a(a(f(b, a(x)))) → f(a(a(a(x))), b)
a(a(x)) → f(b, a(f(a(x), b)))
f(a(x), b) → f(b, a(x))
↳ QTRS
↳ DependencyPairsProof
a(a(f(b, a(x)))) → f(a(a(a(x))), b)
a(a(x)) → f(b, a(f(a(x), b)))
f(a(x), b) → f(b, a(x))
A(a(x)) → F(a(x), b)
A(a(x)) → F(b, a(f(a(x), b)))
A(a(f(b, a(x)))) → F(a(a(a(x))), b)
A(a(f(b, a(x)))) → A(a(x))
A(a(x)) → A(f(a(x), b))
A(a(f(b, a(x)))) → A(a(a(x)))
F(a(x), b) → F(b, a(x))
a(a(f(b, a(x)))) → f(a(a(a(x))), b)
a(a(x)) → f(b, a(f(a(x), b)))
f(a(x), b) → f(b, a(x))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
A(a(x)) → F(a(x), b)
A(a(x)) → F(b, a(f(a(x), b)))
A(a(f(b, a(x)))) → F(a(a(a(x))), b)
A(a(f(b, a(x)))) → A(a(x))
A(a(x)) → A(f(a(x), b))
A(a(f(b, a(x)))) → A(a(a(x)))
F(a(x), b) → F(b, a(x))
a(a(f(b, a(x)))) → f(a(a(a(x))), b)
a(a(x)) → f(b, a(f(a(x), b)))
f(a(x), b) → f(b, a(x))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
A(a(f(b, a(x)))) → A(a(x))
A(a(f(b, a(x)))) → A(a(a(x)))
a(a(f(b, a(x)))) → f(a(a(a(x))), b)
a(a(x)) → f(b, a(f(a(x), b)))
f(a(x), b) → f(b, a(x))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(a(f(b, a(x)))) → A(a(x))
Used ordering: Polynomial interpretation [25,35]:
A(a(f(b, a(x)))) → A(a(a(x)))
The value of delta used in the strict ordering is 16.
POL(a(x1)) = 2 + (4)x_1
POL(f(x1, x2)) = x_1 + x_2
POL(A(x1)) = (2)x_1
POL(b) = 0
a(a(f(b, a(x)))) → f(a(a(a(x))), b)
a(a(x)) → f(b, a(f(a(x), b)))
f(a(x), b) → f(b, a(x))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
A(a(f(b, a(x)))) → A(a(a(x)))
a(a(f(b, a(x)))) → f(a(a(a(x))), b)
a(a(x)) → f(b, a(f(a(x), b)))
f(a(x), b) → f(b, a(x))