Problem:
__(__(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
Proof:
Complexity Transformation Processor:
strict:
__(__(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
weak:
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[u] = 0,
[o] = 0,
[i] = 0,
[e] = 0,
[a] = 0,
[n__u] = 8,
[n__o] = 12,
[n__i] = 1,
[n__e] = 0,
[n__a] = 0,
[isPal](x0) = x0,
[n__isPal](x0) = x0,
[isNePal](x0) = x0,
[n__isNeList](x0) = x0 + 12,
[isQid](x0) = x0 + 4,
[n__isList](x0) = x0,
[n____](x0, x1) = x0 + x1 + 13,
[n__nil] = 5,
[isNeList](x0) = x0 + 1,
[isList](x0) = x0,
[activate](x0) = x0 + 8,
[and](x0, x1) = x0 + x1 + 3,
[tt] = 0,
[nil] = 4,
[__](x0, x1) = x0 + x1 + 13
orientation:
__(__(X,Y),Z) = X + Y + Z + 26 >= X + Y + Z + 26 = __(X,__(Y,Z))
__(X,nil()) = X + 17 >= X = X
__(nil(),X) = X + 17 >= X = X
and(tt(),X) = X + 3 >= X + 8 = activate(X)
isList(V) = V >= V + 9 = isNeList(activate(V))
isList(n__nil()) = 5 >= 0 = tt()
isList(n____(V1,V2)) = V1 + V2 + 13 >= V1 + V2 + 19 = and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) = V + 1 >= V + 12 = isQid(activate(V))
isNeList(n____(V1,V2)) = V1 + V2 + 14 >= V1 + V2 + 31 = and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) = V1 + V2 + 14 >= V1 + V2 + 20 = and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) = V >= V + 12 = isQid(activate(V))
isNePal(n____(I,__(P,I))) = 2I + P + 26 >= I + P + 23 = and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) = V >= V + 8 = isNePal(activate(V))
isPal(n__nil()) = 5 >= 0 = tt()
isQid(n__a()) = 4 >= 0 = tt()
isQid(n__e()) = 4 >= 0 = tt()
isQid(n__i()) = 5 >= 0 = tt()
isQid(n__o()) = 16 >= 0 = tt()
isQid(n__u()) = 12 >= 0 = tt()
nil() = 4 >= 5 = n__nil()
__(X1,X2) = X1 + X2 + 13 >= X1 + X2 + 13 = n____(X1,X2)
isList(X) = X >= X = n__isList(X)
isNeList(X) = X + 1 >= X + 12 = n__isNeList(X)
isPal(X) = X >= X = n__isPal(X)
a() = 0 >= 0 = n__a()
e() = 0 >= 0 = n__e()
i() = 0 >= 1 = n__i()
o() = 0 >= 12 = n__o()
u() = 0 >= 8 = n__u()
activate(n__nil()) = 13 >= 4 = nil()
activate(n____(X1,X2)) = X1 + X2 + 21 >= X1 + X2 + 13 = __(X1,X2)
activate(n__isList(X)) = X + 8 >= X = isList(X)
activate(n__isNeList(X)) = X + 20 >= X + 1 = isNeList(X)
activate(n__isPal(X)) = X + 8 >= X = isPal(X)
activate(n__a()) = 8 >= 0 = a()
activate(n__e()) = 8 >= 0 = e()
activate(n__i()) = 9 >= 0 = i()
activate(n__o()) = 20 >= 0 = o()
activate(n__u()) = 16 >= 0 = u()
activate(X) = X + 8 >= X = X
problem:
strict:
__(__(X,Y),Z) -> __(X,__(Y,Z))
and(tt(),X) -> activate(X)
isList(V) -> isNeList(activate(V))
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))
isPal(V) -> isNePal(activate(V))
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()
weak:
__(X,nil()) -> X
__(nil(),X) -> X
isList(n__nil()) -> tt()
isNePal(n____(I,__(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
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
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[u] = 3,
[o] = 0,
[i] = 2,
[e] = 0,
[a] = 0,
[n__u] = 2,
[n__o] = 10,
[n__i] = 0,
[n__e] = 0,
[n__a] = 0,
[isPal](x0) = x0 + 8,
[n__isPal](x0) = x0 + 8,
[isNePal](x0) = x0 + 12,
