active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(and(tt, X)) → mark(X)
active(isNePal(__(I, __(P, I)))) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(and(X1, X2)) → active(and(mark(X1), X2))
mark(tt) → active(tt)
mark(isNePal(X)) → active(isNePal(mark(X)))
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
and(mark(X1), X2) → and(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
↳ QTRS
↳ DependencyPairsProof
active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(and(tt, X)) → mark(X)
active(isNePal(__(I, __(P, I)))) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(and(X1, X2)) → active(and(mark(X1), X2))
mark(tt) → active(tt)
mark(isNePal(X)) → active(isNePal(mark(X)))
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
and(mark(X1), X2) → and(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
MARK(tt) → ACTIVE(tt)
__1(X1, active(X2)) → __1(X1, X2)
ISNEPAL(mark(X)) → ISNEPAL(X)
MARK(isNePal(X)) → MARK(X)
ACTIVE(__(nil, X)) → MARK(X)
ACTIVE(__(X, nil)) → MARK(X)
AND(X1, mark(X2)) → AND(X1, X2)
MARK(and(X1, X2)) → ACTIVE(and(mark(X1), X2))
MARK(__(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → ACTIVE(__(mark(X1), mark(X2)))
MARK(and(X1, X2)) → MARK(X1)
ACTIVE(__(__(X, Y), Z)) → MARK(__(X, __(Y, Z)))
MARK(and(X1, X2)) → AND(mark(X1), X2)
__1(active(X1), X2) → __1(X1, X2)
MARK(isNePal(X)) → ISNEPAL(mark(X))
ACTIVE(__(__(X, Y), Z)) → __1(X, __(Y, Z))
MARK(__(X1, X2)) → __1(mark(X1), mark(X2))
MARK(isNePal(X)) → ACTIVE(isNePal(mark(X)))
ISNEPAL(active(X)) → ISNEPAL(X)
__1(X1, mark(X2)) → __1(X1, X2)
AND(X1, active(X2)) → AND(X1, X2)
AND(mark(X1), X2) → AND(X1, X2)
ACTIVE(__(__(X, Y), Z)) → __1(Y, Z)
ACTIVE(isNePal(__(I, __(P, I)))) → MARK(tt)
AND(active(X1), X2) → AND(X1, X2)
ACTIVE(and(tt, X)) → MARK(X)
__1(mark(X1), X2) → __1(X1, X2)
MARK(nil) → ACTIVE(nil)
MARK(__(X1, X2)) → MARK(X2)
active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(and(tt, X)) → mark(X)
active(isNePal(__(I, __(P, I)))) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(and(X1, X2)) → active(and(mark(X1), X2))
mark(tt) → active(tt)
mark(isNePal(X)) → active(isNePal(mark(X)))
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
and(mark(X1), X2) → and(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
MARK(tt) → ACTIVE(tt)
__1(X1, active(X2)) → __1(X1, X2)
ISNEPAL(mark(X)) → ISNEPAL(X)
MARK(isNePal(X)) → MARK(X)
ACTIVE(__(nil, X)) → MARK(X)
ACTIVE(__(X, nil)) → MARK(X)
AND(X1, mark(X2)) → AND(X1, X2)
MARK(and(X1, X2)) → ACTIVE(and(mark(X1), X2))
MARK(__(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → ACTIVE(__(mark(X1), mark(X2)))
MARK(and(X1, X2)) → MARK(X1)
ACTIVE(__(__(X, Y), Z)) → MARK(__(X, __(Y, Z)))
MARK(and(X1, X2)) → AND(mark(X1), X2)
__1(active(X1), X2) → __1(X1, X2)
MARK(isNePal(X)) → ISNEPAL(mark(X))
ACTIVE(__(__(X, Y), Z)) → __1(X, __(Y, Z))
MARK(__(X1, X2)) → __1(mark(X1), mark(X2))
MARK(isNePal(X)) → ACTIVE(isNePal(mark(X)))
ISNEPAL(active(X)) → ISNEPAL(X)
__1(X1, mark(X2)) → __1(X1, X2)
AND(X1, active(X2)) → AND(X1, X2)
AND(mark(X1), X2) → AND(X1, X2)
ACTIVE(__(__(X, Y), Z)) → __1(Y, Z)
ACTIVE(isNePal(__(I, __(P, I)))) → MARK(tt)
AND(active(X1), X2) → AND(X1, X2)
ACTIVE(and(tt, X)) → MARK(X)
__1(mark(X1), X2) → __1(X1, X2)
MARK(nil) → ACTIVE(nil)
MARK(__(X1, X2)) → MARK(X2)
active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(and(tt, X)) → mark(X)
