__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
isNeList(V) → isQid(activate(V))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isNePal(V) → isQid(activate(V))
isNePal(n____(I, __(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isPal(V) → isNePal(activate(V))
isPal(n__nil) → tt
isQid(n__a) → tt
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
isNeList(V) → isQid(activate(V))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isNePal(V) → isQid(activate(V))
isNePal(n____(I, __(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isPal(V) → isNePal(activate(V))
isPal(n__nil) → tt
isQid(n__a) → tt
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
ISLIST(V) → ISNELIST(activate(V))
ISNEPAL(n____(I, __(P, I))) → ACTIVATE(I)
ISNEPAL(n____(I, __(P, I))) → ISQID(activate(I))
ISNELIST(V) → ACTIVATE(V)
__1(__(X, Y), Z) → __1(X, __(Y, Z))
ISNELIST(n____(V1, V2)) → AND(isNeList(activate(V1)), n__isList(activate(V2)))
ISNELIST(n____(V1, V2)) → ISNELIST(activate(V1))
ISNEPAL(n____(I, __(P, I))) → ACTIVATE(P)
ISNEPAL(V) → ACTIVATE(V)
ISNELIST(n____(V1, V2)) → ISLIST(activate(V1))
ACTIVATE(n__isList(X)) → ISLIST(X)
ACTIVATE(n____(X1, X2)) → __1(X1, X2)
ACTIVATE(n__o) → O
ISLIST(n____(V1, V2)) → AND(isList(activate(V1)), n__isList(activate(V2)))
ACTIVATE(n__a) → A
ISNELIST(n____(V1, V2)) → ACTIVATE(V1)
ISNEPAL(n____(I, __(P, I))) → AND(isQid(activate(I)), n__isPal(activate(P)))
ISNELIST(V) → ISQID(activate(V))
__1(__(X, Y), Z) → __1(Y, Z)
ACTIVATE(n__isNeList(X)) → ISNELIST(X)
ACTIVATE(n__u) → U
ISPAL(V) → ISNEPAL(activate(V))
ISLIST(n____(V1, V2)) → ACTIVATE(V1)
ACTIVATE(n__isPal(X)) → ISPAL(X)
ACTIVATE(n__nil) → NIL
ISNELIST(n____(V1, V2)) → AND(isList(activate(V1)), n__isNeList(activate(V2)))
ISLIST(n____(V1, V2)) → ISLIST(activate(V1))
AND(tt, X) → ACTIVATE(X)
ISPAL(V) → ACTIVATE(V)
ISLIST(n____(V1, V2)) → ACTIVATE(V2)
ACTIVATE(n__i) → I
ACTIVATE(n__e) → E
ISNEPAL(V) → ISQID(activate(V))
ISLIST(V) → ACTIVATE(V)
ISNELIST(n____(V1, V2)) → ACTIVATE(V2)
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
isNeList(V) → isQid(activate(V))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isNePal(V) → isQid(activate(V))
isNePal(n____(I, __(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isPal(V) → isNePal(activate(V))
isPal(n__nil) → tt
isQid(n__a) → tt
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
ISLIST(V) → ISNELIST(activate(V))
ISNEPAL(n____(I, __(P, I))) → ACTIVATE(I)
ISNEPAL(n____(I, __(P, I))) → ISQID(activate(I))
ISNELIST(V) → ACTIVATE(V)
__1(__(X, Y), Z) → __1(X, __(Y, Z))
ISNELIST(n____(V1, V2)) → AND(isNeList(activate(V1)), n__isList(activate(V2)))
ISNELIST(n____(V1, V2)) → ISNELIST(activate(V1))
ISNEPAL(n____(I, __(P, I))) → ACTIVATE(P)
ISNEPAL(V) → ACTIVATE(V)
ISNELIST(n____(V1, V2)) → ISLIST(activate(V1))
ACTIVATE(n__isList(X)) → ISLIST(X)
ACTIVATE(n____(X1, X2)) → __1(X1, X2)
ACTIVATE(n__o) → O
ISLIST(n____(V1, V2)) → AND(isList(activate(V1)), n__isList(activate(V2)))
ACTIVATE(n__a) → A
ISNELIST(n____(V1, V2)) → ACTIVATE(V1)
ISNEPAL(n____(I, __(P, I))) → AND(isQid(activate(I)), n__isPal(activate(P)))
ISNELIST(V) → ISQID(activate(V))
__1(__(X, Y), Z) → __1(Y, Z)
ACTIVATE(n__isNeList(X)) → ISNELIST(X)
ACTIVATE(n__u) → U
ISPAL(V) → ISNEPAL(activate(V))
ISLIST(n____(V1, V2)) → ACTIVATE(V1)
ACTIVATE(n__isPal(X)) → ISPAL(X)
