a(a(d(d(x1)))) → d(d(b(b(x1))))
a(a(x1)) → b(b(b(b(b(b(x1))))))
b(b(d(d(b(b(x1)))))) → a(a(c(c(x1))))
c(c(x1)) → d(d(x1))
↳ QTRS
↳ DependencyPairsProof
a(a(d(d(x1)))) → d(d(b(b(x1))))
a(a(x1)) → b(b(b(b(b(b(x1))))))
b(b(d(d(b(b(x1)))))) → a(a(c(c(x1))))
c(c(x1)) → d(d(x1))
B(b(d(d(b(b(x1)))))) → C(x1)
B(b(d(d(b(b(x1)))))) → A(c(c(x1)))
A(a(x1)) → B(b(x1))
A(a(d(d(x1)))) → B(x1)
A(a(d(d(x1)))) → B(b(x1))
A(a(x1)) → B(b(b(b(b(x1)))))
B(b(d(d(b(b(x1)))))) → A(a(c(c(x1))))
A(a(x1)) → B(b(b(x1)))
B(b(d(d(b(b(x1)))))) → C(c(x1))
A(a(x1)) → B(b(b(b(x1))))
A(a(x1)) → B(b(b(b(b(b(x1))))))
A(a(x1)) → B(x1)
a(a(d(d(x1)))) → d(d(b(b(x1))))
a(a(x1)) → b(b(b(b(b(b(x1))))))
b(b(d(d(b(b(x1)))))) → a(a(c(c(x1))))
c(c(x1)) → d(d(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
B(b(d(d(b(b(x1)))))) → C(x1)
B(b(d(d(b(b(x1)))))) → A(c(c(x1)))
A(a(x1)) → B(b(x1))
A(a(d(d(x1)))) → B(x1)
A(a(d(d(x1)))) → B(b(x1))
A(a(x1)) → B(b(b(b(b(x1)))))
B(b(d(d(b(b(x1)))))) → A(a(c(c(x1))))
A(a(x1)) → B(b(b(x1)))
B(b(d(d(b(b(x1)))))) → C(c(x1))
A(a(x1)) → B(b(b(b(x1))))
A(a(x1)) → B(b(b(b(b(b(x1))))))
A(a(x1)) → B(x1)
a(a(d(d(x1)))) → d(d(b(b(x1))))
a(a(x1)) → b(b(b(b(b(b(x1))))))
b(b(d(d(b(b(x1)))))) → a(a(c(c(x1))))
c(c(x1)) → d(d(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
B(b(d(d(b(b(x1)))))) → A(c(c(x1)))
A(a(x1)) → B(b(x1))
A(a(d(d(x1)))) → B(x1)
A(a(d(d(x1)))) → B(b(x1))
A(a(x1)) → B(b(b(b(b(x1)))))
A(a(x1)) → B(b(b(x1)))
B(b(d(d(b(b(x1)))))) → A(a(c(c(x1))))
A(a(x1)) → B(b(b(b(x1))))
A(a(x1)) → B(b(b(b(b(b(x1))))))
A(a(x1)) → B(x1)
a(a(d(d(x1)))) → d(d(b(b(x1))))
a(a(x1)) → b(b(b(b(b(b(x1))))))
b(b(d(d(b(b(x1)))))) → a(a(c(c(x1))))
c(c(x1)) → d(d(x1))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(b(d(d(b(b(x1)))))) → A(c(c(x1)))
Used ordering: Polynomial interpretation [25,35]:
A(a(x1)) → B(b(x1))
A(a(d(d(x1)))) → B(x1)
A(a(d(d(x1)))) → B(b(x1))
A(a(x1)) → B(b(b(b(b(x1)))))
A(a(x1)) → B(b(b(x1)))
B(b(d(d(b(b(x1)))))) → A(a(c(c(x1))))
A(a(x1)) → B(b(b(b(x1))))
A(a(x1)) → B(b(b(b(b(b(x1))))))
A(a(x1)) → B(x1)
The value of delta used in the strict ordering is 1.
POL(c(x1)) = 0
POL(B(x1)) = 1
POL(a(x1)) = 1
POL(A(x1)) = x_1
POL(b(x1)) = 1
POL(d(x1)) = 0
a(a(d(d(x1)))) → d(d(b(b(x1))))
a(a(x1)) → b(b(b(b(b(b(x1))))))
b(b(d(d(b(b(x1)))))) → a(a(c(c(x1))))
c(c(x1)) → d(d(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
A(a(d(d(x1)))) → B(b(x1))
A(a(d(d(x1)))) → B(x1)
A(a(x1)) → B(b(x1))
A(a(x1)) → B(b(b(b(b(x1)))))
B(b(d(d(b(b(x1)))))) → A(a(c(c(x1))))
A(a(x1)) → B(b(b(x1)))
A(a(x1)) → B(b(b(b(x1))))
A(a(x1)) → B(b(b(b(b(b(x1))))))
A(a(x1)) → B(x1)
a(a(d(d(x1)))) → d(d(b(b(x1))))
a(a(x1)) → b(b(b(b(b(b(x1))))))
b(b(d(d(b(b(x1)))))) → a(a(c(c(x1))))
c(c(x1)) → d(d(x1))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(a(d(d(x1)))) → B(b(x1))
A(a(d(d(x1)))) → B(x1)
Used ordering: Polynomial interpretation [25,35]:
A(a(x1)) → B(b(x1))
A(a(x1)) → B(b(b(b(b(x1)))))
B(b(d(d(b(b(x1)))))) → A(a(c(c(x1))))
A(a(x1)) → B(b(b(x1)))
A(a(x1)) → B(b(b(b(x1))))
A(a(x1)) → B(b(b(b(b(b(x1))))))
A(a(x1)) → B(x1)
The value of delta used in the strict ordering is 24.
