a(c(x1)) → c(b(c(c(a(x1)))))
b(b(b(x1))) → c(b(x1))
d(d(x1)) → d(b(d(b(d(x1)))))
a(a(x1)) → a(d(a(x1)))
a(b(x1)) → c(c(a(x1)))
c(c(x1)) → c(b(c(b(c(x1)))))
c(c(c(x1))) → c(b(b(x1)))
↳ QTRS
↳ DependencyPairsProof
a(c(x1)) → c(b(c(c(a(x1)))))
b(b(b(x1))) → c(b(x1))
d(d(x1)) → d(b(d(b(d(x1)))))
a(a(x1)) → a(d(a(x1)))
a(b(x1)) → c(c(a(x1)))
c(c(x1)) → c(b(c(b(c(x1)))))
c(c(c(x1))) → c(b(b(x1)))
A(b(x1)) → C(c(a(x1)))
C(c(x1)) → B(c(b(c(x1))))
A(c(x1)) → C(b(c(c(a(x1)))))
C(c(x1)) → C(b(c(b(c(x1)))))
C(c(c(x1))) → B(b(x1))
A(b(x1)) → C(a(x1))
D(d(x1)) → B(d(b(d(x1))))
C(c(x1)) → C(b(c(x1)))
A(c(x1)) → C(a(x1))
A(b(x1)) → A(x1)
A(c(x1)) → C(c(a(x1)))
D(d(x1)) → B(d(x1))
D(d(x1)) → D(b(d(x1)))
C(c(c(x1))) → B(x1)
A(a(x1)) → A(d(a(x1)))
C(c(x1)) → B(c(x1))
A(c(x1)) → A(x1)
A(c(x1)) → B(c(c(a(x1))))
D(d(x1)) → D(b(d(b(d(x1)))))
C(c(c(x1))) → C(b(b(x1)))
B(b(b(x1))) → C(b(x1))
A(a(x1)) → D(a(x1))
a(c(x1)) → c(b(c(c(a(x1)))))
b(b(b(x1))) → c(b(x1))
d(d(x1)) → d(b(d(b(d(x1)))))
a(a(x1)) → a(d(a(x1)))
a(b(x1)) → c(c(a(x1)))
c(c(x1)) → c(b(c(b(c(x1)))))
c(c(c(x1))) → c(b(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
A(b(x1)) → C(c(a(x1)))
C(c(x1)) → B(c(b(c(x1))))
A(c(x1)) → C(b(c(c(a(x1)))))
C(c(x1)) → C(b(c(b(c(x1)))))
C(c(c(x1))) → B(b(x1))
A(b(x1)) → C(a(x1))
D(d(x1)) → B(d(b(d(x1))))
C(c(x1)) → C(b(c(x1)))
A(c(x1)) → C(a(x1))
A(b(x1)) → A(x1)
A(c(x1)) → C(c(a(x1)))
D(d(x1)) → B(d(x1))
D(d(x1)) → D(b(d(x1)))
C(c(c(x1))) → B(x1)
A(a(x1)) → A(d(a(x1)))
C(c(x1)) → B(c(x1))
A(c(x1)) → A(x1)
A(c(x1)) → B(c(c(a(x1))))
D(d(x1)) → D(b(d(b(d(x1)))))
C(c(c(x1))) → C(b(b(x1)))
B(b(b(x1))) → C(b(x1))
A(a(x1)) → D(a(x1))
a(c(x1)) → c(b(c(c(a(x1)))))
b(b(b(x1))) → c(b(x1))
d(d(x1)) → d(b(d(b(d(x1)))))
a(a(x1)) → a(d(a(x1)))
a(b(x1)) → c(c(a(x1)))
c(c(x1)) → c(b(c(b(c(x1)))))
c(c(c(x1))) → c(b(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
C(c(x1)) → C(b(c(b(c(x1)))))
C(c(c(x1))) → B(x1)
C(c(c(x1))) → B(b(x1))
B(b(b(x1))) → C(b(x1))
C(c(c(x1))) → C(b(b(x1)))
C(c(x1)) → C(b(c(x1)))
a(c(x1)) → c(b(c(c(a(x1)))))
b(b(b(x1))) → c(b(x1))
d(d(x1)) → d(b(d(b(d(x1)))))
a(a(x1)) → a(d(a(x1)))
a(b(x1)) → c(c(a(x1)))
c(c(x1)) → c(b(c(b(c(x1)))))
c(c(c(x1))) → c(b(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
D(d(x1)) → D(b(d(x1)))
D(d(x1)) → D(b(d(b(d(x1)))))
a(c(x1)) → c(b(c(c(a(x1)))))
b(b(b(x1))) → c(b(x1))
d(d(x1)) → d(b(d(b(d(x1)))))
a(a(x1)) → a(d(a(x1)))
a(b(x1)) → c(c(a(x1)))
c(c(x1)) → c(b(c(b(c(x1)))))
c(c(c(x1))) → c(b(b(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
D(d(x1)) → D(b(d(x1)))
D(d(x1)) → D(b(d(b(d(x1)))))
The value of delta used in the strict ordering is 13.
POL(c(x1)) = 3/4
POL(D(x1)) = (4)x_1
POL(d(x1)) = 4
POL(b(x1)) = 3/4
b(b(b(x1))) → c(b(x1))
c(c(x1)) → c(b(c(b(c(x1)))))
c(c(c(x1))) → c(b(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
a(c(x1)) → c(b(c(c(a(x1)))))
b(b(b(x1))) → c(b(x1))
d(d(x1)) → d(b(d(b(d(x1)))))
a(a(x1)) → a(d(a(x1)))
a(b(x1)) → c(c(a(x1)))
c(c(x1)) → c(b(c(b(c(x1)))))
c(c(c(x1))) → c(b(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
A(a(x1)) → A(d(a(x1)))
A(c(x1)) → A(x1)
A(b(x1)) → A(x1)
a(c(x1)) → c(b(c(c(a(x1)))))
b(b(b(x1))) → c(b(x1))
d(d(x1)) → d(b(d(b(d(x1)))))
a(a(x1)) → a(d(a(x1)))
a(b(x1)) → c(c(a(x1)))
c(c(x1)) → c(b(c(b(c(x1)))))
c(c(c(x1))) → c(b(b(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(a(x1)) → A(d(a(x1)))
A(c(x1)) → A(x1)
A(b(x1)) → A(x1)
The value of delta used in the strict ordering is 1/16.
POL(c(x1)) = 1/4 + (4)x_1
POL(a(x1)) = 4 + (1/4)x_1
POL(A(x1)) = (1/4)x_1
POL(d(x1)) = 0
POL(b(x1)) = 7/4 + (11/4)x_1
d(d(x1)) → d(b(d(b(d(x1)))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
a(c(x1)) → c(b(c(c(a(x1)))))
b(b(b(x1))) → c(b(x1))
d(d(x1)) → d(b(d(b(d(x1)))))
a(a(x1)) → a(d(a(x1)))
a(b(x1)) → c(c(a(x1)))
c(c(x1)) → c(b(c(b(c(x1)))))
c(c(c(x1))) → c(b(b(x1)))