ACTIVATE(n__nil) → NIL
ISNELIST(n____(V1, V2)) → AND(isList(activate(V1)), n__isNeList(activate(V2)))
ISLIST(n____(V1, V2)) → ISLIST(activate(V1))
AND(tt, X) → ACTIVATE(X)
ISPAL(V) → ACTIVATE(V)
ISLIST(n____(V1, V2)) → ACTIVATE(V2)
ACTIVATE(n__i) → I
ACTIVATE(n__e) → E
ISNEPAL(V) → ISQID(activate(V))
ISLIST(V) → ACTIVATE(V)
ISNELIST(n____(V1, V2)) → ACTIVATE(V2)
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
isNeList(V) → isQid(activate(V))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isNePal(V) → isQid(activate(V))
isNePal(n____(I, __(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isPal(V) → isNePal(activate(V))
isPal(n__nil) → tt
isQid(n__a) → tt
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
__1(__(X, Y), Z) → __1(Y, Z)
__1(__(X, Y), Z) → __1(X, __(Y, Z))
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
isNeList(V) → isQid(activate(V))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isNePal(V) → isQid(activate(V))
isNePal(n____(I, __(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isPal(V) → isNePal(activate(V))
isPal(n__nil) → tt
isQid(n__a) → tt
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
__1(__(X, Y), Z) → __1(Y, Z)
__1(__(X, Y), Z) → __1(X, __(Y, Z))
The value of delta used in the strict ordering is 3.
POL(__(x1, x2)) = 3 + (4)x_1 + x_2
POL(__1(x1, x2)) = x_1
POL(n____(x1, x2)) = 1 + (3)x_1 + (4)x_2
POL(nil) = 0
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
isNeList(V) → isQid(activate(V))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isNePal(V) → isQid(activate(V))
isNePal(n____(I, __(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isPal(V) → isNePal(activate(V))
isPal(n__nil) → tt
isQid(n__a) → tt
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
ISLIST(V) → ISNELIST(activate(V))
ISNEPAL(n____(I, __(P, I))) → ACTIVATE(I)
ACTIVATE(n__isNeList(X)) → ISNELIST(X)
ISPAL(V) → ISNEPAL(activate(V))
ISNELIST(n____(V1, V2)) → AND(isNeList(activate(V1)), n__isList(activate(V2)))
ISNELIST(V) → ACTIVATE(V)
ISLIST(n____(V1, V2)) → ACTIVATE(V1)
ISNELIST(n____(V1, V2)) → ISNELIST(activate(V1))
ISLIST(n____(V1, V2)) → ISLIST(activate(V1))
ISNELIST(n____(V1, V2)) → AND(isList(activate(V1)), n__isNeList(activate(V2)))
ACTIVATE(n__isPal(X)) → ISPAL(X)
ISNEPAL(n____(I, __(P, I))) → ACTIVATE(P)
AND(tt, X) → ACTIVATE(X)
ISPAL(V) → ACTIVATE(V)
ISNEPAL(V) → ACTIVATE(V)
ISLIST(n____(V1, V2)) → ACTIVATE(V2)
ISNELIST(n____(V1, V2)) → ISLIST(activate(V1))
ACTIVATE(n__isList(X)) → ISLIST(X)
ISLIST(n____(V1, V2)) → AND(isList(activate(V1)), n__isList(activate(V2)))
ISNELIST(n____(V1, V2)) → ACTIVATE(V1)
ISNEPAL(n____(I, __(P, I))) → AND(isQid(activate(I)), n__isPal(activate(P)))
ISLIST(V) → ACTIVATE(V)
ISNELIST(n____(V1, V2)) → ACTIVATE(V2)
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
isNeList(V) → isQid(activate(V))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isNePal(V) → isQid(activate(V))
isNePal(n____(I, __(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isPal(V) → isNePal(activate(V))
isPal(n__nil) → tt
isQid(n__a) → tt
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ISLIST(V) → ISNELIST(activate(V))
ISNEPAL(n____(I, __(P, I))) → ACTIVATE(I)
ISLIST(n____(V1, V2)) → ACTIVATE(V1)
ISNELIST(n____(V1, V2)) → ISNELIST(activate(V1))
ISLIST(n____(V1, V2)) → ISLIST(activate(V1))
