a(a(x1)) → c(b(x1))
b(b(x1)) → c(a(x1))
c(c(x1)) → b(a(x1))
↳ QTRS
↳ DependencyPairsProof
a(a(x1)) → c(b(x1))
b(b(x1)) → c(a(x1))
c(c(x1)) → b(a(x1))
B(b(x1)) → A(x1)
C(c(x1)) → A(x1)
A(a(x1)) → C(b(x1))
C(c(x1)) → B(a(x1))
B(b(x1)) → C(a(x1))
A(a(x1)) → B(x1)
a(a(x1)) → c(b(x1))
b(b(x1)) → c(a(x1))
c(c(x1)) → b(a(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
B(b(x1)) → A(x1)
C(c(x1)) → A(x1)
A(a(x1)) → C(b(x1))
C(c(x1)) → B(a(x1))
B(b(x1)) → C(a(x1))
A(a(x1)) → B(x1)
a(a(x1)) → c(b(x1))
b(b(x1)) → c(a(x1))
c(c(x1)) → b(a(x1))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(b(x1)) → A(x1)
C(c(x1)) → A(x1)
A(a(x1)) → C(b(x1))
A(a(x1)) → B(x1)
Used ordering: Polynomial interpretation [25,35]:
C(c(x1)) → B(a(x1))
B(b(x1)) → C(a(x1))
The value of delta used in the strict ordering is 5.
POL(C(x1)) = 3 + (2)x_1
POL(c(x1)) = 3 + (2)x_1
POL(B(x1)) = 3 + (2)x_1
POL(a(x1)) = 3 + (2)x_1
POL(A(x1)) = 4 + (4)x_1
POL(b(x1)) = 3 + (2)x_1
a(a(x1)) → c(b(x1))
c(c(x1)) → b(a(x1))
b(b(x1)) → c(a(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
B(b(x1)) → C(a(x1))
C(c(x1)) → B(a(x1))
a(a(x1)) → c(b(x1))
b(b(x1)) → c(a(x1))
c(c(x1)) → b(a(x1))