f(a, f(b, x)) → f(a, f(a, f(a, x)))
f(b, f(a, x)) → f(b, f(b, f(b, x)))
↳ QTRS
↳ DependencyPairsProof
f(a, f(b, x)) → f(a, f(a, f(a, x)))
f(b, f(a, x)) → f(b, f(b, f(b, x)))
F(b, f(a, x)) → F(b, f(b, f(b, x)))
F(a, f(b, x)) → F(a, f(a, f(a, x)))
F(a, f(b, x)) → F(a, f(a, x))
F(b, f(a, x)) → F(b, x)
F(a, f(b, x)) → F(a, x)
F(b, f(a, x)) → F(b, f(b, x))
f(a, f(b, x)) → f(a, f(a, f(a, x)))
f(b, f(a, x)) → f(b, f(b, f(b, x)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
F(b, f(a, x)) → F(b, f(b, f(b, x)))
F(a, f(b, x)) → F(a, f(a, f(a, x)))
F(a, f(b, x)) → F(a, f(a, x))
F(b, f(a, x)) → F(b, x)
F(a, f(b, x)) → F(a, x)
F(b, f(a, x)) → F(b, f(b, x))
f(a, f(b, x)) → f(a, f(a, f(a, x)))
f(b, f(a, x)) → f(b, f(b, f(b, x)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
F(b, f(a, x)) → F(b, f(b, f(b, x)))
F(b, f(a, x)) → F(b, x)
F(b, f(a, x)) → F(b, f(b, x))
f(a, f(b, x)) → f(a, f(a, f(a, x)))
f(b, f(a, x)) → f(b, f(b, f(b, x)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
F(b, f(a, x)) → F(b, f(b, f(b, x)))
F(b, f(a, x)) → F(b, x)
F(b, f(a, x)) → F(b, f(b, x))
The value of delta used in the strict ordering is 1/64.
POL(a) = 1/4
POL(f(x1, x2)) = (1/4)x_1 + x_2
POL(b) = 0
POL(F(x1, x2)) = (1/4)x_2
f(b, f(a, x)) → f(b, f(b, f(b, x)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
f(a, f(b, x)) → f(a, f(a, f(a, x)))
f(b, f(a, x)) → f(b, f(b, f(b, x)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
F(a, f(b, x)) → F(a, f(a, f(a, x)))
F(a, f(b, x)) → F(a, f(a, x))
F(a, f(b, x)) → F(a, x)
f(a, f(b, x)) → f(a, f(a, f(a, x)))
f(b, f(a, x)) → f(b, f(b, f(b, 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, f(a, x))
F(a, f(b, x)) → F(a, x)
Used ordering: Polynomial interpretation [25,35]:
F(a, f(b, x)) → F(a, f(a, f(a, x)))
The value of delta used in the strict ordering is 1/32.
POL(a) = 1/2
POL(f(x1, x2)) = (1/4)x_1 + x_2
POL(b) = 1
POL(F(x1, x2)) = (1/4)x_2
f(a, f(b, x)) → f(a, f(a, f(a, x)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
F(a, f(b, x)) → F(a, f(a, f(a, x)))
f(a, f(b, x)) → f(a, f(a, f(a, x)))
f(b, f(a, x)) → f(b, f(b, f(b, 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, f(a, f(a, x)))
The value of delta used in the strict ordering is 1/4.
POL(a) = 0
POL(f(x1, x2)) = (1/2)x_1
POL(b) = 2
POL(F(x1, x2)) = (1/4)x_2
f(a, f(b, x)) → f(a, f(a, f(a, x)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
f(a, f(b, x)) → f(a, f(a, f(a, x)))
f(b, f(a, x)) → f(b, f(b, f(b, x)))