ISNELIST(n____(V1, V2)) → AND(isList(activate(V1)), n__isNeList(activate(V2)))
ISNEPAL(n____(I, __(P, I))) → ACTIVATE(P)
ISLIST(n____(V1, V2)) → ACTIVATE(V2)
ISNELIST(n____(V1, V2)) → ISLIST(activate(V1))
ACTIVATE(n__isList(X)) → ISLIST(X)
ISLIST(n____(V1, V2)) → AND(isList(activate(V1)), n__isList(activate(V2)))
ISNELIST(n____(V1, V2)) → ACTIVATE(V1)
ISNEPAL(n____(I, __(P, I))) → AND(isQid(activate(I)), n__isPal(activate(P)))
ISLIST(V) → ACTIVATE(V)
ISNELIST(n____(V1, V2)) → ACTIVATE(V2)
Used ordering: Polynomial interpretation [25,35]:
ACTIVATE(n__isNeList(X)) → ISNELIST(X)
ISPAL(V) → ISNEPAL(activate(V))
ISNELIST(n____(V1, V2)) → AND(isNeList(activate(V1)), n__isList(activate(V2)))
ISNELIST(V) → ACTIVATE(V)
ACTIVATE(n__isPal(X)) → ISPAL(X)
AND(tt, X) → ACTIVATE(X)
ISPAL(V) → ACTIVATE(V)
ISNEPAL(V) → ACTIVATE(V)
The value of delta used in the strict ordering is 2.
POL(i) = 0
POL(n__u) = 1
POL(__(x1, x2)) = 2 + (4)x_1 + x_2
POL(n__i) = 0
POL(activate(x1)) = x_1
POL(and(x1, x2)) = x_1 + x_2
POL(n__nil) = 0
POL(n__a) = 0
POL(tt) = 0
POL(ISPAL(x1)) = (4)x_1
POL(AND(x1, x2)) = (4)x_2
POL(n__isList(x1)) = 2 + x_1
POL(ACTIVATE(x1)) = (4)x_1
POL(nil) = 0
POL(a) = 0
POL(isList(x1)) = 2 + x_1
POL(ISNELIST(x1)) = (4)x_1
POL(n__isPal(x1)) = (4)x_1
POL(e) = 4
POL(n__e) = 4
POL(isNePal(x1)) = x_1
POL(o) = 0
POL(n____(x1, x2)) = 2 + (4)x_1 + x_2
POL(isQid(x1)) = 0
POL(n__isNeList(x1)) = x_1
POL(isPal(x1)) = (4)x_1
POL(n__o) = 0
POL(u) = 1
POL(isNeList(x1)) = x_1
POL(ISLIST(x1)) = 2 + (4)x_1
POL(ISNEPAL(x1)) = (4)x_1
activate(n__a) → a
activate(n__e) → e
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
isNePal(n____(I, __(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isPal(V) → isNePal(activate(V))
activate(n__isPal(X)) → isPal(X)
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
__(nil, X) → X
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
isNeList(V) → isQid(activate(V))
isList(n__nil) → tt
isNePal(V) → isQid(activate(V))
isQid(n__e) → tt
isQid(n__a) → tt
isPal(n__nil) → tt
nil → n__nil
isQid(n__u) → tt
isQid(n__o) → tt
isQid(n__i) → tt
isPal(X) → n__isPal(X)
isNeList(X) → n__isNeList(X)
isList(X) → n__isList(X)
__(X1, X2) → n____(X1, X2)
o → n__o
i → n__i
e → n__e
a → n__a
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
ACTIVATE(n__isNeList(X)) → ISNELIST(X)
ISPAL(V) → ISNEPAL(activate(V))
ISNELIST(V) → ACTIVATE(V)
ISNELIST(n____(V1, V2)) → AND(isNeList(activate(V1)), n__isList(activate(V2)))
ACTIVATE(n__isPal(X)) → ISPAL(X)
ISPAL(V) → ACTIVATE(V)
AND(tt, X) → ACTIVATE(X)
ISNEPAL(V) → ACTIVATE(V)
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
isNeList(V) → isQid(activate(V))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isNePal(V) → isQid(activate(V))
isNePal(n____(I, __(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isPal(V) → isNePal(activate(V))
isPal(n__nil) → tt
isQid(n__a) → tt
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
AND(tt, X) → ACTIVATE(X)
Used ordering: Polynomial interpretation [25,35]:
ACTIVATE(n__isNeList(X)) → ISNELIST(X)
ISPAL(V) → ISNEPAL(activate(V))
ISNELIST(V) → ACTIVATE(V)
ISNELIST(n____(V1, V2)) → AND(isNeList(activate(V1)), n__isList(activate(V2)))
ACTIVATE(n__isPal(X)) → ISPAL(X)
ISPAL(V) → ACTIVATE(V)
ISNEPAL(V) → ACTIVATE(V)
The value of delta used in the strict ordering is 4.