active(isNePal(__(I, __(P, I)))) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(and(X1, X2)) → active(and(mark(X1), X2))
mark(tt) → active(tt)
mark(isNePal(X)) → active(isNePal(mark(X)))
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
and(mark(X1), X2) → and(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
↳ QDP
ISNEPAL(mark(X)) → ISNEPAL(X)
ISNEPAL(active(X)) → ISNEPAL(X)
active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(and(tt, X)) → mark(X)
active(isNePal(__(I, __(P, I)))) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(and(X1, X2)) → active(and(mark(X1), X2))
mark(tt) → active(tt)
mark(isNePal(X)) → active(isNePal(mark(X)))
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
and(mark(X1), X2) → and(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ISNEPAL(mark(X)) → ISNEPAL(X)
ISNEPAL(active(X)) → ISNEPAL(X)
The value of delta used in the strict ordering is 16.
POL(active(x1)) = 4 + x_1
POL(mark(x1)) = 4 + (4)x_1
POL(ISNEPAL(x1)) = (4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
↳ QDP
active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(and(tt, X)) → mark(X)
active(isNePal(__(I, __(P, I)))) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(and(X1, X2)) → active(and(mark(X1), X2))
mark(tt) → active(tt)
mark(isNePal(X)) → active(isNePal(mark(X)))
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
and(mark(X1), X2) → and(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
AND(mark(X1), X2) → AND(X1, X2)
AND(active(X1), X2) → AND(X1, X2)
AND(X1, mark(X2)) → AND(X1, X2)
AND(X1, active(X2)) → AND(X1, X2)
active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(and(tt, X)) → mark(X)
active(isNePal(__(I, __(P, I)))) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(and(X1, X2)) → active(and(mark(X1), X2))
mark(tt) → active(tt)
mark(isNePal(X)) → active(isNePal(mark(X)))
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
and(mark(X1), X2) → and(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
AND(mark(X1), X2) → AND(X1, X2)
AND(active(X1), X2) → AND(X1, X2)
AND(X1, mark(X2)) → AND(X1, X2)
AND(X1, active(X2)) → AND(X1, X2)
The value of delta used in the strict ordering is 1.
POL(active(x1)) = 1 + (4)x_1
POL(AND(x1, x2)) = (2)x_1 + x_2
POL(mark(x1)) = 1 + (2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(and(tt, X)) → mark(X)
active(isNePal(__(I, __(P, I)))) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(and(X1, X2)) → active(and(mark(X1), X2))
mark(tt) → active(tt)
mark(isNePal(X)) → active(isNePal(mark(X)))
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
and(mark(X1), X2) → and(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
__1(X1, active(X2)) → __1(X1, X2)
__1(active(X1), X2) → __1(X1, X2)
__1(X1, mark(X2)) → __1(X1, X2)
__1(mark(X1), X2) → __1(X1, X2)
active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(and(tt, X)) → mark(X)
active(isNePal(__(I, __(P, I)))) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(and(X1, X2)) → active(and(mark(X1), X2))
mark(tt) → active(tt)
mark(isNePal(X)) → active(isNePal(mark(X)))
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
and(mark(X1), X2) → and(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
__1(X1, active(X2)) → __1(X1, X2)
__1(active(X1), X2) → __1(X1, X2)
__1(X1, mark(X2)) → __1(X1, X2)
__1(mark(X1), X2) → __1(X1, X2)
The value of delta used in the strict ordering is 12.
