0 QTRS
↳1 DependencyPairsProof (⇔)
↳2 QDP
↳3 DependencyGraphProof (⇔)
↳4 QDP
↳5 QDPOrderProof (⇔)
↳6 QDP
↳7 QDPOrderProof (⇔)
↳8 QDP
↳9 DependencyGraphProof (⇔)
↳10 QDP
↳11 QDPOrderProof (⇔)
↳12 QDP
↳13 PisEmptyProof (⇔)
↳14 TRUE
a__zeros → cons(0, zeros)
a__tail(cons(X, XS)) → mark(XS)
mark(zeros) → a__zeros
mark(tail(X)) → a__tail(mark(X))
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(0) → 0
a__zeros → zeros
a__tail(X) → tail(X)
A__TAIL(cons(X, XS)) → MARK(XS)
MARK(zeros) → A__ZEROS
MARK(tail(X)) → A__TAIL(mark(X))
MARK(tail(X)) → MARK(X)
MARK(cons(X1, X2)) → MARK(X1)
a__zeros → cons(0, zeros)
a__tail(cons(X, XS)) → mark(XS)
mark(zeros) → a__zeros
mark(tail(X)) → a__tail(mark(X))
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(0) → 0
a__zeros → zeros
a__tail(X) → tail(X)
MARK(tail(X)) → A__TAIL(mark(X))
A__TAIL(cons(X, XS)) → MARK(XS)
MARK(tail(X)) → MARK(X)
MARK(cons(X1, X2)) → MARK(X1)
a__zeros → cons(0, zeros)
a__tail(cons(X, XS)) → mark(XS)
mark(zeros) → a__zeros
mark(tail(X)) → a__tail(mark(X))
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(0) → 0
a__zeros → zeros
a__tail(X) → tail(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(tail(X)) → MARK(X)
POL(0) = 0
POL(a__tail(x1)) = 1 + x1
POL(a__zeros) = 0
POL(cons(x1, x2)) = x1 + x2
POL(mark(x1)) = 1 + x1
POL(tail(x1)) = 1 + x1
POL(zeros) = 0
mark(zeros) → a__zeros
mark(tail(X)) → a__tail(mark(X))
a__tail(cons(X, XS)) → mark(XS)
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(0) → 0
a__tail(X) → tail(X)
a__zeros → cons(0, zeros)
a__zeros → zeros
MARK(tail(X)) → A__TAIL(mark(X))
A__TAIL(cons(X, XS)) → MARK(XS)
MARK(cons(X1, X2)) → MARK(X1)
a__zeros → cons(0, zeros)
a__tail(cons(X, XS)) → mark(XS)
mark(zeros) → a__zeros
mark(tail(X)) → a__tail(mark(X))
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(0) → 0
a__zeros → zeros
a__tail(X) → tail(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(tail(X)) → A__TAIL(mark(X))
POL(0) = 0
POL(a__tail(x1)) = 1 + x1
POL(a__zeros) = 1
POL(cons(x1, x2)) = x1 + x2
POL(mark(x1)) = x1
POL(tail(x1)) = 1 + x1
POL(zeros) = 1
mark(zeros) → a__zeros
mark(tail(X)) → a__tail(mark(X))
a__tail(cons(X, XS)) → mark(XS)
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(0) → 0
a__tail(X) → tail(X)
a__zeros → cons(0, zeros)
a__zeros → zeros
A__TAIL(cons(X, XS)) → MARK(XS)
MARK(cons(X1, X2)) → MARK(X1)
a__zeros → cons(0, zeros)
a__tail(cons(X, XS)) → mark(XS)
mark(zeros) → a__zeros
mark(tail(X)) → a__tail(mark(X))
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(0) → 0
a__zeros → zeros
a__tail(X) → tail(X)
MARK(cons(X1, X2)) → MARK(X1)
a__zeros → cons(0, zeros)
a__tail(cons(X, XS)) → mark(XS)
mark(zeros) → a__zeros
mark(tail(X)) → a__tail(mark(X))
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(0) → 0
a__zeros → zeros
a__tail(X) → tail(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(cons(X1, X2)) → MARK(X1)
POL(cons(x1, x2)) = 1 + x1
a__zeros → cons(0, zeros)
a__tail(cons(X, XS)) → mark(XS)
mark(zeros) → a__zeros
mark(tail(X)) → a__tail(mark(X))
mark(cons(X1, X2)) → cons(mark(X1), X2)
mark(0) → 0
a__zeros → zeros
a__tail(X) → tail(X)