a(a(x1)) → b(a(c(x1)))
b(b(x1)) → a(a(x1))
c(b(x1)) → a(x1)
↳ QTRS
↳ DependencyPairsProof
a(a(x1)) → b(a(c(x1)))
b(b(x1)) → a(a(x1))
c(b(x1)) → a(x1)
C(b(x1)) → A(x1)
A(a(x1)) → A(c(x1))
B(b(x1)) → A(x1)
A(a(x1)) → C(x1)
B(b(x1)) → A(a(x1))
A(a(x1)) → B(a(c(x1)))
a(a(x1)) → b(a(c(x1)))
b(b(x1)) → a(a(x1))
c(b(x1)) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
C(b(x1)) → A(x1)
A(a(x1)) → A(c(x1))
B(b(x1)) → A(x1)
A(a(x1)) → C(x1)
B(b(x1)) → A(a(x1))
A(a(x1)) → B(a(c(x1)))
a(a(x1)) → b(a(c(x1)))
b(b(x1)) → a(a(x1))
c(b(x1)) → a(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(x1)) → A(c(x1))
B(b(x1)) → A(x1)
A(a(x1)) → C(x1)
Used ordering: Polynomial interpretation [25,35]:
B(b(x1)) → A(a(x1))
A(a(x1)) → B(a(c(x1)))
The value of delta used in the strict ordering is 4.
POL(C(x1)) = (2)x_1
POL(c(x1)) = x_1
POL(B(x1)) = (4)x_1
POL(a(x1)) = 2 + (4)x_1
POL(A(x1)) = (4)x_1
POL(b(x1)) = 2 + (4)x_1
b(b(x1)) → a(a(x1))
a(a(x1)) → b(a(c(x1)))
c(b(x1)) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
B(b(x1)) → A(a(x1))
A(a(x1)) → B(a(c(x1)))
a(a(x1)) → b(a(c(x1)))
b(b(x1)) → a(a(x1))
c(b(x1)) → a(x1)