a(b(c(x1))) → c(b(a(x1)))
C(B(A(x1))) → A(B(C(x1)))
b(a(C(x1))) → C(a(b(x1)))
c(A(B(x1))) → B(A(c(x1)))
A(c(b(x1))) → b(c(A(x1)))
B(C(a(x1))) → a(C(B(x1)))
a(A(x1)) → x1
A(a(x1)) → x1
b(B(x1)) → x1
B(b(x1)) → x1
c(C(x1)) → x1
C(c(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
a(b(c(x1))) → c(b(a(x1)))
C(B(A(x1))) → A(B(C(x1)))
b(a(C(x1))) → C(a(b(x1)))
c(A(B(x1))) → B(A(c(x1)))
A(c(b(x1))) → b(c(A(x1)))
B(C(a(x1))) → a(C(B(x1)))
a(A(x1)) → x1
A(a(x1)) → x1
b(B(x1)) → x1
B(b(x1)) → x1
c(C(x1)) → x1
C(c(x1)) → x1
B1(a(C(x1))) → C2(a(b(x1)))
C1(A(B(x1))) → A2(c(x1))
C1(A(B(x1))) → C1(x1)
B1(a(C(x1))) → B1(x1)
A2(c(b(x1))) → C1(A(x1))
B2(C(a(x1))) → A1(C(B(x1)))
A1(b(c(x1))) → A1(x1)
C2(B(A(x1))) → B2(C(x1))
B2(C(a(x1))) → B2(x1)
A2(c(b(x1))) → B1(c(A(x1)))
B1(a(C(x1))) → A1(b(x1))
C2(B(A(x1))) → C2(x1)
A2(c(b(x1))) → A2(x1)
B2(C(a(x1))) → C2(B(x1))
A1(b(c(x1))) → B1(a(x1))
A1(b(c(x1))) → C1(b(a(x1)))
C2(B(A(x1))) → A2(B(C(x1)))
C1(A(B(x1))) → B2(A(c(x1)))
a(b(c(x1))) → c(b(a(x1)))
C(B(A(x1))) → A(B(C(x1)))
b(a(C(x1))) → C(a(b(x1)))
c(A(B(x1))) → B(A(c(x1)))
A(c(b(x1))) → b(c(A(x1)))
B(C(a(x1))) → a(C(B(x1)))
a(A(x1)) → x1
A(a(x1)) → x1
b(B(x1)) → x1
B(b(x1)) → x1
c(C(x1)) → x1
C(c(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
B1(a(C(x1))) → C2(a(b(x1)))
C1(A(B(x1))) → A2(c(x1))
C1(A(B(x1))) → C1(x1)
B1(a(C(x1))) → B1(x1)
A2(c(b(x1))) → C1(A(x1))
B2(C(a(x1))) → A1(C(B(x1)))
A1(b(c(x1))) → A1(x1)
C2(B(A(x1))) → B2(C(x1))
B2(C(a(x1))) → B2(x1)
A2(c(b(x1))) → B1(c(A(x1)))
B1(a(C(x1))) → A1(b(x1))
C2(B(A(x1))) → C2(x1)
A2(c(b(x1))) → A2(x1)
B2(C(a(x1))) → C2(B(x1))
A1(b(c(x1))) → B1(a(x1))
A1(b(c(x1))) → C1(b(a(x1)))
C2(B(A(x1))) → A2(B(C(x1)))
C1(A(B(x1))) → B2(A(c(x1)))
a(b(c(x1))) → c(b(a(x1)))
C(B(A(x1))) → A(B(C(x1)))
b(a(C(x1))) → C(a(b(x1)))
c(A(B(x1))) → B(A(c(x1)))
A(c(b(x1))) → b(c(A(x1)))
B(C(a(x1))) → a(C(B(x1)))
a(A(x1)) → x1
A(a(x1)) → x1
b(B(x1)) → x1
B(b(x1)) → x1
c(C(x1)) → x1
C(c(x1)) → x1
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
C1(A(B(x1))) → A2(c(x1))
C1(A(B(x1))) → C1(x1)
B1(a(C(x1))) → B1(x1)
A1(b(c(x1))) → A1(x1)
B2(C(a(x1))) → B2(x1)
B1(a(C(x1))) → A1(b(x1))
C2(B(A(x1))) → C2(x1)
A2(c(b(x1))) → A2(x1)
B2(C(a(x1))) → C2(B(x1))
A1(b(c(x1))) → B1(a(x1))
Used ordering: Polynomial interpretation [25,35]:
B1(a(C(x1))) → C2(a(b(x1)))
A2(c(b(x1))) → C1(A(x1))
B2(C(a(x1))) → A1(C(B(x1)))
C2(B(A(x1))) → B2(C(x1))
A2(c(b(x1))) → B1(c(A(x1)))
A1(b(c(x1))) → C1(b(a(x1)))
C2(B(A(x1))) → A2(B(C(x1)))
C1(A(B(x1))) → B2(A(c(x1)))
The value of delta used in the strict ordering is 4.
