b(b(b(x1))) → a(x1)
a(a(x1)) → a(b(a(x1)))
b(c(x1)) → c(a(a(x1)))
a(c(x1)) → c(b(b(x1)))
a(a(a(x1))) → b(a(a(x1)))
↳ QTRS
↳ DependencyPairsProof
b(b(b(x1))) → a(x1)
a(a(x1)) → a(b(a(x1)))
b(c(x1)) → c(a(a(x1)))
a(c(x1)) → c(b(b(x1)))
a(a(a(x1))) → b(a(a(x1)))
A(a(a(x1))) → B(a(a(x1)))
B(c(x1)) → A(x1)
A(c(x1)) → B(x1)
A(a(x1)) → A(b(a(x1)))
B(b(b(x1))) → A(x1)
A(c(x1)) → B(b(x1))
B(c(x1)) → A(a(x1))
A(a(x1)) → B(a(x1))
b(b(b(x1))) → a(x1)
a(a(x1)) → a(b(a(x1)))
b(c(x1)) → c(a(a(x1)))
a(c(x1)) → c(b(b(x1)))
a(a(a(x1))) → b(a(a(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
A(a(a(x1))) → B(a(a(x1)))
B(c(x1)) → A(x1)
A(c(x1)) → B(x1)
A(a(x1)) → A(b(a(x1)))
B(b(b(x1))) → A(x1)
A(c(x1)) → B(b(x1))
B(c(x1)) → A(a(x1))
A(a(x1)) → B(a(x1))
b(b(b(x1))) → a(x1)
a(a(x1)) → a(b(a(x1)))
b(c(x1)) → c(a(a(x1)))
a(c(x1)) → c(b(b(x1)))
a(a(a(x1))) → b(a(a(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(c(x1)) → A(x1)
A(c(x1)) → B(x1)
A(c(x1)) → B(b(x1))
B(c(x1)) → A(a(x1))
Used ordering: Polynomial interpretation [25,35]:
A(a(a(x1))) → B(a(a(x1)))
A(a(x1)) → A(b(a(x1)))
B(b(b(x1))) → A(x1)
A(a(x1)) → B(a(x1))
The value of delta used in the strict ordering is 1/16.
POL(c(x1)) = 1/4 + (2)x_1
POL(B(x1)) = (1/4)x_1
POL(a(x1)) = x_1
POL(A(x1)) = (1/4)x_1
POL(b(x1)) = x_1
a(a(x1)) → a(b(a(x1)))
a(a(a(x1))) → b(a(a(x1)))
b(b(b(x1))) → a(x1)
b(c(x1)) → c(a(a(x1)))
a(c(x1)) → c(b(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
A(a(a(x1))) → B(a(a(x1)))
A(a(x1)) → A(b(a(x1)))
B(b(b(x1))) → A(x1)
A(a(x1)) → B(a(x1))
b(b(b(x1))) → a(x1)
a(a(x1)) → a(b(a(x1)))
b(c(x1)) → c(a(a(x1)))
a(c(x1)) → c(b(b(x1)))
a(a(a(x1))) → b(a(a(x1)))