[n__isNeList](x0) = x0,
[isQid](x0) = x0 + 1,
[n__isList](x0) = x0 + 2,
[n____](x0, x1) = x0 + x1 + 10,
[n__nil] = 0,
[isNeList](x0) = x0 + 2,
[isList](x0) = x0,
[activate](x0) = x0 + 2,
[and](x0, x1) = x0 + x1 + 9,
[tt] = 0,
[nil] = 0,
[__](x0, x1) = x0 + x1
orientation:
__(__(X,Y),Z) = X + Y + Z >= X + Y + Z = __(X,__(Y,Z))
and(tt(),X) = X + 9 >= X + 2 = activate(X)
isList(V) = V >= V + 4 = isNeList(activate(V))
isList(n____(V1,V2)) = V1 + V2 + 10 >= V1 + V2 + 15 = and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) = V + 2 >= V + 3 = isQid(activate(V))
isNeList(n____(V1,V2)) = V1 + V2 + 12 >= V1 + V2 + 13 = and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) = V1 + V2 + 12 >= V1 + V2 + 17 = and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) = V + 12 >= V + 3 = isQid(activate(V))
isPal(V) = V + 8 >= V + 14 = isNePal(activate(V))
nil() = 0 >= 0 = n__nil()
__(X1,X2) = X1 + X2 >= X1 + X2 + 10 = n____(X1,X2)
isList(X) = X >= X + 2 = n__isList(X)
isNeList(X) = X + 2 >= X = n__isNeList(X)
isPal(X) = X + 8 >= X + 8 = n__isPal(X)
a() = 0 >= 0 = n__a()
e() = 0 >= 0 = n__e()
i() = 2 >= 0 = n__i()
o() = 0 >= 10 = n__o()
u() = 3 >= 2 = n__u()
__(X,nil()) = X >= X = X
__(nil(),X) = X >= X = X
isList(n__nil()) = 0 >= 0 = tt()
isNePal(n____(I,__(P,I))) = 2I + P + 22 >= I + P + 22 = and(isQid(activate(I)),n__isPal(activate(P)))
isPal(n__nil()) = 8 >= 0 = tt()
isQid(n__a()) = 1 >= 0 = tt()
isQid(n__e()) = 1 >= 0 = tt()
isQid(n__i()) = 1 >= 0 = tt()
isQid(n__o()) = 11 >= 0 = tt()
isQid(n__u()) = 3 >= 0 = tt()
activate(n__nil()) = 2 >= 0 = nil()
activate(n____(X1,X2)) = X1 + X2 + 12 >= X1 + X2 = __(X1,X2)
activate(n__isList(X)) = X + 4 >= X = isList(X)
activate(n__isNeList(X)) = X + 2 >= X + 2 = isNeList(X)
activate(n__isPal(X)) = X + 10 >= X + 8 = isPal(X)
activate(n__a()) = 2 >= 0 = a()
activate(n__e()) = 2 >= 0 = e()
activate(n__i()) = 2 >= 2 = i()
activate(n__o()) = 12 >= 0 = o()
activate(n__u()) = 4 >= 3 = u()
activate(X) = X + 2 >= X = X
problem:
strict:
__(__(X,Y),Z) -> __(X,__(Y,Z))
isList(V) -> isNeList(activate(V))
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)))
isPal(V) -> isNePal(activate(V))
nil() -> n__nil()
__(X1,X2) -> n____(X1,X2)
isList(X) -> n__isList(X)
isPal(X) -> n__isPal(X)
a() -> n__a()
e() -> n__e()
o() -> n__o()
weak:
and(tt(),X) -> activate(X)
isNePal(V) -> isQid(activate(V))
isNeList(X) -> n__isNeList(X)
i() -> n__i()
u() -> n__u()
__(X,nil()) -> X
__(nil(),X) -> X
isList(n__nil()) -> tt()
isNePal(n____(I,__(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
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
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[u] = 7,
[o] = 0,
[i] = 0,
[e] = 0,
[a] = 1,
[n__u] = 7,
[n__o] = 1,
[n__i] = 0,
[n__e] = 10,
[n__a] = 0,
[isPal](x0) = x0 + 5,
[n__isPal](x0) = x0 + 4,
[isNePal](x0) = x0 + 2,
[n__isNeList](x0) = x0 + 15,
[isQid](x0) = x0 + 1,
[n__isList](x0) = x0 + 6,
[n____](x0, x1) = x0 + x1 + 7,
[n__nil] = 1,
[isNeList](x0) = x0 + 15,
[isList](x0) = x0,
[activate](x0) = x0 + 1,
[and](x0, x1) = x0 + x1,
[tt] = 1,
[nil] = 0,
