f(x, f(a, y)) → f(a, f(f(f(a, x), h(a)), y))
↳ QTRS
↳ DependencyPairsProof
f(x, f(a, y)) → f(a, f(f(f(a, x), h(a)), y))
F(x, f(a, y)) → F(a, x)
F(x, f(a, y)) → F(f(f(a, x), h(a)), y)
F(x, f(a, y)) → F(a, f(f(f(a, x), h(a)), y))
F(x, f(a, y)) → F(f(a, x), h(a))
f(x, f(a, y)) → f(a, f(f(f(a, x), h(a)), y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
F(x, f(a, y)) → F(a, x)
F(x, f(a, y)) → F(f(f(a, x), h(a)), y)
F(x, f(a, y)) → F(a, f(f(f(a, x), h(a)), y))
F(x, f(a, y)) → F(f(a, x), h(a))
f(x, f(a, y)) → f(a, f(f(f(a, x), h(a)), y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
F(x, f(a, y)) → F(a, x)
F(x, f(a, y)) → F(f(f(a, x), h(a)), y)
F(x, f(a, y)) → F(a, f(f(f(a, x), h(a)), y))
f(x, f(a, y)) → f(a, f(f(f(a, x), h(a)), y))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
F(x, f(a, y)) → F(a, x)
Used ordering: Polynomial interpretation [25,35]:
F(x, f(a, y)) → F(f(f(a, x), h(a)), y)
F(x, f(a, y)) → F(a, f(f(f(a, x), h(a)), y))
The value of delta used in the strict ordering is 8.
POL(a) = 0
POL(f(x1, x2)) = 4 + (2)x_2
POL(h(x1)) = (3/2)x_1
POL(F(x1, x2)) = (2)x_1 + (2)x_2
f(x, f(a, y)) → f(a, f(f(f(a, x), h(a)), y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
F(x, f(a, y)) → F(f(f(a, x), h(a)), y)
F(x, f(a, y)) → F(a, f(f(f(a, x), h(a)), y))
f(x, f(a, y)) → f(a, f(f(f(a, x), h(a)), y))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
F(x, f(a, y)) → F(f(f(a, x), h(a)), y)
Used ordering: Polynomial interpretation [25,35]:
F(x, f(a, y)) → F(a, f(f(f(a, x), h(a)), y))
The value of delta used in the strict ordering is 1/2.
POL(a) = 2
POL(f(x1, x2)) = 2 + (4)x_2
POL(h(x1)) = 7/4 + (7/2)x_1
POL(F(x1, x2)) = (1/4)x_2
f(x, f(a, y)) → f(a, f(f(f(a, x), h(a)), y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
F(x, f(a, y)) → F(a, f(f(f(a, x), h(a)), y))
f(x, f(a, y)) → f(a, f(f(f(a, x), h(a)), y))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
F(x, f(a, y)) → F(a, f(f(f(a, x), h(a)), y))
The value of delta used in the strict ordering is 13/512.
POL(a) = 1/4
POL(f(x1, x2)) = (1/4)x_1 + (2)x_2
POL(h(x1)) = 0
POL(F(x1, x2)) = (1/4)x_1 + (3/2)x_2
f(x, f(a, y)) → f(a, f(f(f(a, x), h(a)), y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
f(x, f(a, y)) → f(a, f(f(f(a, x), h(a)), y))