a(a(a(a(x1)))) → a(b(a(b(x1))))
b(a(b(x1))) → a(b(a(x1)))
↳ QTRS
↳ DependencyPairsProof
a(a(a(a(x1)))) → a(b(a(b(x1))))
b(a(b(x1))) → a(b(a(x1)))
B(a(b(x1))) → A(x1)
A(a(a(a(x1)))) → A(b(a(b(x1))))
B(a(b(x1))) → A(b(a(x1)))
A(a(a(a(x1)))) → B(x1)
B(a(b(x1))) → B(a(x1))
A(a(a(a(x1)))) → B(a(b(x1)))
A(a(a(a(x1)))) → A(b(x1))
a(a(a(a(x1)))) → a(b(a(b(x1))))
b(a(b(x1))) → a(b(a(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
B(a(b(x1))) → A(x1)
A(a(a(a(x1)))) → A(b(a(b(x1))))
B(a(b(x1))) → A(b(a(x1)))
A(a(a(a(x1)))) → B(x1)
B(a(b(x1))) → B(a(x1))
A(a(a(a(x1)))) → B(a(b(x1)))
A(a(a(a(x1)))) → A(b(x1))
a(a(a(a(x1)))) → a(b(a(b(x1))))
b(a(b(x1))) → a(b(a(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(a(b(x1))) → A(x1)
B(a(b(x1))) → A(b(a(x1)))
A(a(a(a(x1)))) → B(x1)
B(a(b(x1))) → B(a(x1))
A(a(a(a(x1)))) → B(a(b(x1)))
A(a(a(a(x1)))) → A(b(x1))
Used ordering: Polynomial interpretation [25,35]:
A(a(a(a(x1)))) → A(b(a(b(x1))))
The value of delta used in the strict ordering is 3.
POL(B(x1)) = (3)x_1
POL(a(x1)) = 1 + (3)x_1
POL(A(x1)) = 1 + (2)x_1
POL(b(x1)) = 1 + (3)x_1
a(a(a(a(x1)))) → a(b(a(b(x1))))
b(a(b(x1))) → a(b(a(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
A(a(a(a(x1)))) → A(b(a(b(x1))))
a(a(a(a(x1)))) → a(b(a(b(x1))))
b(a(b(x1))) → a(b(a(x1)))