POL(active(x1)) = 4 + (4)x_1
POL(__1(x1, x2)) = (4)x_1 + (3)x_2
POL(mark(x1)) = 4 + (4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(and(tt, X)) → mark(X)
active(isNePal(__(I, __(P, I)))) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(and(X1, X2)) → active(and(mark(X1), X2))
mark(tt) → active(tt)
mark(isNePal(X)) → active(isNePal(mark(X)))
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
and(mark(X1), X2) → and(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
MARK(__(X1, X2)) → MARK(X1)
MARK(isNePal(X)) → MARK(X)
MARK(__(X1, X2)) → ACTIVE(__(mark(X1), mark(X2)))
MARK(and(X1, X2)) → MARK(X1)
MARK(isNePal(X)) → ACTIVE(isNePal(mark(X)))
ACTIVE(and(tt, X)) → MARK(X)
ACTIVE(__(nil, X)) → MARK(X)
ACTIVE(__(X, nil)) → MARK(X)
ACTIVE(__(__(X, Y), Z)) → MARK(__(X, __(Y, Z)))
MARK(and(X1, X2)) → ACTIVE(and(mark(X1), X2))
MARK(__(X1, X2)) → MARK(X2)
active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(and(tt, X)) → mark(X)
active(isNePal(__(I, __(P, I)))) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(and(X1, X2)) → active(and(mark(X1), X2))
mark(tt) → active(tt)
mark(isNePal(X)) → active(isNePal(mark(X)))
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
and(mark(X1), X2) → and(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(isNePal(X)) → ACTIVE(isNePal(mark(X)))
Used ordering: Polynomial interpretation [25,35]:
MARK(__(X1, X2)) → MARK(X1)
MARK(isNePal(X)) → MARK(X)
MARK(__(X1, X2)) → ACTIVE(__(mark(X1), mark(X2)))
MARK(and(X1, X2)) → MARK(X1)
ACTIVE(and(tt, X)) → MARK(X)
ACTIVE(__(nil, X)) → MARK(X)
ACTIVE(__(X, nil)) → MARK(X)
ACTIVE(__(__(X, Y), Z)) → MARK(__(X, __(Y, Z)))
MARK(and(X1, X2)) → ACTIVE(and(mark(X1), X2))
MARK(__(X1, X2)) → MARK(X2)
The value of delta used in the strict ordering is 7/8.
POL(active(x1)) = 7/2 + (5/4)x_1
POL(MARK(x1)) = 1
POL(__(x1, x2)) = 4
POL(tt) = 1/4
POL(mark(x1)) = 4
POL(isNePal(x1)) = 1/2
POL(and(x1, x2)) = 4
POL(ACTIVE(x1)) = (1/4)x_1
POL(nil) = 0
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
and(mark(X1), X2) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
isNePal(active(X)) → isNePal(X)
isNePal(mark(X)) → isNePal(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
MARK(__(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → ACTIVE(__(mark(X1), mark(X2)))
MARK(isNePal(X)) → MARK(X)
MARK(and(X1, X2)) → MARK(X1)
ACTIVE(__(__(X, Y), Z)) → MARK(__(X, __(Y, Z)))
ACTIVE(__(X, nil)) → MARK(X)
ACTIVE(__(nil, X)) → MARK(X)
ACTIVE(and(tt, X)) → MARK(X)
MARK(__(X1, X2)) → MARK(X2)
MARK(and(X1, X2)) → ACTIVE(and(mark(X1), X2))
active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(and(tt, X)) → mark(X)
active(isNePal(__(I, __(P, I)))) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(and(X1, X2)) → active(and(mark(X1), X2))
mark(tt) → active(tt)
mark(isNePal(X)) → active(isNePal(mark(X)))
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
and(mark(X1), X2) → and(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(isNePal(X)) → MARK(X)
Used ordering: Polynomial interpretation [25,35]:
MARK(__(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → ACTIVE(__(mark(X1), mark(X2)))
MARK(and(X1, X2)) → MARK(X1)
ACTIVE(__(__(X, Y), Z)) → MARK(__(X, __(Y, Z)))
ACTIVE(__(X, nil)) → MARK(X)
ACTIVE(__(nil, X)) → MARK(X)
ACTIVE(and(tt, X)) → MARK(X)
MARK(__(X1, X2)) → MARK(X2)
MARK(and(X1, X2)) → ACTIVE(and(mark(X1), X2))
The value of delta used in the strict ordering is 2.
