YES
0 QTRS
↳1 DependencyPairsProof (⇔, 14 ms)
↳2 QDP
↳3 QDPOrderProof (⇔, 15 ms)
↳4 QDP
↳5 QDPSizeChangeProof (⇔, 0 ms)
↳6 YES
a(lambda(x), y) → lambda(a(x, p(1, a(y, t))))
a(p(x, y), z) → p(a(x, z), a(y, z))
a(a(x, y), z) → a(x, a(y, z))
a(id, x) → x
a(1, id) → 1
a(t, id) → t
a(1, p(x, y)) → x
a(t, p(x, y)) → y
A(lambda(x), y) → A(x, p(1, a(y, t)))
A(lambda(x), y) → A(y, t)
A(p(x, y), z) → A(x, z)
A(p(x, y), z) → A(y, z)
A(a(x, y), z) → A(x, a(y, z))
A(a(x, y), z) → A(y, z)
a(lambda(x), y) → lambda(a(x, p(1, a(y, t))))
a(p(x, y), z) → p(a(x, z), a(y, z))
a(a(x, y), z) → a(x, a(y, z))
a(id, x) → x
a(1, id) → 1
a(t, id) → t
a(1, p(x, y)) → x
a(t, p(x, y)) → y
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(lambda(x), y) → A(x, p(1, a(y, t)))
A(lambda(x), y) → A(y, t)
POL(1) = 0
POL(A(x1, x2)) = x1 + x2
POL(a(x1, x2)) = x1 + x2
POL(id) = 0
POL(lambda(x1)) = 1 + x1
POL(p(x1, x2)) = max(x1, x2)
POL(t) = 0
a(lambda(x), y) → lambda(a(x, p(1, a(y, t))))
a(p(x, y), z) → p(a(x, z), a(y, z))
a(a(x, y), z) → a(x, a(y, z))
a(id, x) → x
a(1, id) → 1
a(t, id) → t
a(1, p(x, y)) → x
a(t, p(x, y)) → y
A(p(x, y), z) → A(x, z)
A(p(x, y), z) → A(y, z)
A(a(x, y), z) → A(x, a(y, z))
A(a(x, y), z) → A(y, z)
a(lambda(x), y) → lambda(a(x, p(1, a(y, t))))
a(p(x, y), z) → p(a(x, z), a(y, z))
a(a(x, y), z) → a(x, a(y, z))
a(id, x) → x
a(1, id) → 1
a(t, id) → t
a(1, p(x, y)) → x
a(t, p(x, y)) → y
From the DPs we obtained the following set of size-change graphs: