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,n____(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)) -> __(activate(X1),activate(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: [n__o] = 0, [activate](x0) = x0, [n__a] = 0, [n____](x0, x1) = 4x0 + x1, [nil] = 0, [and](x0, x1) = 4x0 + x1, [n__e] = 0, [e] = 0, [n__u] = 0, [n__i] = 2, [i] = 2, [isList](x0) = 4x0, [isQid](x0) = 2x0, [__](x0, x1) = 4x0 + x1, [n__nil] = 0, [a] = 0, [isPal](x0) = 3x0 + 3, [isNePal](x0) = 2x0 + 3, [o] = 0, [u] = 0, [n__isNeList](x0) = 4x0, [n__isList](x0) = 4x0, [n__isPal](x0) = 3x0 + 3, [isNeList](x0) = 4x0, [tt] = 0 orientation: __(__(X,Y),Z) = 16X + 4Y + Z >= 4X + 4Y + Z = __(X,__(Y,Z)) __(X,nil()) = 4X >= X = X __(nil(),X) = X >= X = X and(tt(),X) = X >= X = activate(X) isList(V) = 4V >= 4V = isNeList(activate(V)) isList(n__nil()) = 0 >= 0 = tt() isList(n____(V1,V2)) = 16V1 + 4V2 >= 16V1 + 4V2 = and(isList(activate(V1)),n__isList(activate(V2))) isNeList(V) = 4V >= 2V = isQid(activate(V)) isNeList(n____(V1,V2)) = 16V1 + 4V2 >= 16V1 + 4V2 = and(isList(activate(V1)),n__isNeList(activate(V2))) isNeList(n____(V1,V2)) = 16V1 + 4V2 >= 16V1 + 4V2 = and(isNeList(activate(V1)),n__isList(activate(V2))) isNePal(V) = 2V + 3 >= 2V = isQid(activate(V)) isNePal(n____(I,n____(P,I))) = 10I + 8P + 3 >= 8I + 3P + 3 = and(isQid(activate(I)),n__isPal(activate(P))) isPal(V) = 3V + 3 >= 2V + 3 = isNePal(activate(V)) isPal(n__nil()) = 3 >= 0 = tt() isQid(n__a()) = 0 >= 0 = tt() isQid(n__e()) = 0 >= 0 = tt() isQid(n__i()) = 4 >= 0 = tt() isQid(n__o()) = 0 >= 0 = tt() isQid(n__u()) = 0 >= 0 = tt() nil() = 0 >= 0 = n__nil() __(X1,X2) = 4X1 + X2 >= 4X1 + X2 = n____(X1,X2) isList(X) = 4X >= 4X = n__isList(X) isNeList(X) = 4X >= 4X = n__isNeList(X) isPal(X) = 3X + 3 >= 3X + 3 = n__isPal(X) a() = 0 >= 0 = n__a() e() = 0 >= 0 = n__e() i() = 2 >= 2 = n__i() o() = 0 >= 0 = n__o() u() = 0 >= 0 = n__u() activate(n__nil()) = 0 >= 0 = nil() activate(n____(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(activate(X1),activate(X2)) activate(n__isList(X)) = 4X >= 4X = isList(X) activate(n__isNeList(X)) = 4X >= 4X = isNeList(X) activate(n__isPal(X)) = 3X + 3 >= 3X + 3 = isPal(X) activate(n__a()) = 0 >= 0 = a() activate(n__e()) = 0 >= 0 = e() activate(n__i()) = 2 >= 2 = i() activate(n__o()) = 0 >= 0 = o() activate(n__u()) = 0 >= 0 = u() activate(X) = X >= X = X 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(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P))) isPal(V) -> isNePal(activate(V)) isQid(n__a()) -> tt() isQid(n__e()) -> 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)) -> __(activate(X1),activate(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: [n__o] = 3, [activate](x0) = x0, [n__a] = 0, [n____](x0, x1) = 4x0 + x1 + 3, [nil] = 6, [and](x0, x1) = 2x0 + x1 + 