POL(c(x1)) = 4 + (2)x_1
POL(B(x1)) = (2)x_1
POL(a(x1)) = x_1
POL(A(x1)) = (2)x_1
POL(d(x1)) = 4 + (2)x_1
POL(b(x1)) = x_1
a(a(d(d(x1)))) → d(d(b(b(x1))))
a(a(x1)) → b(b(b(b(b(b(x1))))))
b(b(d(d(b(b(x1)))))) → a(a(c(c(x1))))
c(c(x1)) → d(d(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
A(a(x1)) → B(b(x1))
A(a(x1)) → B(b(b(b(b(x1)))))
A(a(x1)) → B(b(b(x1)))
B(b(d(d(b(b(x1)))))) → A(a(c(c(x1))))
A(a(x1)) → B(b(b(b(x1))))
A(a(x1)) → B(b(b(b(b(b(x1))))))
A(a(x1)) → B(x1)
a(a(d(d(x1)))) → d(d(b(b(x1))))
a(a(x1)) → b(b(b(b(b(b(x1))))))
b(b(d(d(b(b(x1)))))) → a(a(c(c(x1))))
c(c(x1)) → d(d(x1))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(a(x1)) → B(x1)
Used ordering: Polynomial interpretation [25,35]:
A(a(x1)) → B(b(x1))
A(a(x1)) → B(b(b(b(b(x1)))))
A(a(x1)) → B(b(b(x1)))
B(b(d(d(b(b(x1)))))) → A(a(c(c(x1))))
A(a(x1)) → B(b(b(b(x1))))
A(a(x1)) → B(b(b(b(b(b(x1))))))
The value of delta used in the strict ordering is 3.
POL(c(x1)) = 0
POL(B(x1)) = 1 + x_1
POL(a(x1)) = 1 + (2)x_1
POL(A(x1)) = 2 + (2)x_1
POL(b(x1)) = 3
POL(d(x1)) = 0
a(a(d(d(x1)))) → d(d(b(b(x1))))
a(a(x1)) → b(b(b(b(b(b(x1))))))
b(b(d(d(b(b(x1)))))) → a(a(c(c(x1))))
c(c(x1)) → d(d(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
A(a(x1)) → B(b(x1))
A(a(x1)) → B(b(b(b(b(x1)))))
B(b(d(d(b(b(x1)))))) → A(a(c(c(x1))))
A(a(x1)) → B(b(b(x1)))
A(a(x1)) → B(b(b(b(x1))))
A(a(x1)) → B(b(b(b(b(b(x1))))))
a(a(d(d(x1)))) → d(d(b(b(x1))))
a(a(x1)) → b(b(b(b(b(b(x1))))))
b(b(d(d(b(b(x1)))))) → a(a(c(c(x1))))
c(c(x1)) → d(d(x1))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(a(x1)) → B(b(x1))
A(a(x1)) → B(b(b(b(b(x1)))))
B(b(d(d(b(b(x1)))))) → A(a(c(c(x1))))
A(a(x1)) → B(b(b(x1)))
A(a(x1)) → B(b(b(b(x1))))
Used ordering: Polynomial interpretation [25,35]:
A(a(x1)) → B(b(b(b(b(b(x1))))))
The value of delta used in the strict ordering is 1.
POL(c(x1)) = (2)x_1
POL(B(x1)) = x_1
POL(a(x1)) = 4 + x_1
POL(A(x1)) = 1 + x_1
POL(b(x1)) = 1 + x_1
POL(d(x1)) = (2)x_1
c(c(x1)) → d(d(x1))
a(a(d(d(x1)))) → d(d(b(b(x1))))
a(a(x1)) → b(b(b(b(b(b(x1))))))
b(b(d(d(b(b(x1)))))) → a(a(c(c(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
A(a(x1)) → B(b(b(b(b(b(x1))))))
a(a(d(d(x1)))) → d(d(b(b(x1))))
a(a(x1)) → b(b(b(b(b(b(x1))))))
b(b(d(d(b(b(x1)))))) → a(a(c(c(x1))))
c(c(x1)) → d(d(x1))