[__](x0, x1) = x0 + x1
orientation:
__(__(X,Y),Z) = X + Y + Z >= X + Y + Z = __(X,__(Y,Z))
isList(V) = V >= V + 16 = isNeList(activate(V))
isList(n____(V1,V2)) = V1 + V2 + 7 >= V1 + V2 + 8 = and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) = V + 15 >= V + 2 = isQid(activate(V))
isNeList(n____(V1,V2)) = V1 + V2 + 22 >= V1 + V2 + 17 = and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) = V1 + V2 + 22 >= V1 + V2 + 23 = and(isNeList(activate(V1)),n__isList(activate(V2)))
isPal(V) = V + 5 >= V + 3 = isNePal(activate(V))
nil() = 0 >= 1 = n__nil()
__(X1,X2) = X1 + X2 >= X1 + X2 + 7 = n____(X1,X2)
isList(X) = X >= X + 6 = n__isList(X)
isPal(X) = X + 5 >= X + 4 = n__isPal(X)
a() = 1 >= 0 = n__a()
e() = 0 >= 10 = n__e()
o() = 0 >= 1 = n__o()
and(tt(),X) = X + 1 >= X + 1 = activate(X)
isNePal(V) = V + 2 >= V + 2 = isQid(activate(V))
isNeList(X) = X + 15 >= X + 15 = n__isNeList(X)
i() = 0 >= 0 = n__i()
u() = 7 >= 7 = n__u()
__(X,nil()) = X >= X = X
__(nil(),X) = X >= X = X
isList(n__nil()) = 1 >= 1 = tt()
isNePal(n____(I,__(P,I))) = 2I + P + 9 >= I + P + 7 = and(isQid(activate(I)),n__isPal(activate(P)))
isPal(n__nil()) = 6 >= 1 = tt()
isQid(n__a()) = 1 >= 1 = tt()
isQid(n__e()) = 11 >= 1 = tt()
isQid(n__i()) = 1 >= 1 = tt()
isQid(n__o()) = 2 >= 1 = tt()
isQid(n__u()) = 8 >= 1 = tt()
activate(n__nil()) = 2 >= 0 = nil()
activate(n____(X1,X2)) = X1 + X2 + 8 >= X1 + X2 = __(X1,X2)
activate(n__isList(X)) = X + 7 >= X = isList(X)
activate(n__isNeList(X)) = X + 16 >= X + 15 = isNeList(X)
activate(n__isPal(X)) = X + 5 >= X + 5 = isPal(X)
activate(n__a()) = 1 >= 1 = a()
activate(n__e()) = 11 >= 0 = e()
activate(n__i()) = 1 >= 0 = i()
activate(n__o()) = 2 >= 0 = o()
activate(n__u()) = 8 >= 7 = u()
activate(X) = X + 1 >= X = X
problem:
strict:
__(__(X,Y),Z) -> __(X,__(Y,Z))
isList(V) -> isNeList(activate(V))
isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
nil() -> n__nil()
__(X1,X2) -> n____(X1,X2)
isList(X) -> n__isList(X)
e() -> n__e()
o() -> n__o()
weak:
isNeList(V) -> isQid(activate(V))
isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
isPal(V) -> isNePal(activate(V))
isPal(X) -> n__isPal(X)
a() -> n__a()
and(tt(),X) -> activate(X)
isNePal(V) -> isQid(activate(V))
isNeList(X) -> n__isNeList(X)
i() -> n__i()
u() -> n__u()
__(X,nil()) -> X
__(nil(),X) -> X
isList(n__nil()) -> tt()
isNePal(n____(I,__(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
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
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[u] = 4,
[o] = 3,
[i] = 14,
[e] = 0,
[a] = 5,
[n__u] = 4,
[n__o] = 2,
[n__i] = 12,
[n__e] = 6,
[n__a] = 5,
[isPal](x0) = x0 + 4,
[n__isPal](x0) = x0 + 4,
[isNePal](x0) = x0 + 2,
[n__isNeList](x0) = x0 + 2,
[isQid](x0) = x0,
[n__isList](x0) = x0 + 8,
[n____](x0, x1) = x0 + x1 + 10,
[n__nil] = 11,
[isNeList](x0) = x0 + 2,
[isList](x0) = x0 + 6,
[activate](x0) = x0 + 2,
[and](x0, x1) = x0 + x1,
[tt] = 2,
[nil] = 8,
[__](x0, x1) = x0 + x1 + 1
orientation:
__(__(X,Y),Z) = X + Y + Z + 2 >= X + Y + Z + 2 = __(X,__(Y,Z))
isList(V) = V + 6 >= V + 4 = isNeList(activate(V))
