_1}(z00, f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → g_{s_1,s_1}(z00, f_{s_1,f_2}(x, z1))
g_{f_2,s_1}(f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{f_2,s_1}(f_{s_1,f_2}(x, z1), z10)
g_{f_2,s_1}(z00, f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → g_{f_2,s_1}(z00, f_{s_1,f_2}(x, z1))
f_{g_2,s_1}(f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{g_2,s_1}(f_{s_1,f_2}(x, z1), z10)
f_{g_2,s_1}(z00, f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → f_{g_2,s_1}(z00, f_{s_1,f_2}(x, z1))
g_{s_1,f_2}(f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{s_1,f_2}(f_{s_1,f_2}(x, z1), z10)
g_{s_1,f_2}(z00, f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → g_{s_1,f_2}(z00, f_{s_1,f_2}(x, z1))
g_{f_2,f_2}(f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{f_2,f_2}(f_{s_1,f_2}(x, z1), z10)
g_{f_2,f_2}(z00, f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → g_{f_2,f_2}(z00, f_{s_1,f_2}(x, z1))
f_{g_2,f_2}(f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{g_2,f_2}(f_{s_1,f_2}(x, z1), z10)
f_{g_2,f_2}(z00, f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → f_{g_2,f_2}(z00, f_{s_1,f_2}(x, z1))
s_{s_1}(f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → s_{s_1}(f_{s_1,f_2}(x, z1))
f_{s_1,g_2}(f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{s_1,g_2}(f_{s_1,f_2}(x, z1), z10)
f_{s_1,g_2}(z00, f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → f_{s_1,g_2}(z00, f_{s_1,f_2}(x, z1))
f_{s_1,s_1}(f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{s_1,s_1}(f_{s_1,f_2}(x, z1), z10)
f_{s_1,s_1}(z00, f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → f_{s_1,s_1}(z00, f_{s_1,f_2}(x, z1))
f_{s_1,f_2}(f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{s_1,f_2}(f_{s_1,f_2}(x, z1), z10)
f_{s_1,f_2}(z00, f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → f_{s_1,f_2}(z00, f_{s_1,f_2}(x, z1))
s_{f_2}(f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → s_{f_2}(f_{s_1,f_2}(x, z1))
f_{f_2,g_2}(f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{f_2,g_2}(f_{s_1,f_2}(x, z1), z10)
f_{f_2,g_2}(z00, f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → f_{f_2,g_2}(z00, f_{s_1,f_2}(x, z1))
f_{f_2,s_1}(f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{f_2,s_1}(f_{s_1,f_2}(x, z1), z10)
f_{f_2,s_1}(z00, f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → f_{f_2,s_1}(z00, f_{s_1,f_2}(x, z1))
f_{f_2,f_2}(f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → f_{f_2,f_2}(f_{s_1,f_2}(x, z1), z10)
f_{f_2,f_2}(z00, f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → f_{f_2,f_2}(z00, f_{s_1,f_2}(x, z1))
g_{g_2,g_2}(f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{g_2,g_2}(f_{s_1,f_2}(x, z1), z10)
g_{g_2,g_2}(z00, f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → g_{g_2,g_2}(z00, f_{s_1,f_2}(x, z1))
g_{g_2,s_1}(f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{g_2,s_1}(f_{s_1,f_2}(x, z1), z10)
g_{g_2,s_1}(z00, f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → g_{g_2,s_1}(z00, f_{s_1,f_2}(x, z1))
g_{g_2,f_2}(f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1), z10) → g_{g_2,f_2}(f_{s_1,f_2}(x, z1), z10)
g_{g_2,f_2}(z00, f_{f_2,f_2}(f_{s_1,s_1}(x, y), z1)) → g_{g_2,f_2}(z00, f_{s_1,f_2}(x, z1))
g_{s_1,g_2}(f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{s_1,g_2}(f_{s_1,g_2}(x, z1), z10)
g_{s_1,g_2}(z00, f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → g_{s_1,g_2}(z00, f_{s_1,g_2}(x, z1))
s_{g_2}(f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → s_{g_2}(f_{s_1,g_2}(x, z1))
g_{f_2,g_2}(f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{f_2,g_2}(f_{s_1,g_2}(x, z1), z10)
g_{f_2,g_2}(z00, f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → g_{f_2,g_2}(z00, f_{s_1,g_2}(x, z1))
f_{g_2,g_2}(f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{g_2,g_2}(f_{s_1,g_2}(x, z1), z10)
f_{g_2,g_2}(z00, f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → f_{g_2,g_2}(z00, f_{s_1,g_2}(x, z1))
g_{s_1,s_1}(f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{s_1,s_1}(f_{s_1,g_2}(x, z1), z10)
g_{s_1,s_1}(z00, f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → g_{s_1,s_1}(z00, f_{s_1,g_2}(x, z1))
g_{f_2,s_1}(f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{f_2,s_1}(f_{s_1,g_2}(x, z1), z10)
g_{f_2,s_1}(z00, f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → g_{f_2,s_1}(z00, f_{s_1,g_2}(x, z1))
f_{g_2,s_1}(f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{g_2,s_1}(f_{s_1,g_2}(x, z1), z10)
f_{g_2,s_1}(z00, f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → f_{g_2,s_1}(z00, f_{s_1,g_2}(x, z1))
g_{s_1,f_2}(f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{s_1,f_2}(f_{s_1,g_2}(x, z1), z10)
g_{s_1,f_2}(z00, f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → g_{s_1,f_2}(z00, f_{s_1,g_2}(x, z1))
g_{f_2,f_2}(f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{f_2,f_2}(f_{s_1,g_2}(x, z1), z10)
g_{f_2,f_2}(z00, f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → g_{f_2,f_2}(z00, f_{s_1,g_2}(x, z1))
f_{g_2,f_2}(f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{g_2,f_2}(f_{s_1,g_2}(x, z1), z10)
f_{g_2,f_2}(z00, f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → f_{g_2,f_2}(z00, f_{s_1,g_2}(x, z1))
s_{s_1}(f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → s_{s_1}(f_{s_1,g_2}(x, z1))
f_{s_1,g_2}(f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{s_1,g_2}(f_{s_1,g_2}(x, z1), z10)
f_{s_1,g_2}(z00, f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → f_{s_1,g_2}(z00, f_{s_1,g_2}(x, z1))
f_{s_1,s_1}(f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{s_1,s_1}(f_{s_1,g_2}(x, z1), z10)
f_{s_1,s_1}(z00, f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → f_{s_1,s_1}(z00, f_{s_1,g_2}(x, z1))
f_{s_1,f_2}(f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{s_1,f_2}(f_{s_1,g_2}(x, z1), z10)
f_{s_1,f_2}(z00, f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → f_{s_1,f_2}(z00, f_{s_1,g_2}(x, z1))
s_{f_2}(f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → s_{f_2}(f_{s_1,g_2}(x, z1))
f_{f_2,g_2}(f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{f_2,g_2}(f_{s_1,g_2}(x, z1), z10)
f_{f_2,g_2}(z00, f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → f_{f_2,g_2}(z00, f_{s_1,g_2}(x, z1))
f_{f_2,s_1}(f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{f_2,s_1}(f_{s_1,g_2}(x, z1), z10)
f_{f_2,s_1}(z00, f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → f_{f_2,s_1}(z00, f_{s_1,g_2}(x, z1))
f_{f_2,f_2}(f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{f_2,f_2}(f_{s_1,g_2}(x, z1), z10)
f_{f_2,f_2}(z00, f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → f_{f_2,f_2}(z00, f_{s_1,g_2}(x, z1))
g_{g_2,g_2}(f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{g_2,g_2}(f_{s_1,g_2}(x, z1), z10)
g_{g_2,g_2}(z00, f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → g_{g_2,g_2}(z00, f_{s_1,g_2}(x, z1))
g_{g_2,s_1}(f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{g_2,s_1}(f_{s_1,g_2}(x, z1), z10)
g_{g_2,s_1}(z00, f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → g_{g_2,s_1}(z00, f_{s_1,g_2}(x, z1))
g_{g_2,f_2}(f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{g_2,f_2}(f_{s_1,g_2}(x, z1), z10)
g_{g_2,f_2}(z00, f_{f_2,g_2}(f_{s_1,f_2}(x, y), z1)) → g_{g_2,f_2}(z00, f_{s_1,g_2}(x, z1))
g_{s_1,g_2}(f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → g_{s_1,g_2}(f_{s_1,s_1}(x, z1), z10)
g_{s_1,g_2}(z00, f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → g_{s_1,g_2}(z00, f_{s_1,s_1}(x, z1))
s_{g_2}(f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → s_{g_2}(f_{s_1,s_1}(x, z1))
g_{f_2,g_2}(f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → g_{f_2,g_2}(f_{s_1,s_1}(x, z1), z10)
g_{f_2,g_2}(z00, f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → g_{f_2,g_2}(z00, f_{s_1,s_1}(x, z1))
f_{g_2,g_2}(f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → f_{g_2,g_2}(f_{s_1,s_1}(x, z1), z10)
f_{g_2,g_2}(z00, f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → f_{g_2,g_2}(z00, f_{s_1,s_1}(x, z1))
g_{s_1,s_1}(f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → g_{s_1,s_1}(f_{s_1,s_1}(x, z1), z10)
g_{s_1,s_1}(z00, f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → g_{s_1,s_1}(z00, f_{s_1,s_1}(x, z1))
g_{f_2,s_1}(f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → g_{f_2,s_1}(f_{s_1,s_1}(x, z1), z10)
g_{f_2,s_1}(z00, f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → g_{f_2,s_1}(z00, f_{s_1,s_1}(x, z1))
f_{g_2,s_1}(f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → f_{g_2,s_1}(f_{s_1,s_1}(x, z1), z10)
f_{g_2,s_1}(z00, f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → f_{g_2,s_1}(z00, f_{s_1,s_1}(x, z1))
g_{s_1,f_2}(f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → g_{s_1,f_2}(f_{s_1,s_1}(x, z1), z10)
g_{s_1,f_2}(z00, f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → g_{s_1,f_2}(z00, f_{s_1,s_1}(x, z1))
g_{f_2,f_2}(f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → g_{f_2,f_2}(f_{s_1,s_1}(x, z1), z10)
g_{f_2,f_2}(z00, f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → g_{f_2,f_2}(z00, f_{s_1,s_1}(x, z1))
f_{g_2,f_2}(f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → f_{g_2,f_2}(f_{s_1,s_1}(x, z1), z10)
f_{g_2,f_2}(z00, f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → f_{g_2,f_2}(z00, f_{s_1,s_1}(x, z1))
s_{s_1}(f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → s_{s_1}(f_{s_1,s_1}(x, z1))
f_{s_1,g_2}(f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → f_{s_1,g_2}(f_{s_1,s_1}(x, z1), z10)
f_{s_1,g_2}(z00, f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → f_{s_1,g_2}(z00, f_{s_1,s_1}(x, z1))
f_{s_1,s_1}(f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → f_{s_1,s_1}(f_{s_1,s_1}(x, z1), z10)
f_{s_1,s_1}(z00, f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → f_{s_1,s_1}(z00, f_{s_1,s_1}(x, z1))
f_{s_1,f_2}(f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → f_{s_1,f_2}(f_{s_1,s_1}(x, z1), z10)
f_{s_1,f_2}(z00, f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → f_{s_1,f_2}(z00, f_{s_1,s_1}(x, z1))
s_{f_2}(f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → s_{f_2}(f_{s_1,s_1}(x, z1))
f_{f_2,g_2}(f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → f_{f_2,g_2}(f_{s_1,s_1}(x, z1), z10)
f_{f_2,g_2}(z00, f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → f_{f_2,g_2}(z00, f_{s_1,s_1}(x, z1))
f_{f_2,s_1}(f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → f_{f_2,s_1}(f_{s_1,s_1}(x, z1), z10)
f_{f_2,s_1}(z00, f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → f_{f_2,s_1}(z00, f_{s_1,s_1}(x, z1))
f_{f_2,f_2}(f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → f_{f_2,f_2}(f_{s_1,s_1}(x, z1), z10)
f_{f_2,f_2}(z00, f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → f_{f_2,f_2}(z00, f_{s_1,s_1}(x, z1))
g_{g_2,g_2}(f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → g_{g_2,g_2}(f_{s_1,s_1}(x, z1), z10)
