C(C(x1)) → c(c(x1))
c(c(c(c(x1)))) → x1
b(b(b(b(x1)))) → B(B(x1))
B(B(B(B(x1)))) → b(b(x1))
c(c(B(B(c(c(b(b(c(c(x1)))))))))) → B(B(c(c(b(b(c(c(B(B(c(c(b(b(x1))))))))))))))
b(b(B(B(x1)))) → x1
B(B(b(b(x1)))) → x1
c(c(C(C(x1)))) → x1
C(C(c(c(x1)))) → x1
↳ QTRS
↳ DependencyPairsProof
C(C(x1)) → c(c(x1))
c(c(c(c(x1)))) → x1
b(b(b(b(x1)))) → B(B(x1))
B(B(B(B(x1)))) → b(b(x1))
c(c(B(B(c(c(b(b(c(c(x1)))))))))) → B(B(c(c(b(b(c(c(B(B(c(c(b(b(x1))))))))))))))
b(b(B(B(x1)))) → x1
B(B(b(b(x1)))) → x1
c(c(C(C(x1)))) → x1
C(C(c(c(x1)))) → x1
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → B2(B(c(c(b(b(x1))))))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(B(B(c(c(b(b(x1)))))))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(b(b(x1)))
B1(b(b(b(x1)))) → B2(B(x1))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → B2(B(c(c(b(b(c(c(B(B(c(c(b(b(x1))))))))))))))
B2(B(B(B(x1)))) → B1(x1)
C1(C(x1)) → C2(x1)
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(b(b(c(c(B(B(c(c(b(b(x1)))))))))))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → B1(b(c(c(B(B(c(c(b(b(x1))))))))))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(c(B(B(c(c(b(b(x1))))))))
B2(B(B(B(x1)))) → B1(b(x1))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(c(b(b(x1))))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → B1(x1)
B1(b(b(b(x1)))) → B2(x1)
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → B1(b(x1))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → B1(c(c(B(B(c(c(b(b(x1)))))))))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(c(b(b(c(c(B(B(c(c(b(b(x1))))))))))))
C1(C(x1)) → C2(c(x1))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → B2(c(c(b(b(c(c(B(B(c(c(b(b(x1)))))))))))))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → B2(c(c(b(b(x1)))))
C(C(x1)) → c(c(x1))
c(c(c(c(x1)))) → x1
b(b(b(b(x1)))) → B(B(x1))
B(B(B(B(x1)))) → b(b(x1))
c(c(B(B(c(c(b(b(c(c(x1)))))))))) → B(B(c(c(b(b(c(c(B(B(c(c(b(b(x1))))))))))))))
b(b(B(B(x1)))) → x1
B(B(b(b(x1)))) → x1
c(c(C(C(x1)))) → x1
C(C(c(c(x1)))) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → B2(B(c(c(b(b(x1))))))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(B(B(c(c(b(b(x1)))))))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(b(b(x1)))
B1(b(b(b(x1)))) → B2(B(x1))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → B2(B(c(c(b(b(c(c(B(B(c(c(b(b(x1))))))))))))))
B2(B(B(B(x1)))) → B1(x1)
C1(C(x1)) → C2(x1)
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(b(b(c(c(B(B(c(c(b(b(x1)))))))))))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → B1(b(c(c(B(B(c(c(b(b(x1))))))))))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(c(B(B(c(c(b(b(x1))))))))
B2(B(B(B(x1)))) → B1(b(x1))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(c(b(b(x1))))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → B1(x1)
B1(b(b(b(x1)))) → B2(x1)
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → B1(b(x1))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → B1(c(c(B(B(c(c(b(b(x1)))))))))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(c(b(b(c(c(B(B(c(c(b(b(x1))))))))))))
C1(C(x1)) → C2(c(x1))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → B2(c(c(b(b(c(c(B(B(c(c(b(b(x1)))))))))))))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → B2(c(c(b(b(x1)))))
C(C(x1)) → c(c(x1))
c(c(c(c(x1)))) → x1
b(b(b(b(x1)))) → B(B(x1))
B(B(B(B(x1)))) → b(b(x1))
c(c(B(B(c(c(b(b(c(c(x1)))))))))) → B(B(c(c(b(b(c(c(B(B(c(c(b(b(x1))))))))))))))
b(b(B(B(x1)))) → x1
B(B(b(b(x1)))) → x1
c(c(C(C(x1)))) → x1
C(C(c(c(x1)))) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
B2(B(B(B(x1)))) → B1(b(x1))
B1(b(b(b(x1)))) → B2(B(x1))
B1(b(b(b(x1)))) → B2(x1)
B2(B(B(B(x1)))) → B1(x1)
C(C(x1)) → c(c(x1))
c(c(c(c(x1)))) → x1
b(b(b(b(x1)))) → B(B(x1))
B(B(B(B(x1)))) → b(b(x1))
c(c(B(B(c(c(b(b(c(c(x1)))))))))) → B(B(c(c(b(b(c(c(B(B(c(c(b(b(x1))))))))))))))
b(b(B(B(x1)))) → x1
B(B(b(b(x1)))) → x1
c(c(C(C(x1)))) → x1
C(C(c(c(x1)))) → x1
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B2(B(B(B(x1)))) → B1(b(x1))
B1(b(b(b(x1)))) → B2(B(x1))
B1(b(b(b(x1)))) → B2(x1)
B2(B(B(B(x1)))) → B1(x1)
The value of delta used in the strict ordering is 152.
