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