g_{g_2,g_2}(z00, f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → g_{g_2,g_2}(z00, f_{s_1,s_1}(x, z1))
g_{g_2,s_1}(f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → g_{g_2,s_1}(f_{s_1,s_1}(x, z1), z10)
g_{g_2,s_1}(z00, f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → g_{g_2,s_1}(z00, f_{s_1,s_1}(x, z1))
g_{g_2,f_2}(f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1), z10) → g_{g_2,f_2}(f_{s_1,s_1}(x, z1), z10)
g_{g_2,f_2}(z00, f_{f_2,s_1}(f_{s_1,f_2}(x, y), z1)) → g_{g_2,f_2}(z00, f_{s_1,s_1}(x, z1))
g_{s_1,g_2}(f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{s_1,g_2}(f_{s_1,f_2}(x, z1), z10)
g_{s_1,g_2}(z00, f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → g_{s_1,g_2}(z00, f_{s_1,f_2}(x, z1))
s_{g_2}(f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → s_{g_2}(f_{s_1,f_2}(x, z1))
g_{f_2,g_2}(f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{f_2,g_2}(f_{s_1,f_2}(x, z1), z10)
g_{f_2,g_2}(z00, f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → g_{f_2,g_2}(z00, f_{s_1,f_2}(x, z1))
f_{g_2,g_2}(f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{g_2,g_2}(f_{s_1,f_2}(x, z1), z10)
f_{g_2,g_2}(z00, f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → f_{g_2,g_2}(z00, f_{s_1,f_2}(x, z1))
g_{s_1,s_1}(f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{s_1,s_1}(f_{s_1,f_2}(x, z1), z10)
g_{s_1,s_1}(z00, f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → g_{s_1,s_1}(z00, f_{s_1,f_2}(x, z1))
g_{f_2,s_1}(f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{f_2,s_1}(f_{s_1,f_2}(x, z1), z10)
g_{f_2,s_1}(z00, f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → g_{f_2,s_1}(z00, f_{s_1,f_2}(x, z1))
f_{g_2,s_1}(f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{g_2,s_1}(f_{s_1,f_2}(x, z1), z10)
f_{g_2,s_1}(z00, f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → f_{g_2,s_1}(z00, f_{s_1,f_2}(x, z1))
g_{s_1,f_2}(f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{s_1,f_2}(f_{s_1,f_2}(x, z1), z10)
g_{s_1,f_2}(z00, f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → g_{s_1,f_2}(z00, f_{s_1,f_2}(x, z1))
g_{f_2,f_2}(f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{f_2,f_2}(f_{s_1,f_2}(x, z1), z10)
g_{f_2,f_2}(z00, f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → g_{f_2,f_2}(z00, f_{s_1,f_2}(x, z1))
f_{g_2,f_2}(f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{g_2,f_2}(f_{s_1,f_2}(x, z1), z10)
f_{g_2,f_2}(z00, f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → f_{g_2,f_2}(z00, f_{s_1,f_2}(x, z1))
s_{s_1}(f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → s_{s_1}(f_{s_1,f_2}(x, z1))
f_{s_1,g_2}(f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{s_1,g_2}(f_{s_1,f_2}(x, z1), z10)
f_{s_1,g_2}(z00, f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → f_{s_1,g_2}(z00, f_{s_1,f_2}(x, z1))
f_{s_1,s_1}(f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{s_1,s_1}(f_{s_1,f_2}(x, z1), z10)
f_{s_1,s_1}(z00, f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → f_{s_1,s_1}(z00, f_{s_1,f_2}(x, z1))
f_{s_1,f_2}(f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{s_1,f_2}(f_{s_1,f_2}(x, z1), z10)
f_{s_1,f_2}(z00, f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → f_{s_1,f_2}(z00, f_{s_1,f_2}(x, z1))
s_{f_2}(f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → s_{f_2}(f_{s_1,f_2}(x, z1))
f_{f_2,g_2}(f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{f_2,g_2}(f_{s_1,f_2}(x, z1), z10)
f_{f_2,g_2}(z00, f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → f_{f_2,g_2}(z00, f_{s_1,f_2}(x, z1))
f_{f_2,s_1}(f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{f_2,s_1}(f_{s_1,f_2}(x, z1), z10)
f_{f_2,s_1}(z00, f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → f_{f_2,s_1}(z00, f_{s_1,f_2}(x, z1))
f_{f_2,f_2}(f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → f_{f_2,f_2}(f_{s_1,f_2}(x, z1), z10)
f_{f_2,f_2}(z00, f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → f_{f_2,f_2}(z00, f_{s_1,f_2}(x, z1))
g_{g_2,g_2}(f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{g_2,g_2}(f_{s_1,f_2}(x, z1), z10)
g_{g_2,g_2}(z00, f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → g_{g_2,g_2}(z00, f_{s_1,f_2}(x, z1))
g_{g_2,s_1}(f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{g_2,s_1}(f_{s_1,f_2}(x, z1), z10)
g_{g_2,s_1}(z00, f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → g_{g_2,s_1}(z00, f_{s_1,f_2}(x, z1))
g_{g_2,f_2}(f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1), z10) → g_{g_2,f_2}(f_{s_1,f_2}(x, z1), z10)
g_{g_2,f_2}(z00, f_{f_2,f_2}(f_{s_1,f_2}(x, y), z1)) → g_{g_2,f_2}(z00, f_{s_1,f_2}(x, z1))
g_{s_1,g_2}(f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{s_1,g_2}(f_{g_2,g_2}(z0, x), z10)
g_{s_1,g_2}(z00, f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{s_1,g_2}(z00, f_{g_2,g_2}(z0, x))
s_{g_2}(f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → s_{g_2}(f_{g_2,g_2}(z0, x))
g_{f_2,g_2}(f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{f_2,g_2}(f_{g_2,g_2}(z0, x), z10)
g_{f_2,g_2}(z00, f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{f_2,g_2}(z00, f_{g_2,g_2}(z0, x))
f_{g_2,g_2}(f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{g_2,g_2}(f_{g_2,g_2}(z0, x), z10)
f_{g_2,g_2}(z00, f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{g_2,g_2}(z00, f_{g_2,g_2}(z0, x))
g_{s_1,s_1}(f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{s_1,s_1}(f_{g_2,g_2}(z0, x), z10)
g_{s_1,s_1}(z00, f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{s_1,s_1}(z00, f_{g_2,g_2}(z0, x))
g_{f_2,s_1}(f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{f_2,s_1}(f_{g_2,g_2}(z0, x), z10)
g_{f_2,s_1}(z00, f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{f_2,s_1}(z00, f_{g_2,g_2}(z0, x))
f_{g_2,s_1}(f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{g_2,s_1}(f_{g_2,g_2}(z0, x), z10)
f_{g_2,s_1}(z00, f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{g_2,s_1}(z00, f_{g_2,g_2}(z0, x))
g_{s_1,f_2}(f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{s_1,f_2}(f_{g_2,g_2}(z0, x), z10)
g_{s_1,f_2}(z00, f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{s_1,f_2}(z00, f_{g_2,g_2}(z0, x))
g_{f_2,f_2}(f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{f_2,f_2}(f_{g_2,g_2}(z0, x), z10)
g_{f_2,f_2}(z00, f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{f_2,f_2}(z00, f_{g_2,g_2}(z0, x))
f_{g_2,f_2}(f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{g_2,f_2}(f_{g_2,g_2}(z0, x), z10)
f_{g_2,f_2}(z00, f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{g_2,f_2}(z00, f_{g_2,g_2}(z0, x))
s_{s_1}(f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → s_{s_1}(f_{g_2,g_2}(z0, x))
f_{s_1,g_2}(f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{s_1,g_2}(f_{g_2,g_2}(z0, x), z10)
f_{s_1,g_2}(z00, f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{s_1,g_2}(z00, f_{g_2,g_2}(z0, x))
f_{s_1,s_1}(f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{s_1,s_1}(f_{g_2,g_2}(z0, x), z10)
f_{s_1,s_1}(z00, f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{s_1,s_1}(z00, f_{g_2,g_2}(z0, x))
f_{s_1,f_2}(f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{s_1,f_2}(f_{g_2,g_2}(z0, x), z10)
f_{s_1,f_2}(z00, f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{s_1,f_2}(z00, f_{g_2,g_2}(z0, x))
s_{f_2}(f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → s_{f_2}(f_{g_2,g_2}(z0, x))
f_{f_2,g_2}(f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{f_2,g_2}(f_{g_2,g_2}(z0, x), z10)
f_{f_2,g_2}(z00, f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{f_2,g_2}(z00, f_{g_2,g_2}(z0, x))
f_{f_2,s_1}(f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{f_2,s_1}(f_{g_2,g_2}(z0, x), z10)
f_{f_2,s_1}(z00, f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{f_2,s_1}(z00, f_{g_2,g_2}(z0, x))
f_{f_2,f_2}(f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{f_2,f_2}(f_{g_2,g_2}(z0, x), z10)
f_{f_2,f_2}(z00, f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{f_2,f_2}(z00, f_{g_2,g_2}(z0, x))
g_{g_2,g_2}(f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{g_2,g_2}(f_{g_2,g_2}(z0, x), z10)
g_{g_2,g_2}(z00, f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{g_2,g_2}(z00, f_{g_2,g_2}(z0, x))
g_{g_2,s_1}(f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{g_2,s_1}(f_{g_2,g_2}(z0, x), z10)
g_{g_2,s_1}(z00, f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{g_2,s_1}(z00, f_{g_2,g_2}(z0, x))
g_{g_2,f_2}(f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{g_2,f_2}(f_{g_2,g_2}(z0, x), z10)
g_{g_2,f_2}(z00, f_{g_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{g_2,f_2}(z00, f_{g_2,g_2}(z0, x))
g_{s_1,g_2}(f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{s_1,g_2}(f_{g_2,g_2}(z0, x), z10)
g_{s_1,g_2}(z00, f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{s_1,g_2}(z00, f_{g_2,g_2}(z0, x))
s_{g_2}(f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → s_{g_2}(f_{g_2,g_2}(z0, x))
g_{f_2,g_2}(f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{f_2,g_2}(f_{g_2,g_2}(z0, x), z10)
g_{f_2,g_2}(z00, f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{f_2,g_2}(z00, f_{g_2,g_2}(z0, x))
f_{g_2,g_2}(f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{g_2,g_2}(f_{g_2,g_2}(z0, x), z10)
f_{g_2,g_2}(z00, f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{g_2,g_2}(z00, f_{g_2,g_2}(z0, x))
g_{s_1,s_1}(f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{s_1,s_1}(f_{g_2,g_2}(z0, x), z10)
g_{s_1,s_1}(z00, f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{s_1,s_1}(z00, f_{g_2,g_2}(z0, x))
g_{f_2,s_1}(f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{f_2,s_1}(f_{g_2,g_2}(z0, x), z10)
g_{f_2,s_1}(z00, f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{f_2,s_1}(z00, f_{g_2,g_2}(z0, x))
f_{g_2,s_1}(f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{g_2,s_1}(f_{g_2,g_2}(z0, x), z10)
f_{g_2,s_1}(z00, f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{g_2,s_1}(z00, f_{g_2,g_2}(z0, x))
g_{s_1,f_2}(f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{s_1,f_2}(f_{g_2,g_2}(z0, x), z10)
g_{s_1,f_2}(z00, f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{s_1,f_2}(z00, f_{g_2,g_2}(z0, x))
g_{f_2,f_2}(f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{f_2,f_2}(f_{g_2,g_2}(z0, x), z10)
g_{f_2,f_2}(z00, f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{f_2,f_2}(z00, f_{g_2,g_2}(z0, x))
f_{g_2,f_2}(f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{g_2,f_2}(f_{g_2,g_2}(z0, x), z10)
f_{g_2,f_2}(z00, f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{g_2,f_2}(z00, f_{g_2,g_2}(z0, x))
s_{s_1}(f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → s_{s_1}(f_{g_2,g_2}(z0, x))
f_{s_1,g_2}(f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{s_1,g_2}(f_{g_2,g_2}(z0, x), z10)
f_{s_1,g_2}(z00, f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{s_1,g_2}(z00, f_{g_2,g_2}(z0, x))
f_{s_1,s_1}(f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{s_1,s_1}(f_{g_2,g_2}(z0, x), z10)
