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