isList(n____(V1,V2)) = V1 + V2 + 16 >= V1 + V2 + 18 = and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(n____(V1,V2)) = V1 + V2 + 12 >= V1 + V2 + 14 = and(isNeList(activate(V1)),n__isList(activate(V2)))
nil() = 8 >= 11 = n__nil()
__(X1,X2) = X1 + X2 + 1 >= X1 + X2 + 10 = n____(X1,X2)
isList(X) = X + 6 >= X + 8 = n__isList(X)
e() = 0 >= 6 = n__e()
o() = 3 >= 2 = n__o()
isNeList(V) = V + 2 >= V + 2 = isQid(activate(V))
isNeList(n____(V1,V2)) = V1 + V2 + 12 >= V1 + V2 + 12 = and(isList(activate(V1)),n__isNeList(activate(V2)))
isPal(V) = V + 4 >= V + 4 = isNePal(activate(V))
isPal(X) = X + 4 >= X + 4 = n__isPal(X)
a() = 5 >= 5 = n__a()
and(tt(),X) = X + 2 >= X + 2 = activate(X)
isNePal(V) = V + 2 >= V + 2 = isQid(activate(V))
isNeList(X) = X + 2 >= X + 2 = n__isNeList(X)
i() = 14 >= 12 = n__i()
u() = 4 >= 4 = n__u()
__(X,nil()) = X + 9 >= X = X
__(nil(),X) = X + 9 >= X = X
isList(n__nil()) = 17 >= 2 = tt()
isNePal(n____(I,__(P,I))) = 2I + P + 13 >= I + P + 8 = and(isQid(activate(I)),n__isPal(activate(P)))
isPal(n__nil()) = 15 >= 2 = tt()
isQid(n__a()) = 5 >= 2 = tt()
isQid(n__e()) = 6 >= 2 = tt()
isQid(n__i()) = 12 >= 2 = tt()
isQid(n__o()) = 2 >= 2 = tt()
isQid(n__u()) = 4 >= 2 = tt()
activate(n__nil()) = 13 >= 8 = nil()
activate(n____(X1,X2)) = X1 + X2 + 12 >= X1 + X2 + 1 = __(X1,X2)
activate(n__isList(X)) = X + 10 >= X + 6 = isList(X)
activate(n__isNeList(X)) = X + 4 >= X + 2 = isNeList(X)
activate(n__isPal(X)) = X + 6 >= X + 4 = isPal(X)
activate(n__a()) = 7 >= 5 = a()
activate(n__e()) = 8 >= 0 = e()
activate(n__i()) = 14 >= 14 = i()
activate(n__o()) = 4 >= 3 = o()
activate(n__u()) = 6 >= 4 = u()
activate(X) = X + 2 >= X = X
problem:
strict:
__(__(X,Y),Z) -> __(X,__(Y,Z))
isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
nil() -> n__nil()
__(X1,X2) -> n____(X1,X2)
isList(X) -> n__isList(X)
e() -> n__e()
weak:
isList(V) -> isNeList(activate(V))
o() -> n__o()
isNeList(V) -> isQid(activate(V))
isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
isPal(V) -> isNePal(activate(V))
isPal(X) -> n__isPal(X)
a() -> n__a()
and(tt(),X) -> activate(X)
isNePal(V) -> isQid(activate(V))
isNeList(X) -> n__isNeList(X)
i() -> n__i()
u() -> n__u()
__(X,nil()) -> X
__(nil(),X) -> X
isList(n__nil()) -> tt()
isNePal(n____(I,__(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
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
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[u] = 9,
[o] = 8,
[i] = 12,
[e] = 13,
[a] = 8,
[n__u] = 9,
[n__o] = 8,
[n__i] = 12,
[n__e] = 12,
[n__a] = 8,
[isPal](x0) = x0 + 15,
[n__isPal](x0) = x0 + 15,
[isNePal](x0) = x0 + 14,
[n__isNeList](x0) = x0 + 2,
[isQid](x0) = x0 + 1,
[n__isList](x0) = x0 + 2,
[n____](x0, x1) = x0 + x1 + 5,
[n__nil] = 8,
[isNeList](x0) = x0 + 2,
[isList](x0) = x0 + 3,
[activate](x0) = x0 + 1,
[and](x0, x1) = x0 + x1,
[tt] = 1,
[nil] = 0,
[__](x0, x1) = x0 + x1
orientation:
__(__(X,Y),Z) = X + Y + Z >= X + Y + Z = __(X,__(Y,Z))
isList(n____(V1,V2)) = V1 + V2 + 8 >= V1 + V2 + 7 = and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(n____(V1,V2)) = V1 + V2 + 7 >= V1 + V2 + 6 = and(isNeList(activate(V1)),n__isList(activate(V2)))