POL(C(x1)) = 4 + x_1
POL(B2(x1)) = (2)x_1
POL(c(x1)) = x_1
POL(A1(x1)) = (2)x_1
POL(B(x1)) = x_1
POL(a(x1)) = x_1
POL(C2(x1)) = 4 + (2)x_1
POL(B1(x1)) = (2)x_1
POL(A(x1)) = 2 + x_1
POL(b(x1)) = 2 + x_1
POL(A2(x1)) = (2)x_1
POL(C1(x1)) = (2)x_1
C(B(A(x1))) → A(B(C(x1)))
b(a(C(x1))) → C(a(b(x1)))
A(c(b(x1))) → b(c(A(x1)))
a(b(c(x1))) → c(b(a(x1)))
c(A(B(x1))) → B(A(c(x1)))
B(C(a(x1))) → a(C(B(x1)))
a(A(x1)) → x1
b(B(x1)) → x1
A(a(x1)) → x1
c(C(x1)) → x1
B(b(x1)) → x1
C(c(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
B1(a(C(x1))) → C2(a(b(x1)))
A2(c(b(x1))) → B1(c(A(x1)))
A2(c(b(x1))) → C1(A(x1))
B2(C(a(x1))) → A1(C(B(x1)))
C2(B(A(x1))) → B2(C(x1))
C1(A(B(x1))) → B2(A(c(x1)))
C2(B(A(x1))) → A2(B(C(x1)))
A1(b(c(x1))) → C1(b(a(x1)))
a(b(c(x1))) → c(b(a(x1)))
C(B(A(x1))) → A(B(C(x1)))
b(a(C(x1))) → C(a(b(x1)))
c(A(B(x1))) → B(A(c(x1)))
A(c(b(x1))) → b(c(A(x1)))
B(C(a(x1))) → a(C(B(x1)))
a(A(x1)) → x1
A(a(x1)) → x1
b(B(x1)) → x1
B(b(x1)) → x1
c(C(x1)) → x1
C(c(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
B2(C(a(x1))) → A1(C(B(x1)))
C1(A(B(x1))) → B2(A(c(x1)))
A1(b(c(x1))) → C1(b(a(x1)))
a(b(c(x1))) → c(b(a(x1)))
C(B(A(x1))) → A(B(C(x1)))
b(a(C(x1))) → C(a(b(x1)))
c(A(B(x1))) → B(A(c(x1)))
A(c(b(x1))) → b(c(A(x1)))
B(C(a(x1))) → a(C(B(x1)))
a(A(x1)) → x1
A(a(x1)) → x1
b(B(x1)) → x1
B(b(x1)) → x1
c(C(x1)) → x1
C(c(x1)) → x1
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B2(C(a(x1))) → A1(C(B(x1)))
A1(b(c(x1))) → C1(b(a(x1)))
Used ordering: Polynomial interpretation [25,35]:
C1(A(B(x1))) → B2(A(c(x1)))
The value of delta used in the strict ordering is 3.
