a(a(x1)) → c(b(a(b(a(x1)))))
b(a(b(x1))) → b(x1)
a(a(a(x1))) → c(c(a(x1)))
c(c(x1)) → a(b(c(b(a(x1)))))
a(c(a(x1))) → c(c(a(x1)))
c(a(c(x1))) → a(a(c(x1)))
↳ QTRS
↳ DependencyPairsProof
a(a(x1)) → c(b(a(b(a(x1)))))
b(a(b(x1))) → b(x1)
a(a(a(x1))) → c(c(a(x1)))
c(c(x1)) → a(b(c(b(a(x1)))))
a(c(a(x1))) → c(c(a(x1)))
c(a(c(x1))) → a(a(c(x1)))
A(c(a(x1))) → C(c(a(x1)))
A(a(x1)) → A(b(a(x1)))
A(a(x1)) → B(a(x1))
C(c(x1)) → A(b(c(b(a(x1)))))
C(c(x1)) → C(b(a(x1)))
A(a(x1)) → C(b(a(b(a(x1)))))
C(c(x1)) → A(x1)
C(a(c(x1))) → A(a(c(x1)))
A(a(a(x1))) → C(a(x1))
C(c(x1)) → B(c(b(a(x1))))
A(a(x1)) → B(a(b(a(x1))))
C(c(x1)) → B(a(x1))
A(a(a(x1))) → C(c(a(x1)))
a(a(x1)) → c(b(a(b(a(x1)))))
b(a(b(x1))) → b(x1)
a(a(a(x1))) → c(c(a(x1)))
c(c(x1)) → a(b(c(b(a(x1)))))
a(c(a(x1))) → c(c(a(x1)))
c(a(c(x1))) → a(a(c(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
A(c(a(x1))) → C(c(a(x1)))
A(a(x1)) → A(b(a(x1)))
A(a(x1)) → B(a(x1))
C(c(x1)) → A(b(c(b(a(x1)))))
C(c(x1)) → C(b(a(x1)))
A(a(x1)) → C(b(a(b(a(x1)))))
C(c(x1)) → A(x1)
C(a(c(x1))) → A(a(c(x1)))
A(a(a(x1))) → C(a(x1))
C(c(x1)) → B(c(b(a(x1))))
A(a(x1)) → B(a(b(a(x1))))
C(c(x1)) → B(a(x1))
A(a(a(x1))) → C(c(a(x1)))
a(a(x1)) → c(b(a(b(a(x1)))))
b(a(b(x1))) → b(x1)
a(a(a(x1))) → c(c(a(x1)))
c(c(x1)) → a(b(c(b(a(x1)))))
a(c(a(x1))) → c(c(a(x1)))
c(a(c(x1))) → a(a(c(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
C(c(x1)) → C(b(a(x1)))
C(c(x1)) → A(b(c(b(a(x1)))))
A(c(a(x1))) → C(c(a(x1)))
C(c(x1)) → A(x1)
A(a(x1)) → C(b(a(b(a(x1)))))
A(a(x1)) → A(b(a(x1)))
C(a(c(x1))) → A(a(c(x1)))
A(a(a(x1))) → C(a(x1))
A(a(a(x1))) → C(c(a(x1)))
a(a(x1)) → c(b(a(b(a(x1)))))
b(a(b(x1))) → b(x1)
a(a(a(x1))) → c(c(a(x1)))
c(c(x1)) → a(b(c(b(a(x1)))))
a(c(a(x1))) → c(c(a(x1)))
c(a(c(x1))) → a(a(c(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
C(c(x1)) → C(b(a(x1)))
A(a(x1)) → C(b(a(b(a(x1)))))
Used ordering: Polynomial interpretation [25,35]:
C(c(x1)) → A(b(c(b(a(x1)))))
A(c(a(x1))) → C(c(a(x1)))
C(c(x1)) → A(x1)
A(a(x1)) → A(b(a(x1)))
C(a(c(x1))) → A(a(c(x1)))
A(a(a(x1))) → C(a(x1))
A(a(a(x1))) → C(c(a(x1)))
The value of delta used in the strict ordering is 2.
