c(c(c(a(x1)))) → d(d(x1))
d(b(x1)) → c(c(x1))
c(x1) → a(a(a(a(x1))))
d(x1) → b(b(b(b(x1))))
b(d(x1)) → c(c(x1))
a(c(c(c(x1)))) → d(d(x1))
↳ QTRS
↳ DependencyPairsProof
c(c(c(a(x1)))) → d(d(x1))
d(b(x1)) → c(c(x1))
c(x1) → a(a(a(a(x1))))
d(x1) → b(b(b(b(x1))))
b(d(x1)) → c(c(x1))
a(c(c(c(x1)))) → d(d(x1))
B(d(x1)) → C(x1)
C(c(c(a(x1)))) → D(x1)
D(x1) → B(x1)
D(x1) → B(b(b(b(x1))))
A(c(c(c(x1)))) → D(x1)
D(b(x1)) → C(c(x1))
D(x1) → B(b(x1))
C(c(c(a(x1)))) → D(d(x1))
D(x1) → B(b(b(x1)))
B(d(x1)) → C(c(x1))
C(x1) → A(x1)
C(x1) → A(a(x1))
C(x1) → A(a(a(a(x1))))
C(x1) → A(a(a(x1)))
A(c(c(c(x1)))) → D(d(x1))
D(b(x1)) → C(x1)
c(c(c(a(x1)))) → d(d(x1))
d(b(x1)) → c(c(x1))
c(x1) → a(a(a(a(x1))))
d(x1) → b(b(b(b(x1))))
b(d(x1)) → c(c(x1))
a(c(c(c(x1)))) → d(d(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
B(d(x1)) → C(x1)
C(c(c(a(x1)))) → D(x1)
D(x1) → B(x1)
D(x1) → B(b(b(b(x1))))
A(c(c(c(x1)))) → D(x1)
D(b(x1)) → C(c(x1))
D(x1) → B(b(x1))
C(c(c(a(x1)))) → D(d(x1))
D(x1) → B(b(b(x1)))
B(d(x1)) → C(c(x1))
C(x1) → A(x1)
C(x1) → A(a(x1))
C(x1) → A(a(a(a(x1))))
C(x1) → A(a(a(x1)))
A(c(c(c(x1)))) → D(d(x1))
D(b(x1)) → C(x1)
c(c(c(a(x1)))) → d(d(x1))
d(b(x1)) → c(c(x1))
c(x1) → a(a(a(a(x1))))
d(x1) → b(b(b(b(x1))))
b(d(x1)) → c(c(x1))
a(c(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(d(x1)) → C(x1)
C(c(c(a(x1)))) → D(x1)
D(x1) → B(x1)
A(c(c(c(x1)))) → D(x1)
D(x1) → B(b(x1))
D(x1) → B(b(b(x1)))
C(x1) → A(x1)
C(x1) → A(a(x1))
C(x1) → A(a(a(x1)))
A(c(c(c(x1)))) → D(d(x1))
D(b(x1)) → C(x1)
Used ordering: Polynomial interpretation [25,35]:
D(x1) → B(b(b(b(x1))))
D(b(x1)) → C(c(x1))
C(c(c(a(x1)))) → D(d(x1))
B(d(x1)) → C(c(x1))
C(x1) → A(a(a(a(x1))))
The value of delta used in the strict ordering is 1/2.
POL(C(x1)) = 3/2 + (2)x_1
POL(c(x1)) = 5/4 + x_1
POL(B(x1)) = (2)x_1
POL(D(x1)) = 3 + (2)x_1
POL(a(x1)) = 1/4 + x_1
POL(A(x1)) = (2)x_1
POL(d(x1)) = 2 + x_1
POL(b(x1)) = 1/2 + x_1
c(c(c(a(x1)))) → d(d(x1))
d(b(x1)) → c(c(x1))
d(x1) → b(b(b(b(x1))))
a(c(c(c(x1)))) → d(d(x1))
c(x1) → a(a(a(a(x1))))
b(d(x1)) → c(c(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
C(c(c(a(x1)))) → D(d(x1))
B(d(x1)) → C(c(x1))
D(x1) → B(b(b(b(x1))))
C(x1) → A(a(a(a(x1))))
D(b(x1)) → C(c(x1))
c(c(c(a(x1)))) → d(d(x1))
d(b(x1)) → c(c(x1))
c(x1) → a(a(a(a(x1))))
d(x1) → b(b(b(b(x1))))
b(d(x1)) → c(c(x1))
a(c(c(c(x1)))) → d(d(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
C(c(c(a(x1)))) → D(d(x1))
B(d(x1)) → C(c(x1))
D(x1) → B(b(b(b(x1))))
D(b(x1)) → C(c(x1))
c(c(c(a(x1)))) → d(d(x1))
d(b(x1)) → c(c(x1))
c(x1) → a(a(a(a(x1))))
d(x1) → b(b(b(b(x1))))
b(d(x1)) → c(c(x1))
a(c(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.
D(x1) → B(b(b(b(x1))))
Used ordering: Polynomial interpretation [25,35]:
C(c(c(a(x1)))) → D(d(x1))
B(d(x1)) → C(c(x1))
D(b(x1)) → C(c(x1))
The value of delta used in the strict ordering is 1/4.
POL(C(x1)) = 5/4 + x_1
POL(c(x1)) = 2 + x_1
POL(D(x1)) = 5/2 + x_1
POL(B(x1)) = x_1
POL(a(x1)) = 1/2 + x_1
POL(d(x1)) = 13/4 + x_1
POL(b(x1)) = 3/4 + x_1
c(c(c(a(x1)))) → d(d(x1))
d(b(x1)) → c(c(x1))
d(x1) → b(b(b(b(x1))))
a(c(c(c(x1)))) → d(d(x1))
c(x1) → a(a(a(a(x1))))
b(d(x1)) → c(c(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
C(c(c(a(x1)))) → D(d(x1))
B(d(x1)) → C(c(x1))
D(b(x1)) → C(c(x1))
c(c(c(a(x1)))) → d(d(x1))
d(b(x1)) → c(c(x1))
c(x1) → a(a(a(a(x1))))
d(x1) → b(b(b(b(x1))))
b(d(x1)) → c(c(x1))
a(c(c(c(x1)))) → d(d(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
C(c(c(a(x1)))) → D(d(x1))
D(b(x1)) → C(c(x1))
c(c(c(a(x1)))) → d(d(x1))
d(b(x1)) → c(c(x1))
c(x1) → a(a(a(a(x1))))
d(x1) → b(b(b(b(x1))))
b(d(x1)) → c(c(x1))
a(c(c(c(x1)))) → d(d(x1))