f(a, x) → f(b, f(c, x))
f(a, f(b, x)) → f(b, f(a, x))
f(d, f(c, x)) → f(d, f(a, x))
f(a, f(c, x)) → f(c, f(a, x))
↳ QTRS
↳ DependencyPairsProof
f(a, x) → f(b, f(c, x))
f(a, f(b, x)) → f(b, f(a, x))
f(d, f(c, x)) → f(d, f(a, x))
f(a, f(c, x)) → f(c, f(a, x))
F(a, f(b, x)) → F(b, f(a, x))
F(a, x) → F(b, f(c, x))
F(d, f(c, x)) → F(a, x)
F(a, f(c, x)) → F(c, f(a, x))
F(a, x) → F(c, x)
F(d, f(c, x)) → F(d, f(a, x))
F(a, f(b, x)) → F(a, x)
F(a, f(c, x)) → F(a, x)
f(a, x) → f(b, f(c, x))
f(a, f(b, x)) → f(b, f(a, x))
f(d, f(c, x)) → f(d, f(a, x))
f(a, f(c, x)) → f(c, f(a, x))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
F(a, f(b, x)) → F(b, f(a, x))
F(a, x) → F(b, f(c, x))
F(d, f(c, x)) → F(a, x)
F(a, f(c, x)) → F(c, f(a, x))
F(a, x) → F(c, x)
F(d, f(c, x)) → F(d, f(a, x))
F(a, f(b, x)) → F(a, x)
F(a, f(c, x)) → F(a, x)
f(a, x) → f(b, f(c, x))
f(a, f(b, x)) → f(b, f(a, x))
f(d, f(c, x)) → f(d, f(a, x))
f(a, f(c, x)) → f(c, f(a, x))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
F(a, f(b, x)) → F(a, x)
F(a, f(c, x)) → F(a, x)
f(a, x) → f(b, f(c, x))
f(a, f(b, x)) → f(b, f(a, x))
f(d, f(c, x)) → f(d, f(a, x))
f(a, f(c, x)) → f(c, f(a, x))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
F(a, f(b, x)) → F(a, x)
F(a, f(c, x)) → F(a, x)
The value of delta used in the strict ordering is 4.
POL(c) = 0
POL(a) = 0
POL(f(x1, x2)) = 1 + (4)x_1 + (4)x_2
POL(b) = 4
POL(F(x1, x2)) = (4)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
f(a, x) → f(b, f(c, x))
f(a, f(b, x)) → f(b, f(a, x))
f(d, f(c, x)) → f(d, f(a, x))
f(a, f(c, x)) → f(c, f(a, x))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
F(d, f(c, x)) → F(d, f(a, x))
f(a, x) → f(b, f(c, x))
f(a, f(b, x)) → f(b, f(a, x))
f(d, f(c, x)) → f(d, f(a, x))
f(a, f(c, x)) → f(c, f(a, x))