b(c(a(x1))) → a(b(a(b(c(x1)))))
b(x1) → c(c(x1))
c(d(x1)) → a(b(c(a(x1))))
a(a(x1)) → a(c(b(a(x1))))
↳ QTRS
↳ DependencyPairsProof
b(c(a(x1))) → a(b(a(b(c(x1)))))
b(x1) → c(c(x1))
c(d(x1)) → a(b(c(a(x1))))
a(a(x1)) → a(c(b(a(x1))))
B(c(a(x1))) → A(b(a(b(c(x1)))))
B(c(a(x1))) → A(b(c(x1)))
A(a(x1)) → A(c(b(a(x1))))
A(a(x1)) → B(a(x1))
B(c(a(x1))) → B(a(b(c(x1))))
B(x1) → C(x1)
B(x1) → C(c(x1))
C(d(x1)) → A(x1)
A(a(x1)) → C(b(a(x1)))
C(d(x1)) → C(a(x1))
C(d(x1)) → B(c(a(x1)))
B(c(a(x1))) → B(c(x1))
C(d(x1)) → A(b(c(a(x1))))
B(c(a(x1))) → C(x1)
b(c(a(x1))) → a(b(a(b(c(x1)))))
b(x1) → c(c(x1))
c(d(x1)) → a(b(c(a(x1))))
a(a(x1)) → a(c(b(a(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
B(c(a(x1))) → A(b(a(b(c(x1)))))
B(c(a(x1))) → A(b(c(x1)))
A(a(x1)) → A(c(b(a(x1))))
A(a(x1)) → B(a(x1))
B(c(a(x1))) → B(a(b(c(x1))))
B(x1) → C(x1)
B(x1) → C(c(x1))
C(d(x1)) → A(x1)
A(a(x1)) → C(b(a(x1)))
C(d(x1)) → C(a(x1))
C(d(x1)) → B(c(a(x1)))
B(c(a(x1))) → B(c(x1))
C(d(x1)) → A(b(c(a(x1))))
B(c(a(x1))) → C(x1)
b(c(a(x1))) → a(b(a(b(c(x1)))))
b(x1) → c(c(x1))
c(d(x1)) → a(b(c(a(x1))))
a(a(x1)) → a(c(b(a(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
C(d(x1)) → A(x1)
C(d(x1)) → B(c(a(x1)))
B(c(a(x1))) → A(b(a(b(c(x1)))))
B(c(a(x1))) → B(c(x1))
B(c(a(x1))) → A(b(c(x1)))
C(d(x1)) → A(b(c(a(x1))))
A(a(x1)) → A(c(b(a(x1))))
B(c(a(x1))) → C(x1)
B(x1) → C(x1)
B(c(a(x1))) → B(a(b(c(x1))))
A(a(x1)) → B(a(x1))
b(c(a(x1))) → a(b(a(b(c(x1)))))
b(x1) → c(c(x1))
c(d(x1)) → a(b(c(a(x1))))
a(a(x1)) → a(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(c(a(x1)))
C(d(x1)) → A(b(c(a(x1))))
Used ordering: Polynomial interpretation [25,35]:
B(c(a(x1))) → A(b(a(b(c(x1)))))
B(c(a(x1))) → B(c(x1))
B(c(a(x1))) → A(b(c(x1)))
A(a(x1)) → A(c(b(a(x1))))
B(c(a(x1))) → C(x1)
B(x1) → C(x1)
B(c(a(x1))) → B(a(b(c(x1))))
A(a(x1)) → B(a(x1))
The value of delta used in the strict ordering is 3/16.
