c(c(b(x1))) → a(c(b(x1)))
a(c(b(a(x1)))) → b(c(c(x1)))
b(a(c(x1))) → a(b(c(a(x1))))
b(c(a(x1))) → c(a(b(x1)))
↳ QTRS
↳ DependencyPairsProof
c(c(b(x1))) → a(c(b(x1)))
a(c(b(a(x1)))) → b(c(c(x1)))
b(a(c(x1))) → a(b(c(a(x1))))
b(c(a(x1))) → c(a(b(x1)))
A(c(b(a(x1)))) → C(x1)
A(c(b(a(x1)))) → B(c(c(x1)))
B(c(a(x1))) → B(x1)
B(a(c(x1))) → C(a(x1))
B(a(c(x1))) → B(c(a(x1)))
C(c(b(x1))) → A(c(b(x1)))
B(a(c(x1))) → A(b(c(a(x1))))
B(c(a(x1))) → A(b(x1))
B(a(c(x1))) → A(x1)
B(c(a(x1))) → C(a(b(x1)))
A(c(b(a(x1)))) → C(c(x1))
c(c(b(x1))) → a(c(b(x1)))
a(c(b(a(x1)))) → b(c(c(x1)))
b(a(c(x1))) → a(b(c(a(x1))))
b(c(a(x1))) → c(a(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
A(c(b(a(x1)))) → C(x1)
A(c(b(a(x1)))) → B(c(c(x1)))
B(c(a(x1))) → B(x1)
B(a(c(x1))) → C(a(x1))
B(a(c(x1))) → B(c(a(x1)))
C(c(b(x1))) → A(c(b(x1)))
B(a(c(x1))) → A(b(c(a(x1))))
B(c(a(x1))) → A(b(x1))
B(a(c(x1))) → A(x1)
B(c(a(x1))) → C(a(b(x1)))
A(c(b(a(x1)))) → C(c(x1))
c(c(b(x1))) → a(c(b(x1)))
a(c(b(a(x1)))) → b(c(c(x1)))
b(a(c(x1))) → a(b(c(a(x1))))
b(c(a(x1))) → c(a(b(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(c(b(a(x1)))) → C(x1)
B(a(c(x1))) → C(a(x1))
B(a(c(x1))) → A(x1)
A(c(b(a(x1)))) → C(c(x1))
Used ordering: Polynomial interpretation [25,35]:
A(c(b(a(x1)))) → B(c(c(x1)))
B(c(a(x1))) → B(x1)
B(a(c(x1))) → B(c(a(x1)))
C(c(b(x1))) → A(c(b(x1)))
B(a(c(x1))) → A(b(c(a(x1))))
B(c(a(x1))) → A(b(x1))
B(c(a(x1))) → C(a(b(x1)))
The value of delta used in the strict ordering is 2.
POL(C(x1)) = (1/2)x_1
POL(c(x1)) = x_1
POL(B(x1)) = 2 + (2)x_1
POL(a(x1)) = x_1
POL(A(x1)) = (1/2)x_1
POL(b(x1)) = 4 + (4)x_1
a(c(b(a(x1)))) → b(c(c(x1)))
b(a(c(x1))) → a(b(c(a(x1))))
c(c(b(x1))) → a(c(b(x1)))
b(c(a(x1))) → c(a(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
A(c(b(a(x1)))) → B(c(c(x1)))
B(c(a(x1))) → B(x1)
B(a(c(x1))) → B(c(a(x1)))
C(c(b(x1))) → A(c(b(x1)))
B(a(c(x1))) → A(b(c(a(x1))))
B(c(a(x1))) → A(b(x1))
B(c(a(x1))) → C(a(b(x1)))
c(c(b(x1))) → a(c(b(x1)))
a(c(b(a(x1)))) → b(c(c(x1)))
b(a(c(x1))) → a(b(c(a(x1))))
b(c(a(x1))) → c(a(b(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(a(c(x1))) → A(b(c(a(x1))))
B(c(a(x1))) → A(b(x1))
Used ordering: Polynomial interpretation [25,35]:
A(c(b(a(x1)))) → B(c(c(x1)))
B(c(a(x1))) → B(x1)
B(a(c(x1))) → B(c(a(x1)))
C(c(b(x1))) → A(c(b(x1)))
B(c(a(x1))) → C(a(b(x1)))
The value of delta used in the strict ordering is 1/8.
POL(C(x1)) = 1/4
POL(c(x1)) = (2)x_1
POL(B(x1)) = 1/4
POL(a(x1)) = (1/2)x_1
POL(A(x1)) = (1/4)x_1
POL(b(x1)) = 1/2
a(c(b(a(x1)))) → b(c(c(x1)))
b(a(c(x1))) → a(b(c(a(x1))))
c(c(b(x1))) → a(c(b(x1)))
b(c(a(x1))) → c(a(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
A(c(b(a(x1)))) → B(c(c(x1)))
B(c(a(x1))) → B(x1)
B(a(c(x1))) → B(c(a(x1)))
C(c(b(x1))) → A(c(b(x1)))
B(c(a(x1))) → C(a(b(x1)))
c(c(b(x1))) → a(c(b(x1)))
a(c(b(a(x1)))) → b(c(c(x1)))
b(a(c(x1))) → a(b(c(a(x1))))
b(c(a(x1))) → c(a(b(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(c(b(a(x1)))) → B(c(c(x1)))
B(c(a(x1))) → C(a(b(x1)))
Used ordering: Polynomial interpretation [25,35]:
B(c(a(x1))) → B(x1)
B(a(c(x1))) → B(c(a(x1)))
C(c(b(x1))) → A(c(b(x1)))
The value of delta used in the strict ordering is 3/8.
POL(C(x1)) = (1/4)x_1
POL(c(x1)) = (4)x_1
POL(B(x1)) = 1/2
POL(a(x1)) = (1/4)x_1
POL(A(x1)) = 2
POL(b(x1)) = 2
a(c(b(a(x1)))) → b(c(c(x1)))
b(a(c(x1))) → a(b(c(a(x1))))
c(c(b(x1))) → a(c(b(x1)))
b(c(a(x1))) → c(a(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
B(c(a(x1))) → B(x1)
B(a(c(x1))) → B(c(a(x1)))
C(c(b(x1))) → A(c(b(x1)))
c(c(b(x1))) → a(c(b(x1)))
a(c(b(a(x1)))) → b(c(c(x1)))
b(a(c(x1))) → a(b(c(a(x1))))
b(c(a(x1))) → c(a(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
B(c(a(x1))) → B(x1)
B(a(c(x1))) → B(c(a(x1)))
c(c(b(x1))) → a(c(b(x1)))
a(c(b(a(x1)))) → b(c(c(x1)))
b(a(c(x1))) → a(b(c(a(x1))))
b(c(a(x1))) → c(a(b(x1)))