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