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