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