c(a(a(x1))) → a(c(x1))
a(c(b(x1))) → a(d(b(x1)))
a(d(x1)) → d(a(a(a(x1))))
b(d(x1)) → b(c(x1))
↳ QTRS
↳ DependencyPairsProof
c(a(a(x1))) → a(c(x1))
a(c(b(x1))) → a(d(b(x1)))
a(d(x1)) → d(a(a(a(x1))))
b(d(x1)) → b(c(x1))
B(d(x1)) → C(x1)
A(d(x1)) → A(x1)
A(c(b(x1))) → A(d(b(x1)))
A(d(x1)) → A(a(a(x1)))
C(a(a(x1))) → A(c(x1))
B(d(x1)) → B(c(x1))
C(a(a(x1))) → C(x1)
A(d(x1)) → A(a(x1))
c(a(a(x1))) → a(c(x1))
a(c(b(x1))) → a(d(b(x1)))
a(d(x1)) → d(a(a(a(x1))))
b(d(x1)) → b(c(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
B(d(x1)) → C(x1)
A(d(x1)) → A(x1)
A(c(b(x1))) → A(d(b(x1)))
A(d(x1)) → A(a(a(x1)))
C(a(a(x1))) → A(c(x1))
B(d(x1)) → B(c(x1))
C(a(a(x1))) → C(x1)
A(d(x1)) → A(a(x1))
c(a(a(x1))) → a(c(x1))
a(c(b(x1))) → a(d(b(x1)))
a(d(x1)) → d(a(a(a(x1))))
b(d(x1)) → b(c(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
A(d(x1)) → A(x1)
A(c(b(x1))) → A(d(b(x1)))
A(d(x1)) → A(a(a(x1)))
A(d(x1)) → A(a(x1))
c(a(a(x1))) → a(c(x1))
a(c(b(x1))) → a(d(b(x1)))
a(d(x1)) → d(a(a(a(x1))))
b(d(x1)) → b(c(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)
A(c(b(x1))) → A(d(b(x1)))
A(d(x1)) → A(a(a(x1)))
A(d(x1)) → A(a(x1))
The value of delta used in the strict ordering is 1.
POL(c(x1)) = 3
POL(a(x1)) = x_1
POL(A(x1)) = x_1
POL(d(x1)) = 1 + (4)x_1
POL(b(x1)) = 0
c(a(a(x1))) → a(c(x1))
a(c(b(x1))) → a(d(b(x1)))
a(d(x1)) → d(a(a(a(x1))))
b(d(x1)) → b(c(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
c(a(a(x1))) → a(c(x1))
a(c(b(x1))) → a(d(b(x1)))
a(d(x1)) → d(a(a(a(x1))))
b(d(x1)) → b(c(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
C(a(a(x1))) → C(x1)
c(a(a(x1))) → a(c(x1))
a(c(b(x1))) → a(d(b(x1)))
a(d(x1)) → d(a(a(a(x1))))
b(d(x1)) → b(c(x1))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
C(a(a(x1))) → C(x1)
The value of delta used in the strict ordering is 6.
POL(C(x1)) = (2)x_1
POL(a(x1)) = 1 + (2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
c(a(a(x1))) → a(c(x1))
a(c(b(x1))) → a(d(b(x1)))
a(d(x1)) → d(a(a(a(x1))))
b(d(x1)) → b(c(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
B(d(x1)) → B(c(x1))
c(a(a(x1))) → a(c(x1))
a(c(b(x1))) → a(d(b(x1)))
a(d(x1)) → d(a(a(a(x1))))
b(d(x1)) → b(c(x1))