0 QTRS
↳1 DependencyPairsProof (⇔)
↳2 QDP
↳3 DependencyGraphProof (⇔)
↳4 QDP
↳5 QDPOrderProof (⇔)
↳6 QDP
↳7 QDPOrderProof (⇔)
↳8 QDP
↳9 PisEmptyProof (⇔)
↳10 TRUE
a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt) → a__U12(tt)
a__U12(tt) → tt
a__isNePal(__(I, __(P, I))) → a__U11(tt)
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X)) → a__U11(mark(X))
mark(U12(X)) → a__U12(mark(X))
mark(isNePal(X)) → a__isNePal(mark(X))
mark(nil) → nil
mark(tt) → tt
a____(X1, X2) → __(X1, X2)
a__U11(X) → U11(X)
a__U12(X) → U12(X)
a__isNePal(X) → isNePal(X)
A____(__(X, Y), Z) → A____(mark(X), a____(mark(Y), mark(Z)))
A____(__(X, Y), Z) → MARK(X)
A____(__(X, Y), Z) → A____(mark(Y), mark(Z))
A____(__(X, Y), Z) → MARK(Y)
A____(__(X, Y), Z) → MARK(Z)
A____(X, nil) → MARK(X)
A____(nil, X) → MARK(X)
A__U11(tt) → A__U12(tt)
A__ISNEPAL(__(I, __(P, I))) → A__U11(tt)
MARK(__(X1, X2)) → A____(mark(X1), mark(X2))
MARK(__(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → MARK(X2)
MARK(U11(X)) → A__U11(mark(X))
MARK(U11(X)) → MARK(X)
MARK(U12(X)) → A__U12(mark(X))
MARK(U12(X)) → MARK(X)
MARK(isNePal(X)) → A__ISNEPAL(mark(X))
MARK(isNePal(X)) → MARK(X)
a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt) → a__U12(tt)
a__U12(tt) → tt
a__isNePal(__(I, __(P, I))) → a__U11(tt)
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X)) → a__U11(mark(X))
mark(U12(X)) → a__U12(mark(X))
mark(isNePal(X)) → a__isNePal(mark(X))
mark(nil) → nil
mark(tt) → tt
a____(X1, X2) → __(X1, X2)
a__U11(X) → U11(X)
a__U12(X) → U12(X)
a__isNePal(X) → isNePal(X)
A____(__(X, Y), Z) → MARK(X)
MARK(__(X1, X2)) → A____(mark(X1), mark(X2))
A____(__(X, Y), Z) → A____(mark(X), a____(mark(Y), mark(Z)))
A____(__(X, Y), Z) → A____(mark(Y), mark(Z))
A____(__(X, Y), Z) → MARK(Y)
MARK(__(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → MARK(X2)
MARK(U11(X)) → MARK(X)
MARK(U12(X)) → MARK(X)
MARK(isNePal(X)) → MARK(X)
A____(__(X, Y), Z) → MARK(Z)
A____(X, nil) → MARK(X)
A____(nil, X) → MARK(X)
a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt) → a__U12(tt)
a__U12(tt) → tt
a__isNePal(__(I, __(P, I))) → a__U11(tt)
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X)) → a__U11(mark(X))
mark(U12(X)) → a__U12(mark(X))
mark(isNePal(X)) → a__isNePal(mark(X))
mark(nil) → nil
mark(tt) → tt
a____(X1, X2) → __(X1, X2)
a__U11(X) → U11(X)
a__U12(X) → U12(X)
a__isNePal(X) → isNePal(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A____(__(X, Y), Z) → MARK(X)
MARK(__(X1, X2)) → A____(mark(X1), mark(X2))
A____(__(X, Y), Z) → A____(mark(Y), mark(Z))
A____(__(X, Y), Z) → MARK(Y)
MARK(__(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → MARK(X2)
MARK(U11(X)) → MARK(X)
MARK(U12(X)) → MARK(X)
MARK(isNePal(X)) → MARK(X)
A____(__(X, Y), Z) → MARK(Z)
A____(X, nil) → MARK(X)
A____(nil, X) → MARK(X)
POL(A____(x1, x2)) = x1 + x2
POL(MARK(x1)) = x1
POL(U11(x1)) = 1 + x1
POL(U12(x1)) = 1 + x1
POL(__(x1, x2)) = 1 + x1 + x2
POL(a__U11(x1)) = 1 + x1
POL(a__U12(x1)) = 1 + x1
POL(a____(x1, x2)) = 1 + x1 + x2
POL(a__isNePal(x1)) = 1 + x1
POL(isNePal(x1)) = 1 + x1
POL(mark(x1)) = x1
POL(nil) = 1
POL(tt) = 1
a____(X, nil) → mark(X)
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(nil, X) → mark(X)
mark(U11(X)) → a__U11(mark(X))
mark(U12(X)) → a__U12(mark(X))
mark(isNePal(X)) → a__isNePal(mark(X))
mark(nil) → nil
mark(tt) → tt
a____(X1, X2) → __(X1, X2)
a__U11(tt) → a__U12(tt)
a__U11(X) → U11(X)
a__U12(tt) → tt
a__U12(X) → U12(X)
a__isNePal(__(I, __(P, I))) → a__U11(tt)
a__isNePal(X) → isNePal(X)
A____(__(X, Y), Z) → A____(mark(X), a____(mark(Y), mark(Z)))
a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt) → a__U12(tt)
a__U12(tt) → tt
a__isNePal(__(I, __(P, I))) → a__U11(tt)
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X)) → a__U11(mark(X))
mark(U12(X)) → a__U12(mark(X))
mark(isNePal(X)) → a__isNePal(mark(X))
mark(nil) → nil
mark(tt) → tt
a____(X1, X2) → __(X1, X2)
a__U11(X) → U11(X)
a__U12(X) → U12(X)
a__isNePal(X) → isNePal(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A____(__(X, Y), Z) → A____(mark(X), a____(mark(Y), mark(Z)))
POL(A____(x1, x2)) = x1
POL(U11(x1)) = 1
POL(U12(x1)) = x1
POL(__(x1, x2)) = 1 + x1 + x2
POL(a__U11(x1)) = 1
POL(a__U12(x1)) = x1
POL(a____(x1, x2)) = 1 + x1 + x2
POL(a__isNePal(x1)) = 1
POL(isNePal(x1)) = 1
POL(mark(x1)) = x1
POL(nil) = 0
POL(tt) = 0
a____(X, nil) → mark(X)
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(nil, X) → mark(X)
mark(U11(X)) → a__U11(mark(X))
mark(U12(X)) → a__U12(mark(X))
mark(isNePal(X)) → a__isNePal(mark(X))
mark(nil) → nil
mark(tt) → tt
a____(X1, X2) → __(X1, X2)
a__U11(tt) → a__U12(tt)
a__U11(X) → U11(X)
a__U12(tt) → tt
a__U12(X) → U12(X)
a__isNePal(__(I, __(P, I))) → a__U11(tt)
a__isNePal(X) → isNePal(X)
a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt) → a__U12(tt)
a__U12(tt) → tt
a__isNePal(__(I, __(P, I))) → a__U11(tt)
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X)) → a__U11(mark(X))
mark(U12(X)) → a__U12(mark(X))
mark(isNePal(X)) → a__isNePal(mark(X))
mark(nil) → nil
mark(tt) → tt
a____(X1, X2) → __(X1, X2)
a__U11(X) → U11(X)
a__U12(X) → U12(X)
a__isNePal(X) → isNePal(X)