a(a(a(a(x1)))) → b(b(x1))
b(b(a(a(x1)))) → a(a(b(b(x1))))
b(b(b(b(c(c(x1)))))) → c(c(a(a(x1))))
b(b(b(b(x1)))) → a(a(a(a(a(a(x1))))))
c(c(a(a(x1)))) → b(b(a(a(c(c(x1))))))
↳ QTRS
↳ DependencyPairsProof
a(a(a(a(x1)))) → b(b(x1))
b(b(a(a(x1)))) → a(a(b(b(x1))))
b(b(b(b(c(c(x1)))))) → c(c(a(a(x1))))
b(b(b(b(x1)))) → a(a(a(a(a(a(x1))))))
c(c(a(a(x1)))) → b(b(a(a(c(c(x1))))))
C(c(a(a(x1)))) → C(c(x1))
C(c(a(a(x1)))) → A(a(c(c(x1))))
C(c(a(a(x1)))) → B(b(a(a(c(c(x1))))))
A(a(a(a(x1)))) → B(b(x1))
B(b(b(b(x1)))) → A(x1)
B(b(b(b(x1)))) → A(a(a(x1)))
B(b(a(a(x1)))) → A(b(b(x1)))
B(b(a(a(x1)))) → B(b(x1))
B(b(b(b(c(c(x1)))))) → A(a(x1))
B(b(a(a(x1)))) → B(x1)
B(b(b(b(c(c(x1)))))) → C(c(a(a(x1))))
C(c(a(a(x1)))) → B(a(a(c(c(x1)))))
B(b(a(a(x1)))) → A(a(b(b(x1))))
B(b(b(b(x1)))) → A(a(a(a(a(a(x1))))))
B(b(b(b(x1)))) → A(a(x1))
A(a(a(a(x1)))) → B(x1)
C(c(a(a(x1)))) → A(c(c(x1)))
B(b(b(b(c(c(x1)))))) → C(a(a(x1)))
B(b(b(b(x1)))) → A(a(a(a(x1))))
B(b(b(b(c(c(x1)))))) → A(x1)
C(c(a(a(x1)))) → C(x1)
B(b(b(b(x1)))) → A(a(a(a(a(x1)))))
a(a(a(a(x1)))) → b(b(x1))
b(b(a(a(x1)))) → a(a(b(b(x1))))
b(b(b(b(c(c(x1)))))) → c(c(a(a(x1))))
b(b(b(b(x1)))) → a(a(a(a(a(a(x1))))))
c(c(a(a(x1)))) → b(b(a(a(c(c(x1))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
C(c(a(a(x1)))) → C(c(x1))
C(c(a(a(x1)))) → A(a(c(c(x1))))
C(c(a(a(x1)))) → B(b(a(a(c(c(x1))))))
A(a(a(a(x1)))) → B(b(x1))
B(b(b(b(x1)))) → A(x1)
B(b(b(b(x1)))) → A(a(a(x1)))
B(b(a(a(x1)))) → A(b(b(x1)))
B(b(a(a(x1)))) → B(b(x1))
B(b(b(b(c(c(x1)))))) → A(a(x1))
B(b(a(a(x1)))) → B(x1)
B(b(b(b(c(c(x1)))))) → C(c(a(a(x1))))
C(c(a(a(x1)))) → B(a(a(c(c(x1)))))
B(b(a(a(x1)))) → A(a(b(b(x1))))
B(b(b(b(x1)))) → A(a(a(a(a(a(x1))))))
B(b(b(b(x1)))) → A(a(x1))
A(a(a(a(x1)))) → B(x1)
C(c(a(a(x1)))) → A(c(c(x1)))
B(b(b(b(c(c(x1)))))) → C(a(a(x1)))
B(b(b(b(x1)))) → A(a(a(a(x1))))
B(b(b(b(c(c(x1)))))) → A(x1)
C(c(a(a(x1)))) → C(x1)
B(b(b(b(x1)))) → A(a(a(a(a(x1)))))
a(a(a(a(x1)))) → b(b(x1))
b(b(a(a(x1)))) → a(a(b(b(x1))))
b(b(b(b(c(c(x1)))))) → c(c(a(a(x1))))
b(b(b(b(x1)))) → a(a(a(a(a(a(x1))))))
c(c(a(a(x1)))) → b(b(a(a(c(c(x1))))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(b(b(b(c(c(x1)))))) → A(a(x1))
B(b(b(b(c(c(x1)))))) → C(a(a(x1)))
B(b(b(b(c(c(x1)))))) → A(x1)
C(c(a(a(x1)))) → C(x1)
Used ordering: Polynomial interpretation [25,35]:
C(c(a(a(x1)))) → C(c(x1))
C(c(a(a(x1)))) → A(a(c(c(x1))))
C(c(a(a(x1)))) → B(b(a(a(c(c(x1))))))
A(a(a(a(x1)))) → B(b(x1))
B(b(b(b(x1)))) → A(x1)
B(b(b(b(x1)))) → A(a(a(x1)))
B(b(a(a(x1)))) → A(b(b(x1)))
B(b(a(a(x1)))) → B(b(x1))
B(b(a(a(x1)))) → B(x1)
B(b(b(b(c(c(x1)))))) → C(c(a(a(x1))))
C(c(a(a(x1)))) → B(a(a(c(c(x1)))))
B(b(a(a(x1)))) → A(a(b(b(x1))))
B(b(b(b(x1)))) → A(a(a(a(a(a(x1))))))
B(b(b(b(x1)))) → A(a(x1))
A(a(a(a(x1)))) → B(x1)
C(c(a(a(x1)))) → A(c(c(x1)))
B(b(b(b(x1)))) → A(a(a(a(x1))))
B(b(b(b(x1)))) → A(a(a(a(a(x1)))))
The value of delta used in the strict ordering is 2.
