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