nil() = 0 >= 8 = n__nil()
__(X1,X2) = X1 + X2 >= X1 + X2 + 5 = n____(X1,X2)
isList(X) = X + 3 >= X + 2 = n__isList(X)
e() = 13 >= 12 = n__e()
isList(V) = V + 3 >= V + 3 = isNeList(activate(V))
o() = 8 >= 8 = n__o()
isNeList(V) = V + 2 >= V + 2 = isQid(activate(V))
isNeList(n____(V1,V2)) = V1 + V2 + 7 >= V1 + V2 + 7 = and(isList(activate(V1)),n__isNeList(activate(V2)))
isPal(V) = V + 15 >= V + 15 = isNePal(activate(V))
isPal(X) = X + 15 >= X + 15 = n__isPal(X)
a() = 8 >= 8 = n__a()
and(tt(),X) = X + 1 >= X + 1 = activate(X)
isNePal(V) = V + 14 >= V + 2 = isQid(activate(V))
isNeList(X) = X + 2 >= X + 2 = n__isNeList(X)
i() = 12 >= 12 = n__i()
u() = 9 >= 9 = n__u()
__(X,nil()) = X >= X = X
__(nil(),X) = X >= X = X
isList(n__nil()) = 11 >= 1 = tt()
isNePal(n____(I,__(P,I))) = 2I + P + 19 >= I + P + 18 = and(isQid(activate(I)),n__isPal(activate(P)))
isPal(n__nil()) = 23 >= 1 = tt()
isQid(n__a()) = 9 >= 1 = tt()
isQid(n__e()) = 13 >= 1 = tt()
isQid(n__i()) = 13 >= 1 = tt()
isQid(n__o()) = 9 >= 1 = tt()
isQid(n__u()) = 10 >= 1 = tt()
activate(n__nil()) = 9 >= 0 = nil()
activate(n____(X1,X2)) = X1 + X2 + 6 >= X1 + X2 = __(X1,X2)
activate(n__isList(X)) = X + 3 >= X + 3 = isList(X)
activate(n__isNeList(X)) = X + 3 >= X + 2 = isNeList(X)
activate(n__isPal(X)) = X + 16 >= X + 15 = isPal(X)
activate(n__a()) = 9 >= 8 = a()
activate(n__e()) = 13 >= 13 = e()
activate(n__i()) = 13 >= 12 = i()
activate(n__o()) = 9 >= 8 = o()
activate(n__u()) = 10 >= 9 = u()
activate(X) = X + 1 >= X = X
problem:
strict:
__(__(X,Y),Z) -> __(X,__(Y,Z))
nil() -> n__nil()
__(X1,X2) -> n____(X1,X2)
weak:
isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
isList(X) -> n__isList(X)
e() -> n__e()
isList(V) -> isNeList(activate(V))
o() -> n__o()
isNeList(V) -> isQid(activate(V))
isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
isPal(V) -> isNePal(activate(V))
isPal(X) -> n__isPal(X)
a() -> n__a()
and(tt(),X) -> activate(X)
isNePal(V) -> isQid(activate(V))
isNeList(X) -> n__isNeList(X)
i() -> n__i()
u() -> n__u()
__(X,nil()) -> X
__(nil(),X) -> X
isList(n__nil()) -> tt()
isNePal(n____(I,__(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
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
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[u] = 56,
[o] = 60,
[i] = 57,
[e] = 56,
[a] = 56,
[n__u] = 56,
[n__o] = 60,
[n__i] = 56,
[n__e] = 56,
[n__a] = 56,
[isPal](x0) = x0 + 8,
[n__isPal](x0) = x0 + 8,
[isNePal](x0) = x0 + 2,
[n__isNeList](x0) = x0,
[isQid](x0) = x0,
[n__isList](x0) = x0 + 3,
[n____](x0, x1) = x0 + x1 + 54,
[n__nil] = 58,
[isNeList](x0) = x0 + 1,
[isList](x0) = x0 + 4,
[activate](x0) = x0 + 1,
[and](x0, x1) = x0 + x1 + 6,
[tt] = 56,
[nil] = 59,
[__](x0, x1) = x0 + x1
orientation:
__(__(X,Y),Z) = X + Y + Z >= X + Y + Z = __(X,__(Y,Z))
nil() = 59 >= 58 = n__nil()
__(X1,X2) = X1 + X2 >= X1 + X2 + 54 = n____(X1,X2)
isList(n____(V1,V2)) = V1 + V2 + 58 >= V1 + V2 + 15 = and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(n____(V1,V2)) = V1 + V2 + 55 >= V1 + V2 + 12 = and(isNeList(activate(V1)),n__isList(activate(V2)))