f_{s_1,s_1}(z00, f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{s_1,s_1}(z00, f_{g_2,g_2}(z0, x))
f_{s_1,f_2}(f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{s_1,f_2}(f_{g_2,g_2}(z0, x), z10)
f_{s_1,f_2}(z00, f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{s_1,f_2}(z00, f_{g_2,g_2}(z0, x))
s_{f_2}(f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → s_{f_2}(f_{g_2,g_2}(z0, x))
f_{f_2,g_2}(f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{f_2,g_2}(f_{g_2,g_2}(z0, x), z10)
f_{f_2,g_2}(z00, f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{f_2,g_2}(z00, f_{g_2,g_2}(z0, x))
f_{f_2,s_1}(f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{f_2,s_1}(f_{g_2,g_2}(z0, x), z10)
f_{f_2,s_1}(z00, f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{f_2,s_1}(z00, f_{g_2,g_2}(z0, x))
f_{f_2,f_2}(f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{f_2,f_2}(f_{g_2,g_2}(z0, x), z10)
f_{f_2,f_2}(z00, f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{f_2,f_2}(z00, f_{g_2,g_2}(z0, x))
g_{g_2,g_2}(f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{g_2,g_2}(f_{g_2,g_2}(z0, x), z10)
g_{g_2,g_2}(z00, f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{g_2,g_2}(z00, f_{g_2,g_2}(z0, x))
g_{g_2,s_1}(f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{g_2,s_1}(f_{g_2,g_2}(z0, x), z10)
g_{g_2,s_1}(z00, f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{g_2,s_1}(z00, f_{g_2,g_2}(z0, x))
g_{g_2,f_2}(f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{g_2,f_2}(f_{g_2,g_2}(z0, x), z10)
g_{g_2,f_2}(z00, f_{g_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{g_2,f_2}(z00, f_{g_2,g_2}(z0, x))
g_{s_1,g_2}(f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{s_1,g_2}(f_{g_2,g_2}(z0, x), z10)
g_{s_1,g_2}(z00, f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{s_1,g_2}(z00, f_{g_2,g_2}(z0, x))
s_{g_2}(f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → s_{g_2}(f_{g_2,g_2}(z0, x))
g_{f_2,g_2}(f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{f_2,g_2}(f_{g_2,g_2}(z0, x), z10)
g_{f_2,g_2}(z00, f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{f_2,g_2}(z00, f_{g_2,g_2}(z0, x))
f_{g_2,g_2}(f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{g_2,g_2}(f_{g_2,g_2}(z0, x), z10)
f_{g_2,g_2}(z00, f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{g_2,g_2}(z00, f_{g_2,g_2}(z0, x))
g_{s_1,s_1}(f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{s_1,s_1}(f_{g_2,g_2}(z0, x), z10)
g_{s_1,s_1}(z00, f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{s_1,s_1}(z00, f_{g_2,g_2}(z0, x))
g_{f_2,s_1}(f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{f_2,s_1}(f_{g_2,g_2}(z0, x), z10)
g_{f_2,s_1}(z00, f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{f_2,s_1}(z00, f_{g_2,g_2}(z0, x))
f_{g_2,s_1}(f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{g_2,s_1}(f_{g_2,g_2}(z0, x), z10)
f_{g_2,s_1}(z00, f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{g_2,s_1}(z00, f_{g_2,g_2}(z0, x))
g_{s_1,f_2}(f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{s_1,f_2}(f_{g_2,g_2}(z0, x), z10)
g_{s_1,f_2}(z00, f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{s_1,f_2}(z00, f_{g_2,g_2}(z0, x))
g_{f_2,f_2}(f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{f_2,f_2}(f_{g_2,g_2}(z0, x), z10)
g_{f_2,f_2}(z00, f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{f_2,f_2}(z00, f_{g_2,g_2}(z0, x))
f_{g_2,f_2}(f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{g_2,f_2}(f_{g_2,g_2}(z0, x), z10)
f_{g_2,f_2}(z00, f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{g_2,f_2}(z00, f_{g_2,g_2}(z0, x))
s_{s_1}(f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → s_{s_1}(f_{g_2,g_2}(z0, x))
f_{s_1,g_2}(f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{s_1,g_2}(f_{g_2,g_2}(z0, x), z10)
f_{s_1,g_2}(z00, f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{s_1,g_2}(z00, f_{g_2,g_2}(z0, x))
f_{s_1,s_1}(f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{s_1,s_1}(f_{g_2,g_2}(z0, x), z10)
f_{s_1,s_1}(z00, f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{s_1,s_1}(z00, f_{g_2,g_2}(z0, x))
f_{s_1,f_2}(f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{s_1,f_2}(f_{g_2,g_2}(z0, x), z10)
f_{s_1,f_2}(z00, f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{s_1,f_2}(z00, f_{g_2,g_2}(z0, x))
s_{f_2}(f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → s_{f_2}(f_{g_2,g_2}(z0, x))
f_{f_2,g_2}(f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{f_2,g_2}(f_{g_2,g_2}(z0, x), z10)
f_{f_2,g_2}(z00, f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{f_2,g_2}(z00, f_{g_2,g_2}(z0, x))
f_{f_2,s_1}(f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{f_2,s_1}(f_{g_2,g_2}(z0, x), z10)
f_{f_2,s_1}(z00, f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{f_2,s_1}(z00, f_{g_2,g_2}(z0, x))
f_{f_2,f_2}(f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{f_2,f_2}(f_{g_2,g_2}(z0, x), z10)
f_{f_2,f_2}(z00, f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{f_2,f_2}(z00, f_{g_2,g_2}(z0, x))
g_{g_2,g_2}(f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{g_2,g_2}(f_{g_2,g_2}(z0, x), z10)
g_{g_2,g_2}(z00, f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{g_2,g_2}(z00, f_{g_2,g_2}(z0, x))
g_{g_2,s_1}(f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{g_2,s_1}(f_{g_2,g_2}(z0, x), z10)
g_{g_2,s_1}(z00, f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{g_2,s_1}(z00, f_{g_2,g_2}(z0, x))
g_{g_2,f_2}(f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{g_2,f_2}(f_{g_2,g_2}(z0, x), z10)
g_{g_2,f_2}(z00, f_{g_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{g_2,f_2}(z00, f_{g_2,g_2}(z0, x))
g_{s_1,g_2}(f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{s_1,g_2}(f_{g_2,s_1}(z0, x), z10)
g_{s_1,g_2}(z00, f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{s_1,g_2}(z00, f_{g_2,s_1}(z0, x))
s_{g_2}(f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → s_{g_2}(f_{g_2,s_1}(z0, x))
g_{f_2,g_2}(f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{f_2,g_2}(f_{g_2,s_1}(z0, x), z10)
g_{f_2,g_2}(z00, f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{f_2,g_2}(z00, f_{g_2,s_1}(z0, x))
f_{g_2,g_2}(f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{g_2,g_2}(f_{g_2,s_1}(z0, x), z10)
f_{g_2,g_2}(z00, f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{g_2,g_2}(z00, f_{g_2,s_1}(z0, x))
g_{s_1,s_1}(f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{s_1,s_1}(f_{g_2,s_1}(z0, x), z10)
g_{s_1,s_1}(z00, f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{s_1,s_1}(z00, f_{g_2,s_1}(z0, x))
g_{f_2,s_1}(f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{f_2,s_1}(f_{g_2,s_1}(z0, x), z10)
g_{f_2,s_1}(z00, f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{f_2,s_1}(z00, f_{g_2,s_1}(z0, x))
f_{g_2,s_1}(f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{g_2,s_1}(f_{g_2,s_1}(z0, x), z10)
f_{g_2,s_1}(z00, f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{g_2,s_1}(z00, f_{g_2,s_1}(z0, x))
g_{s_1,f_2}(f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{s_1,f_2}(f_{g_2,s_1}(z0, x), z10)
g_{s_1,f_2}(z00, f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{s_1,f_2}(z00, f_{g_2,s_1}(z0, x))
g_{f_2,f_2}(f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{f_2,f_2}(f_{g_2,s_1}(z0, x), z10)
g_{f_2,f_2}(z00, f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{f_2,f_2}(z00, f_{g_2,s_1}(z0, x))
f_{g_2,f_2}(f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{g_2,f_2}(f_{g_2,s_1}(z0, x), z10)
f_{g_2,f_2}(z00, f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{g_2,f_2}(z00, f_{g_2,s_1}(z0, x))
s_{s_1}(f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → s_{s_1}(f_{g_2,s_1}(z0, x))
f_{s_1,g_2}(f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{s_1,g_2}(f_{g_2,s_1}(z0, x), z10)
f_{s_1,g_2}(z00, f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{s_1,g_2}(z00, f_{g_2,s_1}(z0, x))
f_{s_1,s_1}(f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{s_1,s_1}(f_{g_2,s_1}(z0, x), z10)
f_{s_1,s_1}(z00, f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{s_1,s_1}(z00, f_{g_2,s_1}(z0, x))
f_{s_1,f_2}(f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{s_1,f_2}(f_{g_2,s_1}(z0, x), z10)
f_{s_1,f_2}(z00, f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{s_1,f_2}(z00, f_{g_2,s_1}(z0, x))
s_{f_2}(f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → s_{f_2}(f_{g_2,s_1}(z0, x))
f_{f_2,g_2}(f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{f_2,g_2}(f_{g_2,s_1}(z0, x), z10)
f_{f_2,g_2}(z00, f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{f_2,g_2}(z00, f_{g_2,s_1}(z0, x))
f_{f_2,s_1}(f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{f_2,s_1}(f_{g_2,s_1}(z0, x), z10)
f_{f_2,s_1}(z00, f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{f_2,s_1}(z00, f_{g_2,s_1}(z0, x))
f_{f_2,f_2}(f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{f_2,f_2}(f_{g_2,s_1}(z0, x), z10)
f_{f_2,f_2}(z00, f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{f_2,f_2}(z00, f_{g_2,s_1}(z0, x))
g_{g_2,g_2}(f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{g_2,g_2}(f_{g_2,s_1}(z0, x), z10)
g_{g_2,g_2}(z00, f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{g_2,g_2}(z00, f_{g_2,s_1}(z0, x))
g_{g_2,s_1}(f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{g_2,s_1}(f_{g_2,s_1}(z0, x), z10)
g_{g_2,s_1}(z00, f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{g_2,s_1}(z00, f_{g_2,s_1}(z0, x))
g_{g_2,f_2}(f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{g_2,f_2}(f_{g_2,s_1}(z0, x), z10)
g_{g_2,f_2}(z00, f_{g_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{g_2,f_2}(z00, f_{g_2,s_1}(z0, x))
g_{s_1,g_2}(f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{s_1,g_2}(f_{g_2,s_1}(z0, x), z10)
g_{s_1,g_2}(z00, f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{s_1,g_2}(z00, f_{g_2,s_1}(z0, x))
s_{g_2}(f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → s_{g_2}(f_{g_2,s_1}(z0, x))
g_{f_2,g_2}(f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{f_2,g_2}(f_{g_2,s_1}(z0, x), z10)
g_{f_2,g_2}(z00, f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{f_2,g_2}(z00, f_{g_2,s_1}(z0, x))
f_{g_2,g_2}(f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{g_2,g_2}(f_{g_2,s_1}(z0, x), z10)
f_{g_2,g_2}(z00, f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{g_2,g_2}(z00, f_{g_2,s_1}(z0, x))
g_{s_1,s_1}(f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{s_1,s_1}(f_{g_2,s_1}(z0, x), z10)
g_{s_1,s_1}(z00, f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{s_1,s_1}(z00, f_{g_2,s_1}(z0, x))
g_{f_2,s_1}(f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{f_2,s_1}(f_{g_2,s_1}(z0, x), z10)
g_{f_2,s_1}(z00, f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{f_2,s_1}(z00, f_{g_2,s_1}(z0, x))
f_{g_2,s_1}(f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{g_2,s_1}(f_{g_2,s_1}(z0, x), z10)
f_{g_2,s_1}(z00, f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{g_2,s_1}(z00, f_{g_2,s_1}(z0, x))