POL(C(x1)) = (1/4)x_1
POL(c(x1)) = (1/2)x_1
POL(B(x1)) = (1/4)x_1
POL(a(x1)) = (2)x_1
POL(A(x1)) = (1/2)x_1
POL(d(x1)) = 3/4 + (2)x_1
POL(b(x1)) = (1/2)x_1
b(c(a(x1))) → a(b(a(b(c(x1)))))
c(d(x1)) → a(b(c(a(x1))))
b(x1) → c(c(x1))
a(a(x1)) → a(c(b(a(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
B(c(a(x1))) → A(b(a(b(c(x1)))))
B(c(a(x1))) → A(b(c(x1)))
B(c(a(x1))) → B(c(x1))
A(a(x1)) → A(c(b(a(x1))))
B(c(a(x1))) → C(x1)
A(a(x1)) → B(a(x1))
B(c(a(x1))) → B(a(b(c(x1))))
B(x1) → C(x1)
b(c(a(x1))) → a(b(a(b(c(x1)))))
b(x1) → c(c(x1))
c(d(x1)) → a(b(c(a(x1))))
a(a(x1)) → a(c(b(a(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
B(c(a(x1))) → A(b(a(b(c(x1)))))
B(c(a(x1))) → B(c(x1))
B(c(a(x1))) → A(b(c(x1)))
A(a(x1)) → A(c(b(a(x1))))
B(c(a(x1))) → B(a(b(c(x1))))
A(a(x1)) → B(a(x1))
b(c(a(x1))) → a(b(a(b(c(x1)))))
b(x1) → c(c(x1))
c(d(x1)) → a(b(c(a(x1))))
a(a(x1)) → a(c(b(a(x1))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(c(a(x1))) → B(a(b(c(x1))))
A(a(x1)) → B(a(x1))
Used ordering: Polynomial interpretation [25,35]:
B(c(a(x1))) → A(b(a(b(c(x1)))))
B(c(a(x1))) → B(c(x1))
B(c(a(x1))) → A(b(c(x1)))
A(a(x1)) → A(c(b(a(x1))))
The value of delta used in the strict ordering is 1/2.
POL(c(x1)) = 1
POL(B(x1)) = (1/2)x_1
POL(a(x1)) = 0
POL(A(x1)) = 1/2
POL(b(x1)) = 4
POL(d(x1)) = 13/4 + (2)x_1
c(d(x1)) → a(b(c(a(x1))))
b(x1) → c(c(x1))
a(a(x1)) → a(c(b(a(x1))))
b(c(a(x1))) → a(b(a(b(c(x1)))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
B(c(a(x1))) → A(b(a(b(c(x1)))))
B(c(a(x1))) → A(b(c(x1)))
B(c(a(x1))) → B(c(x1))
A(a(x1)) → A(c(b(a(x1))))
b(c(a(x1))) → a(b(a(b(c(x1)))))
b(x1) → c(c(x1))
c(d(x1)) → a(b(c(a(x1))))
a(a(x1)) → a(c(b(a(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
A(a(x1)) → A(c(b(a(x1))))
b(c(a(x1))) → a(b(a(b(c(x1)))))
b(x1) → c(c(x1))
c(d(x1)) → a(b(c(a(x1))))
a(a(x1)) → a(c(b(a(x1))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(a(x1)) → A(c(b(a(x1))))
The value of delta used in the strict ordering is 5/8.
POL(c(x1)) = (1/4)x_1
POL(a(x1)) = 1
POL(A(x1)) = x_1
POL(b(x1)) = 1 + (1/2)x_1
POL(d(x1)) = 4
c(d(x1)) → a(b(c(a(x1))))
b(x1) → c(c(x1))
a(a(x1)) → a(c(b(a(x1))))
b(c(a(x1))) → a(b(a(b(c(x1)))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
b(c(a(x1))) → a(b(a(b(c(x1)))))
b(x1) → c(c(x1))
c(d(x1)) → a(b(c(a(x1))))
a(a(x1)) → a(c(b(a(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
B(c(a(x1))) → B(c(x1))
b(c(a(x1))) → a(b(a(b(c(x1)))))
b(x1) → c(c(x1))
c(d(x1)) → a(b(c(a(x1))))
a(a(x1)) → a(c(b(a(x1))))