YES Problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(U11(tt())) -> mark(U12(tt())) active(U12(tt())) -> mark(tt()) active(isNePal(__(I,__(P,I)))) -> mark(U11(tt())) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) 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) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Proof: Matrix Interpretation Processor: dim=1 interpretation: [isNePal](x0) = 2x0 + 6, [U12](x0) = 2x0 + 1, [U11](x0) = x0 + 4, [tt] = 2, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = 2x0 + x1 orientation: active(__(__(X,Y),Z)) = 4X + 2Y + Z >= 2X + 2Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = 2X >= X = mark(X) active(__(nil(),X)) = X >= X = mark(X) active(U11(tt())) = 6 >= 5 = mark(U12(tt())) active(U12(tt())) = 5 >= 2 = mark(tt()) active(isNePal(__(I,__(P,I)))) = 6I + 4P + 6 >= 6 = mark(U11(tt())) mark(__(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 0 >= 0 = active(nil()) mark(U11(X)) = X + 4 >= X + 4 = active(U11(mark(X))) mark(tt()) = 2 >= 2 = active(tt()) mark(U12(X)) = 2X + 1 >= 2X + 1 = active(U12(mark(X))) mark(isNePal(X)) = 2X + 6 >= 2X + 6 = active(isNePal(mark(X))) __(mark(X1),X2) = 2X1 + X2 >= 2X1 + X2 = __(X1,X2) __(X1,mark(X2)) = 2X1 + X2 >= 2X1 + X2 = __(X1,X2) __(active(X1),X2) = 2X1 + X2 >= 2X1 + X2 = __(X1,X2) __(X1,active(X2)) = 2X1 + X2 >= 2X1 + X2 = __(X1,X2) U11(mark(X)) = X + 4 >= X + 4 = U11(X) U11(active(X)) = X + 4 >= X + 4 = U11(X) U12(mark(X)) = 2X + 1 >= 2X + 1 = U12(X) U12(active(X)) = 2X + 1 >= 2X + 1 = U12(X) isNePal(mark(X)) = 2X + 6 >= 2X + 6 = isNePal(X) isNePal(active(X)) = 2X + 6 >= 2X + 6 = isNePal(X) problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(__(X,nil())) -> mark(X) active(__(nil(),X)) -> mark(X) active(isNePal(__(I,__(P,I)))) -> mark(U11(tt())) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) 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) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [isNePal](x0) = x0 + 2, [U12](x0) = x0, [U11](x0) = x0 + 1, [tt] = 1, [nil] = 2, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = 2x0 + x1 orientation: active(__(__(X,Y),Z)) = 4X + 2Y + Z >= 2X + 2Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = 2X + 2 >= X = mark(X) active(__(nil(),X)) = X + 4 >= X = mark(X) active(isNePal(__(I,__(P,I)))) = 3I + 2P + 2 >= 2 = mark(U11(tt())) mark(__(X1,X2)) = 2X1 + X2 >= 2X1 + X2 = active(__(mark(X1),mark(X2))) mark(nil()) = 2 >= 2 = active(nil()) mark(U11(X)) = X + 1 >= X + 1 = active(U11(mark(X))) mark(tt()) = 1 >= 1 = active(tt()) mark(U12(X)) = X >= X = active(U12(mark(X))) mark(isNePal(X)) = X + 2 >= X + 2 = active(isNePal(mark(X))) __(mark(X1),X2) = 2X1 + X2 >= 2X1 + X2 = __(X1,X2) __(X1,mark(X2)) = 2X1 + X2 >= 2X1 + X2 = __(X1,X2) __(active(X1),X2) = 2X1 + X2 >= 2X1 + X2 = __(X1,X2) __(X1,active(X2)) = 2X1 + X2 >= 2X1 + X2 = __(X1,X2) U11(mark(X)) = X + 1 >= X + 1 = U11(X) U11(active(X)) = X + 1 >= X + 1 = U11(X) U12(mark(X)) = X >= X = U12(X) U12(active(X)) = X >= X = U12(X) isNePal(mark(X)) = X + 2 >= X + 2 = isNePal(X) isNePal(active(X)) = X + 2 >= X + 2 = isNePal(X) problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(isNePal(__(I,__(P,I)))) -> mark(U11(tt())) mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) 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) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=1 interpretation: [isNePal](x0) = 2x0, [U12](x0) = x0 + 1, [U11](x0) = x0 + 2, [tt] = 3, [nil] = 4, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = 2x0 + x1 + 2 orientation: active(__(__(X,Y),Z)) = 4X + 2Y + Z + 6 >= 2X + 2Y + Z + 4 = mark(__(X,__(Y,Z))) active(isNePal(__(I,__(P,I)))) = 6I + 4P + 8 >= 5 = mark(U11(tt())) mark(__(X1,X2)) = 2X1 + X2 + 2 >= 2X1 + X2 + 2 = active(__(mark(X1),mark(X2))) mark(nil()) = 4 >= 4 = active(nil()) mark(U11(X)) = X + 2 >= X + 2 = active(U11(mark(X))) mark(tt()) = 3 >= 3 = active(tt()) mark(U12(X)) = X + 1 >= X + 1 = active(U12(mark(X))) mark(isNePal(X)) = 2X >= 2X = active(isNePal(mark(X))) __(mark(X1),X2) = 2X1 + X2 + 2 >= 2X1 + X2 + 2 = __(X1,X2) __(X1,mark(X2)) = 2X1 + X2 + 2 >= 2X1 + X2 + 2 = __(X1,X2) __(active(X1),X2) = 2X1 + X2 + 2 >= 2X1 + X2 + 2 = __(X1,X2) __(X1,active(X2)) = 2X1 + X2 + 2 >= 2X1 + X2 + 2 = __(X1,X2) U11(mark(X)) = X + 2 >= X + 2 = U11(X) U11(active(X)) = X + 2 >= X + 2 = U11(X) U12(mark(X)) = X + 1 >= X + 1 = U12(X) U12(active(X)) = X + 1 >= X + 1 = U12(X) isNePal(mark(X)) = 2X >= 2X = isNePal(X) isNePal(active(X)) = 2X >= 2X = isNePal(X) problem: mark(__(X1,X2)) -> active(__(mark(X1),mark(X2))) mark(nil()) -> active(nil()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) 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) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [isNePal](x0) = [0 0 1]x0 [0 0 1] , [1 1 0] [U12](x0) = [0 0 1]x0 [0 0 1] , [1 1 0] [U11](x0) = [0 0 1]x0 [0 0 1] , [0] [tt] = [0] [0], [1] [nil] = [0] [0], [1 1 0] [mark](x0) = [0 0 1]x0 [0 0 1] , [active](x0) = x0 , [1 1 0] [1 1 0] [0] [__](x0, x1) = [0 0 1]x0 + [0 0 1]x1 + [1] [0 0 1] [0 0 1] [1] orientation: [1 1 1] [1 1 1] [1] [1 1 1] [1 1 1] [0] mark(__(X1,X2)) = [0 0 1]X1 + [0 0 1]X2 + [1] >= [0 0 1]X1 + [0 0 1]X2 + [1] = active(__(mark(X1),mark(X2))) [0 0 1] [0 0 1] [1] [0 0 1] [0 0 1] [1] [1] [1] mark(nil()) = [0] >= [0] = active(nil()) [0] [0] [1 1 1] [1 1 1] mark(U11(X)) = [0 0 1]X >= [0 0 1]X = active(U11(mark(X))) [0 0 1] [0 0 1] [0] [0] mark(tt()) = [0] >= [0] = active(tt()) [0] [0] [1 1 1] [1 1 1] mark(U12(X)) = [0 0 1]X >= [0 0 1]X = active(U12(mark(X))) [0 0 1] [0 0 1] [1 1 1] [1 1 1] mark(isNePal(X)) = [0 0 1]X >= [0 0 1]X = active(isNePal(mark(X))) [0 0 1] [0 0 1] [1 1 1] [1 1 0] [0] [1 1 0] [1 1 0] [0] __(mark(X1),X2) = [0 0 1]X1 + [0 0 1]X2 + [1] >= [0 0 1]X1 + [0 0 1]X2 + [1] = __(X1,X2) [0 0 1] [0 0 1] [1] [0 0 1] [0 0 1] [1] [1 1 0] [1 1 1] [0] [1 1 0] [1 1 0] [0] __(X1,mark(X2)) = [0 0 1]X1 + [0 0 1]X2 + [1] >= [0 0 1]X1 + [0 0 1]X2 + [1] = __(X1,X2) [0 0 1] [0 0 1] [1] [0 0 1] [0 0 1] [1] [1 1 0] [1 1 