POL(active(x1)) = x_1
POL(MARK(x1)) = 4 + (1/2)x_1
POL(__(x1, x2)) = (2)x_1 + x_2
POL(tt) = 0
POL(mark(x1)) = x_1
POL(isNePal(x1)) = 4 + (4)x_1
POL(and(x1, x2)) = x_1 + (4)x_2
POL(ACTIVE(x1)) = 4 + (1/2)x_1
POL(nil) = 0
active(isNePal(__(I, __(P, I)))) → mark(tt)
mark(and(X1, X2)) → active(and(mark(X1), X2))
mark(isNePal(X)) → active(isNePal(mark(X)))
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(and(tt, X)) → mark(X)
mark(tt) → active(tt)
mark(nil) → active(nil)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
and(mark(X1), X2) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
isNePal(active(X)) → isNePal(X)
isNePal(mark(X)) → isNePal(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
MARK(__(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → ACTIVE(__(mark(X1), mark(X2)))
MARK(and(X1, X2)) → MARK(X1)
ACTIVE(and(tt, X)) → MARK(X)
ACTIVE(__(nil, X)) → MARK(X)
ACTIVE(__(X, nil)) → MARK(X)
ACTIVE(__(__(X, Y), Z)) → MARK(__(X, __(Y, Z)))
MARK(and(X1, X2)) → ACTIVE(and(mark(X1), X2))
MARK(__(X1, X2)) → MARK(X2)
active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(and(tt, X)) → mark(X)
active(isNePal(__(I, __(P, I)))) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(and(X1, X2)) → active(and(mark(X1), X2))
mark(tt) → active(tt)
mark(isNePal(X)) → active(isNePal(mark(X)))
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
and(mark(X1), X2) → and(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(and(X1, X2)) → MARK(X1)
ACTIVE(and(tt, X)) → MARK(X)
Used ordering: Polynomial interpretation [25,35]:
MARK(__(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → ACTIVE(__(mark(X1), mark(X2)))
ACTIVE(__(nil, X)) → MARK(X)
ACTIVE(__(X, nil)) → MARK(X)
ACTIVE(__(__(X, Y), Z)) → MARK(__(X, __(Y, Z)))
MARK(and(X1, X2)) → ACTIVE(and(mark(X1), X2))
MARK(__(X1, X2)) → MARK(X2)
The value of delta used in the strict ordering is 16.
POL(active(x1)) = x_1
POL(MARK(x1)) = (4)x_1
POL(__(x1, x2)) = (4)x_1 + x_2
POL(tt) = 0
POL(mark(x1)) = x_1
POL(isNePal(x1)) = 0
POL(and(x1, x2)) = 4 + (4)x_1 + (4)x_2
POL(ACTIVE(x1)) = (4)x_1
POL(nil) = 0
active(isNePal(__(I, __(P, I)))) → mark(tt)
mark(and(X1, X2)) → active(and(mark(X1), X2))
mark(isNePal(X)) → active(isNePal(mark(X)))
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(and(tt, X)) → mark(X)
mark(tt) → active(tt)
mark(nil) → active(nil)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
and(mark(X1), X2) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
isNePal(active(X)) → isNePal(X)
isNePal(mark(X)) → isNePal(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
MARK(__(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → ACTIVE(__(mark(X1), mark(X2)))
ACTIVE(__(__(X, Y), Z)) → MARK(__(X, __(Y, Z)))
ACTIVE(__(X, nil)) → MARK(X)
ACTIVE(__(nil, X)) → MARK(X)
MARK(__(X1, X2)) → MARK(X2)
MARK(and(X1, X2)) → ACTIVE(and(mark(X1), X2))
active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(and(tt, X)) → mark(X)
active(isNePal(__(I, __(P, I)))) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(and(X1, X2)) → active(and(mark(X1), X2))
mark(tt) → active(tt)
mark(isNePal(X)) → active(isNePal(mark(X)))
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
and(mark(X1), X2) → and(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(and(X1, X2)) → ACTIVE(and(mark(X1), X2))
Used ordering: Polynomial interpretation [25,35]:
MARK(__(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → ACTIVE(__(mark(X1), mark(X2)))
ACTIVE(__(__(X, Y), Z)) → MARK(__(X, __(Y, Z)))
ACTIVE(__(X, nil)) → MARK(X)
ACTIVE(__(nil, X)) → MARK(X)
MARK(__(X1, X2)) → MARK(X2)
The value of delta used in the strict ordering is 1/4.
