YES Problem: 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) Proof: Matrix Interpretation Processor: dim=1 interpretation: [isNePal](x0) = x0 + 2, [and](x0, x1) = x0 + 4x1, [tt] = 1, [nil] = 1, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = 4x0 + x1 + 6 orientation: active(__(__(X,Y),Z)) = 16X + 4Y + Z + 30 >= 4X + 4Y + Z + 12 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 4X + 7 >= X = mark(X) active(__(nil(),X)) = X + 10 >= X = mark(X) active(and(tt(),X)) = 4X + 1 >= X = mark(X) active(isNePal(__(I,__(P,I)))) = 5I + 4P + 14 >= 1 = mark(tt()) mark(__(X1,X2)) = 4X1 + X2 + 6 >= 4X1 + X2 + 6 = active(__(mark(X1),mark(X2))) mark(nil()) = 1 >= 1 = active(nil()) mark(and(X1,X2)) = X1 + 4X2 >= X1 + 4X2 = active(and(mark(X1),X2)) mark(tt()) = 1 >= 1 = active(tt()) mark(isNePal(X)) = X + 2 >= X + 2 = active(isNePal(mark(X))) __(mark(X1),X2) = 4X1 + X2 + 6 >= 4X1 + X2 + 6 = __(X1,X2) __(X1,mark(X2)) = 4X1 + X2 + 6 >= 4X1 + X2 + 6 = __(X1,X2) __(active(X1),X2) = 4X1 + X2 + 6 >= 4X1 + X2 + 6 = __(X1,X2) __(X1,active(X2)) = 4X1 + X2 + 6 >= 4X1 + X2 + 6 = __(X1,X2) and(mark(X1),X2) = X1 + 4X2 >= X1 + 4X2 = and(X1,X2) and(X1,mark(X2)) = X1 + 4X2 >= X1 + 4X2 = and(X1,X2) and(active(X1),X2) = X1 + 4X2 >= X1 + 4X2 = and(X1,X2) and(X1,active(X2)) = X1 + 4X2 >= X1 + 4X2 = and(X1,X2) isNePal(mark(X)) = X + 2 >= X + 2 = isNePal(X) isNePal(active(X)) = X + 2 >= X + 2 = isNePal(X) problem: 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) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1] [isNePal](x0) = [0 1 0]x0 + [0] [0 0 0] [0], [1 0 0] [1 0 0] [and](x0, x1) = [0 1 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [tt] = [0] [0], [0] [nil] = [1] [0], [1 1 0] [0] [mark](x0) = [0 1 0]x0 + [0] [0 0 1] [1], [1 0 1] [active](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [1 0 1] [0] [__](x0, x1) = [0 1 0]x0 + [0 1 0]x1 + [1] [0 0 0] [0 0 0] [0] orientation: [1 1 0] [1 1 1] [1] [1 1 0] [1 1 1] [1] mark(__(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [1] = active(__(mark(X1),mark(X2))) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0] [1] [0] mark(nil()) = [1] >= [1] = active(nil()) [1] [0] [1 1 0] [1 0 0] [0] [1 1 0] [1 0 0] mark(and(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 + [0] >= [0 1 0]X1 + [0 0 0]X2 = active(and(mark(X1),X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0] [0] mark(tt()) = [0] >= [0] = active(tt()) [1] [0] [1 1 0] [1] [1 1 0] [1] mark(isNePal(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = active(isNePal(mark(X))) [0 0 0] [1] [0 0 0] [0] [1 1 0] [1 0 1] [0] [1 0 0] [1 0 1] [0] __(mark(X1),X2) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [1] = __(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 1 1] [1] [1 0 0] [1 0 1] [0] __(X1,mark(X2)) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [1] = __(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 1] [0] [1 0 0] [1 0 1] [0] __(active(X1),X2) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [1] = __(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 1] [0] [1 0 0] [1 0 1] [0] __(X1,active(X2)) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [1] = __(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 0 0] [1 0 0] [1 0 0] and(mark(X1),X2) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 1 0] [1 0 0] [1 0 0] and(X1,mark(X2)) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 0] [1 0 0] [1 0 0] and(active(X1),X2) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 1] [1 0 0] [1 0 0] and(X1,active(X2)) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1] [1 0 0] [1] isNePal(mark(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = isNePal(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1] [1 0 0] [1] isNePal(active(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = isNePal(X) [0 0 0] [0] [0 0 0] [0] problem: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) 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) __(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) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [isNePal](x0) = [0 0 0]x0 + [1] [0 1 1] [0], [1 0 0] [1 0 0] [1] [and](x0, x1) = [0 0 0]x0 + [0 1 0]x1 + [0] [0 1 1] [0 0 0] [0], [0] [tt] = [0] [0], [1 1 