YES
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:
Matrix Interpretation Processor: dim=1
interpretation:
[u] = 0,
[o] = 4,
[i] = 0,
[e] = 0,
[a] = 2,
[n__u] = 0,
[n__o] = 4,
[n__i] = 0,
[n__e] = 0,
[n__a] = 2,
[isPal](x0) = 4x0,
[n__isPal](x0) = 4x0,
[isNePal](x0) = x0,
[n__isNeList](x0) = x0,
[isQid](x0) = x0,
[n__isList](x0) = x0,
[n____](x0, x1) = 4x0 + x1 + 3,
[n__nil] = 0,
[isNeList](x0) = x0,
[isList](x0) = x0,
[activate](x0) = x0,
[and](x0, x1) = 2x0 + x1 + 1,
[tt] = 0,
[nil] = 0,
[__](x0, x1) = 4x0 + x1 + 3
orientation:
__(__(X,Y),Z) = 16X + 4Y + Z + 15 >= 4X + 4Y + Z + 6 = __(X,__(Y,Z))
__(X,nil()) = 4X + 3 >= X = X
__(nil(),X) = X + 3 >= X = X
and(tt(),X) = X + 1 >= X = activate(X)
isList(V) = V >= V = isNeList(activate(V))
isList(n__nil()) = 0 >= 0 = tt()
isList(n____(V1,V2)) = 4V1 + V2 + 3 >= 2V1 + V2 + 1 = and(isList(activate(V1)),n__isList(activate(V2)))
isNeList(V) = V >= V = isQid(activate(V))
isNeList(n____(V1,V2)) = 4V1 + V2 + 3 >= 2V1 + V2 + 1 = and(isList(activate(V1)),n__isNeList(activate(V2)))
isNeList(n____(V1,V2)) = 4V1 + V2 + 3 >= 2V1 + V2 + 1 = and(isNeList(activate(V1)),n__isList(activate(V2)))
isNePal(V) = V >= V = isQid(activate(V))
isNePal(n____(I,__(P,I))) = 5I + 4P + 6 >= 2I + 4P + 1 = and(isQid(activate(I)),n__isPal(activate(P)))
isPal(V) = 4V >= V = isNePal(activate(V))
isPal(n__nil()) = 0 >= 0 = tt()
isQid(n__a()) = 2 >= 0 = tt()
isQid(n__e()) = 0 >= 0 = tt()
isQid(n__i()) = 0 >= 0 = tt()
isQid(n__o()) = 4 >= 0 = tt()
isQid(n__u()) = 0 >= 0 = tt()
nil() = 0 >= 0 = n__nil()
__(X1,X2) = 4X1 + X2 + 3 >= 4X1 + X2 + 3 = n____(X1,X2)
isList(X) = X >= X = n__isList(X)
isNeList(X) = X >= X = n__isNeList(X)
isPal(X) = 4X >= 4X = n__isPal(X)
a() = 2 >= 2 = n__a()
e() = 0 >= 0 = n__e()
i() = 0 >= 0 = n__i()
o() = 4 >= 4 = n__o()
u() = 0 >= 0 = n__u()
activate(n__nil()) = 0 >= 0 = nil()
activate(n____(X1,X2)) = 4X1 + X2 + 3 >= 4X1 + X2 + 3 = __(X1,X2)
activate(n__isList(X)) = X >= X = isList(X)
activate(n__isNeList(X)) = X >= X = isNeList(X)
activate(n__isPal(X)) = 4X >= 4X = isPal(X)
activate(n__a()) = 2 >= 2 = a()
activate(n__e()) = 0 >= 0 = e()
activate(n__i()) = 0 >= 0 = i()
activate(n__o()) = 4 >= 4 = o()
activate(n__u()) = 0 >= 0 = u()
activate(X) = X >= X = X
problem:
isList(V) -> isNeList(activate(V))
isList(n__nil()) -> tt()
isNeList(V) -> isQid(activate(V))
isNePal(V) -> isQid(activate(V))