g_{s_1,f_2}(f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{s_1,f_2}(f_{g_2,s_1}(z0, x), z10)
g_{s_1,f_2}(z00, f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{s_1,f_2}(z00, f_{g_2,s_1}(z0, x))
g_{f_2,f_2}(f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{f_2,f_2}(f_{g_2,s_1}(z0, x), z10)
g_{f_2,f_2}(z00, f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{f_2,f_2}(z00, f_{g_2,s_1}(z0, x))
f_{g_2,f_2}(f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{g_2,f_2}(f_{g_2,s_1}(z0, x), z10)
f_{g_2,f_2}(z00, f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{g_2,f_2}(z00, f_{g_2,s_1}(z0, x))
s_{s_1}(f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → s_{s_1}(f_{g_2,s_1}(z0, x))
f_{s_1,g_2}(f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{s_1,g_2}(f_{g_2,s_1}(z0, x), z10)
f_{s_1,g_2}(z00, f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{s_1,g_2}(z00, f_{g_2,s_1}(z0, x))
f_{s_1,s_1}(f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{s_1,s_1}(f_{g_2,s_1}(z0, x), z10)
f_{s_1,s_1}(z00, f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{s_1,s_1}(z00, f_{g_2,s_1}(z0, x))
f_{s_1,f_2}(f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{s_1,f_2}(f_{g_2,s_1}(z0, x), z10)
f_{s_1,f_2}(z00, f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{s_1,f_2}(z00, f_{g_2,s_1}(z0, x))
s_{f_2}(f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → s_{f_2}(f_{g_2,s_1}(z0, x))
f_{f_2,g_2}(f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{f_2,g_2}(f_{g_2,s_1}(z0, x), z10)
f_{f_2,g_2}(z00, f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{f_2,g_2}(z00, f_{g_2,s_1}(z0, x))
f_{f_2,s_1}(f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{f_2,s_1}(f_{g_2,s_1}(z0, x), z10)
f_{f_2,s_1}(z00, f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{f_2,s_1}(z00, f_{g_2,s_1}(z0, x))
f_{f_2,f_2}(f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{f_2,f_2}(f_{g_2,s_1}(z0, x), z10)
f_{f_2,f_2}(z00, f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{f_2,f_2}(z00, f_{g_2,s_1}(z0, x))
g_{g_2,g_2}(f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{g_2,g_2}(f_{g_2,s_1}(z0, x), z10)
g_{g_2,g_2}(z00, f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{g_2,g_2}(z00, f_{g_2,s_1}(z0, x))
g_{g_2,s_1}(f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{g_2,s_1}(f_{g_2,s_1}(z0, x), z10)
g_{g_2,s_1}(z00, f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{g_2,s_1}(z00, f_{g_2,s_1}(z0, x))
g_{g_2,f_2}(f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{g_2,f_2}(f_{g_2,s_1}(z0, x), z10)
g_{g_2,f_2}(z00, f_{g_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{g_2,f_2}(z00, f_{g_2,s_1}(z0, x))
g_{s_1,g_2}(f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{s_1,g_2}(f_{g_2,s_1}(z0, x), z10)
g_{s_1,g_2}(z00, f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{s_1,g_2}(z00, f_{g_2,s_1}(z0, x))
s_{g_2}(f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → s_{g_2}(f_{g_2,s_1}(z0, x))
g_{f_2,g_2}(f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{f_2,g_2}(f_{g_2,s_1}(z0, x), z10)
g_{f_2,g_2}(z00, f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{f_2,g_2}(z00, f_{g_2,s_1}(z0, x))
f_{g_2,g_2}(f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{g_2,g_2}(f_{g_2,s_1}(z0, x), z10)
f_{g_2,g_2}(z00, f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{g_2,g_2}(z00, f_{g_2,s_1}(z0, x))
g_{s_1,s_1}(f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{s_1,s_1}(f_{g_2,s_1}(z0, x), z10)
g_{s_1,s_1}(z00, f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{s_1,s_1}(z00, f_{g_2,s_1}(z0, x))
g_{f_2,s_1}(f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{f_2,s_1}(f_{g_2,s_1}(z0, x), z10)
g_{f_2,s_1}(z00, f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{f_2,s_1}(z00, f_{g_2,s_1}(z0, x))
f_{g_2,s_1}(f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{g_2,s_1}(f_{g_2,s_1}(z0, x), z10)
f_{g_2,s_1}(z00, f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{g_2,s_1}(z00, f_{g_2,s_1}(z0, x))
g_{s_1,f_2}(f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{s_1,f_2}(f_{g_2,s_1}(z0, x), z10)
g_{s_1,f_2}(z00, f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{s_1,f_2}(z00, f_{g_2,s_1}(z0, x))
g_{f_2,f_2}(f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{f_2,f_2}(f_{g_2,s_1}(z0, x), z10)
g_{f_2,f_2}(z00, f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{f_2,f_2}(z00, f_{g_2,s_1}(z0, x))
f_{g_2,f_2}(f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{g_2,f_2}(f_{g_2,s_1}(z0, x), z10)
f_{g_2,f_2}(z00, f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{g_2,f_2}(z00, f_{g_2,s_1}(z0, x))
s_{s_1}(f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → s_{s_1}(f_{g_2,s_1}(z0, x))
f_{s_1,g_2}(f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{s_1,g_2}(f_{g_2,s_1}(z0, x), z10)
f_{s_1,g_2}(z00, f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{s_1,g_2}(z00, f_{g_2,s_1}(z0, x))
f_{s_1,s_1}(f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{s_1,s_1}(f_{g_2,s_1}(z0, x), z10)
f_{s_1,s_1}(z00, f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{s_1,s_1}(z00, f_{g_2,s_1}(z0, x))
f_{s_1,f_2}(f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{s_1,f_2}(f_{g_2,s_1}(z0, x), z10)
f_{s_1,f_2}(z00, f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{s_1,f_2}(z00, f_{g_2,s_1}(z0, x))
s_{f_2}(f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → s_{f_2}(f_{g_2,s_1}(z0, x))
f_{f_2,g_2}(f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{f_2,g_2}(f_{g_2,s_1}(z0, x), z10)
f_{f_2,g_2}(z00, f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{f_2,g_2}(z00, f_{g_2,s_1}(z0, x))
f_{f_2,s_1}(f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{f_2,s_1}(f_{g_2,s_1}(z0, x), z10)
f_{f_2,s_1}(z00, f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{f_2,s_1}(z00, f_{g_2,s_1}(z0, x))
f_{f_2,f_2}(f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{f_2,f_2}(f_{g_2,s_1}(z0, x), z10)
f_{f_2,f_2}(z00, f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{f_2,f_2}(z00, f_{g_2,s_1}(z0, x))
g_{g_2,g_2}(f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{g_2,g_2}(f_{g_2,s_1}(z0, x), z10)
g_{g_2,g_2}(z00, f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{g_2,g_2}(z00, f_{g_2,s_1}(z0, x))
g_{g_2,s_1}(f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{g_2,s_1}(f_{g_2,s_1}(z0, x), z10)
g_{g_2,s_1}(z00, f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{g_2,s_1}(z00, f_{g_2,s_1}(z0, x))
g_{g_2,f_2}(f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{g_2,f_2}(f_{g_2,s_1}(z0, x), z10)
g_{g_2,f_2}(z00, f_{g_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{g_2,f_2}(z00, f_{g_2,s_1}(z0, x))
g_{s_1,g_2}(f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{s_1,g_2}(f_{s_1,g_2}(z0, x), z10)
g_{s_1,g_2}(z00, f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{s_1,g_2}(z00, f_{s_1,g_2}(z0, x))
s_{g_2}(f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → s_{g_2}(f_{s_1,g_2}(z0, x))
g_{f_2,g_2}(f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{f_2,g_2}(f_{s_1,g_2}(z0, x), z10)
g_{f_2,g_2}(z00, f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{f_2,g_2}(z00, f_{s_1,g_2}(z0, x))
f_{g_2,g_2}(f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{g_2,g_2}(f_{s_1,g_2}(z0, x), z10)
f_{g_2,g_2}(z00, f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{g_2,g_2}(z00, f_{s_1,g_2}(z0, x))
g_{s_1,s_1}(f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{s_1,s_1}(f_{s_1,g_2}(z0, x), z10)
g_{s_1,s_1}(z00, f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{s_1,s_1}(z00, f_{s_1,g_2}(z0, x))
g_{f_2,s_1}(f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{f_2,s_1}(f_{s_1,g_2}(z0, x), z10)
g_{f_2,s_1}(z00, f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{f_2,s_1}(z00, f_{s_1,g_2}(z0, x))
f_{g_2,s_1}(f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{g_2,s_1}(f_{s_1,g_2}(z0, x), z10)
f_{g_2,s_1}(z00, f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{g_2,s_1}(z00, f_{s_1,g_2}(z0, x))
g_{s_1,f_2}(f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{s_1,f_2}(f_{s_1,g_2}(z0, x), z10)
g_{s_1,f_2}(z00, f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{s_1,f_2}(z00, f_{s_1,g_2}(z0, x))
g_{f_2,f_2}(f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{f_2,f_2}(f_{s_1,g_2}(z0, x), z10)
g_{f_2,f_2}(z00, f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{f_2,f_2}(z00, f_{s_1,g_2}(z0, x))
f_{g_2,f_2}(f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{g_2,f_2}(f_{s_1,g_2}(z0, x), z10)
f_{g_2,f_2}(z00, f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{g_2,f_2}(z00, f_{s_1,g_2}(z0, x))
s_{s_1}(f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → s_{s_1}(f_{s_1,g_2}(z0, x))
f_{s_1,g_2}(f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{s_1,g_2}(f_{s_1,g_2}(z0, x), z10)
f_{s_1,g_2}(z00, f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{s_1,g_2}(z00, f_{s_1,g_2}(z0, x))
f_{s_1,s_1}(f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{s_1,s_1}(f_{s_1,g_2}(z0, x), z10)
f_{s_1,s_1}(z00, f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{s_1,s_1}(z00, f_{s_1,g_2}(z0, x))
f_{s_1,f_2}(f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{s_1,f_2}(f_{s_1,g_2}(z0, x), z10)
f_{s_1,f_2}(z00, f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{s_1,f_2}(z00, f_{s_1,g_2}(z0, x))
s_{f_2}(f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → s_{f_2}(f_{s_1,g_2}(z0, x))
f_{f_2,g_2}(f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{f_2,g_2}(f_{s_1,g_2}(z0, x), z10)
f_{f_2,g_2}(z00, f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{f_2,g_2}(z00, f_{s_1,g_2}(z0, x))
f_{f_2,s_1}(f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{f_2,s_1}(f_{s_1,g_2}(z0, x), z10)
f_{f_2,s_1}(z00, f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{f_2,s_1}(z00, f_{s_1,g_2}(z0, x))
f_{f_2,f_2}(f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{f_2,f_2}(f_{s_1,g_2}(z0, x), z10)
f_{f_2,f_2}(z00, f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{f_2,f_2}(z00, f_{s_1,g_2}(z0, x))
g_{g_2,g_2}(f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{g_2,g_2}(f_{s_1,g_2}(z0, x), z10)
g_{g_2,g_2}(z00, f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{g_2,g_2}(z00, f_{s_1,g_2}(z0, x))
g_{g_2,s_1}(f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{g_2,s_1}(f_{s_1,g_2}(z0, x), z10)
g_{g_2,s_1}(z00, f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{g_2,s_1}(z00, f_{s_1,g_2}(z0, x))
g_{g_2,f_2}(f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{g_2,f_2}(f_{s_1,g_2}(z0, x), z10)
g_{g_2,f_2}(z00, f_{s_1,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{g_2,f_2}(z00, f_{s_1,g_2}(z0, x))
g_{s_1,g_2}(f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{s_1,g_2}(f_{s_1,g_2}(z0, x), z10)
g_{s_1,g_2}(z00, f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{s_1,g_2}(z00, f_{s_1,g_2}(z0, x))
s_{g_2}(f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → s_{g_2}(f_{s_1,g_2}(z0, x))