isList(X) = X + 4 >= X + 3 = n__isList(X)
e() = 56 >= 56 = n__e()
isList(V) = V + 4 >= V + 2 = isNeList(activate(V))
o() = 60 >= 60 = n__o()
isNeList(V) = V + 1 >= V + 1 = isQid(activate(V))
isNeList(n____(V1,V2)) = V1 + V2 + 55 >= V1 + V2 + 12 = and(isList(activate(V1)),n__isNeList(activate(V2)))
isPal(V) = V + 8 >= V + 3 = isNePal(activate(V))
isPal(X) = X + 8 >= X + 8 = n__isPal(X)
a() = 56 >= 56 = n__a()
and(tt(),X) = X + 62 >= X + 1 = activate(X)
isNePal(V) = V + 2 >= V + 1 = isQid(activate(V))
isNeList(X) = X + 1 >= X = n__isNeList(X)
i() = 57 >= 56 = n__i()
u() = 56 >= 56 = n__u()
__(X,nil()) = X + 59 >= X = X
__(nil(),X) = X + 59 >= X = X
isList(n__nil()) = 62 >= 56 = tt()
isNePal(n____(I,__(P,I))) = 2I + P + 56 >= I + P + 16 = and(isQid(activate(I)),n__isPal(activate(P)))
isPal(n__nil()) = 66 >= 56 = tt()
isQid(n__a()) = 56 >= 56 = tt()
isQid(n__e()) = 56 >= 56 = tt()
isQid(n__i()) = 56 >= 56 = tt()
isQid(n__o()) = 60 >= 56 = tt()
isQid(n__u()) = 56 >= 56 = tt()
activate(n__nil()) = 59 >= 59 = nil()
activate(n____(X1,X2)) = X1 + X2 + 55 >= X1 + X2 = __(X1,X2)
activate(n__isList(X)) = X + 4 >= X + 4 = isList(X)
activate(n__isNeList(X)) = X + 1 >= X + 1 = isNeList(X)
activate(n__isPal(X)) = X + 9 >= X + 8 = isPal(X)
activate(n__a()) = 57 >= 56 = a()
activate(n__e()) = 57 >= 56 = e()
activate(n__i()) = 57 >= 57 = i()
activate(n__o()) = 61 >= 60 = o()
activate(n__u()) = 57 >= 56 = u()
activate(X) = X + 1 >= X = X
problem:
strict:
__(__(X,Y),Z) -> __(X,__(Y,Z))
__(X1,X2) -> n____(X1,X2)
weak:
nil() -> n__nil()
isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
isList(X) -> n__isList(X)
e() -> n__e()
isList(V) -> isNeList(activate(V))
o() -> n__o()
isNeList(V) -> isQid(activate(V))
isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
isPal(V) -> isNePal(activate(V))
isPal(X) -> n__isPal(X)
a() -> n__a()
and(tt(),X) -> activate(X)
isNePal(V) -> isQid(activate(V))
isNeList(X) -> n__isNeList(X)
i() -> n__i()
u() -> n__u()
__(X,nil()) -> X
__(nil(),X) -> X
isList(n__nil()) -> tt()
isNePal(n____(I,__(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
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
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[u] = 0,
[o] = 0,
[i] = 0,
[e] = 0,
[a] = 0,
[n__u] = 0,
[n__o] = 0,
[n__i] = 0,
[n__e] = 0,
[n__a] = 0,
[isPal](x0) = x0 + 62,
[n__isPal](x0) = x0 + 61,
[isNePal](x0) = x0 + 39,
[n__isNeList](x0) = x0 + 2,
[isQid](x0) = x0 + 1,
[n__isList](x0) = x0 + 4,
[n____](x0, x1) = x0 + x1 + 18,
[n__nil] = 0,
[isNeList](x0) = x0 + 2,
[isList](x0) = x0 + 4,
[activate](x0) = x0 + 1,
[and](x0, x1) = x0 + x1 + 12,
[tt] = 0,
[nil] = 0,
[__](x0, x1) = x0 + x1 + 19
orientation:
__(__(X,Y),Z) = X + Y + Z + 38 >= X + Y + Z + 38 = __(X,__(Y,Z))
__(X1,X2) = X1 + X2 + 19 >= X1 + X2 + 18 = n____(X1,X2)
nil() = 0 >= 0 = n__nil()
isList(n____(V1,V2)) = V1 + V2 + 22 >= V1 + V2 + 22 = and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(n____(V1,V2)) = V1 + V2 + 20 >= V1 + V2 + 20 = and(isNeList(activate(V1)),n__isList(activate(V2)))