POL(i) = 2
POL(__(x1, x2)) = (4)x_1 + x_2
POL(n__u) = 1
POL(n__i) = 2
POL(activate(x1)) = x_1
POL(and(x1, x2)) = (2)x_1 + x_2
POL(n__nil) = 1
POL(n__a) = 4
POL(tt) = 1
POL(ISPAL(x1)) = x_1
POL(AND(x1, x2)) = (4)x_1 + x_2
POL(n__isList(x1)) = x_1
POL(ACTIVATE(x1)) = x_1
POL(nil) = 1
POL(a) = 4
POL(ISNELIST(x1)) = x_1
POL(isList(x1)) = x_1
POL(n__isPal(x1)) = x_1
POL(e) = 3
POL(n__e) = 3
POL(isNePal(x1)) = x_1
POL(o) = 1
POL(n____(x1, x2)) = (4)x_1 + x_2
POL(isQid(x1)) = x_1
POL(n__isNeList(x1)) = x_1
POL(isPal(x1)) = x_1
POL(n__o) = 1
POL(u) = 1
POL(isNeList(x1)) = x_1
POL(ISNEPAL(x1)) = x_1
activate(n__a) → a
activate(n__e) → e
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
isNePal(n____(I, __(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isPal(V) → isNePal(activate(V))
activate(n__isPal(X)) → isPal(X)
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
__(nil, X) → X
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
isNeList(V) → isQid(activate(V))
isList(n__nil) → tt
isNePal(V) → isQid(activate(V))
isQid(n__e) → tt
isQid(n__a) → tt
isPal(n__nil) → tt
nil → n__nil
isQid(n__u) → tt
isQid(n__o) → tt
isQid(n__i) → tt
isPal(X) → n__isPal(X)
isNeList(X) → n__isNeList(X)
isList(X) → n__isList(X)
__(X1, X2) → n____(X1, X2)
o → n__o
i → n__i
e → n__e
a → n__a
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
ACTIVATE(n__isNeList(X)) → ISNELIST(X)
ISPAL(V) → ISNEPAL(activate(V))
ISNELIST(n____(V1, V2)) → AND(isNeList(activate(V1)), n__isList(activate(V2)))
ISNELIST(V) → ACTIVATE(V)
ACTIVATE(n__isPal(X)) → ISPAL(X)
ISPAL(V) → ACTIVATE(V)
ISNEPAL(V) → ACTIVATE(V)
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
isNeList(V) → isQid(activate(V))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isNePal(V) → isQid(activate(V))
isNePal(n____(I, __(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isPal(V) → isNePal(activate(V))
isPal(n__nil) → tt
isQid(n__a) → tt
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
ACTIVATE(n__isNeList(X)) → ISNELIST(X)
ISPAL(V) → ISNEPAL(activate(V))
ISNELIST(V) → ACTIVATE(V)
ACTIVATE(n__isPal(X)) → ISPAL(X)
ISPAL(V) → ACTIVATE(V)
ISNEPAL(V) → ACTIVATE(V)
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
isNeList(V) → isQid(activate(V))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isNePal(V) → isQid(activate(V))
isNePal(n____(I, __(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isPal(V) → isNePal(activate(V))
isPal(n__nil) → tt
isQid(n__a) → tt
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVATE(n__isNeList(X)) → ISNELIST(X)
ISNELIST(V) → ACTIVATE(V)
Used ordering: Polynomial interpretation [25,35]:
ISPAL(V) → ISNEPAL(activate(V))
ACTIVATE(n__isPal(X)) → ISPAL(X)
ISPAL(V) → ACTIVATE(V)
ISNEPAL(V) → ACTIVATE(V)
The value of delta used in the strict ordering is 1.