POL(B2(x1)) = (2)x_1
POL(B(x1)) = 4 + (4)x_1
POL(B1(x1)) = 4 + (4)x_1
POL(b(x1)) = 3 + (4)x_1
B(B(B(B(x1)))) → b(b(x1))
b(b(b(b(x1)))) → B(B(x1))
B(B(b(b(x1)))) → x1
b(b(B(B(x1)))) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
C(C(x1)) → c(c(x1))
c(c(c(c(x1)))) → x1
b(b(b(b(x1)))) → B(B(x1))
B(B(B(B(x1)))) → b(b(x1))
c(c(B(B(c(c(b(b(c(c(x1)))))))))) → B(B(c(c(b(b(c(c(B(B(c(c(b(b(x1))))))))))))))
b(b(B(B(x1)))) → x1
B(B(b(b(x1)))) → x1
c(c(C(C(x1)))) → x1
C(C(c(c(x1)))) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(B(B(c(c(b(b(x1)))))))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(b(b(x1)))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(c(b(b(x1))))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(c(b(b(c(c(B(B(c(c(b(b(x1))))))))))))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(b(b(c(c(B(B(c(c(b(b(x1)))))))))))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(c(B(B(c(c(b(b(x1))))))))
C(C(x1)) → c(c(x1))
c(c(c(c(x1)))) → x1
b(b(b(b(x1)))) → B(B(x1))
B(B(B(B(x1)))) → b(b(x1))
c(c(B(B(c(c(b(b(c(c(x1)))))))))) → B(B(c(c(b(b(c(c(B(B(c(c(b(b(x1))))))))))))))
b(b(B(B(x1)))) → x1
B(B(b(b(x1)))) → x1
c(c(C(C(x1)))) → x1
C(C(c(c(x1)))) → x1
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(B(B(c(c(b(b(x1)))))))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(b(b(x1)))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(c(b(b(x1))))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(b(b(c(c(B(B(c(c(b(b(x1)))))))))))
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(c(B(B(c(c(b(b(x1))))))))
Used ordering: Polynomial interpretation [25,35]:
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(c(b(b(c(c(B(B(c(c(b(b(x1))))))))))))
The value of delta used in the strict ordering is 1.
POL(C(x1)) = x_1
POL(c(x1)) = 1 + x_1
POL(B(x1)) = x_1
POL(C2(x1)) = x_1
POL(b(x1)) = x_1
c(c(c(c(x1)))) → x1
c(c(B(B(c(c(b(b(c(c(x1)))))))))) → B(B(c(c(b(b(c(c(B(B(c(c(b(b(x1))))))))))))))
B(B(B(B(x1)))) → b(b(x1))
b(b(b(b(x1)))) → B(B(x1))
B(B(b(b(x1)))) → x1
b(b(B(B(x1)))) → x1
c(c(C(C(x1)))) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
C2(c(B(B(c(c(b(b(c(c(x1)))))))))) → C2(c(b(b(c(c(B(B(c(c(b(b(x1))))))))))))
C(C(x1)) → c(c(x1))
c(c(c(c(x1)))) → x1
b(b(b(b(x1)))) → B(B(x1))
B(B(B(B(x1)))) → b(b(x1))
c(c(B(B(c(c(b(b(c(c(x1)))))))))) → B(B(c(c(b(b(c(c(B(B(c(c(b(b(x1))))))))))))))
b(b(B(B(x1)))) → x1
B(B(b(b(x1)))) → x1
c(c(C(C(x1)))) → x1
C(C(c(c(x1)))) → x1