POL(B2(x1)) = (2)x_1
POL(C(x1)) = 4 + (2)x_1
POL(c(x1)) = (1/2)x_1
POL(A1(x1)) = 4 + (2)x_1
POL(B(x1)) = (4)x_1
POL(a(x1)) = 4 + (4)x_1
POL(A(x1)) = (1/4)x_1
POL(b(x1)) = x_1
POL(C1(x1)) = (1/4)x_1
C(B(A(x1))) → A(B(C(x1)))
b(a(C(x1))) → C(a(b(x1)))
A(c(b(x1))) → b(c(A(x1)))
a(b(c(x1))) → c(b(a(x1)))
c(A(B(x1))) → B(A(c(x1)))
B(C(a(x1))) → a(C(B(x1)))
a(A(x1)) → x1
b(B(x1)) → x1
A(a(x1)) → x1
c(C(x1)) → x1
B(b(x1)) → x1
C(c(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
C1(A(B(x1))) → B2(A(c(x1)))
a(b(c(x1))) → c(b(a(x1)))
C(B(A(x1))) → A(B(C(x1)))
b(a(C(x1))) → C(a(b(x1)))
c(A(B(x1))) → B(A(c(x1)))
A(c(b(x1))) → b(c(A(x1)))
B(C(a(x1))) → a(C(B(x1)))
a(A(x1)) → x1
A(a(x1)) → x1
b(B(x1)) → x1
B(b(x1)) → x1
c(C(x1)) → x1
C(c(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
B1(a(C(x1))) → C2(a(b(x1)))
A2(c(b(x1))) → B1(c(A(x1)))
C2(B(A(x1))) → A2(B(C(x1)))
a(b(c(x1))) → c(b(a(x1)))
C(B(A(x1))) → A(B(C(x1)))
b(a(C(x1))) → C(a(b(x1)))
c(A(B(x1))) → B(A(c(x1)))
A(c(b(x1))) → b(c(A(x1)))
B(C(a(x1))) → a(C(B(x1)))
a(A(x1)) → x1
A(a(x1)) → x1
b(B(x1)) → x1
B(b(x1)) → x1
c(C(x1)) → x1
C(c(x1)) → x1
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B1(a(C(x1))) → C2(a(b(x1)))
Used ordering: Polynomial interpretation [25,35]:
A2(c(b(x1))) → B1(c(A(x1)))
C2(B(A(x1))) → A2(B(C(x1)))
The value of delta used in the strict ordering is 4.
POL(C(x1)) = 1 + x_1
POL(c(x1)) = (4)x_1
POL(B(x1)) = 2 + (4)x_1
POL(a(x1)) = (2)x_1
POL(C2(x1)) = 4 + (4)x_1
POL(B1(x1)) = (4)x_1
POL(A(x1)) = (1/2)x_1
POL(b(x1)) = x_1
POL(A2(x1)) = (2)x_1
C(B(A(x1))) → A(B(C(x1)))
b(a(C(x1))) → C(a(b(x1)))
A(c(b(x1))) → b(c(A(x1)))
a(b(c(x1))) → c(b(a(x1)))
c(A(B(x1))) → B(A(c(x1)))
B(C(a(x1))) → a(C(B(x1)))
a(A(x1)) → x1
b(B(x1)) → x1
A(a(x1)) → x1
c(C(x1)) → x1
B(b(x1)) → x1
C(c(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
A2(c(b(x1))) → B1(c(A(x1)))
C2(B(A(x1))) → A2(B(C(x1)))
a(b(c(x1))) → c(b(a(x1)))
C(B(A(x1))) → A(B(C(x1)))
b(a(C(x1))) → C(a(b(x1)))
c(A(B(x1))) → B(A(c(x1)))
A(c(b(x1))) → b(c(A(x1)))
B(C(a(x1))) → a(C(B(x1)))
a(A(x1)) → x1
A(a(x1)) → x1
b(B(x1)) → x1
B(b(x1)) → x1
c(C(x1)) → x1
C(c(x1)) → x1