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