g_{f_2,g_2}(f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{f_2,g_2}(f_{s_1,g_2}(z0, x), z10)
g_{f_2,g_2}(z00, f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{f_2,g_2}(z00, f_{s_1,g_2}(z0, x))
f_{g_2,g_2}(f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{g_2,g_2}(f_{s_1,g_2}(z0, x), z10)
f_{g_2,g_2}(z00, f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{g_2,g_2}(z00, f_{s_1,g_2}(z0, x))
g_{s_1,s_1}(f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{s_1,s_1}(f_{s_1,g_2}(z0, x), z10)
g_{s_1,s_1}(z00, f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{s_1,s_1}(z00, f_{s_1,g_2}(z0, x))
g_{f_2,s_1}(f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{f_2,s_1}(f_{s_1,g_2}(z0, x), z10)
g_{f_2,s_1}(z00, f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{f_2,s_1}(z00, f_{s_1,g_2}(z0, x))
f_{g_2,s_1}(f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{g_2,s_1}(f_{s_1,g_2}(z0, x), z10)
f_{g_2,s_1}(z00, f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{g_2,s_1}(z00, f_{s_1,g_2}(z0, x))
g_{s_1,f_2}(f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{s_1,f_2}(f_{s_1,g_2}(z0, x), z10)
g_{s_1,f_2}(z00, f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{s_1,f_2}(z00, f_{s_1,g_2}(z0, x))
g_{f_2,f_2}(f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{f_2,f_2}(f_{s_1,g_2}(z0, x), z10)
g_{f_2,f_2}(z00, f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{f_2,f_2}(z00, f_{s_1,g_2}(z0, x))
f_{g_2,f_2}(f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{g_2,f_2}(f_{s_1,g_2}(z0, x), z10)
f_{g_2,f_2}(z00, f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{g_2,f_2}(z00, f_{s_1,g_2}(z0, x))
s_{s_1}(f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → s_{s_1}(f_{s_1,g_2}(z0, x))
f_{s_1,g_2}(f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{s_1,g_2}(f_{s_1,g_2}(z0, x), z10)
f_{s_1,g_2}(z00, f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{s_1,g_2}(z00, f_{s_1,g_2}(z0, x))
f_{s_1,s_1}(f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{s_1,s_1}(f_{s_1,g_2}(z0, x), z10)
f_{s_1,s_1}(z00, f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{s_1,s_1}(z00, f_{s_1,g_2}(z0, x))
f_{s_1,f_2}(f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{s_1,f_2}(f_{s_1,g_2}(z0, x), z10)
f_{s_1,f_2}(z00, f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{s_1,f_2}(z00, f_{s_1,g_2}(z0, x))
s_{f_2}(f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → s_{f_2}(f_{s_1,g_2}(z0, x))
f_{f_2,g_2}(f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{f_2,g_2}(f_{s_1,g_2}(z0, x), z10)
f_{f_2,g_2}(z00, f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{f_2,g_2}(z00, f_{s_1,g_2}(z0, x))
f_{f_2,s_1}(f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{f_2,s_1}(f_{s_1,g_2}(z0, x), z10)
f_{f_2,s_1}(z00, f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{f_2,s_1}(z00, f_{s_1,g_2}(z0, x))
f_{f_2,f_2}(f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{f_2,f_2}(f_{s_1,g_2}(z0, x), z10)
f_{f_2,f_2}(z00, f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{f_2,f_2}(z00, f_{s_1,g_2}(z0, x))
g_{g_2,g_2}(f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{g_2,g_2}(f_{s_1,g_2}(z0, x), z10)
g_{g_2,g_2}(z00, f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{g_2,g_2}(z00, f_{s_1,g_2}(z0, x))
g_{g_2,s_1}(f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{g_2,s_1}(f_{s_1,g_2}(z0, x), z10)
g_{g_2,s_1}(z00, f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{g_2,s_1}(z00, f_{s_1,g_2}(z0, x))
g_{g_2,f_2}(f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{g_2,f_2}(f_{s_1,g_2}(z0, x), z10)
g_{g_2,f_2}(z00, f_{s_1,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{g_2,f_2}(z00, f_{s_1,g_2}(z0, x))
g_{s_1,g_2}(f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{s_1,g_2}(f_{s_1,g_2}(z0, x), z10)
g_{s_1,g_2}(z00, f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{s_1,g_2}(z00, f_{s_1,g_2}(z0, x))
s_{g_2}(f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → s_{g_2}(f_{s_1,g_2}(z0, x))
g_{f_2,g_2}(f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{f_2,g_2}(f_{s_1,g_2}(z0, x), z10)
g_{f_2,g_2}(z00, f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{f_2,g_2}(z00, f_{s_1,g_2}(z0, x))
f_{g_2,g_2}(f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{g_2,g_2}(f_{s_1,g_2}(z0, x), z10)
f_{g_2,g_2}(z00, f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{g_2,g_2}(z00, f_{s_1,g_2}(z0, x))
g_{s_1,s_1}(f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{s_1,s_1}(f_{s_1,g_2}(z0, x), z10)
g_{s_1,s_1}(z00, f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{s_1,s_1}(z00, f_{s_1,g_2}(z0, x))
g_{f_2,s_1}(f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{f_2,s_1}(f_{s_1,g_2}(z0, x), z10)
g_{f_2,s_1}(z00, f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{f_2,s_1}(z00, f_{s_1,g_2}(z0, x))
f_{g_2,s_1}(f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{g_2,s_1}(f_{s_1,g_2}(z0, x), z10)
f_{g_2,s_1}(z00, f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{g_2,s_1}(z00, f_{s_1,g_2}(z0, x))
g_{s_1,f_2}(f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{s_1,f_2}(f_{s_1,g_2}(z0, x), z10)
g_{s_1,f_2}(z00, f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{s_1,f_2}(z00, f_{s_1,g_2}(z0, x))
g_{f_2,f_2}(f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{f_2,f_2}(f_{s_1,g_2}(z0, x), z10)
g_{f_2,f_2}(z00, f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{f_2,f_2}(z00, f_{s_1,g_2}(z0, x))
f_{g_2,f_2}(f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{g_2,f_2}(f_{s_1,g_2}(z0, x), z10)
f_{g_2,f_2}(z00, f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{g_2,f_2}(z00, f_{s_1,g_2}(z0, x))
s_{s_1}(f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → s_{s_1}(f_{s_1,g_2}(z0, x))
f_{s_1,g_2}(f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{s_1,g_2}(f_{s_1,g_2}(z0, x), z10)
f_{s_1,g_2}(z00, f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{s_1,g_2}(z00, f_{s_1,g_2}(z0, x))
f_{s_1,s_1}(f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{s_1,s_1}(f_{s_1,g_2}(z0, x), z10)
f_{s_1,s_1}(z00, f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{s_1,s_1}(z00, f_{s_1,g_2}(z0, x))
f_{s_1,f_2}(f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{s_1,f_2}(f_{s_1,g_2}(z0, x), z10)
f_{s_1,f_2}(z00, f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{s_1,f_2}(z00, f_{s_1,g_2}(z0, x))
s_{f_2}(f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → s_{f_2}(f_{s_1,g_2}(z0, x))
f_{f_2,g_2}(f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{f_2,g_2}(f_{s_1,g_2}(z0, x), z10)
f_{f_2,g_2}(z00, f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{f_2,g_2}(z00, f_{s_1,g_2}(z0, x))
f_{f_2,s_1}(f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{f_2,s_1}(f_{s_1,g_2}(z0, x), z10)
f_{f_2,s_1}(z00, f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{f_2,s_1}(z00, f_{s_1,g_2}(z0, x))
f_{f_2,f_2}(f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{f_2,f_2}(f_{s_1,g_2}(z0, x), z10)
f_{f_2,f_2}(z00, f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{f_2,f_2}(z00, f_{s_1,g_2}(z0, x))
g_{g_2,g_2}(f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{g_2,g_2}(f_{s_1,g_2}(z0, x), z10)
g_{g_2,g_2}(z00, f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{g_2,g_2}(z00, f_{s_1,g_2}(z0, x))
g_{g_2,s_1}(f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{g_2,s_1}(f_{s_1,g_2}(z0, x), z10)
g_{g_2,s_1}(z00, f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{g_2,s_1}(z00, f_{s_1,g_2}(z0, x))
g_{g_2,f_2}(f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{g_2,f_2}(f_{s_1,g_2}(z0, x), z10)
g_{g_2,f_2}(z00, f_{s_1,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{g_2,f_2}(z00, f_{s_1,g_2}(z0, x))
g_{s_1,g_2}(f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{s_1,g_2}(f_{s_1,s_1}(z0, x), z10)
g_{s_1,g_2}(z00, f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{s_1,g_2}(z00, f_{s_1,s_1}(z0, x))
s_{g_2}(f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → s_{g_2}(f_{s_1,s_1}(z0, x))
g_{f_2,g_2}(f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{f_2,g_2}(f_{s_1,s_1}(z0, x), z10)
g_{f_2,g_2}(z00, f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{f_2,g_2}(z00, f_{s_1,s_1}(z0, x))
f_{g_2,g_2}(f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{g_2,g_2}(f_{s_1,s_1}(z0, x), z10)
f_{g_2,g_2}(z00, f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{g_2,g_2}(z00, f_{s_1,s_1}(z0, x))
g_{s_1,s_1}(f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{s_1,s_1}(f_{s_1,s_1}(z0, x), z10)
g_{s_1,s_1}(z00, f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{s_1,s_1}(z00, f_{s_1,s_1}(z0, x))
g_{f_2,s_1}(f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{f_2,s_1}(f_{s_1,s_1}(z0, x), z10)
g_{f_2,s_1}(z00, f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{f_2,s_1}(z00, f_{s_1,s_1}(z0, x))
f_{g_2,s_1}(f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{g_2,s_1}(f_{s_1,s_1}(z0, x), z10)
f_{g_2,s_1}(z00, f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{g_2,s_1}(z00, f_{s_1,s_1}(z0, x))
g_{s_1,f_2}(f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{s_1,f_2}(f_{s_1,s_1}(z0, x), z10)
g_{s_1,f_2}(z00, f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{s_1,f_2}(z00, f_{s_1,s_1}(z0, x))
g_{f_2,f_2}(f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{f_2,f_2}(f_{s_1,s_1}(z0, x), z10)
g_{f_2,f_2}(z00, f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{f_2,f_2}(z00, f_{s_1,s_1}(z0, x))
f_{g_2,f_2}(f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{g_2,f_2}(f_{s_1,s_1}(z0, x), z10)
f_{g_2,f_2}(z00, f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{g_2,f_2}(z00, f_{s_1,s_1}(z0, x))
s_{s_1}(f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → s_{s_1}(f_{s_1,s_1}(z0, x))
f_{s_1,g_2}(f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{s_1,g_2}(f_{s_1,s_1}(z0, x), z10)
f_{s_1,g_2}(z00, f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{s_1,g_2}(z00, f_{s_1,s_1}(z0, x))
f_{s_1,s_1}(f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{s_1,s_1}(f_{s_1,s_1}(z0, x), z10)
f_{s_1,s_1}(z00, f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{s_1,s_1}(z00, f_{s_1,s_1}(z0, x))
f_{s_1,f_2}(f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{s_1,f_2}(f_{s_1,s_1}(z0, x), z10)
f_{s_1,f_2}(z00, f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{s_1,f_2}(z00, f_{s_1,s_1}(z0, x))
s_{f_2}(f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → s_{f_2}(f_{s_1,s_1}(z0, x))
f_{f_2,g_2}(f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{f_2,g_2}(f_{s_1,s_1}(z0, x), z10)
f_{f_2,g_2}(z00, f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{f_2,g_2}(z00, f_{s_1,s_1}(z0, x))
f_{f_2,s_1}(f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{f_2,s_1}(f_{s_1,s_1}(z0, x), z10)
f_{f_2,s_1}(z00, f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{f_2,s_1}(z00, f_{s_1,s_1}(z0, x))
