a(b(x1)) → b(c(a(x1)))
b(c(x1)) → c(b(b(x1)))
c(a(x1)) → a(c(x1))
↳ QTRS
↳ DependencyPairsProof
a(b(x1)) → b(c(a(x1)))
b(c(x1)) → c(b(b(x1)))
c(a(x1)) → a(c(x1))
C(a(x1)) → C(x1)
A(b(x1)) → B(c(a(x1)))
A(b(x1)) → C(a(x1))
C(a(x1)) → A(c(x1))
B(c(x1)) → B(x1)
B(c(x1)) → B(b(x1))
B(c(x1)) → C(b(b(x1)))
A(b(x1)) → A(x1)
a(b(x1)) → b(c(a(x1)))
b(c(x1)) → c(b(b(x1)))
c(a(x1)) → a(c(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
C(a(x1)) → C(x1)
A(b(x1)) → B(c(a(x1)))
A(b(x1)) → C(a(x1))
C(a(x1)) → A(c(x1))
B(c(x1)) → B(x1)
B(c(x1)) → B(b(x1))
B(c(x1)) → C(b(b(x1)))
A(b(x1)) → A(x1)
a(b(x1)) → b(c(a(x1)))
b(c(x1)) → c(b(b(x1)))
c(a(x1)) → a(c(x1))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(b(x1)) → B(c(a(x1)))
A(b(x1)) → C(a(x1))
A(b(x1)) → A(x1)
Used ordering: Polynomial interpretation [25,35]:
C(a(x1)) → C(x1)
C(a(x1)) → A(c(x1))
B(c(x1)) → B(x1)
B(c(x1)) → B(b(x1))
B(c(x1)) → C(b(b(x1)))
The value of delta used in the strict ordering is 1/16.
POL(C(x1)) = 0
POL(c(x1)) = 0
POL(B(x1)) = 0
POL(a(x1)) = (2)x_1
POL(A(x1)) = (1/4)x_1
POL(b(x1)) = 1/4 + (4)x_1
b(c(x1)) → c(b(b(x1)))
c(a(x1)) → a(c(x1))
a(b(x1)) → b(c(a(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
C(a(x1)) → C(x1)
C(a(x1)) → A(c(x1))
B(c(x1)) → C(b(b(x1)))
B(c(x1)) → B(b(x1))
B(c(x1)) → B(x1)
a(b(x1)) → b(c(a(x1)))
b(c(x1)) → c(b(b(x1)))
c(a(x1)) → a(c(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
C(a(x1)) → C(x1)
a(b(x1)) → b(c(a(x1)))
b(c(x1)) → c(b(b(x1)))
c(a(x1)) → a(c(x1))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
C(a(x1)) → C(x1)
The value of delta used in the strict ordering is 1/16.
POL(C(x1)) = (1/4)x_1
POL(a(x1)) = 1/4 + (2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
a(b(x1)) → b(c(a(x1)))
b(c(x1)) → c(b(b(x1)))
c(a(x1)) → a(c(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
B(c(x1)) → B(x1)
B(c(x1)) → B(b(x1))
a(b(x1)) → b(c(a(x1)))
b(c(x1)) → c(b(b(x1)))
c(a(x1)) → a(c(x1))