b(a(b(x1))) → a(b(a(x1)))
b(b(a(x1))) → b(b(b(x1)))
c(a(x1)) → a(b(c(x1)))
c(b(x1)) → b(a(c(x1)))
↳ QTRS
↳ DependencyPairsProof
b(a(b(x1))) → a(b(a(x1)))
b(b(a(x1))) → b(b(b(x1)))
c(a(x1)) → a(b(c(x1)))
c(b(x1)) → b(a(c(x1)))
B(b(a(x1))) → B(b(x1))
C(b(x1)) → B(a(c(x1)))
B(b(a(x1))) → B(x1)
C(a(x1)) → B(c(x1))
C(a(x1)) → C(x1)
B(b(a(x1))) → B(b(b(x1)))
B(a(b(x1))) → B(a(x1))
C(b(x1)) → C(x1)
b(a(b(x1))) → a(b(a(x1)))
b(b(a(x1))) → b(b(b(x1)))
c(a(x1)) → a(b(c(x1)))
c(b(x1)) → b(a(c(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
B(b(a(x1))) → B(b(x1))
C(b(x1)) → B(a(c(x1)))
B(b(a(x1))) → B(x1)
C(a(x1)) → B(c(x1))
C(a(x1)) → C(x1)
B(b(a(x1))) → B(b(b(x1)))
B(a(b(x1))) → B(a(x1))
C(b(x1)) → C(x1)
b(a(b(x1))) → a(b(a(x1)))
b(b(a(x1))) → b(b(b(x1)))
c(a(x1)) → a(b(c(x1)))
c(b(x1)) → b(a(c(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
B(a(b(x1))) → B(a(x1))
b(a(b(x1))) → a(b(a(x1)))
b(b(a(x1))) → b(b(b(x1)))
c(a(x1)) → a(b(c(x1)))
c(b(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(b(x1))) → B(a(x1))
The value of delta used in the strict ordering is 1.
POL(B(x1)) = (2)x_1
POL(a(x1)) = (2)x_1
POL(b(x1)) = 1/4 + (11/4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
b(a(b(x1))) → a(b(a(x1)))
b(b(a(x1))) → b(b(b(x1)))
c(a(x1)) → a(b(c(x1)))
c(b(x1)) → b(a(c(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
B(b(a(x1))) → B(b(x1))
B(b(a(x1))) → B(x1)
B(b(a(x1))) → B(b(b(x1)))
b(a(b(x1))) → a(b(a(x1)))
b(b(a(x1))) → b(b(b(x1)))
c(a(x1)) → a(b(c(x1)))
c(b(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(a(x1))) → B(b(x1))
B(b(a(x1))) → B(x1)
Used ordering: Polynomial interpretation [25,35]:
B(b(a(x1))) → B(b(b(x1)))
The value of delta used in the strict ordering is 1/4.
POL(B(x1)) = (1/4)x_1
POL(a(x1)) = 1/4 + (4)x_1
POL(b(x1)) = 1/4 + (4)x_1
b(a(b(x1))) → a(b(a(x1)))
b(b(a(x1))) → b(b(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
B(b(a(x1))) → B(b(b(x1)))
b(a(b(x1))) → a(b(a(x1)))
b(b(a(x1))) → b(b(b(x1)))
c(a(x1)) → a(b(c(x1)))
c(b(x1)) → b(a(c(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
C(a(x1)) → C(x1)
C(b(x1)) → C(x1)
b(a(b(x1))) → a(b(a(x1)))
b(b(a(x1))) → b(b(b(x1)))
c(a(x1)) → a(b(c(x1)))
c(b(x1)) → b(a(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(x1)
C(b(x1)) → C(x1)
The value of delta used in the strict ordering is 1/4.
POL(C(x1)) = (1/2)x_1
POL(a(x1)) = 1/2 + (3/2)x_1
POL(b(x1)) = 9/4 + x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
b(a(b(x1))) → a(b(a(x1)))
b(b(a(x1))) → b(b(b(x1)))
c(a(x1)) → a(b(c(x1)))
c(b(x1)) → b(a(c(x1)))