a(b(x1)) → b(b(a(x1)))
b(c(x1)) → c(b(b(x1)))
c(a(x1)) → a(c(c(x1)))
↳ QTRS
↳ DependencyPairsProof
a(b(x1)) → b(b(a(x1)))
b(c(x1)) → c(b(b(x1)))
c(a(x1)) → a(c(c(x1)))
C(a(x1)) → C(c(x1))
C(a(x1)) → C(x1)
A(b(x1)) → B(b(a(x1)))
A(b(x1)) → B(a(x1))
C(a(x1)) → A(c(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(b(a(x1)))
b(c(x1)) → c(b(b(x1)))
c(a(x1)) → a(c(c(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
C(a(x1)) → C(c(x1))
C(a(x1)) → C(x1)
A(b(x1)) → B(b(a(x1)))
A(b(x1)) → B(a(x1))
C(a(x1)) → A(c(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(b(a(x1)))
b(c(x1)) → c(b(b(x1)))
c(a(x1)) → a(c(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(b(a(x1)))
A(b(x1)) → B(a(x1))
C(a(x1)) → A(c(c(x1)))
A(b(x1)) → A(x1)
Used ordering: Polynomial interpretation [25,35]:
C(a(x1)) → C(c(x1))
C(a(x1)) → 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 1/4.
POL(C(x1)) = 4
POL(c(x1)) = 0
POL(B(x1)) = 4
POL(a(x1)) = (2)x_1
POL(A(x1)) = 15/4 + (9/4)x_1
POL(b(x1)) = 1/4 + x_1
b(c(x1)) → c(b(b(x1)))
a(b(x1)) → b(b(a(x1)))
c(a(x1)) → a(c(c(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
C(a(x1)) → C(c(x1))
C(a(x1)) → C(x1)
B(c(x1)) → C(b(b(x1)))
B(c(x1)) → B(b(x1))
B(c(x1)) → B(x1)
a(b(x1)) → b(b(a(x1)))
b(c(x1)) → c(b(b(x1)))
c(a(x1)) → a(c(c(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
C(a(x1)) → C(c(x1))
C(a(x1)) → C(x1)
a(b(x1)) → b(b(a(x1)))
b(c(x1)) → c(b(b(x1)))
c(a(x1)) → a(c(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(c(x1))
C(a(x1)) → C(x1)
The value of delta used in the strict ordering is 1.
POL(C(x1)) = (4)x_1
POL(c(x1)) = x_1
POL(a(x1)) = 1/4 + x_1
POL(b(x1)) = 0
b(c(x1)) → c(b(b(x1)))
a(b(x1)) → b(b(a(x1)))
c(a(x1)) → a(c(c(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
a(b(x1)) → b(b(a(x1)))
b(c(x1)) → c(b(b(x1)))
c(a(x1)) → a(c(c(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
B(c(x1)) → B(x1)
B(c(x1)) → B(b(x1))
a(b(x1)) → b(b(a(x1)))
b(c(x1)) → c(b(b(x1)))
c(a(x1)) → a(c(c(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(c(x1)) → B(x1)
B(c(x1)) → B(b(x1))
The value of delta used in the strict ordering is 2.
POL(c(x1)) = 1/2 + x_1
POL(B(x1)) = (4)x_1
POL(a(x1)) = 0
POL(b(x1)) = x_1
b(c(x1)) → c(b(b(x1)))
a(b(x1)) → b(b(a(x1)))
c(a(x1)) → a(c(c(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
a(b(x1)) → b(b(a(x1)))
b(c(x1)) → c(b(b(x1)))
c(a(x1)) → a(c(c(x1)))