1] [mark](x0) = [0 1 1]x0 [0 0 0] , [1 1 0] [active](x0) = [0 1 1]x0 [0 0 0] , [1 0 0] [1 0 0] [0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 1 1] [0 1 1] [1] orientation: [1 1 1] [1 1 1] [1] [1 1 1] [1 1 1] [0] mark(__(X1,X2)) = [0 1 1]X1 + [0 1 1]X2 + [1] >= [0 1 1]X1 + [0 1 1]X2 + [1] = active(__(mark(X1),mark(X2))) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 1] [1 1 0] [1] [1 1 1] [1 1 0] [1] mark(and(X1,X2)) = [0 1 1]X1 + [0 1 0]X2 + [0] >= [0 1 1]X1 + [0 1 0]X2 + [0] = active(and(mark(X1),X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [0] [0] mark(tt()) = [0] >= [0] = active(tt()) [0] [0] [1 1 1] [1] [1 1 1] [1] mark(isNePal(X)) = [0 1 1]X + [1] >= [0 1 1]X + [1] = active(isNePal(mark(X))) [0 0 0] [0] [0 0 0] [0] [1 1 1] [1 0 0] [0] [1 0 0] [1 0 0] [0] __(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = __(X1,X2) [0 1 1] [0 1 1] [1] [0 1 1] [0 1 1] [1] [1 1 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] __(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = __(X1,X2) [0 1 1] [0 1 1] [1] [0 1 1] [0 1 1] [1] [1 0 0] [1 1 0] [0] [1 0 0] [1 0 0] [0] __(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = __(X1,X2) [0 1 1] [0 1 1] [1] [0 1 1] [0 1 1] [1] [1 1 1] [1 0 0] [1] [1 0 0] [1 0 0] [1] and(mark(X1),X2) = [0 0 0]X1 + [0 1 0]X2 + [0] >= [0 0 0]X1 + [0 1 0]X2 + [0] = and(X1,X2) [0 1 1] [0 0 0] [0] [0 1 1] [0 0 0] [0] [1 0 0] [1 1 1] [1] [1 0 0] [1 0 0] [1] and(X1,mark(X2)) = [0 0 0]X1 + [0 1 1]X2 + [0] >= [0 0 0]X1 + [0 1 0]X2 + [0] = and(X1,X2) [0 1 1] [0 0 0] [0] [0 1 1] [0 0 0] [0] [1 1 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] and(active(X1),X2) = [0 0 0]X1 + [0 1 0]X2 + [0] >= [0 0 0]X1 + [0 1 0]X2 + [0] = and(X1,X2) [0 1 1] [0 0 0] [0] [0 1 1] [0 0 0] [0] [1 0 0] [1 1 0] [1] [1 0 0] [1 0 0] [1] and(X1,active(X2)) = [0 0 0]X1 + [0 1 1]X2 + [0] >= [0 0 0]X1 + [0 1 0]X2 + [0] = and(X1,X2) [0 1 1] [0 0 0] [0] [0 1 1] [0 0 0] [0] [1 1 1] [0] [1 0 0] [0] isNePal(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isNePal(X) [0 1 1] [0] [0 1 1] [0] [1 1 0] [0] [1 0 0] [0] isNePal(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isNePal(X) [0 1 1] [0] [0 1 1] [0] problem: 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) __(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) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [isNePal](x0) = [0 0 0]x0 + [1] [0 0 1] [1], [1 1 0] [1 1 0] [0] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 0 1] [0 0 0] [1], [0] [tt] = [1] [1], [1 0 1] [mark](x0) = [0 1 0]x0 [0 0 1] , [1 1 0] [0] [active](x0) = [0 0 0]x0 + [1] [0 0 1] [0], [1 0 0] [1 0 0] [1] [__](x0, x1) = [0 0 0]x0 + [1 1 0]x1 + [0] [0 0 0] [0 0 0] [0] orientation: [1 1 1] [1 1 0] [1] [1 1 1] [1 1 0] [1] mark(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = active(and(mark(X1),X2)) [0 0 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] [1] [1] mark(tt()) = [1] >= [1] = active(tt()) [1] [1] [1 0 1] [1] [1 0 1] [1] mark(isNePal(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = active(isNePal(mark(X))) [0 0 1] [1] [0 0 1] [1] [1 0 1] [1 0 0] [1] [1 0 0] [1 0 0] [1] __(mark(X1),X2) = [0 0 0]X1 + [1 1 0]X2 + [0] >= [0 0 0]X1 + [1 1 0]X2 + [0] = __(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] __(active(X1),X2) = [0 0 0]X1 + [1 1 0]X2 + [0] >= [0 0 0]X1 + [1 1 0]X2 + [0] = __(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 1 0] [1] [1 0 0] [1 0 0] [1] __(X1,active(X2)) = [0 0 0]X1 + [1 1 0]X2 + [1] >= [0 0 0]X1 + [1 1 0]X2 + [0] = __(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 1] [1 1 0] [0] [1 1 0] [1 1 0] [0] and(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = and(X1,X2) [0 0 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] [1 1 0] [1 1 1] [0] [1 1 0] [1 1 0] [0] and(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = and(X1,X2) [0 0 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] [1 1 0] [1 1 0] [1] [1 1 0] [1 1 0] [0] and(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = and(X1,X2) [0 0 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] [1 1 0] [1 1 0] [1] [1 1 0] [1 1 0] [0] and(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = and(X1,X2) [0 0 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] [1 