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