1, [n__e] = 0, [e] = 0, [n__u] = 0, [n__i] = 0, [i] = 0, [isList](x0) = 4x0 + 5, [isQid](x0) = 4x0 + 5, [__](x0, x1) = 4x0 + x1 + 3, [n__nil] = 6, [a] = 0, [isPal](x0) = 4x0 + 4, [isNePal](x0) = 2x0 + 3, [o] = 3, [u] = 0, [n__isNeList](x0) = 4x0 + 5, [n__isList](x0) = 4x0 + 5, [n__isPal](x0) = 4x0 + 4, [isNeList](x0) = 4x0 + 5, [tt] = 2 orientation: __(__(X,Y),Z) = 16X + 4Y + Z + 15 >= 4X + 4Y + Z + 6 = __(X,__(Y,Z)) __(X,nil()) = 4X + 9 >= X = X __(nil(),X) = X + 27 >= X = X and(tt(),X) = X + 5 >= X = activate(X) isList(V) = 4V + 5 >= 4V + 5 = isNeList(activate(V)) isList(n__nil()) = 29 >= 2 = tt() isList(n____(V1,V2)) = 16V1 + 4V2 + 17 >= 8V1 + 4V2 + 16 = and(isList(activate(V1)),n__isList(activate(V2))) isNeList(V) = 4V + 5 >= 4V + 5 = isQid(activate(V)) isNeList(n____(V1,V2)) = 16V1 + 4V2 + 17 >= 8V1 + 4V2 + 16 = and(isList(activate(V1)),n__isNeList(activate(V2))) isNeList(n____(V1,V2)) = 16V1 + 4V2 + 17 >= 8V1 + 4V2 + 16 = and(isNeList(activate(V1)),n__isList(activate(V2))) isNePal(n____(I,n____(P,I))) = 10I + 8P + 15 >= 8I + 4P + 15 = and(isQid(activate(I)),n__isPal(activate(P))) isPal(V) = 4V + 4 >= 2V + 3 = isNePal(activate(V)) isQid(n__a()) = 5 >= 2 = tt() isQid(n__e()) = 5 >= 2 = tt() isQid(n__o()) = 17 >= 2 = tt() isQid(n__u()) = 5 >= 2 = tt() nil() = 6 >= 6 = n__nil() __(X1,X2) = 4X1 + X2 + 3 >= 4X1 + X2 + 3 = n____(X1,X2) isList(X) = 4X + 5 >= 4X + 5 = n__isList(X) isNeList(X) = 4X + 5 >= 4X + 5 = n__isNeList(X) isPal(X) = 4X + 4 >= 4X + 4 = n__isPal(X) a() = 0 >= 0 = n__a() e() = 0 >= 0 = n__e() i() = 0 >= 0 = n__i() o() = 3 >= 3 = n__o() u() = 0 >= 0 = n__u() activate(n__nil()) = 6 >= 6 = nil() activate(n____(X1,X2)) = 4X1 + X2 + 3 >= 4X1 + X2 + 3 = __(activate(X1),activate(X2)) activate(n__isList(X)) = 4X + 5 >= 4X + 5 = isList(X) activate(n__isNeList(X)) = 4X + 5 >= 4X + 5 = isNeList(X) activate(n__isPal(X)) = 4X + 4 >= 4X + 4 = isPal(X) activate(n__a()) = 0 >= 0 = a() activate(n__e()) = 0 >= 0 = e() activate(n__i()) = 0 >= 0 = i() activate(n__o()) = 3 >= 3 = o() activate(n__u()) = 0 >= 0 = u() activate(X) = X >= X = X problem: isList(V) -> isNeList(activate(V)) isNeList(V) -> isQid(activate(V)) isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P))) 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)) -> __(activate(X1),activate(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: [n__o] = 0, [activate](x0) = 2x0, [n__a] = 0, [n____](x0, x1) = 2x0 + 2x1 + 1, [nil] = 4, [and](x0, x1) = 4x0 + 4x1 + 2, [n__e] = 1, [e] = 1, [n__u] = 0, [n__i] = 1, [i] = 1, [isList](x0) = 4x0 + 5, [isQid](x0) = x0, [__](x0, x1) = 2x0 + 2x1 + 2, [n__nil] = 3, [a] = 0, [isPal](x0) = 4x0 + 6, [isNePal](x0) = 4x0 + 6, [o] = 0, [u] = 0, [n__isNeList](x0) = x0 + 5, [n__isList](x0) = 2x0 + 3, [n__isPal](x0) = 2x0 + 4, [isNeList](x0) = 2x0 + 5 orientation: isList(V) = 4V + 5 >= 4V + 5 = isNeList(activate(V)) isNeList(V) = 2V + 5 >= 2V = isQid(activate(V)) isNePal(n____(I,n____(P,I))) = 24I + 16P + 18 >= 8I + 16P + 18 = and(isQid(activate(I)),n__isPal(activate(P))) nil() = 4 >= 3 = n__nil() __(X1,X2) = 2X1 + 2X2 + 2 >= 2X1 + 2X2 + 1 = n____(X1,X2) isList(X) = 4X + 5 >= 2X + 3 = n__isList(X) isNeList(X) = 2X + 5 >= X + 5 = n__isNeList(X) isPal(X) = 4X + 6 >= 2X + 4 = n__isPal(X) a() = 0 >= 0 = n__a() e() = 1 >= 1 = n__e() i() = 1 >= 1 = n__i() o() = 0 >= 0 = n__o() u() = 0 >= 0 = n__u() activate(n__nil()) = 6 >= 4 = nil() activate(n____(X1,X2)) = 4X1 + 4X2 + 2 >= 4X1 + 4X2 + 2 = __(activate(X1),activate(X2)) activate(n__isList(X)) = 4X + 6 >= 4X + 5 = isList(X) activate(n__isNeList(X)) = 2X + 10 >= 2X + 5 = isNeList(X) activate(n__isPal(X)) = 4X + 8 >= 4X + 6 = isPal(X) activate(n__a()) = 0 >= 0 = a() activate(n__e()) = 2 >= 1 = e() activate(n__i()) = 2 >= 1 = i() activate(n__o()) = 0 >= 0 = o() activate(n__u()) = 0 >= 0 = u() activate(X) = 2X >= X = X problem: isList(V) -> isNeList(activate(V)) isNePal(n____(I,n____(P,I))) -> and(isQid(activate(I)),n__isPal(activate(P))) isNeList(X) -> n__isNeList(X) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n____(X1,X2)) -> __(activate(X1),activate(X2)) activate(n__a()) -> a() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Matrix Interpretation Processor: dim=1 interpretation: [n__o] = 0, [activate](x0) = x0, [n__a] = 4, [n____](x0, x1) = 2x0 + 3x1 + 3, [and](x0, x1) = x0 + x1, [n__e] = 0, [e] = 0, [n__u] = 0, [n__i] = 0, [i] = 0, [isList](x0) = 5x0, [isQid](x0) = 2x0 + 4, [__](x0, x1) = 2x0 + 2x1 + 2, [a] = 4, [isNePal](x0) = x0 + 4, [o] = 0, [u] = 0, [n__isNeList](x0) = 2x0, [n__isPal](x0) = 6x0, [isNeList](x0) = 4x0 orientation: isList(V) = 5V >= 4V = isNeList(activate(V)) isNePal(n____(I,n____(P,I))) = 11I + 6P + 16 >= 2I + 6P + 4 = and(isQid(activate(I)),n__isPal(activate(P))) isNeList(X) = 4X >= 2X = n__isNeList(X) a() = 4 >= 4 = n__a() e() = 0 >= 0 = n__e() i() = 0 >= 0 = n__i() o() = 0 >= 0 = n__o() u() = 0 >= 0 = n__u() activate(n____(X1,X2)) = 2X1 + 3X2 + 3 >= 2X1 + 2X2 + 2 = __(activate(X1),activate(X2)) activate(n__a()) = 4 >= 4 = a() activate(n__o()) = 0 >= 0 = o() activate(n__u()) = 0 >= 0 = u() activate(X) = X >= X = X problem: isList(V) -> isNeList(activate(V)) isNeList(X) -> n__isNeList(X) a() -> n__a() e() -> n__e() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__a()) -> a() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [0] [n__o] = [1] [0], [activate](x0) = x0 , [0] [n__a] = [0] [0], [0] [n__e] = [0] [0], [1] [e] = [1] [0], [0] [n__u] = [0] [1], [0] [n__i] = [0] [0], [0] [i] = [1] [0], [1 0 1] [0] [isList](x0) = [1 0 0]x0 + [0] [0 0 0] [1], [0] [a] = [0] [0], [0] [o] = [1] [0], [0] [u] = [0] [1], [1 0 