a(a(x1)) → b(x1)
b(a(x1)) → a(b(x1))
b(b(c(x1))) → c(a(x1))
b(b(x1)) → a(a(a(x1)))
c(a(x1)) → b(a(c(x1)))
↳ QTRS
↳ DependencyPairsProof
a(a(x1)) → b(x1)
b(a(x1)) → a(b(x1))
b(b(c(x1))) → c(a(x1))
b(b(x1)) → a(a(a(x1)))
c(a(x1)) → b(a(c(x1)))
B(b(x1)) → A(a(a(x1)))
B(a(x1)) → A(b(x1))
C(a(x1)) → C(x1)
C(a(x1)) → B(a(c(x1)))
B(b(x1)) → A(x1)
B(b(c(x1))) → C(a(x1))
B(b(c(x1))) → A(x1)
B(b(x1)) → A(a(x1))
B(a(x1)) → B(x1)
C(a(x1)) → A(c(x1))
A(a(x1)) → B(x1)
a(a(x1)) → b(x1)
b(a(x1)) → a(b(x1))
b(b(c(x1))) → c(a(x1))
b(b(x1)) → a(a(a(x1)))
c(a(x1)) → b(a(c(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
B(b(x1)) → A(a(a(x1)))
B(a(x1)) → A(b(x1))
C(a(x1)) → C(x1)
C(a(x1)) → B(a(c(x1)))
B(b(x1)) → A(x1)
B(b(c(x1))) → C(a(x1))
B(b(c(x1))) → A(x1)
B(b(x1)) → A(a(x1))
B(a(x1)) → B(x1)
C(a(x1)) → A(c(x1))
A(a(x1)) → B(x1)
a(a(x1)) → b(x1)
b(a(x1)) → a(b(x1))
b(b(c(x1))) → c(a(x1))
b(b(x1)) → a(a(a(x1)))
c(a(x1)) → b(a(c(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(b(c(x1))) → A(x1)
Used ordering: Polynomial interpretation [25,35]:
B(b(x1)) → A(a(a(x1)))
B(a(x1)) → A(b(x1))
C(a(x1)) → C(x1)
C(a(x1)) → B(a(c(x1)))
B(b(x1)) → A(x1)
B(b(c(x1))) → C(a(x1))
B(b(x1)) → A(a(x1))
B(a(x1)) → B(x1)
C(a(x1)) → A(c(x1))
A(a(x1)) → B(x1)
The value of delta used in the strict ordering is 4.
POL(C(x1)) = 4 + (4)x_1
POL(c(x1)) = 1 + x_1
POL(B(x1)) = (4)x_1
POL(a(x1)) = x_1
POL(A(x1)) = (4)x_1
POL(b(x1)) = x_1
b(a(x1)) → a(b(x1))
b(b(x1)) → a(a(a(x1)))
b(b(c(x1))) → c(a(x1))
c(a(x1)) → b(a(c(x1)))
a(a(x1)) → b(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
B(b(x1)) → A(a(a(x1)))
B(a(x1)) → A(b(x1))
C(a(x1)) → B(a(c(x1)))
C(a(x1)) → C(x1)
B(b(x1)) → A(x1)
B(b(c(x1))) → C(a(x1))
B(b(x1)) → A(a(x1))
B(a(x1)) → B(x1)
C(a(x1)) → A(c(x1))
A(a(x1)) → B(x1)
a(a(x1)) → b(x1)
b(a(x1)) → a(b(x1))
b(b(c(x1))) → c(a(x1))
b(b(x1)) → a(a(a(x1)))
c(a(x1)) → b(a(c(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(b(x1)) → A(a(a(x1)))
C(a(x1)) → B(a(c(x1)))
C(a(x1)) → C(x1)
B(b(x1)) → A(x1)
B(b(x1)) → A(a(x1))
B(a(x1)) → B(x1)
C(a(x1)) → A(c(x1))
Used ordering: Polynomial interpretation [25,35]:
B(a(x1)) → A(b(x1))
B(b(c(x1))) → C(a(x1))
A(a(x1)) → B(x1)
The value of delta used in the strict ordering is 1/4.
POL(C(x1)) = 2 + (4)x_1
POL(c(x1)) = 1 + (4)x_1
POL(B(x1)) = 3/2 + x_1
POL(a(x1)) = 1/4 + x_1
POL(A(x1)) = 5/4 + x_1
POL(b(x1)) = 1/2 + x_1
b(a(x1)) → a(b(x1))
b(b(x1)) → a(a(a(x1)))
b(b(c(x1))) → c(a(x1))
c(a(x1)) → b(a(c(x1)))
a(a(x1)) → b(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
B(a(x1)) → A(b(x1))
B(b(c(x1))) → C(a(x1))
A(a(x1)) → B(x1)
a(a(x1)) → b(x1)
b(a(x1)) → a(b(x1))
b(b(c(x1))) → c(a(x1))
b(b(x1)) → a(a(a(x1)))
c(a(x1)) → b(a(c(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
B(a(x1)) → A(b(x1))
A(a(x1)) → B(x1)
a(a(x1)) → b(x1)
b(a(x1)) → a(b(x1))
b(b(c(x1))) → c(a(x1))
b(b(x1)) → a(a(a(x1)))
c(a(x1)) → b(a(c(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(a(x1)) → A(b(x1))
A(a(x1)) → B(x1)
The value of delta used in the strict ordering is 1/4.
POL(c(x1)) = 1/2 + (3)x_1
POL(B(x1)) = 3/2 + (4)x_1
POL(a(x1)) = 1/2 + x_1
POL(A(x1)) = 1/4 + (4)x_1
POL(b(x1)) = 3/4 + x_1
b(a(x1)) → a(b(x1))
b(b(x1)) → a(a(a(x1)))
b(b(c(x1))) → c(a(x1))
c(a(x1)) → b(a(c(x1)))
a(a(x1)) → b(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
a(a(x1)) → b(x1)
b(a(x1)) → a(b(x1))
b(b(c(x1))) → c(a(x1))
b(b(x1)) → a(a(a(x1)))
c(a(x1)) → b(a(c(x1)))