POL(active(x1)) = 3 + (13/4)x_1
POL(MARK(x1)) = 1/4
POL(__(x1, x2)) = 1/4
POL(tt) = 4
POL(mark(x1)) = 3/2
POL(isNePal(x1)) = 2 + (5/2)x_1
POL(and(x1, x2)) = 0
POL(ACTIVE(x1)) = x_1
POL(nil) = 0
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
and(mark(X1), X2) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
MARK(__(X1, X2)) → MARK(X1)
MARK(__(X1, X2)) → ACTIVE(__(mark(X1), mark(X2)))
ACTIVE(__(nil, X)) → MARK(X)
ACTIVE(__(X, nil)) → MARK(X)
ACTIVE(__(__(X, Y), Z)) → MARK(__(X, __(Y, Z)))
MARK(__(X1, X2)) → MARK(X2)
active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(and(tt, X)) → mark(X)
active(isNePal(__(I, __(P, I)))) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(and(X1, X2)) → active(and(mark(X1), X2))
mark(tt) → active(tt)
mark(isNePal(X)) → active(isNePal(mark(X)))
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
and(mark(X1), X2) → and(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(__(X1, X2)) → MARK(X1)
ACTIVE(__(nil, X)) → MARK(X)
ACTIVE(__(X, nil)) → MARK(X)
ACTIVE(__(__(X, Y), Z)) → MARK(__(X, __(Y, Z)))
MARK(__(X1, X2)) → MARK(X2)
Used ordering: Polynomial interpretation [25,35]:
MARK(__(X1, X2)) → ACTIVE(__(mark(X1), mark(X2)))
The value of delta used in the strict ordering is 1/4.
POL(active(x1)) = x_1
POL(MARK(x1)) = (1/4)x_1
POL(__(x1, x2)) = 1 + (5/2)x_1 + x_2
POL(tt) = 2
POL(mark(x1)) = x_1
POL(isNePal(x1)) = 2
POL(and(x1, x2)) = 4 + (2)x_1 + (2)x_2
POL(ACTIVE(x1)) = (1/4)x_1
POL(nil) = 0
active(isNePal(__(I, __(P, I)))) → mark(tt)
mark(and(X1, X2)) → active(and(mark(X1), X2))
mark(isNePal(X)) → active(isNePal(mark(X)))
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(and(tt, X)) → mark(X)
isNePal(active(X)) → isNePal(X)
isNePal(mark(X)) → isNePal(X)
mark(tt) → active(tt)
mark(nil) → active(nil)
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
and(mark(X1), X2) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
MARK(__(X1, X2)) → ACTIVE(__(mark(X1), mark(X2)))
active(__(__(X, Y), Z)) → mark(__(X, __(Y, Z)))
active(__(X, nil)) → mark(X)
active(__(nil, X)) → mark(X)
active(and(tt, X)) → mark(X)
active(isNePal(__(I, __(P, I)))) → mark(tt)
mark(__(X1, X2)) → active(__(mark(X1), mark(X2)))
mark(nil) → active(nil)
mark(and(X1, X2)) → active(and(mark(X1), X2))
mark(tt) → active(tt)
mark(isNePal(X)) → active(isNePal(mark(X)))
__(mark(X1), X2) → __(X1, X2)
__(X1, mark(X2)) → __(X1, X2)
__(active(X1), X2) → __(X1, X2)
__(X1, active(X2)) → __(X1, X2)
and(mark(X1), X2) → and(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
isNePal(mark(X)) → isNePal(X)
isNePal(active(X)) → isNePal(X)