0] [n__isNeList](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [isNeList](x0) = [0 0 0]x0 [0 0 0] orientation: [1 0 1] [0] [1 0 1] isList(V) = [1 0 0]V + [0] >= [0 0 0]V = isNeList(activate(V)) [0 0 0] [1] [0 0 0] [1 0 1] [1 0 0] isNeList(X) = [0 0 0]X >= [0 0 0]X = n__isNeList(X) [0 0 0] [0 0 0] [0] [0] a() = [0] >= [0] = n__a() [0] [0] [1] [0] e() = [1] >= [0] = n__e() [0] [0] [0] [0] i() = [1] >= [0] = n__i() [0] [0] [0] [0] o() = [1] >= [1] = n__o() [0] [0] [0] [0] u() = [0] >= [0] = n__u() [1] [1] [0] [0] activate(n__a()) = [0] >= [0] = a() [0] [0] [0] [0] activate(n__o()) = [1] >= [1] = o() [0] [0] [0] [0] activate(n__u()) = [0] >= [0] = u() [1] [1] activate(X) = X >= X = X problem: isList(V) -> isNeList(activate(V)) isNeList(X) -> n__isNeList(X) a() -> n__a() i() -> n__i() o() -> n__o() u() -> n__u() activate(n__a()) -> a() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [0] [n__o] = [0] [0], [activate](x0) = x0 , [1] [n__a] = [0] [0], [0] [n__u] = [0] [0], [0] [n__i] = [0] [0], [1] [i] = [1] [0], [1 0 1] [isList](x0) = [1 0 0]x0 [0 0 0] , [1] [a] = [0] [0], [0] [o] = [0] [0], [0] [u] = [0] [0], [1 0 0] [n__isNeList](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [isNeList](x0) = [0 0 0]x0 [0 0 0] orientation: [1 0 1] [1 0 1] isList(V) = [1 0 0]V >= [0 0 0]V = isNeList(activate(V)) [0 0 0] [0 0 0] [1 0 1] [1 0 0] isNeList(X) = [0 0 0]X >= [0 0 0]X = n__isNeList(X) [0 0 0] [0 0 0] [1] [1] a() = [0] >= [0] = n__a() [0] [0] [1] [0] i() = [1] >= [0] = n__i() [0] [0] [0] [0] o() = [0] >= [0] = n__o() [0] [0] [0] [0] u() = [0] >= [0] = n__u() [0] [0] [1] [1] activate(n__a()) = [0] >= [0] = a() [0] [0] [0] [0] activate(n__o()) = [0] >= [0] = o() [0] [0] [0] [0] activate(n__u()) = [0] >= [0] = u() [0] [0] activate(X) = X >= X = X problem: isList(V) -> isNeList(activate(V)) isNeList(X) -> n__isNeList(X) a() -> n__a() o() -> n__o() u() -> n__u() activate(n__a()) -> a() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [0] [n__o] = [0] [0], [1 0 1] [0] [activate](x0) = [0 1 0]x0 + [1] [0 0 1] [0], [0] [n__a] = [0] [0], [0] [n__u] = [0] [1], [1 1 1] [isList](x0) = [0 0 0]x0 [0 1 0] , [0] [a] = [1] [0], [0] [o] = [1] [0], [1] [u] = [0] [1], [1 0 0] [n__isNeList](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [isNeList](x0) = [0 0 0]x0 [0 0 0] orientation: [1 1 1] [1 0 1] isList(V) = [0 0 0]V >= [0 0 0]V = isNeList(activate(V)) [0 1 0] [0 0 0] [1 0 0] [1 0 0] isNeList(X) = [0 0 0]X >= [0 0 0]X = n__isNeList(X) [0 0 0] [0 0 0] [0] [0] a() = [1] >= [0] = n__a() [0] [0] [0] [0] o() = [1] >= [0] = n__o() [0] [0] [1] [0] u() = [0] >= [0] = n__u() [1] [1] [0] [0] activate(n__a()) = [1] >= [1] = a() [0] [0] [0] [0] activate(n__o()) = [1] >= [1] = o() [0] [0] [1] [1] activate(n__u()) = [1] >= [0] = u() [1] [1] [1 0 1] [0] activate(X) = [0 1 0]X + [1] >= X = X [0 