a(a(b(b(x1)))) → b(b(c(c(a(a(x1))))))
b(b(c(c(x1)))) → c(c(b(b(b(b(x1))))))
b(b(a(a(x1)))) → a(a(c(c(b(b(x1))))))
↳ QTRS
↳ DependencyPairsProof
a(a(b(b(x1)))) → b(b(c(c(a(a(x1))))))
b(b(c(c(x1)))) → c(c(b(b(b(b(x1))))))
b(b(a(a(x1)))) → a(a(c(c(b(b(x1))))))
B(b(a(a(x1)))) → B(x1)
B(b(a(a(x1)))) → A(a(c(c(b(b(x1))))))
B(b(a(a(x1)))) → A(c(c(b(b(x1)))))
A(a(b(b(x1)))) → B(c(c(a(a(x1)))))
B(b(c(c(x1)))) → B(b(b(x1)))
A(a(b(b(x1)))) → A(a(x1))
A(a(b(b(x1)))) → B(b(c(c(a(a(x1))))))
B(b(c(c(x1)))) → B(b(x1))
B(b(a(a(x1)))) → B(b(x1))
B(b(c(c(x1)))) → B(b(b(b(x1))))
A(a(b(b(x1)))) → A(x1)
B(b(c(c(x1)))) → B(x1)
a(a(b(b(x1)))) → b(b(c(c(a(a(x1))))))
b(b(c(c(x1)))) → c(c(b(b(b(b(x1))))))
b(b(a(a(x1)))) → a(a(c(c(b(b(x1))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
B(b(a(a(x1)))) → B(x1)
B(b(a(a(x1)))) → A(a(c(c(b(b(x1))))))
B(b(a(a(x1)))) → A(c(c(b(b(x1)))))
A(a(b(b(x1)))) → B(c(c(a(a(x1)))))
B(b(c(c(x1)))) → B(b(b(x1)))
A(a(b(b(x1)))) → A(a(x1))
A(a(b(b(x1)))) → B(b(c(c(a(a(x1))))))
B(b(c(c(x1)))) → B(b(x1))
B(b(a(a(x1)))) → B(b(x1))
B(b(c(c(x1)))) → B(b(b(b(x1))))
A(a(b(b(x1)))) → A(x1)
B(b(c(c(x1)))) → B(x1)
a(a(b(b(x1)))) → b(b(c(c(a(a(x1))))))
b(b(c(c(x1)))) → c(c(b(b(b(b(x1))))))
b(b(a(a(x1)))) → a(a(c(c(b(b(x1))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
B(b(a(a(x1)))) → B(x1)
B(b(c(c(x1)))) → B(b(b(x1)))
B(b(c(c(x1)))) → B(b(x1))
B(b(a(a(x1)))) → B(b(x1))
B(b(c(c(x1)))) → B(b(b(b(x1))))
B(b(c(c(x1)))) → B(x1)
a(a(b(b(x1)))) → b(b(c(c(a(a(x1))))))
b(b(c(c(x1)))) → c(c(b(b(b(b(x1))))))
b(b(a(a(x1)))) → a(a(c(c(b(b(x1))))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(b(a(a(x1)))) → B(x1)
B(b(a(a(x1)))) → B(b(x1))
Used ordering: Polynomial interpretation [25,35]:
B(b(c(c(x1)))) → B(b(b(x1)))
B(b(c(c(x1)))) → B(b(x1))
B(b(c(c(x1)))) → B(b(b(b(x1))))
B(b(c(c(x1)))) → B(x1)
The value of delta used in the strict ordering is 5.
POL(c(x1)) = x_1
POL(B(x1)) = (1/4)x_1
POL(a(x1)) = 4 + (4)x_1
POL(b(x1)) = x_1
b(b(c(c(x1)))) → c(c(b(b(b(b(x1))))))
b(b(a(a(x1)))) → a(a(c(c(b(b(x1))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
B(b(c(c(x1)))) → B(b(b(x1)))
B(b(c(c(x1)))) → B(b(x1))
B(b(c(c(x1)))) → B(b(b(b(x1))))
B(b(c(c(x1)))) → B(x1)
a(a(b(b(x1)))) → b(b(c(c(a(a(x1))))))
b(b(c(c(x1)))) → c(c(b(b(b(b(x1))))))
b(b(a(a(x1)))) → a(a(c(c(b(b(x1))))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(b(c(c(x1)))) → B(b(b(x1)))
B(b(c(c(x1)))) → B(b(x1))
B(b(c(c(x1)))) → B(b(b(b(x1))))
B(b(c(c(x1)))) → B(x1)
The value of delta used in the strict ordering is 10.
POL(c(x1)) = 4 + (4)x_1
POL(B(x1)) = (1/2)x_1
POL(a(x1)) = 0
POL(b(x1)) = x_1
b(b(c(c(x1)))) → c(c(b(b(b(b(x1))))))
b(b(a(a(x1)))) → a(a(c(c(b(b(x1))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
a(a(b(b(x1)))) → b(b(c(c(a(a(x1))))))
b(b(c(c(x1)))) → c(c(b(b(b(b(x1))))))
b(b(a(a(x1)))) → a(a(c(c(b(b(x1))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
A(a(b(b(x1)))) → A(a(x1))
A(a(b(b(x1)))) → A(x1)
a(a(b(b(x1)))) → b(b(c(c(a(a(x1))))))
b(b(c(c(x1)))) → c(c(b(b(b(b(x1))))))
b(b(a(a(x1)))) → a(a(c(c(b(b(x1))))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(a(b(b(x1)))) → A(x1)
Used ordering: Polynomial interpretation [25,35]:
A(a(b(b(x1)))) → A(a(x1))
The value of delta used in the strict ordering is 1/8.
POL(c(x1)) = 0
POL(a(x1)) = 1/4 + (1/4)x_1
POL(A(x1)) = (1/2)x_1
POL(b(x1)) = (4)x_1
a(a(b(b(x1)))) → b(b(c(c(a(a(x1))))))
b(b(c(c(x1)))) → c(c(b(b(b(b(x1))))))
b(b(a(a(x1)))) → a(a(c(c(b(b(x1))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
A(a(b(b(x1)))) → A(a(x1))
a(a(b(b(x1)))) → b(b(c(c(a(a(x1))))))
b(b(c(c(x1)))) → c(c(b(b(b(b(x1))))))
b(b(a(a(x1)))) → a(a(c(c(b(b(x1))))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(a(b(b(x1)))) → A(a(x1))
The value of delta used in the strict ordering is 5/32.
POL(c(x1)) = 0
POL(a(x1)) = 4 + (1/2)x_1
POL(A(x1)) = (1/4)x_1
POL(b(x1)) = 1/4 + (4)x_1
a(a(b(b(x1)))) → b(b(c(c(a(a(x1))))))
b(b(c(c(x1)))) → c(c(b(b(b(b(x1))))))
b(b(a(a(x1)))) → a(a(c(c(b(b(x1))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
a(a(b(b(x1)))) → b(b(c(c(a(a(x1))))))
b(b(c(c(x1)))) → c(c(b(b(b(b(x1))))))
b(b(a(a(x1)))) → a(a(c(c(b(b(x1))))))