0 1] [0] [1 0 0] [0] isNePal(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isNePal(X) [0 0 1] [1] [0 0 1] [1] [1 1 0] [0] [1 0 0] [0] isNePal(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isNePal(X) [0 0 1] [1] [0 0 1] [1] problem: 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) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [isNePal](x0) = [0 1 1]x0 [0 0 0] , [1 0 0] [1 0 0] [0] [and](x0, x1) = [0 1 1]x0 + [0 1 1]x1 + [1] [0 0 0] [0 0 0] [0], [0] [tt] = [0] [0], [1 1 0] [mark](x0) = [0 0 1]x0 [0 1 0] , [1 0 1] [active](x0) = [0 0 1]x0 [0 1 0] , [1 0 0] [1 0 1] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [1 1 1] [1 1 1] [1] [1 1 0] [1 0 0] [0] mark(and(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(and(mark(X1),X2)) [0 1 1] [0 1 1] [1] [0 1 1] [0 1 1] [1] [0] [0] mark(tt()) = [0] >= [0] = active(tt()) [0] [0] [1 1 1] [1 1 0] mark(isNePal(X)) = [0 0 0]X >= [0 0 0]X = active(isNePal(mark(X))) [0 1 1] [0 1 1] [1 1 0] [1 0 1] [1 0 0] [1 0 1] __(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1 0 0] [1 0 1] __(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 1 1] [1 0 0] [1 0 1] __(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] and(mark(X1),X2) = [0 1 1]X1 + [0 1 1]X2 + [1] >= [0 1 1]X1 + [0 1 1]X2 + [1] = and(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 1 0] [0] [1 0 0] [1 0 0] [0] and(X1,mark(X2)) = [0 1 1]X1 + [0 1 1]X2 + [1] >= [0 1 1]X1 + [0 1 1]X2 + [1] = and(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1 0 0] isNePal(mark(X)) = [0 1 1]X >= [0 1 1]X = isNePal(X) [0 0 0] [0 0 0] [1 0 1] [1 0 0] isNePal(active(X)) = [0 1 1]X >= [0 1 1]X = isNePal(X) [0 0 0] [0 0 0] problem: mark(tt()) -> active(tt()) mark(isNePal(X)) -> active(isNePal(mark(X))) __(mark(X1),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) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [isNePal](x0) = [0 0 0]x0 + [1] [0 1 1] [1], [1 0 0] [1 0 0] [1] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [0], [0] [tt] = [0] [1], [1 0 1] [mark](x0) = [0 0 1]x0 [0 1 0] , [1 0 0] [active](x0) = [0 0 1]x0 [0 1 0] , [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [1 0 0] [0 0 0] orientation: [1] [0] mark(tt()) = [1] >= [1] = active(tt()) [0] [0] [1 1 1] [1] [1 0 1] [0] mark(isNePal(X)) = [0 1 1]X + [1] >= [0 1 1]X + [1] = active(isNePal(mark(X))) [0 0 0] [1] [0 0 0] [1] [1 0 1] [1 0 0] [1 0 0] [1 0 0] __(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [1 0 1] [0 0 0] [1 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [1 0 0] [0 0 0] [1 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [1 0 0] [0 0 0] [1 0 0] [0 0 0] [1 0 1] [1 0 0] [1] [1 0 0] [1 0 0] [1] and(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = and(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 1] [1] [1 0 0] [1 0 0] [1] and(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = and(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [0] [1 0 0] [0] isNePal(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isNePal(X) [0 1 1] [1] [0 1 1] [1] [1 0 0] [0] [1 0 0] [0] isNePal(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isNePal(X) [0 1 1] [1] [0 1 1] [1] problem: __(mark(X1),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) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [1 0 1] [and](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [mark](x0) = x0 + [1] [1], [0] [active](x0) = x0 + [1] [1], [1 0 1] [1 1 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [1 0 1] [1 1 0] [1] [1 0 1] [1 1 0] __(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 1] [1 1 0] [1] [1 0 1] [1 1 0] __(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 1] [1 1 0] [1] [1 0 1] [1 1 0] __(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 1 0] [1 0 1] [1] [1 1 0] [1 0 1] and(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 1 0] [1 0 1] [1] [1 1 0] [1 0 1] and(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = and(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 1] [1] [1 0 1] isNePal(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = isNePal(X) [0 0 0] [0] [0 0 0] [1 0 1] [1] [1 0 1] isNePal(active(X)) = [0 0 0]X + [0] >= [0 0 0]X = isNePal(X) [0 0 0] [0] [0 0 0] problem: Qed