isPal(V) -> isNePal(activate(V))
isPal(n__nil()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> 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
Matrix Interpretation Processor: dim=1
interpretation:
[u] = 7,
[o] = 2,
[i] = 7,
[e] = 7,
[a] = 2,
[n__u] = 7,
[n__o] = 0,
[n__i] = 7,
[n__e] = 7,
[n__a] = 2,
[isPal](x0) = x0 + 6,
[n__isPal](x0) = x0 + 6,
[isNePal](x0) = x0 + 3,
[n__isNeList](x0) = x0,
[isQid](x0) = x0,
[n__isList](x0) = x0 + 5,
[n____](x0, x1) = x0 + 2x1,
[n__nil] = 1,
[isNeList](x0) = x0 + 3,
[isList](x0) = x0 + 6,
[activate](x0) = x0 + 3,
[tt] = 7,
[nil] = 2,
[__](x0, x1) = x0 + 2x1
orientation:
isList(V) = V + 6 >= V + 6 = isNeList(activate(V))
isList(n__nil()) = 7 >= 7 = tt()
isNeList(V) = V + 3 >= V + 3 = isQid(activate(V))
isNePal(V) = V + 3 >= V + 3 = isQid(activate(V))
isPal(V) = V + 6 >= V + 6 = isNePal(activate(V))
isPal(n__nil()) = 7 >= 7 = tt()
isQid(n__e()) = 7 >= 7 = tt()
isQid(n__i()) = 7 >= 7 = tt()
isQid(n__u()) = 7 >= 7 = tt()
nil() = 2 >= 1 = n__nil()
__(X1,X2) = X1 + 2X2 >= X1 + 2X2 = n____(X1,X2)
isList(X) = X + 6 >= X + 5 = n__isList(X)
isNeList(X) = X + 3 >= X = n__isNeList(X)
isPal(X) = X + 6 >= X + 6 = n__isPal(X)
a() = 2 >= 2 = n__a()
e() = 7 >= 7 = n__e()
i() = 7 >= 7 = n__i()
o() = 2 >= 0 = n__o()
u() = 7 >= 7 = n__u()
activate(n__nil()) = 4 >= 2 = nil()
activate(n____(X1,X2)) = X1 + 2X2 + 3 >= X1 + 2X2 = __(X1,X2)
activate(n__isList(X)) = X + 8 >= X + 6 = isList(X)
activate(n__isNeList(X)) = X + 3 >= X + 3 = isNeList(X)
activate(n__isPal(X)) = X + 9 >= X + 6 = isPal(X)
activate(n__a()) = 5 >= 2 = a()
activate(n__e()) = 10 >= 7 = e()
activate(n__i()) = 10 >= 7 = i()
activate(n__o()) = 3 >= 2 = o()
activate(n__u()) = 10 >= 7 = u()
activate(X) = X + 3 >= X = X
problem:
isList(V) -> isNeList(activate(V))
isList(n__nil()) -> tt()
isNeList(V) -> isQid(activate(V))
isNePal(V) -> isQid(activate(V))
isPal(V) -> isNePal(activate(V))
isPal(n__nil()) -> tt()
isQid(n__e()) -> tt()
isQid(n__i()) -> tt()
isQid(n__u()) -> tt()
__(X1,X2) -> n____(X1,X2)
isPal(X) -> n__isPal(X)
a() -> n__a()
e() -> n__e()
i() -> n__i()
u() -> n__u()
activate(n__isNeList(X)) -> isNeList(X)
Matrix Interpretation Processor: dim=1
interpretation:
[u] = 0,
[i] = 0,
[e] = 3,
[a] = 4,
[n__u] = 0,
[n__i] = 0,
[n__e] = 3,
[n__a] = 0,
[isPal](x0) = 5x0 + 4,
[n__isPal](x0) = x0 + 4,
[isNePal](x0) = 3x0 + 4,
[n__isNeList](x0) = 4x0 + 1,
[isQid](x0) = 3x0,
