a(a(b(x1))) → b(a(b(c(a(x1)))))
b(a(x1)) → a(b(b(x1)))
b(c(a(x1))) → c(a(b(x1)))
↳ QTRS
↳ DependencyPairsProof
a(a(b(x1))) → b(a(b(c(a(x1)))))
b(a(x1)) → a(b(b(x1)))
b(c(a(x1))) → c(a(b(x1)))
B(a(x1)) → B(b(x1))
B(a(x1)) → A(b(b(x1)))
B(c(a(x1))) → B(x1)
A(a(b(x1))) → A(b(c(a(x1))))
A(a(b(x1))) → A(x1)
A(a(b(x1))) → B(a(b(c(a(x1)))))
B(c(a(x1))) → A(b(x1))
A(a(b(x1))) → B(c(a(x1)))
B(a(x1)) → B(x1)
a(a(b(x1))) → b(a(b(c(a(x1)))))
b(a(x1)) → a(b(b(x1)))
b(c(a(x1))) → c(a(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
B(a(x1)) → B(b(x1))
B(a(x1)) → A(b(b(x1)))
B(c(a(x1))) → B(x1)
A(a(b(x1))) → A(b(c(a(x1))))
A(a(b(x1))) → A(x1)
A(a(b(x1))) → B(a(b(c(a(x1)))))
B(c(a(x1))) → A(b(x1))
A(a(b(x1))) → B(c(a(x1)))
B(a(x1)) → B(x1)
a(a(b(x1))) → b(a(b(c(a(x1)))))
b(a(x1)) → a(b(b(x1)))
b(c(a(x1))) → c(a(b(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(a(x1)) → B(b(x1))
B(c(a(x1))) → B(x1)
A(a(b(x1))) → A(x1)
A(a(b(x1))) → B(c(a(x1)))
B(a(x1)) → B(x1)
Used ordering: Polynomial interpretation [25,35]:
B(a(x1)) → A(b(b(x1)))
A(a(b(x1))) → A(b(c(a(x1))))
A(a(b(x1))) → B(a(b(c(a(x1)))))
B(c(a(x1))) → A(b(x1))
The value of delta used in the strict ordering is 1/4.
POL(c(x1)) = x_1
POL(B(x1)) = 1/2 + (1/2)x_1
POL(a(x1)) = 1/2 + (4)x_1
POL(A(x1)) = 3/4 + (2)x_1
POL(b(x1)) = x_1
b(a(x1)) → a(b(b(x1)))
a(a(b(x1))) → b(a(b(c(a(x1)))))
b(c(a(x1))) → c(a(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
B(a(x1)) → A(b(b(x1)))
A(a(b(x1))) → A(b(c(a(x1))))
A(a(b(x1))) → B(a(b(c(a(x1)))))
B(c(a(x1))) → A(b(x1))
a(a(b(x1))) → b(a(b(c(a(x1)))))
b(a(x1)) → a(b(b(x1)))
b(c(a(x1))) → c(a(b(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(c(a(x1))) → A(b(x1))
Used ordering: Polynomial interpretation [25,35]:
B(a(x1)) → A(b(b(x1)))
A(a(b(x1))) → A(b(c(a(x1))))
A(a(b(x1))) → B(a(b(c(a(x1)))))
The value of delta used in the strict ordering is 1/8.
POL(c(x1)) = 1/4
POL(B(x1)) = (1/2)x_1
POL(a(x1)) = 0
POL(A(x1)) = 0
POL(b(x1)) = (5/4)x_1
b(a(x1)) → a(b(b(x1)))
a(a(b(x1))) → b(a(b(c(a(x1)))))
b(c(a(x1))) → c(a(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
B(a(x1)) → A(b(b(x1)))
A(a(b(x1))) → A(b(c(a(x1))))
A(a(b(x1))) → B(a(b(c(a(x1)))))
a(a(b(x1))) → b(a(b(c(a(x1)))))
b(a(x1)) → a(b(b(x1)))
b(c(a(x1))) → c(a(b(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(a(x1)) → A(b(b(x1)))
A(a(b(x1))) → A(b(c(a(x1))))
A(a(b(x1))) → B(a(b(c(a(x1)))))
The value of delta used in the strict ordering is 1/8.
POL(c(x1)) = 0
POL(B(x1)) = (7/4)x_1
POL(a(x1)) = 1/2 + (4)x_1
POL(A(x1)) = (2)x_1
POL(b(x1)) = x_1
b(a(x1)) → a(b(b(x1)))
a(a(b(x1))) → b(a(b(c(a(x1)))))
b(c(a(x1))) → c(a(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
a(a(b(x1))) → b(a(b(c(a(x1)))))
b(a(x1)) → a(b(b(x1)))
b(c(a(x1))) → c(a(b(x1)))