POL(C(x1)) = 2 + (4)x_1
POL(c(x1)) = 1/2 + 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(b(a(a(x1)))) → a(a(b(b(x1))))
b(b(b(b(c(c(x1)))))) → c(c(a(a(x1))))
b(b(b(b(x1)))) → a(a(a(a(a(a(x1))))))
a(a(a(a(x1)))) → b(b(x1))
c(c(a(a(x1)))) → b(b(a(a(c(c(x1))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
C(c(a(a(x1)))) → C(c(x1))
C(c(a(a(x1)))) → A(a(c(c(x1))))
C(c(a(a(x1)))) → B(b(a(a(c(c(x1))))))
A(a(a(a(x1)))) → B(b(x1))
B(b(b(b(x1)))) → A(x1)
B(b(b(b(x1)))) → A(a(a(x1)))
B(b(a(a(x1)))) → A(b(b(x1)))
B(b(a(a(x1)))) → B(b(x1))
B(b(a(a(x1)))) → B(x1)
B(b(b(b(c(c(x1)))))) → C(c(a(a(x1))))
C(c(a(a(x1)))) → B(a(a(c(c(x1)))))
B(b(a(a(x1)))) → A(a(b(b(x1))))
B(b(b(b(x1)))) → A(a(a(a(a(a(x1))))))
A(a(a(a(x1)))) → B(x1)
B(b(b(b(x1)))) → A(a(x1))
B(b(b(b(x1)))) → A(a(a(a(x1))))
C(c(a(a(x1)))) → A(c(c(x1)))
B(b(b(b(x1)))) → A(a(a(a(a(x1)))))
a(a(a(a(x1)))) → b(b(x1))
b(b(a(a(x1)))) → a(a(b(b(x1))))
b(b(b(b(c(c(x1)))))) → c(c(a(a(x1))))
b(b(b(b(x1)))) → a(a(a(a(a(a(x1))))))
c(c(a(a(x1)))) → b(b(a(a(c(c(x1))))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
C(c(a(a(x1)))) → C(c(x1))
C(c(a(a(x1)))) → A(a(c(c(x1))))
C(c(a(a(x1)))) → B(b(a(a(c(c(x1))))))
B(b(b(b(x1)))) → A(x1)
B(b(b(b(x1)))) → A(a(a(x1)))
B(b(a(a(x1)))) → A(b(b(x1)))
B(b(a(a(x1)))) → B(b(x1))
B(b(a(a(x1)))) → B(x1)
B(b(b(b(c(c(x1)))))) → C(c(a(a(x1))))
C(c(a(a(x1)))) → B(a(a(c(c(x1)))))
B(b(b(b(x1)))) → A(a(a(a(a(a(x1))))))
A(a(a(a(x1)))) → B(x1)
B(b(b(b(x1)))) → A(a(x1))
B(b(b(b(x1)))) → A(a(a(a(x1))))
C(c(a(a(x1)))) → A(c(c(x1)))
B(b(b(b(x1)))) → A(a(a(a(a(x1)))))
Used ordering: Polynomial interpretation [25,35]:
A(a(a(a(x1)))) → B(b(x1))
B(b(a(a(x1)))) → A(a(b(b(x1))))
The value of delta used in the strict ordering is 5/16.
POL(C(x1)) = 7/4 + (7/2)x_1
POL(c(x1)) = (7/4)x_1
POL(B(x1)) = 5/2 + (2)x_1
POL(a(x1)) = 1/4 + x_1
POL(A(x1)) = 2 + (2)x_1
POL(b(x1)) = 1/2 + x_1
b(b(a(a(x1)))) → a(a(b(b(x1))))
b(b(b(b(c(c(x1)))))) → c(c(a(a(x1))))
b(b(b(b(x1)))) → a(a(a(a(a(a(x1))))))
a(a(a(a(x1)))) → b(b(x1))
c(c(a(a(x1)))) → b(b(a(a(c(c(x1))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
A(a(a(a(x1)))) → B(b(x1))
B(b(a(a(x1)))) → A(a(b(b(x1))))
a(a(a(a(x1)))) → b(b(x1))
b(b(a(a(x1)))) → a(a(b(b(x1))))
b(b(b(b(c(c(x1)))))) → c(c(a(a(x1))))
b(b(b(b(x1)))) → a(a(a(a(a(a(x1))))))
c(c(a(a(x1)))) → b(b(a(a(c(c(x1))))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(a(a(a(x1)))) → B(b(x1))
B(b(a(a(x1)))) → A(a(b(b(x1))))
The value of delta used in the strict ordering is 3/4.
POL(c(x1)) = (7/4)x_1
POL(B(x1)) = 4 + x_1
POL(a(x1)) = 2 + x_1
POL(A(x1)) = 2 + x_1
POL(b(x1)) = 13/4 + x_1
b(b(a(a(x1)))) → a(a(b(b(x1))))
b(b(b(b(c(c(x1)))))) → c(c(a(a(x1))))
b(b(b(b(x1)))) → a(a(a(a(a(a(x1))))))
a(a(a(a(x1)))) → b(b(x1))
c(c(a(a(x1)))) → b(b(a(a(c(c(x1))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
a(a(a(a(x1)))) → b(b(x1))
b(b(a(a(x1)))) → a(a(b(b(x1))))
b(b(b(b(c(c(x1)))))) → c(c(a(a(x1))))
b(b(b(b(x1)))) → a(a(a(a(a(a(x1))))))
c(c(a(a(x1)))) → b(b(a(a(c(c(x1))))))