f_{f_2,f_2}(f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{f_2,f_2}(f_{s_1,s_1}(z0, x), z10)
f_{f_2,f_2}(z00, f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{f_2,f_2}(z00, f_{s_1,s_1}(z0, x))
g_{g_2,g_2}(f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{g_2,g_2}(f_{s_1,s_1}(z0, x), z10)
g_{g_2,g_2}(z00, f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{g_2,g_2}(z00, f_{s_1,s_1}(z0, x))
g_{g_2,s_1}(f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{g_2,s_1}(f_{s_1,s_1}(z0, x), z10)
g_{g_2,s_1}(z00, f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{g_2,s_1}(z00, f_{s_1,s_1}(z0, x))
g_{g_2,f_2}(f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{g_2,f_2}(f_{s_1,s_1}(z0, x), z10)
g_{g_2,f_2}(z00, f_{s_1,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{g_2,f_2}(z00, f_{s_1,s_1}(z0, x))
g_{s_1,g_2}(f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{s_1,g_2}(f_{s_1,s_1}(z0, x), z10)
g_{s_1,g_2}(z00, f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{s_1,g_2}(z00, f_{s_1,s_1}(z0, x))
s_{g_2}(f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → s_{g_2}(f_{s_1,s_1}(z0, x))
g_{f_2,g_2}(f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{f_2,g_2}(f_{s_1,s_1}(z0, x), z10)
g_{f_2,g_2}(z00, f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{f_2,g_2}(z00, f_{s_1,s_1}(z0, x))
f_{g_2,g_2}(f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{g_2,g_2}(f_{s_1,s_1}(z0, x), z10)
f_{g_2,g_2}(z00, f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{g_2,g_2}(z00, f_{s_1,s_1}(z0, x))
g_{s_1,s_1}(f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{s_1,s_1}(f_{s_1,s_1}(z0, x), z10)
g_{s_1,s_1}(z00, f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{s_1,s_1}(z00, f_{s_1,s_1}(z0, x))
g_{f_2,s_1}(f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{f_2,s_1}(f_{s_1,s_1}(z0, x), z10)
g_{f_2,s_1}(z00, f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{f_2,s_1}(z00, f_{s_1,s_1}(z0, x))
f_{g_2,s_1}(f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{g_2,s_1}(f_{s_1,s_1}(z0, x), z10)
f_{g_2,s_1}(z00, f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{g_2,s_1}(z00, f_{s_1,s_1}(z0, x))
g_{s_1,f_2}(f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{s_1,f_2}(f_{s_1,s_1}(z0, x), z10)
g_{s_1,f_2}(z00, f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{s_1,f_2}(z00, f_{s_1,s_1}(z0, x))
g_{f_2,f_2}(f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{f_2,f_2}(f_{s_1,s_1}(z0, x), z10)
g_{f_2,f_2}(z00, f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{f_2,f_2}(z00, f_{s_1,s_1}(z0, x))
f_{g_2,f_2}(f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{g_2,f_2}(f_{s_1,s_1}(z0, x), z10)
f_{g_2,f_2}(z00, f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{g_2,f_2}(z00, f_{s_1,s_1}(z0, x))
s_{s_1}(f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → s_{s_1}(f_{s_1,s_1}(z0, x))
f_{s_1,g_2}(f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{s_1,g_2}(f_{s_1,s_1}(z0, x), z10)
f_{s_1,g_2}(z00, f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{s_1,g_2}(z00, f_{s_1,s_1}(z0, x))
f_{s_1,s_1}(f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{s_1,s_1}(f_{s_1,s_1}(z0, x), z10)
f_{s_1,s_1}(z00, f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{s_1,s_1}(z00, f_{s_1,s_1}(z0, x))
f_{s_1,f_2}(f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{s_1,f_2}(f_{s_1,s_1}(z0, x), z10)
f_{s_1,f_2}(z00, f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{s_1,f_2}(z00, f_{s_1,s_1}(z0, x))
s_{f_2}(f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → s_{f_2}(f_{s_1,s_1}(z0, x))
f_{f_2,g_2}(f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{f_2,g_2}(f_{s_1,s_1}(z0, x), z10)
f_{f_2,g_2}(z00, f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{f_2,g_2}(z00, f_{s_1,s_1}(z0, x))
f_{f_2,s_1}(f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{f_2,s_1}(f_{s_1,s_1}(z0, x), z10)
f_{f_2,s_1}(z00, f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{f_2,s_1}(z00, f_{s_1,s_1}(z0, x))
f_{f_2,f_2}(f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{f_2,f_2}(f_{s_1,s_1}(z0, x), z10)
f_{f_2,f_2}(z00, f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{f_2,f_2}(z00, f_{s_1,s_1}(z0, x))
g_{g_2,g_2}(f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{g_2,g_2}(f_{s_1,s_1}(z0, x), z10)
g_{g_2,g_2}(z00, f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{g_2,g_2}(z00, f_{s_1,s_1}(z0, x))
g_{g_2,s_1}(f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{g_2,s_1}(f_{s_1,s_1}(z0, x), z10)
g_{g_2,s_1}(z00, f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{g_2,s_1}(z00, f_{s_1,s_1}(z0, x))
g_{g_2,f_2}(f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{g_2,f_2}(f_{s_1,s_1}(z0, x), z10)
g_{g_2,f_2}(z00, f_{s_1,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{g_2,f_2}(z00, f_{s_1,s_1}(z0, x))
g_{s_1,g_2}(f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{s_1,g_2}(f_{s_1,s_1}(z0, x), z10)
g_{s_1,g_2}(z00, f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{s_1,g_2}(z00, f_{s_1,s_1}(z0, x))
s_{g_2}(f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → s_{g_2}(f_{s_1,s_1}(z0, x))
g_{f_2,g_2}(f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{f_2,g_2}(f_{s_1,s_1}(z0, x), z10)
g_{f_2,g_2}(z00, f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{f_2,g_2}(z00, f_{s_1,s_1}(z0, x))
f_{g_2,g_2}(f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{g_2,g_2}(f_{s_1,s_1}(z0, x), z10)
f_{g_2,g_2}(z00, f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{g_2,g_2}(z00, f_{s_1,s_1}(z0, x))
g_{s_1,s_1}(f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{s_1,s_1}(f_{s_1,s_1}(z0, x), z10)
g_{s_1,s_1}(z00, f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{s_1,s_1}(z00, f_{s_1,s_1}(z0, x))
g_{f_2,s_1}(f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{f_2,s_1}(f_{s_1,s_1}(z0, x), z10)
g_{f_2,s_1}(z00, f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{f_2,s_1}(z00, f_{s_1,s_1}(z0, x))
f_{g_2,s_1}(f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{g_2,s_1}(f_{s_1,s_1}(z0, x), z10)
f_{g_2,s_1}(z00, f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{g_2,s_1}(z00, f_{s_1,s_1}(z0, x))
g_{s_1,f_2}(f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{s_1,f_2}(f_{s_1,s_1}(z0, x), z10)
g_{s_1,f_2}(z00, f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{s_1,f_2}(z00, f_{s_1,s_1}(z0, x))
g_{f_2,f_2}(f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{f_2,f_2}(f_{s_1,s_1}(z0, x), z10)
g_{f_2,f_2}(z00, f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{f_2,f_2}(z00, f_{s_1,s_1}(z0, x))
f_{g_2,f_2}(f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{g_2,f_2}(f_{s_1,s_1}(z0, x), z10)
f_{g_2,f_2}(z00, f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{g_2,f_2}(z00, f_{s_1,s_1}(z0, x))
s_{s_1}(f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → s_{s_1}(f_{s_1,s_1}(z0, x))
f_{s_1,g_2}(f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{s_1,g_2}(f_{s_1,s_1}(z0, x), z10)
f_{s_1,g_2}(z00, f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{s_1,g_2}(z00, f_{s_1,s_1}(z0, x))
f_{s_1,s_1}(f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{s_1,s_1}(f_{s_1,s_1}(z0, x), z10)
f_{s_1,s_1}(z00, f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{s_1,s_1}(z00, f_{s_1,s_1}(z0, x))
f_{s_1,f_2}(f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{s_1,f_2}(f_{s_1,s_1}(z0, x), z10)
f_{s_1,f_2}(z00, f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{s_1,f_2}(z00, f_{s_1,s_1}(z0, x))
s_{f_2}(f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → s_{f_2}(f_{s_1,s_1}(z0, x))
f_{f_2,g_2}(f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{f_2,g_2}(f_{s_1,s_1}(z0, x), z10)
f_{f_2,g_2}(z00, f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{f_2,g_2}(z00, f_{s_1,s_1}(z0, x))
f_{f_2,s_1}(f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{f_2,s_1}(f_{s_1,s_1}(z0, x), z10)
f_{f_2,s_1}(z00, f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{f_2,s_1}(z00, f_{s_1,s_1}(z0, x))
f_{f_2,f_2}(f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{f_2,f_2}(f_{s_1,s_1}(z0, x), z10)
f_{f_2,f_2}(z00, f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{f_2,f_2}(z00, f_{s_1,s_1}(z0, x))
g_{g_2,g_2}(f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{g_2,g_2}(f_{s_1,s_1}(z0, x), z10)
g_{g_2,g_2}(z00, f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{g_2,g_2}(z00, f_{s_1,s_1}(z0, x))
g_{g_2,s_1}(f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{g_2,s_1}(f_{s_1,s_1}(z0, x), z10)
g_{g_2,s_1}(z00, f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{g_2,s_1}(z00, f_{s_1,s_1}(z0, x))
g_{g_2,f_2}(f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{g_2,f_2}(f_{s_1,s_1}(z0, x), z10)
g_{g_2,f_2}(z00, f_{s_1,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{g_2,f_2}(z00, f_{s_1,s_1}(z0, x))
g_{s_1,g_2}(f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{s_1,g_2}(f_{f_2,g_2}(z0, x), z10)
g_{s_1,g_2}(z00, f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{s_1,g_2}(z00, f_{f_2,g_2}(z0, x))
s_{g_2}(f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → s_{g_2}(f_{f_2,g_2}(z0, x))
g_{f_2,g_2}(f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{f_2,g_2}(f_{f_2,g_2}(z0, x), z10)
g_{f_2,g_2}(z00, f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{f_2,g_2}(z00, f_{f_2,g_2}(z0, x))
f_{g_2,g_2}(f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{g_2,g_2}(f_{f_2,g_2}(z0, x), z10)
f_{g_2,g_2}(z00, f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{g_2,g_2}(z00, f_{f_2,g_2}(z0, x))
g_{s_1,s_1}(f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{s_1,s_1}(f_{f_2,g_2}(z0, x), z10)
g_{s_1,s_1}(z00, f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{s_1,s_1}(z00, f_{f_2,g_2}(z0, x))
g_{f_2,s_1}(f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{f_2,s_1}(f_{f_2,g_2}(z0, x), z10)
g_{f_2,s_1}(z00, f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{f_2,s_1}(z00, f_{f_2,g_2}(z0, x))
f_{g_2,s_1}(f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{g_2,s_1}(f_{f_2,g_2}(z0, x), z10)
f_{g_2,s_1}(z00, f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{g_2,s_1}(z00, f_{f_2,g_2}(z0, x))
g_{s_1,f_2}(f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{s_1,f_2}(f_{f_2,g_2}(z0, x), z10)
g_{s_1,f_2}(z00, f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{s_1,f_2}(z00, f_{f_2,g_2}(z0, x))
g_{f_2,f_2}(f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{f_2,f_2}(f_{f_2,g_2}(z0, x), z10)
g_{f_2,f_2}(z00, f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{f_2,f_2}(z00, f_{f_2,g_2}(z0, x))
f_{g_2,f_2}(f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{g_2,f_2}(f_{f_2,g_2}(z0, x), z10)
f_{g_2,f_2}(z00, f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{g_2,f_2}(z00, f_{f_2,g_2}(z0, x))
s_{s_1}(f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → s_{s_1}(f_{f_2,g_2}(z0, x))
f_{s_1,g_2}(f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{s_1,g_2}(f_{f_2,g_2}(z0, x), z10)
