YES
0 QTRS
↳1 QTRSRRRProof (⇔, 0 ms)
↳2 QTRS
↳3 QTRSRRRProof (⇔, 0 ms)
↳4 QTRS
↳5 AAECC Innermost (⇔, 0 ms)
↳6 QTRS
↳7 DependencyPairsProof (⇔, 0 ms)
↳8 QDP
↳9 DependencyGraphProof (⇔, 0 ms)
↳10 TRUE
f(s(X)) → f(X)
g(cons(0, Y)) → g(Y)
g(cons(s(X), Y)) → s(X)
h(cons(X, Y)) → h(g(cons(X, Y)))
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
POL(0) = 0
POL(cons(x1, x2)) = 2 + x1 + x2
POL(f(x1)) = x1
POL(g(x1)) = x1
POL(h(x1)) = 2·x1
POL(s(x1)) = 2·x1
g(cons(0, Y)) → g(Y)
g(cons(s(X), Y)) → s(X)
f(s(X)) → f(X)
h(cons(X, Y)) → h(g(cons(X, Y)))
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
POL(cons(x1, x2)) = x1 + x2
POL(f(x1)) = x1
POL(g(x1)) = x1
POL(h(x1)) = 2·x1
POL(s(x1)) = 1 + x1
f(s(X)) → f(X)
h(cons(X, Y)) → h(g(cons(X, Y)))
h(cons(X, Y)) → h(g(cons(X, Y)))
h(cons(X, Y)) → h(g(cons(X, Y)))
h(cons(x0, x1))
H(cons(X, Y)) → H(g(cons(X, Y)))
h(cons(X, Y)) → h(g(cons(X, Y)))
h(cons(x0, x1))