b(c(x1)) → c(b(x1))
c(b(x1)) → a(a(a(x1)))
a(a(a(a(x1)))) → b(c(x1))
↳ QTRS
↳ DependencyPairsProof
b(c(x1)) → c(b(x1))
c(b(x1)) → a(a(a(x1)))
a(a(a(a(x1)))) → b(c(x1))
C(b(x1)) → A(x1)
A(a(a(a(x1)))) → C(x1)
A(a(a(a(x1)))) → B(c(x1))
B(c(x1)) → C(b(x1))
C(b(x1)) → A(a(x1))
C(b(x1)) → A(a(a(x1)))
B(c(x1)) → B(x1)
b(c(x1)) → c(b(x1))
c(b(x1)) → a(a(a(x1)))
a(a(a(a(x1)))) → b(c(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
C(b(x1)) → A(x1)
A(a(a(a(x1)))) → C(x1)
A(a(a(a(x1)))) → B(c(x1))
B(c(x1)) → C(b(x1))
C(b(x1)) → A(a(x1))
C(b(x1)) → A(a(a(x1)))
B(c(x1)) → B(x1)
b(c(x1)) → c(b(x1))
c(b(x1)) → a(a(a(x1)))
a(a(a(a(x1)))) → b(c(x1))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
C(b(x1)) → A(x1)
A(a(a(a(x1)))) → C(x1)
B(c(x1)) → C(b(x1))
C(b(x1)) → A(a(x1))
C(b(x1)) → A(a(a(x1)))
B(c(x1)) → B(x1)
Used ordering: Polynomial interpretation [25,35]:
A(a(a(a(x1)))) → B(c(x1))
The value of delta used in the strict ordering is 1.
POL(C(x1)) = 4 + (3)x_1
POL(c(x1)) = 4 + (4)x_1
POL(B(x1)) = 1 + (4)x_1
POL(a(x1)) = 1 + (2)x_1
POL(A(x1)) = 3 + (2)x_1
POL(b(x1)) = 2 + (3)x_1
c(b(x1)) → a(a(a(x1)))
a(a(a(a(x1)))) → b(c(x1))
b(c(x1)) → c(b(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
A(a(a(a(x1)))) → B(c(x1))
b(c(x1)) → c(b(x1))
c(b(x1)) → a(a(a(x1)))
a(a(a(a(x1)))) → b(c(x1))