f_{s_1,g_2}(z00, f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{s_1,g_2}(z00, f_{f_2,g_2}(z0, x))
f_{s_1,s_1}(f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{s_1,s_1}(f_{f_2,g_2}(z0, x), z10)
f_{s_1,s_1}(z00, f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{s_1,s_1}(z00, f_{f_2,g_2}(z0, x))
f_{s_1,f_2}(f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{s_1,f_2}(f_{f_2,g_2}(z0, x), z10)
f_{s_1,f_2}(z00, f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{s_1,f_2}(z00, f_{f_2,g_2}(z0, x))
s_{f_2}(f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → s_{f_2}(f_{f_2,g_2}(z0, x))
f_{f_2,g_2}(f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{f_2,g_2}(f_{f_2,g_2}(z0, x), z10)
f_{f_2,g_2}(z00, f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{f_2,g_2}(z00, f_{f_2,g_2}(z0, x))
f_{f_2,s_1}(f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{f_2,s_1}(f_{f_2,g_2}(z0, x), z10)
f_{f_2,s_1}(z00, f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{f_2,s_1}(z00, f_{f_2,g_2}(z0, x))
f_{f_2,f_2}(f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → f_{f_2,f_2}(f_{f_2,g_2}(z0, x), z10)
f_{f_2,f_2}(z00, f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → f_{f_2,f_2}(z00, f_{f_2,g_2}(z0, x))
g_{g_2,g_2}(f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{g_2,g_2}(f_{f_2,g_2}(z0, x), z10)
g_{g_2,g_2}(z00, f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{g_2,g_2}(z00, f_{f_2,g_2}(z0, x))
g_{g_2,s_1}(f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{g_2,s_1}(f_{f_2,g_2}(z0, x), z10)
g_{g_2,s_1}(z00, f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{g_2,s_1}(z00, f_{f_2,g_2}(z0, x))
g_{g_2,f_2}(f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y)), z10) → g_{g_2,f_2}(f_{f_2,g_2}(z0, x), z10)
g_{g_2,f_2}(z00, f_{f_2,f_2}(z0, f_{g_2,g_2}(x, y))) → g_{g_2,f_2}(z00, f_{f_2,g_2}(z0, x))
g_{s_1,g_2}(f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{s_1,g_2}(f_{f_2,g_2}(z0, x), z10)
g_{s_1,g_2}(z00, f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{s_1,g_2}(z00, f_{f_2,g_2}(z0, x))
s_{g_2}(f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → s_{g_2}(f_{f_2,g_2}(z0, x))
g_{f_2,g_2}(f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{f_2,g_2}(f_{f_2,g_2}(z0, x), z10)
g_{f_2,g_2}(z00, f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{f_2,g_2}(z00, f_{f_2,g_2}(z0, x))
f_{g_2,g_2}(f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{g_2,g_2}(f_{f_2,g_2}(z0, x), z10)
f_{g_2,g_2}(z00, f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{g_2,g_2}(z00, f_{f_2,g_2}(z0, x))
g_{s_1,s_1}(f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{s_1,s_1}(f_{f_2,g_2}(z0, x), z10)
g_{s_1,s_1}(z00, f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{s_1,s_1}(z00, f_{f_2,g_2}(z0, x))
g_{f_2,s_1}(f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{f_2,s_1}(f_{f_2,g_2}(z0, x), z10)
g_{f_2,s_1}(z00, f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{f_2,s_1}(z00, f_{f_2,g_2}(z0, x))
f_{g_2,s_1}(f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{g_2,s_1}(f_{f_2,g_2}(z0, x), z10)
f_{g_2,s_1}(z00, f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{g_2,s_1}(z00, f_{f_2,g_2}(z0, x))
g_{s_1,f_2}(f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{s_1,f_2}(f_{f_2,g_2}(z0, x), z10)
g_{s_1,f_2}(z00, f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{s_1,f_2}(z00, f_{f_2,g_2}(z0, x))
g_{f_2,f_2}(f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{f_2,f_2}(f_{f_2,g_2}(z0, x), z10)
g_{f_2,f_2}(z00, f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{f_2,f_2}(z00, f_{f_2,g_2}(z0, x))
f_{g_2,f_2}(f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{g_2,f_2}(f_{f_2,g_2}(z0, x), z10)
f_{g_2,f_2}(z00, f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{g_2,f_2}(z00, f_{f_2,g_2}(z0, x))
s_{s_1}(f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → s_{s_1}(f_{f_2,g_2}(z0, x))
f_{s_1,g_2}(f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{s_1,g_2}(f_{f_2,g_2}(z0, x), z10)
f_{s_1,g_2}(z00, f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{s_1,g_2}(z00, f_{f_2,g_2}(z0, x))
f_{s_1,s_1}(f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{s_1,s_1}(f_{f_2,g_2}(z0, x), z10)
f_{s_1,s_1}(z00, f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{s_1,s_1}(z00, f_{f_2,g_2}(z0, x))
f_{s_1,f_2}(f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{s_1,f_2}(f_{f_2,g_2}(z0, x), z10)
f_{s_1,f_2}(z00, f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{s_1,f_2}(z00, f_{f_2,g_2}(z0, x))
s_{f_2}(f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → s_{f_2}(f_{f_2,g_2}(z0, x))
f_{f_2,g_2}(f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{f_2,g_2}(f_{f_2,g_2}(z0, x), z10)
f_{f_2,g_2}(z00, f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{f_2,g_2}(z00, f_{f_2,g_2}(z0, x))
f_{f_2,s_1}(f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{f_2,s_1}(f_{f_2,g_2}(z0, x), z10)
f_{f_2,s_1}(z00, f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{f_2,s_1}(z00, f_{f_2,g_2}(z0, x))
f_{f_2,f_2}(f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → f_{f_2,f_2}(f_{f_2,g_2}(z0, x), z10)
f_{f_2,f_2}(z00, f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → f_{f_2,f_2}(z00, f_{f_2,g_2}(z0, x))
g_{g_2,g_2}(f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{g_2,g_2}(f_{f_2,g_2}(z0, x), z10)
g_{g_2,g_2}(z00, f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{g_2,g_2}(z00, f_{f_2,g_2}(z0, x))
g_{g_2,s_1}(f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{g_2,s_1}(f_{f_2,g_2}(z0, x), z10)
g_{g_2,s_1}(z00, f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{g_2,s_1}(z00, f_{f_2,g_2}(z0, x))
g_{g_2,f_2}(f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y)), z10) → g_{g_2,f_2}(f_{f_2,g_2}(z0, x), z10)
g_{g_2,f_2}(z00, f_{f_2,f_2}(z0, f_{g_2,s_1}(x, y))) → g_{g_2,f_2}(z00, f_{f_2,g_2}(z0, x))
g_{s_1,g_2}(f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{s_1,g_2}(f_{f_2,g_2}(z0, x), z10)
g_{s_1,g_2}(z00, f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{s_1,g_2}(z00, f_{f_2,g_2}(z0, x))
s_{g_2}(f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → s_{g_2}(f_{f_2,g_2}(z0, x))
g_{f_2,g_2}(f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{f_2,g_2}(f_{f_2,g_2}(z0, x), z10)
g_{f_2,g_2}(z00, f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{f_2,g_2}(z00, f_{f_2,g_2}(z0, x))
f_{g_2,g_2}(f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{g_2,g_2}(f_{f_2,g_2}(z0, x), z10)
f_{g_2,g_2}(z00, f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{g_2,g_2}(z00, f_{f_2,g_2}(z0, x))
g_{s_1,s_1}(f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{s_1,s_1}(f_{f_2,g_2}(z0, x), z10)
g_{s_1,s_1}(z00, f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{s_1,s_1}(z00, f_{f_2,g_2}(z0, x))
g_{f_2,s_1}(f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{f_2,s_1}(f_{f_2,g_2}(z0, x), z10)
g_{f_2,s_1}(z00, f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{f_2,s_1}(z00, f_{f_2,g_2}(z0, x))
f_{g_2,s_1}(f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{g_2,s_1}(f_{f_2,g_2}(z0, x), z10)
f_{g_2,s_1}(z00, f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{g_2,s_1}(z00, f_{f_2,g_2}(z0, x))
g_{s_1,f_2}(f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{s_1,f_2}(f_{f_2,g_2}(z0, x), z10)
g_{s_1,f_2}(z00, f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{s_1,f_2}(z00, f_{f_2,g_2}(z0, x))
g_{f_2,f_2}(f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{f_2,f_2}(f_{f_2,g_2}(z0, x), z10)
g_{f_2,f_2}(z00, f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{f_2,f_2}(z00, f_{f_2,g_2}(z0, x))
f_{g_2,f_2}(f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{g_2,f_2}(f_{f_2,g_2}(z0, x), z10)
f_{g_2,f_2}(z00, f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{g_2,f_2}(z00, f_{f_2,g_2}(z0, x))
s_{s_1}(f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → s_{s_1}(f_{f_2,g_2}(z0, x))
f_{s_1,g_2}(f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{s_1,g_2}(f_{f_2,g_2}(z0, x), z10)
f_{s_1,g_2}(z00, f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{s_1,g_2}(z00, f_{f_2,g_2}(z0, x))
f_{s_1,s_1}(f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{s_1,s_1}(f_{f_2,g_2}(z0, x), z10)
f_{s_1,s_1}(z00, f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{s_1,s_1}(z00, f_{f_2,g_2}(z0, x))
f_{s_1,f_2}(f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{s_1,f_2}(f_{f_2,g_2}(z0, x), z10)
f_{s_1,f_2}(z00, f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{s_1,f_2}(z00, f_{f_2,g_2}(z0, x))
s_{f_2}(f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → s_{f_2}(f_{f_2,g_2}(z0, x))
f_{f_2,g_2}(f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{f_2,g_2}(f_{f_2,g_2}(z0, x), z10)
f_{f_2,g_2}(z00, f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{f_2,g_2}(z00, f_{f_2,g_2}(z0, x))
f_{f_2,s_1}(f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{f_2,s_1}(f_{f_2,g_2}(z0, x), z10)
f_{f_2,s_1}(z00, f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{f_2,s_1}(z00, f_{f_2,g_2}(z0, x))
f_{f_2,f_2}(f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → f_{f_2,f_2}(f_{f_2,g_2}(z0, x), z10)
f_{f_2,f_2}(z00, f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → f_{f_2,f_2}(z00, f_{f_2,g_2}(z0, x))
g_{g_2,g_2}(f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{g_2,g_2}(f_{f_2,g_2}(z0, x), z10)
g_{g_2,g_2}(z00, f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{g_2,g_2}(z00, f_{f_2,g_2}(z0, x))
g_{g_2,s_1}(f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{g_2,s_1}(f_{f_2,g_2}(z0, x), z10)
g_{g_2,s_1}(z00, f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{g_2,s_1}(z00, f_{f_2,g_2}(z0, x))
g_{g_2,f_2}(f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y)), z10) → g_{g_2,f_2}(f_{f_2,g_2}(z0, x), z10)
g_{g_2,f_2}(z00, f_{f_2,f_2}(z0, f_{g_2,f_2}(x, y))) → g_{g_2,f_2}(z00, f_{f_2,g_2}(z0, x))
g_{s_1,g_2}(f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{s_1,g_2}(f_{f_2,s_1}(z0, x), z10)
g_{s_1,g_2}(z00, f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{s_1,g_2}(z00, f_{f_2,s_1}(z0, x))
s_{g_2}(f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → s_{g_2}(f_{f_2,s_1}(z0, x))
g_{f_2,g_2}(f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{f_2,g_2}(f_{f_2,s_1}(z0, x), z10)
g_{f_2,g_2}(z00, f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{f_2,g_2}(z00, f_{f_2,s_1}(z0, x))
f_{g_2,g_2}(f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{g_2,g_2}(f_{f_2,s_1}(z0, x), z10)
f_{g_2,g_2}(z00, f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{g_2,g_2}(z00, f_{f_2,s_1}(z0, x))
g_{s_1,s_1}(f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{s_1,s_1}(f_{f_2,s_1}(z0, x), z10)
g_{s_1,s_1}(z00, f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{s_1,s_1}(z00, f_{f_2,s_1}(z0, x))
g_{f_2,s_1}(f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{f_2,s_1}(f_{f_2,s_1}(z0, x), z10)
