a(a(a(x1))) → b(b(b(x1)))
b(b(b(b(x1)))) → a(b(b(a(x1))))
↳ QTRS
↳ DependencyPairsProof
a(a(a(x1))) → b(b(b(x1)))
b(b(b(b(x1)))) → a(b(b(a(x1))))
A(a(a(x1))) → B(x1)
B(b(b(b(x1)))) → A(b(b(a(x1))))
B(b(b(b(x1)))) → B(a(x1))
B(b(b(b(x1)))) → A(x1)
A(a(a(x1))) → B(b(x1))
B(b(b(b(x1)))) → B(b(a(x1)))
A(a(a(x1))) → B(b(b(x1)))
a(a(a(x1))) → b(b(b(x1)))
b(b(b(b(x1)))) → a(b(b(a(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
A(a(a(x1))) → B(x1)
B(b(b(b(x1)))) → A(b(b(a(x1))))
B(b(b(b(x1)))) → B(a(x1))
B(b(b(b(x1)))) → A(x1)
A(a(a(x1))) → B(b(x1))
B(b(b(b(x1)))) → B(b(a(x1)))
A(a(a(x1))) → B(b(b(x1)))
a(a(a(x1))) → b(b(b(x1)))
b(b(b(b(x1)))) → a(b(b(a(x1))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(a(a(x1))) → B(x1)
B(b(b(b(x1)))) → B(a(x1))
B(b(b(b(x1)))) → A(x1)
A(a(a(x1))) → B(b(x1))
B(b(b(b(x1)))) → B(b(a(x1)))
Used ordering: Polynomial interpretation [25,35]:
B(b(b(b(x1)))) → A(b(b(a(x1))))
A(a(a(x1))) → B(b(b(x1)))
The value of delta used in the strict ordering is 32.
POL(B(x1)) = (2)x_1
POL(a(x1)) = 4 + (4)x_1
POL(A(x1)) = (2)x_1
POL(b(x1)) = 4 + (4)x_1
a(a(a(x1))) → b(b(b(x1)))
b(b(b(b(x1)))) → a(b(b(a(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
B(b(b(b(x1)))) → A(b(b(a(x1))))
A(a(a(x1))) → B(b(b(x1)))
a(a(a(x1))) → b(b(b(x1)))
b(b(b(b(x1)))) → a(b(b(a(x1))))