a(a(b(x1))) → b(a(x1))
b(a(a(x1))) → a(a(a(b(x1))))
a(c(x1)) → c(b(x1))
↳ QTRS
↳ DependencyPairsProof
a(a(b(x1))) → b(a(x1))
b(a(a(x1))) → a(a(a(b(x1))))
a(c(x1)) → c(b(x1))
B(a(a(x1))) → A(b(x1))
B(a(a(x1))) → A(a(a(b(x1))))
A(c(x1)) → B(x1)
A(a(b(x1))) → A(x1)
B(a(a(x1))) → B(x1)
B(a(a(x1))) → A(a(b(x1)))
A(a(b(x1))) → B(a(x1))
a(a(b(x1))) → b(a(x1))
b(a(a(x1))) → a(a(a(b(x1))))
a(c(x1)) → c(b(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
B(a(a(x1))) → A(b(x1))
B(a(a(x1))) → A(a(a(b(x1))))
A(c(x1)) → B(x1)
A(a(b(x1))) → A(x1)
B(a(a(x1))) → B(x1)
B(a(a(x1))) → A(a(b(x1)))
A(a(b(x1))) → B(a(x1))
a(a(b(x1))) → b(a(x1))
b(a(a(x1))) → a(a(a(b(x1))))
a(c(x1)) → c(b(x1))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(c(x1)) → B(x1)
Used ordering: Polynomial interpretation [25,35]:
B(a(a(x1))) → A(b(x1))
B(a(a(x1))) → A(a(a(b(x1))))
A(a(b(x1))) → A(x1)
B(a(a(x1))) → B(x1)
B(a(a(x1))) → A(a(b(x1)))
A(a(b(x1))) → B(a(x1))
The value of delta used in the strict ordering is 4.
POL(c(x1)) = 4 + (2)x_1
POL(B(x1)) = 1 + x_1
POL(a(x1)) = x_1
POL(A(x1)) = 1 + x_1
POL(b(x1)) = x_1
b(a(a(x1))) → a(a(a(b(x1))))
a(a(b(x1))) → b(a(x1))
a(c(x1)) → c(b(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
B(a(a(x1))) → A(a(a(b(x1))))
B(a(a(x1))) → A(b(x1))
A(a(b(x1))) → A(x1)
B(a(a(x1))) → A(a(b(x1)))
B(a(a(x1))) → B(x1)
A(a(b(x1))) → B(a(x1))
a(a(b(x1))) → b(a(x1))
b(a(a(x1))) → a(a(a(b(x1))))
a(c(x1)) → c(b(x1))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(a(a(x1))) → A(a(a(b(x1))))
B(a(a(x1))) → A(b(x1))
A(a(b(x1))) → A(x1)
B(a(a(x1))) → A(a(b(x1)))
B(a(a(x1))) → B(x1)
Used ordering: Polynomial interpretation [25,35]:
A(a(b(x1))) → B(a(x1))
The value of delta used in the strict ordering is 8.
POL(c(x1)) = 4
POL(B(x1)) = (4)x_1
POL(a(x1)) = 4 + x_1
POL(A(x1)) = 4 + (2)x_1
POL(b(x1)) = 2 + (2)x_1
b(a(a(x1))) → a(a(a(b(x1))))
a(a(b(x1))) → b(a(x1))
a(c(x1)) → c(b(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
A(a(b(x1))) → B(a(x1))
a(a(b(x1))) → b(a(x1))
b(a(a(x1))) → a(a(a(b(x1))))
a(c(x1)) → c(b(x1))