g_{f_2,s_1}(z00, f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{f_2,s_1}(z00, f_{f_2,s_1}(z0, x))
f_{g_2,s_1}(f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{g_2,s_1}(f_{f_2,s_1}(z0, x), z10)
f_{g_2,s_1}(z00, f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{g_2,s_1}(z00, f_{f_2,s_1}(z0, x))
g_{s_1,f_2}(f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{s_1,f_2}(f_{f_2,s_1}(z0, x), z10)
g_{s_1,f_2}(z00, f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{s_1,f_2}(z00, f_{f_2,s_1}(z0, x))
g_{f_2,f_2}(f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{f_2,f_2}(f_{f_2,s_1}(z0, x), z10)
g_{f_2,f_2}(z00, f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{f_2,f_2}(z00, f_{f_2,s_1}(z0, x))
f_{g_2,f_2}(f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{g_2,f_2}(f_{f_2,s_1}(z0, x), z10)
f_{g_2,f_2}(z00, f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{g_2,f_2}(z00, f_{f_2,s_1}(z0, x))
s_{s_1}(f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → s_{s_1}(f_{f_2,s_1}(z0, x))
f_{s_1,g_2}(f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{s_1,g_2}(f_{f_2,s_1}(z0, x), z10)
f_{s_1,g_2}(z00, f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{s_1,g_2}(z00, f_{f_2,s_1}(z0, x))
f_{s_1,s_1}(f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{s_1,s_1}(f_{f_2,s_1}(z0, x), z10)
f_{s_1,s_1}(z00, f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{s_1,s_1}(z00, f_{f_2,s_1}(z0, x))
f_{s_1,f_2}(f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{s_1,f_2}(f_{f_2,s_1}(z0, x), z10)
f_{s_1,f_2}(z00, f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{s_1,f_2}(z00, f_{f_2,s_1}(z0, x))
s_{f_2}(f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → s_{f_2}(f_{f_2,s_1}(z0, x))
f_{f_2,g_2}(f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{f_2,g_2}(f_{f_2,s_1}(z0, x), z10)
f_{f_2,g_2}(z00, f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{f_2,g_2}(z00, f_{f_2,s_1}(z0, x))
f_{f_2,s_1}(f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{f_2,s_1}(f_{f_2,s_1}(z0, x), z10)
f_{f_2,s_1}(z00, f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{f_2,s_1}(z00, f_{f_2,s_1}(z0, x))
f_{f_2,f_2}(f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → f_{f_2,f_2}(f_{f_2,s_1}(z0, x), z10)
f_{f_2,f_2}(z00, f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → f_{f_2,f_2}(z00, f_{f_2,s_1}(z0, x))
g_{g_2,g_2}(f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{g_2,g_2}(f_{f_2,s_1}(z0, x), z10)
g_{g_2,g_2}(z00, f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{g_2,g_2}(z00, f_{f_2,s_1}(z0, x))
g_{g_2,s_1}(f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{g_2,s_1}(f_{f_2,s_1}(z0, x), z10)
g_{g_2,s_1}(z00, f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{g_2,s_1}(z00, f_{f_2,s_1}(z0, x))
g_{g_2,f_2}(f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y)), z10) → g_{g_2,f_2}(f_{f_2,s_1}(z0, x), z10)
g_{g_2,f_2}(z00, f_{f_2,f_2}(z0, f_{s_1,g_2}(x, y))) → g_{g_2,f_2}(z00, f_{f_2,s_1}(z0, x))
g_{s_1,g_2}(f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{s_1,g_2}(f_{f_2,s_1}(z0, x), z10)
g_{s_1,g_2}(z00, f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{s_1,g_2}(z00, f_{f_2,s_1}(z0, x))
s_{g_2}(f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → s_{g_2}(f_{f_2,s_1}(z0, x))
g_{f_2,g_2}(f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{f_2,g_2}(f_{f_2,s_1}(z0, x), z10)
g_{f_2,g_2}(z00, f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{f_2,g_2}(z00, f_{f_2,s_1}(z0, x))
f_{g_2,g_2}(f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{g_2,g_2}(f_{f_2,s_1}(z0, x), z10)
f_{g_2,g_2}(z00, f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{g_2,g_2}(z00, f_{f_2,s_1}(z0, x))
g_{s_1,s_1}(f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{s_1,s_1}(f_{f_2,s_1}(z0, x), z10)
g_{s_1,s_1}(z00, f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{s_1,s_1}(z00, f_{f_2,s_1}(z0, x))
g_{f_2,s_1}(f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{f_2,s_1}(f_{f_2,s_1}(z0, x), z10)
g_{f_2,s_1}(z00, f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{f_2,s_1}(z00, f_{f_2,s_1}(z0, x))
f_{g_2,s_1}(f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{g_2,s_1}(f_{f_2,s_1}(z0, x), z10)
f_{g_2,s_1}(z00, f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{g_2,s_1}(z00, f_{f_2,s_1}(z0, x))
g_{s_1,f_2}(f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{s_1,f_2}(f_{f_2,s_1}(z0, x), z10)
g_{s_1,f_2}(z00, f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{s_1,f_2}(z00, f_{f_2,s_1}(z0, x))
g_{f_2,f_2}(f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{f_2,f_2}(f_{f_2,s_1}(z0, x), z10)
g_{f_2,f_2}(z00, f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{f_2,f_2}(z00, f_{f_2,s_1}(z0, x))
f_{g_2,f_2}(f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{g_2,f_2}(f_{f_2,s_1}(z0, x), z10)
f_{g_2,f_2}(z00, f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{g_2,f_2}(z00, f_{f_2,s_1}(z0, x))
s_{s_1}(f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → s_{s_1}(f_{f_2,s_1}(z0, x))
f_{s_1,g_2}(f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{s_1,g_2}(f_{f_2,s_1}(z0, x), z10)
f_{s_1,g_2}(z00, f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{s_1,g_2}(z00, f_{f_2,s_1}(z0, x))
f_{s_1,s_1}(f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{s_1,s_1}(f_{f_2,s_1}(z0, x), z10)
f_{s_1,s_1}(z00, f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{s_1,s_1}(z00, f_{f_2,s_1}(z0, x))
f_{s_1,f_2}(f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{s_1,f_2}(f_{f_2,s_1}(z0, x), z10)
f_{s_1,f_2}(z00, f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{s_1,f_2}(z00, f_{f_2,s_1}(z0, x))
s_{f_2}(f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → s_{f_2}(f_{f_2,s_1}(z0, x))
f_{f_2,g_2}(f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{f_2,g_2}(f_{f_2,s_1}(z0, x), z10)
f_{f_2,g_2}(z00, f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{f_2,g_2}(z00, f_{f_2,s_1}(z0, x))
f_{f_2,s_1}(f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{f_2,s_1}(f_{f_2,s_1}(z0, x), z10)
f_{f_2,s_1}(z00, f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{f_2,s_1}(z00, f_{f_2,s_1}(z0, x))
f_{f_2,f_2}(f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → f_{f_2,f_2}(f_{f_2,s_1}(z0, x), z10)
f_{f_2,f_2}(z00, f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → f_{f_2,f_2}(z00, f_{f_2,s_1}(z0, x))
g_{g_2,g_2}(f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{g_2,g_2}(f_{f_2,s_1}(z0, x), z10)
g_{g_2,g_2}(z00, f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{g_2,g_2}(z00, f_{f_2,s_1}(z0, x))
g_{g_2,s_1}(f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{g_2,s_1}(f_{f_2,s_1}(z0, x), z10)
g_{g_2,s_1}(z00, f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{g_2,s_1}(z00, f_{f_2,s_1}(z0, x))
g_{g_2,f_2}(f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y)), z10) → g_{g_2,f_2}(f_{f_2,s_1}(z0, x), z10)
g_{g_2,f_2}(z00, f_{f_2,f_2}(z0, f_{s_1,s_1}(x, y))) → g_{g_2,f_2}(z00, f_{f_2,s_1}(z0, x))
g_{s_1,g_2}(f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{s_1,g_2}(f_{f_2,s_1}(z0, x), z10)
g_{s_1,g_2}(z00, f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{s_1,g_2}(z00, f_{f_2,s_1}(z0, x))
s_{g_2}(f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → s_{g_2}(f_{f_2,s_1}(z0, x))
g_{f_2,g_2}(f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{f_2,g_2}(f_{f_2,s_1}(z0, x), z10)
g_{f_2,g_2}(z00, f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{f_2,g_2}(z00, f_{f_2,s_1}(z0, x))
f_{g_2,g_2}(f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{g_2,g_2}(f_{f_2,s_1}(z0, x), z10)
f_{g_2,g_2}(z00, f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{g_2,g_2}(z00, f_{f_2,s_1}(z0, x))
g_{s_1,s_1}(f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{s_1,s_1}(f_{f_2,s_1}(z0, x), z10)
g_{s_1,s_1}(z00, f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{s_1,s_1}(z00, f_{f_2,s_1}(z0, x))
g_{f_2,s_1}(f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{f_2,s_1}(f_{f_2,s_1}(z0, x), z10)
g_{f_2,s_1}(z00, f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{f_2,s_1}(z00, f_{f_2,s_1}(z0, x))
f_{g_2,s_1}(f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{g_2,s_1}(f_{f_2,s_1}(z0, x), z10)
f_{g_2,s_1}(z00, f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{g_2,s_1}(z00, f_{f_2,s_1}(z0, x))
g_{s_1,f_2}(f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{s_1,f_2}(f_{f_2,s_1}(z0, x), z10)
g_{s_1,f_2}(z00, f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{s_1,f_2}(z00, f_{f_2,s_1}(z0, x))
g_{f_2,f_2}(f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{f_2,f_2}(f_{f_2,s_1}(z0, x), z10)
g_{f_2,f_2}(z00, f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{f_2,f_2}(z00, f_{f_2,s_1}(z0, x))
f_{g_2,f_2}(f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{g_2,f_2}(f_{f_2,s_1}(z0, x), z10)
f_{g_2,f_2}(z00, f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{g_2,f_2}(z00, f_{f_2,s_1}(z0, x))
s_{s_1}(f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → s_{s_1}(f_{f_2,s_1}(z0, x))
f_{s_1,g_2}(f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{s_1,g_2}(f_{f_2,s_1}(z0, x), z10)
f_{s_1,g_2}(z00, f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{s_1,g_2}(z00, f_{f_2,s_1}(z0, x))
f_{s_1,s_1}(f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{s_1,s_1}(f_{f_2,s_1}(z0, x), z10)
f_{s_1,s_1}(z00, f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{s_1,s_1}(z00, f_{f_2,s_1}(z0, x))
f_{s_1,f_2}(f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{s_1,f_2}(f_{f_2,s_1}(z0, x), z10)
f_{s_1,f_2}(z00, f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{s_1,f_2}(z00, f_{f_2,s_1}(z0, x))
s_{f_2}(f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → s_{f_2}(f_{f_2,s_1}(z0, x))
f_{f_2,g_2}(f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{f_2,g_2}(f_{f_2,s_1}(z0, x), z10)
f_{f_2,g_2}(z00, f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{f_2,g_2}(z00, f_{f_2,s_1}(z0, x))
f_{f_2,s_1}(f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{f_2,s_1}(f_{f_2,s_1}(z0, x), z10)
f_{f_2,s_1}(z00, f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{f_2,s_1}(z00, f_{f_2,s_1}(z0, x))
f_{f_2,f_2}(f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → f_{f_2,f_2}(f_{f_2,s_1}(z0, x), z10)
f_{f_2,f_2}(z00, f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → f_{f_2,f_2}(z00, f_{f_2,s_1}(z0, x))
g_{g_2,g_2}(f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{g_2,g_2}(f_{f_2,s_1}(z0, x), z10)
g_{g_2,g_2}(z00, f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{g_2,g_2}(z00, f_{f_2,s_1}(z0, x))
g_{g_2,s_1}(f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{g_2,s_1}(f_{f_2,s_1}(z0, x), z10)
g_{g_2,s_1}(z00, f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{g_2,s_1}(z00, f_{f_2,s_1}(z0, x))
g_{g_2,f_2}(f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y)), z10) → g_{g_2,f_2}(f_{f_2,s_1}(z0, x), z10)
g_{g_2,f_2}(z00, f_{f_2,f_2}(z0, f_{s_1,f_2}(x, y))) → g_{g_2,f_2}(z00, f_{f_2,s_1}(z0, x))