a(a(a(a(x1)))) → b(b(c(c(x1))))
b(b(b(b(x1)))) → a(a(c(c(x1))))
c(c(c(c(x1)))) → b(a(a(a(x1))))
↳ QTRS
↳ DependencyPairsProof
a(a(a(a(x1)))) → b(b(c(c(x1))))
b(b(b(b(x1)))) → a(a(c(c(x1))))
c(c(c(c(x1)))) → b(a(a(a(x1))))
C(c(c(c(x1)))) → A(a(x1))
A(a(a(a(x1)))) → C(c(x1))
A(a(a(a(x1)))) → B(c(c(x1)))
C(c(c(c(x1)))) → A(a(a(x1)))
B(b(b(b(x1)))) → A(a(c(c(x1))))
B(b(b(b(x1)))) → C(c(x1))
A(a(a(a(x1)))) → B(b(c(c(x1))))
A(a(a(a(x1)))) → C(x1)
C(c(c(c(x1)))) → B(a(a(a(x1))))
C(c(c(c(x1)))) → A(x1)
B(b(b(b(x1)))) → C(x1)
B(b(b(b(x1)))) → A(c(c(x1)))
a(a(a(a(x1)))) → b(b(c(c(x1))))
b(b(b(b(x1)))) → a(a(c(c(x1))))
c(c(c(c(x1)))) → b(a(a(a(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
C(c(c(c(x1)))) → A(a(x1))
A(a(a(a(x1)))) → C(c(x1))
A(a(a(a(x1)))) → B(c(c(x1)))
C(c(c(c(x1)))) → A(a(a(x1)))
B(b(b(b(x1)))) → A(a(c(c(x1))))
B(b(b(b(x1)))) → C(c(x1))
A(a(a(a(x1)))) → B(b(c(c(x1))))
A(a(a(a(x1)))) → C(x1)
C(c(c(c(x1)))) → B(a(a(a(x1))))
C(c(c(c(x1)))) → A(x1)
B(b(b(b(x1)))) → C(x1)
B(b(b(b(x1)))) → A(c(c(x1)))
a(a(a(a(x1)))) → b(b(c(c(x1))))
b(b(b(b(x1)))) → a(a(c(c(x1))))
c(c(c(c(x1)))) → b(a(a(a(x1))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
C(c(c(c(x1)))) → A(a(x1))
A(a(a(a(x1)))) → C(c(x1))
A(a(a(a(x1)))) → B(c(c(x1)))
C(c(c(c(x1)))) → A(a(a(x1)))
B(b(b(b(x1)))) → C(c(x1))
A(a(a(a(x1)))) → C(x1)
C(c(c(c(x1)))) → A(x1)
B(b(b(b(x1)))) → C(x1)
B(b(b(b(x1)))) → A(c(c(x1)))
Used ordering: Polynomial interpretation [25,35]:
B(b(b(b(x1)))) → A(a(c(c(x1))))
A(a(a(a(x1)))) → B(b(c(c(x1))))
C(c(c(c(x1)))) → B(a(a(a(x1))))
The value of delta used in the strict ordering is 256.
POL(C(x1)) = (4)x_1
POL(c(x1)) = 4 + (4)x_1
POL(B(x1)) = (4)x_1
POL(a(x1)) = 4 + (4)x_1
POL(A(x1)) = (4)x_1
POL(b(x1)) = 4 + (4)x_1
a(a(a(a(x1)))) → b(b(c(c(x1))))
b(b(b(b(x1)))) → a(a(c(c(x1))))
c(c(c(c(x1)))) → b(a(a(a(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
B(b(b(b(x1)))) → A(a(c(c(x1))))
A(a(a(a(x1)))) → B(b(c(c(x1))))
C(c(c(c(x1)))) → B(a(a(a(x1))))
a(a(a(a(x1)))) → b(b(c(c(x1))))
b(b(b(b(x1)))) → a(a(c(c(x1))))
c(c(c(c(x1)))) → b(a(a(a(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
B(b(b(b(x1)))) → A(a(c(c(x1))))
A(a(a(a(x1)))) → B(b(c(c(x1))))
a(a(a(a(x1)))) → b(b(c(c(x1))))
b(b(b(b(x1)))) → a(a(c(c(x1))))
c(c(c(c(x1)))) → b(a(a(a(x1))))