C(x1) → c(x1)
c(c(x1)) → x1
b(b(x1)) → B(x1)
B(B(x1)) → b(x1)
c(B(c(b(c(x1))))) → B(c(b(c(B(c(b(x1)))))))
b(B(x1)) → x1
B(b(x1)) → x1
c(C(x1)) → x1
C(c(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
C(x1) → c(x1)
c(c(x1)) → x1
b(b(x1)) → B(x1)
B(B(x1)) → b(x1)
c(B(c(b(c(x1))))) → B(c(b(c(B(c(b(x1)))))))
b(B(x1)) → x1
B(b(x1)) → x1
c(C(x1)) → x1
C(c(x1)) → x1
C2(B(c(b(c(x1))))) → B1(c(B(c(b(x1)))))
C1(x1) → C2(x1)
C2(B(c(b(c(x1))))) → B1(x1)
C2(B(c(b(c(x1))))) → C2(b(x1))
C2(B(c(b(c(x1))))) → C2(b(c(B(c(b(x1))))))
C2(B(c(b(c(x1))))) → B2(c(b(x1)))
C2(B(c(b(c(x1))))) → B2(c(b(c(B(c(b(x1)))))))
C2(B(c(b(c(x1))))) → C2(B(c(b(x1))))
B1(b(x1)) → B2(x1)
B2(B(x1)) → B1(x1)
C(x1) → c(x1)
c(c(x1)) → x1
b(b(x1)) → B(x1)
B(B(x1)) → b(x1)
c(B(c(b(c(x1))))) → B(c(b(c(B(c(b(x1)))))))
b(B(x1)) → x1
B(b(x1)) → x1
c(C(x1)) → x1
C(c(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
C2(B(c(b(c(x1))))) → B1(c(B(c(b(x1)))))
C1(x1) → C2(x1)
C2(B(c(b(c(x1))))) → B1(x1)
C2(B(c(b(c(x1))))) → C2(b(x1))
C2(B(c(b(c(x1))))) → C2(b(c(B(c(b(x1))))))
C2(B(c(b(c(x1))))) → B2(c(b(x1)))
C2(B(c(b(c(x1))))) → B2(c(b(c(B(c(b(x1)))))))
C2(B(c(b(c(x1))))) → C2(B(c(b(x1))))
B1(b(x1)) → B2(x1)
B2(B(x1)) → B1(x1)
C(x1) → c(x1)
c(c(x1)) → x1
b(b(x1)) → B(x1)
B(B(x1)) → b(x1)
c(B(c(b(c(x1))))) → B(c(b(c(B(c(b(x1)))))))
b(B(x1)) → x1
B(b(x1)) → x1
c(C(x1)) → x1
C(c(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
B1(b(x1)) → B2(x1)
B2(B(x1)) → B1(x1)
C(x1) → c(x1)
c(c(x1)) → x1
b(b(x1)) → B(x1)
B(B(x1)) → b(x1)
c(B(c(b(c(x1))))) → B(c(b(c(B(c(b(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(b(x1)) → B2(x1)
B2(B(x1)) → B1(x1)
The value of delta used in the strict ordering is 9/4.
POL(B2(x1)) = 3/4 + (4)x_1
POL(B(x1)) = 4 + (3/4)x_1
POL(B1(x1)) = 3/2 + (3)x_1
POL(b(x1)) = 1/2 + (9/4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
C(x1) → c(x1)
c(c(x1)) → x1
b(b(x1)) → B(x1)
B(B(x1)) → b(x1)
c(B(c(b(c(x1))))) → B(c(b(c(B(c(b(x1)))))))
b(B(x1)) → x1
B(b(x1)) → x1
c(C(x1)) → x1
C(c(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
C2(B(c(b(c(x1))))) → C2(b(x1))
C2(B(c(b(c(x1))))) → C2(b(c(B(c(b(x1))))))
C2(B(c(b(c(x1))))) → C2(B(c(b(x1))))
C(x1) → c(x1)
c(c(x1)) → x1
b(b(x1)) → B(x1)
B(B(x1)) → b(x1)
c(B(c(b(c(x1))))) → B(c(b(c(B(c(b(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.
C2(B(c(b(c(x1))))) → C2(b(x1))
C2(B(c(b(c(x1))))) → C2(B(c(b(x1))))
Used ordering: Polynomial interpretation [25,35]:
C2(B(c(b(c(x1))))) → C2(b(c(B(c(b(x1))))))
The value of delta used in the strict ordering is 12.
POL(C(x1)) = (9/4)x_1
POL(c(x1)) = 2 + (3/2)x_1
POL(B(x1)) = x_1
POL(C2(x1)) = (4)x_1
POL(b(x1)) = x_1
B(b(x1)) → x1
b(B(x1)) → x1
c(C(x1)) → x1
c(c(x1)) → x1
B(B(x1)) → b(x1)
b(b(x1)) → B(x1)
c(B(c(b(c(x1))))) → B(c(b(c(B(c(b(x1)))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
C2(B(c(b(c(x1))))) → C2(b(c(B(c(b(x1))))))
C(x1) → c(x1)
c(c(x1)) → x1
b(b(x1)) → B(x1)
B(B(x1)) → b(x1)
c(B(c(b(c(x1))))) → B(c(b(c(B(c(b(x1)))))))
b(B(x1)) → x1
B(b(x1)) → x1
c(C(x1)) → x1
C(c(x1)) → x1