POL(i) = 3
POL(__(x1, x2)) = (4)x_1 + x_2
POL(n__u) = 2
POL(n__i) = 3
POL(activate(x1)) = x_1
POL(and(x1, x2)) = x_2
POL(n__nil) = 2
POL(n__a) = 0
POL(tt) = 0
POL(ISPAL(x1)) = (4)x_1
POL(n__isList(x1)) = 4 + x_1
POL(nil) = 2
POL(ACTIVATE(x1)) = x_1
POL(a) = 0
POL(ISNELIST(x1)) = 1 + x_1
POL(isList(x1)) = 4 + x_1
POL(n__isPal(x1)) = (4)x_1
POL(e) = 0
POL(n__e) = 0
POL(isNePal(x1)) = (4)x_1
POL(o) = 1
POL(n____(x1, x2)) = (4)x_1 + x_2
POL(isQid(x1)) = 0
POL(n__isNeList(x1)) = 4 + x_1
POL(isPal(x1)) = (4)x_1
POL(n__o) = 1
POL(u) = 2
POL(isNeList(x1)) = 4 + x_1
POL(ISNEPAL(x1)) = x_1
activate(n__a) → a
activate(n__e) → e
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
isNePal(n____(I, __(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isPal(V) → isNePal(activate(V))
activate(n__isPal(X)) → isPal(X)
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
__(nil, X) → X
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
isNeList(V) → isQid(activate(V))
isList(n__nil) → tt
isNePal(V) → isQid(activate(V))
isQid(n__e) → tt
isQid(n__a) → tt
isPal(n__nil) → tt
nil → n__nil
isQid(n__u) → tt
isQid(n__o) → tt
isQid(n__i) → tt
isPal(X) → n__isPal(X)
isNeList(X) → n__isNeList(X)
isList(X) → n__isList(X)
__(X1, X2) → n____(X1, X2)
o → n__o
i → n__i
e → n__e
a → n__a
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
ISPAL(V) → ISNEPAL(activate(V))
ACTIVATE(n__isPal(X)) → ISPAL(X)
ISPAL(V) → ACTIVATE(V)
ISNEPAL(V) → ACTIVATE(V)
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
isNeList(V) → isQid(activate(V))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isNePal(V) → isQid(activate(V))
isNePal(n____(I, __(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isPal(V) → isNePal(activate(V))
isPal(n__nil) → tt
isQid(n__a) → tt
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ISPAL(V) → ISNEPAL(activate(V))
ACTIVATE(n__isPal(X)) → ISPAL(X)
ISPAL(V) → ACTIVATE(V)
Used ordering: Polynomial interpretation [25,35]:
ISNEPAL(V) → ACTIVATE(V)
The value of delta used in the strict ordering is 1.
POL(i) = 1
POL(__(x1, x2)) = 3 + (4)x_1 + x_2
POL(n__u) = 1
POL(n__i) = 1
POL(activate(x1)) = x_1
POL(and(x1, x2)) = x_2
POL(n__nil) = 0
POL(n__a) = 0
POL(tt) = 0
POL(ISPAL(x1)) = 3 + x_1
POL(n__isList(x1)) = 0
POL(ACTIVATE(x1)) = 2 + x_1
POL(nil) = 0
POL(a) = 0
POL(isList(x1)) = 0
POL(n__isPal(x1)) = 2 + x_1
POL(e) = 3
POL(n__e) = 3
POL(isNePal(x1)) = 2 + x_1
POL(o) = 0
POL(n____(x1, x2)) = 3 + (4)x_1 + x_2
POL(isQid(x1)) = 0
POL(n__isNeList(x1)) = 0
POL(isPal(x1)) = 2 + x_1
POL(n__o) = 0
POL(u) = 1
POL(isNeList(x1)) = 0
POL(ISNEPAL(x1)) = 2 + x_1
activate(n__a) → a
activate(n__e) → e
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
isNePal(n____(I, __(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isPal(V) → isNePal(activate(V))
activate(n__isPal(X)) → isPal(X)
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
__(nil, X) → X
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
isNeList(V) → isQid(activate(V))
isList(n__nil) → tt
isNePal(V) → isQid(activate(V))
isQid(n__e) → tt
isQid(n__a) → tt
isPal(n__nil) → tt
nil → n__nil
isQid(n__u) → tt
isQid(n__o) → tt
isQid(n__i) → tt
isPal(X) → n__isPal(X)
isNeList(X) → n__isNeList(X)
isList(X) → n__isList(X)
__(X1, X2) → n____(X1, X2)
o → n__o
i → n__i
e → n__e
a → n__a
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
ISNEPAL(V) → ACTIVATE(V)
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
isNeList(V) → isQid(activate(V))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isNePal(V) → isQid(activate(V))
isNePal(n____(I, __(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isPal(V) → isNePal(activate(V))
isPal(n__nil) → tt
isQid(n__a) → tt
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X