0 QTRS
↳1 DependencyPairsProof (⇔)
↳2 QDP
↳3 DependencyGraphProof (⇔)
↳4 QDP
↳5 QDPOrderProof (⇔)
↳6 QDP
↳7 PisEmptyProof (⇔)
↳8 TRUE
f(f(x)) → f(c(f(x)))
f(f(x)) → f(d(f(x)))
g(c(x)) → x
g(d(x)) → x
g(c(h(0))) → g(d(1))
g(c(1)) → g(d(h(0)))
g(h(x)) → g(x)
F(f(x)) → F(c(f(x)))
F(f(x)) → F(d(f(x)))
G(c(h(0))) → G(d(1))
G(c(1)) → G(d(h(0)))
G(h(x)) → G(x)
f(f(x)) → f(c(f(x)))
f(f(x)) → f(d(f(x)))
g(c(x)) → x
g(d(x)) → x
g(c(h(0))) → g(d(1))
g(c(1)) → g(d(h(0)))
g(h(x)) → g(x)
G(h(x)) → G(x)
f(f(x)) → f(c(f(x)))
f(f(x)) → f(d(f(x)))
g(c(x)) → x
g(d(x)) → x
g(c(h(0))) → g(d(1))
g(c(1)) → g(d(h(0)))
g(h(x)) → g(x)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
G(h(x)) → G(x)
f > c1 > h1 > 1 > G1
f > c1 > d1 > G1
f > c1 > 0 > 1 > G1
g1 > h1 > 1 > G1
g1 > d1 > G1
g1 > 0 > 1 > G1
G1: multiset
h1: multiset
f: multiset
c1: multiset
d1: multiset
g1: multiset
0: multiset
1: multiset
f(f(x)) → f(c(f(x)))
f(f(x)) → f(d(f(x)))
g(c(x)) → x
g(d(x)) → x
g(c(h(0))) → g(d(1))
g(c(1)) → g(d(h(0)))
g(h(x)) → g(x)
f(f(x)) → f(c(f(x)))
f(f(x)) → f(d(f(x)))
g(c(x)) → x
g(d(x)) → x
g(c(h(0))) → g(d(1))
g(c(1)) → g(d(h(0)))
g(h(x)) → g(x)