[n____](x0, x1) = x0 + x1,
[n__nil] = 5,
[isNeList](x0) = 4x0 + 1,
[isList](x0) = 4x0 + 2,
[activate](x0) = x0,
[tt] = 0,
[__](x0, x1) = x0 + x1
orientation:
isList(V) = 4V + 2 >= 4V + 1 = isNeList(activate(V))
isList(n__nil()) = 22 >= 0 = tt()
isNeList(V) = 4V + 1 >= 3V = isQid(activate(V))
isNePal(V) = 3V + 4 >= 3V = isQid(activate(V))
isPal(V) = 5V + 4 >= 3V + 4 = isNePal(activate(V))
isPal(n__nil()) = 29 >= 0 = tt()
isQid(n__e()) = 9 >= 0 = tt()
isQid(n__i()) = 0 >= 0 = tt()
isQid(n__u()) = 0 >= 0 = tt()
__(X1,X2) = X1 + X2 >= X1 + X2 = n____(X1,X2)
isPal(X) = 5X + 4 >= X + 4 = n__isPal(X)
a() = 4 >= 0 = n__a()
e() = 3 >= 3 = n__e()
i() = 0 >= 0 = n__i()
u() = 0 >= 0 = n__u()
activate(n__isNeList(X)) = 4X + 1 >= 4X + 1 = isNeList(X)
problem:
isPal(V) -> isNePal(activate(V))
isQid(n__i()) -> tt()
isQid(n__u()) -> tt()
__(X1,X2) -> n____(X1,X2)
isPal(X) -> n__isPal(X)
e() -> n__e()
i() -> n__i()
u() -> n__u()
activate(n__isNeList(X)) -> isNeList(X)
Matrix Interpretation Processor: dim=3
interpretation:
[1]
[u] = [0]
[0],
[1]
[i] = [0]
[0],
[1]
[e] = [0]
[0],
[0]
[n__u] = [0]
[0],
[0]
[n__i] = [0]
[0],
[0]
[n__e] = [0]
[0],
[1 0 0] [1]
[isPal](x0) = [0 0 0]x0 + [0]
[0 0 0] [0],
[1 0 0]
[n__isPal](x0) = [0 0 0]x0
[0 0 0] ,
[1 0 0]
[isNePal](x0) = [0 0 0]x0
[0 0 0] ,
[1 0 0] [1]
[n__isNeList](x0) = [0 0 0]x0 + [0]
[0 0 0] [0],
[1 0 0] [1]
[isQid](x0) = [0 0 0]x0 + [0]
[0 0 0] [0],
[1 0 0] [1 0 0]
[n____](x0, x1) = [0 0 0]x0 + [0 0 0]x1
[0 0 0] [0 0 0] ,
[1 0 0]
[isNeList](x0) = [0 0 0]x0
[0 0 0] ,
[1 0 0]
[activate](x0) = [0 0 0]x0
[0 0 0] ,
[0]
[tt] = [0]
[0],
[1 0 0] [1 0 0] [1]
[__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
[0 0 0] [0 0 0] [0]
orientation:
[1 0 0] [1] [1 0 0]
isPal(V) = [0 0 0]V + [0] >= [0 0 0]V = isNePal(activate(V))
[0 0 0] [0] [0 0 0]
[1] [0]
isQid(n__i()) = [0] >= [0] = tt()
[0] [0]
[1] [0]
isQid(n__u()) = [0] >= [0] = tt()
[0] [0]
[1 0 0] [1 0 0] [1] [1 0 0] [1 0 0]
__(X1,X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = n____(X1,X2)
[0 0 0] [0 0 0] [0] [0 0 0] [0 0 0]
[1 0 0] [1] [1 0 0]
isPal(X) = [0 0 0]X + [0] >= [0 0 0]X = n__isPal(X)
[0 0 0] [0] [0 0 0]
[1] [0]
e() = [0] >= [0] = n__e()
[0] [0]
[1] [0]
i() = [0] >= [0] = n__i()
[0] [0]
[1] [0]
u() = [0] >= [0] = n__u()
[0] [0]
[1 0 0] [1] [1 0 0]
activate(n__isNeList(X)) = [0 0 0]X + [0] >= [0 0 0]X = isNeList(X)
[0 0 0] [0] [0 0 0]
problem:
Qed