0 1] [0] problem: isList(V) -> isNeList(activate(V)) isNeList(X) -> n__isNeList(X) a() -> n__a() o() -> n__o() activate(n__a()) -> a() activate(n__o()) -> o() activate(n__u()) -> u() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [0] [n__o] = [0] [1], [1 0 1] [activate](x0) = [0 1 1]x0 [1 0 1] , [0] [n__a] = [0] [0], [0] [n__u] = [1] [0], [1 0 1] [0] [isList](x0) = [1 1 1]x0 + [1] [1 1 1] [0], [0] [a] = [0] [0], [0] [o] = [0] [1], [0] [u] = [1] [0], [1 0 0] [n__isNeList](x0) = [0 0 0]x0 [0 1 0] , [1 0 0] [0] [isNeList](x0) = [0 0 1]x0 + [1] [0 1 0] [0] orientation: [1 0 1] [0] [1 0 1] [0] isList(V) = [1 1 1]V + [1] >= [1 0 1]V + [1] = isNeList(activate(V)) [1 1 1] [0] [0 1 1] [0] [1 0 0] [0] [1 0 0] isNeList(X) = [0 0 1]X + [1] >= [0 0 0]X = n__isNeList(X) [0 1 0] [0] [0 1 0] [0] [0] a() = [0] >= [0] = n__a() [0] [0] [0] [0] o() = [0] >= [0] = n__o() [1] [1] [0] [0] activate(n__a()) = [0] >= [0] = a() [0] [0] [1] [0] activate(n__o()) = [1] >= [0] = o() [1] [1] [0] [0] activate(n__u()) = [1] >= [1] = u() [0] [0] [1 0 1] activate(X) = [0 1 1]X >= X = X [1 0 1] problem: isList(V) -> isNeList(activate(V)) isNeList(X) -> n__isNeList(X) a() -> n__a() o() -> n__o() activate(n__a()) -> a() activate(n__u()) -> u() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [0] [n__o] = [0] [0], [0] [activate](x0) = x0 + [1] [0], [0] [n__a] = [0] [0], [1] [n__u] = [0] [0], [1 0 1] [isList](x0) = [1 0 0]x0 [0 0 0] , [0] [a] = [1] [0], [0] [o] = [0] [0], [0] [u] = [1] [0], [1 0 0] [n__isNeList](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [isNeList](x0) = [0 0 0]x0 [0 0 0] orientation: [1 0 1] [1 0 1] isList(V) = [1 0 0]V >= [0 0 0]V = isNeList(activate(V)) [0 0 0] [0 0 0] [1 0 1] [1 0 0] isNeList(X) = [0 0 0]X >= [0 0 0]X = n__isNeList(X) [0 0 0] [0 0 0] [0] [0] a() = [1] >= [0] = n__a() [0] [0] [0] [0] o() = [0] >= [0] = n__o() [0] [0] [0] [0] activate(n__a()) = [1] >= [1] = a() [0] [0] [1] [0] activate(n__u()) = [1] >= [1] = u() [0] [0] [0] activate(X) = X + [1] >= X = X [0] problem: isList(V) -> isNeList(activate(V)) isNeList(X) -> n__isNeList(X) a() -> n__a() o() -> n__o() activate(n__a()) -> a() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [0] [n__o] = [0] [0], [0] [activate](x0) = x0 + [1] [0], [0] [n__a] = [0] [0], [1 0 0] [isList](x0) = [0 0 0]x0 [0 0 0] , [0] [a] = [1] [0], [1] [o] = [0] [0], [1 0 0] [n__isNeList](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [isNeList](x0) = [0 0 0]x0 [0 0 0] orientation: [1 0 0] [1 0 0] isList(V) = [0 0 0]V >= [0 0 0]V = isNeList(activate(V)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] isNeList(X) = [0 0 0]X >= [0 0 0]X = n__isNeList(X) [0 0 0] [0 0 0] [0] [0] a() = [1] >= [0] = n__a() [0] [0] [1] [0] o() = [0] >= [0] = n__o() [0] [0] [0] [0] activate(n__a()) = [1] >= [1] = a() [0] [0] [0] activate(X) = X + [1] >= X = X [0] problem: isList(V) -> isNeList(activate(V)) isNeList(X) -> n__isNeList(X) a() -> n__a() activate(n__a()) -> a() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [0] [activate](x0) = [0 1 0]x0 + [1] [0 0 1] [0], [0] [n__a] = [0] [1], [1 0 1] [isList](x0) = [0 0 0]x0 [1 0 0] , [0] [a] = [1] [1], [1 0 0] [n__isNeList](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [isNeList](x0) = [0 0 0]x0 [0 0 0] orientation: [1 0 1] [1 0 1] isList(V) = [0 0 0]V >= [0 0 0]V = isNeList(activate(V)) [1 0 0] [0 0 0] [1 0 0] [1 0 0] isNeList(X) = [0 0 0]X >= [0 0 0]X = n__isNeList(X) [0 0 0] [0 0 0] [0] [0] a() = [1] >= [0] = n__a() [1] [1] [1] [0] activate(n__a()) = [1] >= [1] = a() [1] [1] [1 0 1] [0] activate(X) = [0 1 0]X + [1] >= X = X [0 0 1] [0] problem: isList(V) -> isNeList(activate(V)) isNeList(X) -> n__isNeList(X) a() -> n__a() activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [activate](x0) = x0 , [0] [n__a] = [0] [0], [1 0 0] [0] [isList](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1] [a] = [0] [0], [1 0 0] [n__isNeList](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [isNeList](x0) = [0 0 0]x0 + [1] [0 0 0] [0] orientation: [1 0 0] [0] [1 0 0] [0] isList(V) = [0 0 0]V + [1] >= [0 0 0]V + [1] = isNeList(activate(V)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] isNeList(X) = [0 0 0]X + [1] >= [0 0 0]X = n__isNeList(X) [0 0 0] [0] [0 0 0] [1] [0] a() = [0] >= [0] = n__a() [0] [0] activate(X) = X >= X = X problem: isList(V) -> isNeList(activate(V)) isNeList(X) -> n__isNeList(X) activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [activate](x0) = x0 , [1 0 0] [1] [isList](x0) = [1 0 0]x0 + [1] [0 0 0] [0], [1 0 0] [n__isNeList](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [isNeList](x0) = [0 0 0]x0 + [1] [0 0 0] [0] orientation: [1 0 0] [1] [1 0 0] [0] isList(V) = [1 0 0]V + [1] >= [0 0 0]V + [1] = isNeList(activate(V)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] isNeList(X) = [0 0 0]X + [1] >= [0 0 0]X = n__isNeList(X) [0 0 0] [0] [0 0 0] activate(X) = X >= X = X problem: isNeList(X) -> n__isNeList(X) activate(X) -> X Matrix Interpretation Processor: dim=3 interpretation: [1] [activate](x0) = x0 + [0] [0], [1 0 0] [n__isNeList](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [isNeList](x0) = [0 0 0]x0 [0 0 0] orientation: [1 0 0] [1 0 0] isNeList(X) = [0 0 0]X >= [0 0 0]X = n__isNeList(X) [0 0 0] [0 0 0] [1] activate(X) = X + [0] >= X = X [0] problem: isNeList(X) -> n__isNeList(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [n__isNeList](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1] [isNeList](x0) = [0 0 0]x0 + [0] [0 0 1] [0] orientation: [1 0 0] [1] [1 0 0] isNeList(X) = [0 0 0]X + [0] >= [0 0 0]X = n__isNeList(X) [0 0 1] [0] [0 0 0] problem: Qed