isList(X) = X + 4 >= X + 4 = n__isList(X)
e() = 0 >= 0 = n__e()
isList(V) = V + 4 >= V + 3 = isNeList(activate(V))
o() = 0 >= 0 = n__o()
isNeList(V) = V + 2 >= V + 2 = isQid(activate(V))
isNeList(n____(V1,V2)) = V1 + V2 + 20 >= V1 + V2 + 20 = and(isList(activate(V1)),n__isNeList(activate(V2)))
isPal(V) = V + 62 >= V + 40 = isNePal(activate(V))
isPal(X) = X + 62 >= X + 61 = n__isPal(X)
a() = 0 >= 0 = n__a()
and(tt(),X) = X + 12 >= X + 1 = activate(X)
isNePal(V) = V + 39 >= V + 2 = isQid(activate(V))
isNeList(X) = X + 2 >= X + 2 = n__isNeList(X)
i() = 0 >= 0 = n__i()
u() = 0 >= 0 = n__u()
__(X,nil()) = X + 19 >= X = X
__(nil(),X) = X + 19 >= X = X
isList(n__nil()) = 4 >= 0 = tt()
isNePal(n____(I,__(P,I))) = 2I + P + 76 >= I + P + 76 = and(isQid(activate(I)),n__isPal(activate(P)))
isPal(n__nil()) = 62 >= 0 = tt()
isQid(n__a()) = 1 >= 0 = tt()
isQid(n__e()) = 1 >= 0 = tt()
isQid(n__i()) = 1 >= 0 = tt()
isQid(n__o()) = 1 >= 0 = tt()
isQid(n__u()) = 1 >= 0 = tt()
activate(n__nil()) = 1 >= 0 = nil()
activate(n____(X1,X2)) = X1 + X2 + 19 >= X1 + X2 + 19 = __(X1,X2)
activate(n__isList(X)) = X + 5 >= X + 4 = isList(X)
activate(n__isNeList(X)) = X + 3 >= X + 2 = isNeList(X)
activate(n__isPal(X)) = X + 62 >= X + 62 = isPal(X)
activate(n__a()) = 1 >= 0 = a()
activate(n__e()) = 1 >= 0 = e()
activate(n__i()) = 1 >= 0 = i()
activate(n__o()) = 1 >= 0 = o()
activate(n__u()) = 1 >= 0 = u()
activate(X) = X + 1 >= X = X
problem:
strict:
__(__(X,Y),Z) -> __(X,__(Y,Z))
weak:
__(X1,X2) -> n____(X1,X2)
nil() -> n__nil()
isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
isList(X) -> n__isList(X)
e() -> n__e()
isList(V) -> isNeList(activate(V))
o() -> n__o()
isNeList(V) -> isQid(activate(V))
isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
isPal(V) -> isNePal(activate(V))
isPal(X) -> n__isPal(X)
a() -> n__a()
and(tt(),X) -> activate(X)
isNePal(V) -> isQid(activate(V))
isNeList(X) -> n__isNeList(X)
i() -> n__i()
u() -> n__u()
__(X,nil()) -> X
__(nil(),X) -> X
isList(n__nil()) -> tt()
isNePal(n____(I,__(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
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
Matrix Interpretation Processor:
dimension: 2
max_matrix:
[1 2]
[0 1]
interpretation:
[1]
[u] = [0],
[0]
[o] = [0],
[2]
[i] = [1],
[0]
[e] = [1],
[0]
[a] = [1],
[1]
[n__u] = [0],
[0]
[n__o] = [0],
[2]
[n__i] = [1],
[0]
[n__e] = [1],
[0]
[n__a] = [1],
[1 1] [1]
[isPal](x0) = [0 1]x0 + [0],
[1 1] [1]
[n__isPal](x0) = [0 1]x0 + [0],
[1 1] [1]
[isNePal](x0) = [0 1]x0 + [0],
[n__isNeList](x0) = x0,
[isQid](x0) = x0,
[n__isList](x0) = x0,
[1 2] [2]
[n____](x0, x1) = [0 1]x0 + x1 + [3],
[0]
[n__nil] = [0],
[isNeList](x0) = x0,
[isList](x0) = x0,
[activate](x0) = x0,
[1 2] [1]
[and](x0, x1) = [0 0]x0 + x1 + [2],
[0]
[tt] = [0],
[0]
[nil] = [0],
[1 2] [2]
[__](x0, x1) = [0 1]x0 + x1 + [3]
orientation:
[1 4] [1 2] [10] [1 2] [1 2] [4]
__(__(X,Y),Z) = [0 1]X + [0 1]Y + Z + [6 ] >= [0 1]X + [0 1]Y + Z + [6] = __(X,__(Y,Z))
[1 2] [2] [1 2] [2]
__(X1,X2) = [0 1]X1 + X2 + [3] >= [0 1]X1 + X2 + [3] = n____(X1,X2)
[0] [0]
nil() = [0] >= [0] = n__nil()
