a(b(a(x1))) → b(c(x1))
b(b(b(x1))) → c(b(x1))
c(x1) → a(b(x1))
c(d(x1)) → d(c(b(a(x1))))
↳ QTRS
↳ DependencyPairsProof
a(b(a(x1))) → b(c(x1))
b(b(b(x1))) → c(b(x1))
c(x1) → a(b(x1))
c(d(x1)) → d(c(b(a(x1))))
C(d(x1)) → A(x1)
C(x1) → B(x1)
A(b(a(x1))) → C(x1)
C(x1) → A(b(x1))
C(d(x1)) → B(a(x1))
C(d(x1)) → C(b(a(x1)))
A(b(a(x1))) → B(c(x1))
B(b(b(x1))) → C(b(x1))
a(b(a(x1))) → b(c(x1))
b(b(b(x1))) → c(b(x1))
c(x1) → a(b(x1))
c(d(x1)) → d(c(b(a(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
C(d(x1)) → A(x1)
C(x1) → B(x1)
A(b(a(x1))) → C(x1)
C(x1) → A(b(x1))
C(d(x1)) → B(a(x1))
C(d(x1)) → C(b(a(x1)))
A(b(a(x1))) → B(c(x1))
B(b(b(x1))) → C(b(x1))
a(b(a(x1))) → b(c(x1))
b(b(b(x1))) → c(b(x1))
c(x1) → a(b(x1))
c(d(x1)) → d(c(b(a(x1))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
C(d(x1)) → A(x1)
C(d(x1)) → B(a(x1))
C(d(x1)) → C(b(a(x1)))
Used ordering: Polynomial interpretation [25,35]:
C(x1) → B(x1)
A(b(a(x1))) → C(x1)
C(x1) → A(b(x1))
A(b(a(x1))) → B(c(x1))
B(b(b(x1))) → C(b(x1))
The value of delta used in the strict ordering is 3/16.
POL(C(x1)) = (1/4)x_1
POL(c(x1)) = x_1
POL(B(x1)) = (1/4)x_1
POL(a(x1)) = x_1
POL(A(x1)) = (1/4)x_1
POL(d(x1)) = 3/4 + x_1
POL(b(x1)) = x_1
b(b(b(x1))) → c(b(x1))
c(x1) → a(b(x1))
a(b(a(x1))) → b(c(x1))
c(d(x1)) → d(c(b(a(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
A(b(a(x1))) → C(x1)
C(x1) → B(x1)
C(x1) → A(b(x1))
A(b(a(x1))) → B(c(x1))
B(b(b(x1))) → C(b(x1))
a(b(a(x1))) → b(c(x1))
b(b(b(x1))) → c(b(x1))
c(x1) → a(b(x1))
c(d(x1)) → d(c(b(a(x1))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(b(a(x1))) → C(x1)
C(x1) → B(x1)
Used ordering: Polynomial interpretation [25,35]:
C(x1) → A(b(x1))
A(b(a(x1))) → B(c(x1))
B(b(b(x1))) → C(b(x1))
The value of delta used in the strict ordering is 1.
POL(C(x1)) = 2 + (4)x_1
POL(c(x1)) = 1/2 + x_1
POL(B(x1)) = 1 + (4)x_1
POL(a(x1)) = 1/4 + x_1
POL(A(x1)) = 1 + (4)x_1
POL(b(x1)) = 1/4 + x_1
POL(d(x1)) = 5/2 + (1/2)x_1
b(b(b(x1))) → c(b(x1))
c(x1) → a(b(x1))
a(b(a(x1))) → b(c(x1))
c(d(x1)) → d(c(b(a(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
C(x1) → A(b(x1))
A(b(a(x1))) → B(c(x1))
B(b(b(x1))) → C(b(x1))
a(b(a(x1))) → b(c(x1))
b(b(b(x1))) → c(b(x1))
c(x1) → a(b(x1))
c(d(x1)) → d(c(b(a(x1))))