POL(C(x1)) = 2 + (2)x_1
POL(c(x1)) = 1
POL(a(x1)) = 1
POL(A(x1)) = 4
POL(b(x1)) = 0
b(a(b(x1))) → b(x1)
a(a(x1)) → c(b(a(b(a(x1)))))
a(c(a(x1))) → c(c(a(x1)))
c(c(x1)) → a(b(c(b(a(x1)))))
c(a(c(x1))) → a(a(c(x1)))
a(a(a(x1))) → c(c(a(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
C(c(x1)) → A(b(c(b(a(x1)))))
A(c(a(x1))) → C(c(a(x1)))
C(c(x1)) → A(x1)
A(a(x1)) → A(b(a(x1)))
C(a(c(x1))) → A(a(c(x1)))
A(a(a(x1))) → C(a(x1))
A(a(a(x1))) → C(c(a(x1)))
a(a(x1)) → c(b(a(b(a(x1)))))
b(a(b(x1))) → b(x1)
a(a(a(x1))) → c(c(a(x1)))
c(c(x1)) → a(b(c(b(a(x1)))))
a(c(a(x1))) → c(c(a(x1)))
c(a(c(x1))) → a(a(c(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
C(c(x1)) → A(x1)
A(a(a(x1))) → C(a(x1))
Used ordering: Polynomial interpretation [25,35]:
C(c(x1)) → A(b(c(b(a(x1)))))
A(c(a(x1))) → C(c(a(x1)))
A(a(x1)) → A(b(a(x1)))
C(a(c(x1))) → A(a(c(x1)))
A(a(a(x1))) → C(c(a(x1)))
The value of delta used in the strict ordering is 1/8.
POL(C(x1)) = (1/2)x_1
POL(c(x1)) = 1/4 + (2)x_1
POL(a(x1)) = 1/4 + (2)x_1
POL(A(x1)) = (1/2)x_1
POL(b(x1)) = 1/4
b(a(b(x1))) → b(x1)
a(a(x1)) → c(b(a(b(a(x1)))))
a(c(a(x1))) → c(c(a(x1)))
c(c(x1)) → a(b(c(b(a(x1)))))
c(a(c(x1))) → a(a(c(x1)))
a(a(a(x1))) → c(c(a(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
C(c(x1)) → A(b(c(b(a(x1)))))
A(c(a(x1))) → C(c(a(x1)))
A(a(x1)) → A(b(a(x1)))
C(a(c(x1))) → A(a(c(x1)))
A(a(a(x1))) → C(c(a(x1)))
a(a(x1)) → c(b(a(b(a(x1)))))
b(a(b(x1))) → b(x1)
a(a(a(x1))) → c(c(a(x1)))
c(c(x1)) → a(b(c(b(a(x1)))))
a(c(a(x1))) → c(c(a(x1)))
c(a(c(x1))) → a(a(c(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
C(c(x1)) → A(b(c(b(a(x1)))))
A(a(x1)) → A(b(a(x1)))
Used ordering: Polynomial interpretation [25,35]:
A(c(a(x1))) → C(c(a(x1)))
C(a(c(x1))) → A(a(c(x1)))
A(a(a(x1))) → C(c(a(x1)))
The value of delta used in the strict ordering is 1/16.
POL(C(x1)) = (1/4)x_1
POL(c(x1)) = 1/4
POL(a(x1)) = 1/4
POL(A(x1)) = (1/4)x_1
POL(b(x1)) = 0
a(a(x1)) → c(b(a(b(a(x1)))))
a(c(a(x1))) → c(c(a(x1)))
c(c(x1)) → a(b(c(b(a(x1)))))
c(a(c(x1))) → a(a(c(x1)))
a(a(a(x1))) → c(c(a(x1)))
b(a(b(x1))) → b(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
A(c(a(x1))) → C(c(a(x1)))
C(a(c(x1))) → A(a(c(x1)))
A(a(a(x1))) → C(c(a(x1)))
a(a(x1)) → c(b(a(b(a(x1)))))
b(a(b(x1))) → b(x1)
a(a(a(x1))) → c(c(a(x1)))
c(c(x1)) → a(b(c(b(a(x1)))))
a(c(a(x1))) → c(c(a(x1)))
c(a(c(x1))) → a(a(c(x1)))