[1 2] [2] [1 2] [1]
isList(n____(V1,V2)) = [0 1]V1 + V2 + [3] >= [0 0]V1 + V2 + [2] = and(isList(activate(V1)),n__isList(activate(V2)))
[1 2] [2] [1 2] [1]
isNeList(n____(V1,V2)) = [0 1]V1 + V2 + [3] >= [0 0]V1 + V2 + [2] = and(isNeList(activate(V1)),n__isList(activate(V2)))
isList(X) = X >= X = n__isList(X)
[0] [0]
e() = [1] >= [1] = n__e()
isList(V) = V >= V = isNeList(activate(V))
[0] [0]
o() = [0] >= [0] = n__o()
isNeList(V) = V >= V = isQid(activate(V))
[1 2] [2] [1 2] [1]
isNeList(n____(V1,V2)) = [0 1]V1 + V2 + [3] >= [0 0]V1 + V2 + [2] = and(isList(activate(V1)),n__isNeList(activate(V2)))
[1 1] [1] [1 1] [1]
isPal(V) = [0 1]V + [0] >= [0 1]V + [0] = isNePal(activate(V))
[1 1] [1] [1 1] [1]
isPal(X) = [0 1]X + [0] >= [0 1]X + [0] = n__isPal(X)
[0] [0]
a() = [1] >= [1] = n__a()
[1]
and(tt(),X) = X + [2] >= X = activate(X)
[1 1] [1]
isNePal(V) = [0 1]V + [0] >= V = isQid(activate(V))
isNeList(X) = X >= X = n__isNeList(X)
[2] [2]
i() = [1] >= [1] = n__i()
[1] [1]
u() = [0] >= [0] = n__u()
[1 2] [2]
__(X,nil()) = [0 1]X + [3] >= X = X
[2]
__(nil(),X) = X + [3] >= X = X
[0] [0]
isList(n__nil()) = [0] >= [0] = tt()
[2 4] [1 3] [11] [1 2] [1 1] [2]
isNePal(n____(I,__(P,I))) = [0 2]I + [0 1]P + [6 ] >= [0 0]I + [0 1]P + [2] = and(isQid(activate(I)),n__isPal(activate(P)))
[1] [0]
isPal(n__nil()) = [0] >= [0] = tt()
[0] [0]
isQid(n__a()) = [1] >= [0] = tt()
[0] [0]
isQid(n__e()) = [1] >= [0] = tt()
[2] [0]
isQid(n__i()) = [1] >= [0] = tt()
[0] [0]
isQid(n__o()) = [0] >= [0] = tt()
[1] [0]
isQid(n__u()) = [0] >= [0] = tt()
[0] [0]
activate(n__nil()) = [0] >= [0] = nil()
[1 2] [2] [1 2] [2]
activate(n____(X1,X2)) = [0 1]X1 + X2 + [3] >= [0 1]X1 + X2 + [3] = __(X1,X2)
activate(n__isList(X)) = X >= X = isList(X)
activate(n__isNeList(X)) = X >= X = isNeList(X)
[1 1] [1] [1 1] [1]
activate(n__isPal(X)) = [0 1]X + [0] >= [0 1]X + [0] = isPal(X)
[0] [0]
activate(n__a()) = [1] >= [1] = a()
[0] [0]
activate(n__e()) = [1] >= [1] = e()
[2] [2]
activate(n__i()) = [1] >= [1] = i()
[0] [0]
activate(n__o()) = [0] >= [0] = o()
[1] [1]
activate(n__u()) = [0] >= [0] = u()
activate(X) = X >= X = X
problem:
strict:
weak:
__(__(X,Y),Z) -> __(X,__(Y,Z))
__(X1,X2) -> n____(X1,X2)
nil() -> n__nil()
isList(n____(V1,V2)) -> and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(n____(V1,V2)) -> and(isNeList(activate(V1)),n__isList(activate(V2)))
isList(X) -> n__isList(X)
e() -> n__e()
isList(V) -> isNeList(activate(V))
o() -> n__o()
isNeList(V) -> isQid(activate(V))
isNeList(n____(V1,V2)) -> and(isList(activate(V1)),n__isNeList(activate(V2)))
isPal(V) -> isNePal(activate(V))
isPal(X) -> n__isPal(X)
a() -> n__a()
and(tt(),X) -> activate(X)
isNePal(V) -> isQid(activate(V))
isNeList(X) -> n__isNeList(X)
i() -> n__i()
u() -> n__u()
__(X,nil()) -> X
__(nil(),X) -> X
isList(n__nil()) -> tt()
isNePal(n____(I,__(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P)))
isPal(n__nil()) -> tt()
isQid(n__a()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__o()) -> tt()
isQid(n__u()) -> tt()
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
Qed