0] [0] [1 1 0] [1 1 0] [0] __(active(X1),X2) = [0 0 1]X1 + [0 0 1]X2 + [1] >= [0 0 1]X1 + [0 0 1]X2 + [1] = __(X1,X2) [0 0 1] [0 0 1] [1] [0 0 1] [0 0 1] [1] [1 1 0] [1 1 0] [0] [1 1 0] [1 1 0] [0] __(X1,active(X2)) = [0 0 1]X1 + [0 0 1]X2 + [1] >= [0 0 1]X1 + [0 0 1]X2 + [1] = __(X1,X2) [0 0 1] [0 0 1] [1] [0 0 1] [0 0 1] [1] [1 1 1] [1 1 0] U11(mark(X)) = [0 0 1]X >= [0 0 1]X = U11(X) [0 0 1] [0 0 1] [1 1 0] [1 1 0] U11(active(X)) = [0 0 1]X >= [0 0 1]X = U11(X) [0 0 1] [0 0 1] [1 1 1] [1 1 0] U12(mark(X)) = [0 0 1]X >= [0 0 1]X = U12(X) [0 0 1] [0 0 1] [1 1 0] [1 1 0] U12(active(X)) = [0 0 1]X >= [0 0 1]X = U12(X) [0 0 1] [0 0 1] [1 1 1] [1 1 0] isNePal(mark(X)) = [0 0 1]X >= [0 0 1]X = isNePal(X) [0 0 1] [0 0 1] [1 1 0] [1 1 0] isNePal(active(X)) = [0 0 1]X >= [0 0 1]X = isNePal(X) [0 0 1] [0 0 1] problem: mark(nil()) -> active(nil()) mark(U11(X)) -> active(U11(mark(X))) mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) 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) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1] [isNePal](x0) = [0 0 0]x0 + [0] [0 0 1] [0], [1 0 0] [1] [U12](x0) = [0 0 0]x0 + [0] [0 0 1] [0], [1 0 0] [0] [U11](x0) = [0 0 0]x0 + [0] [0 0 1] [1], [0] [tt] = [0] [0], [0] [nil] = [1] [1], [1 0 1] [0] [mark](x0) = [0 0 0]x0 + [1] [0 0 1] [0], [active](x0) = x0 , [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [1] [0] mark(nil()) = [1] >= [1] = active(nil()) [1] [1] [1 0 1] [1] [1 0 1] [0] mark(U11(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = active(U11(mark(X))) [0 0 1] [1] [0 0 1] [1] [0] [0] mark(tt()) = [1] >= [0] = active(tt()) [0] [0] [1 0 1] [1] [1 0 1] [1] mark(U12(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = active(U12(mark(X))) [0 0 1] [0] [0 0 1] [0] [1 0 1] [1] [1 0 1] [1] mark(isNePal(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = active(isNePal(mark(X))) [0 0 1] [0] [0 0 1] [0] [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) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 1] [1 0 0] [1 0 0] __(X1,mark(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 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) [0 0 0] [0 0 0] [0 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) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [0] [1 0 0] [0] U11(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U11(X) [0 0 1] [1] [0 0 1] [1] [1 0 0] [0] [1 0 0] [0] U11(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U11(X) [0 0 1] [1] [0 0 1] [1] [1 0 1] [1] [1 0 0] [1] U12(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U12(X) [0 0 1] [0] [0 0 1] [0] [1 0 0] [1] [1 0 0] [1] U12(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U12(X) [0 0 1] [0] [0 0 1] [0] [1 0 1] [1] [1 0 0] [1] isNePal(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNePal(X) [0 0 1] [0] [0 0 1] [0] [1 0 0] [1] [1 0 0] [1] isNePal(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = isNePal(X) [0 0 1] [0] [0 0 1] [0] problem: mark(tt()) -> active(tt()) mark(U12(X)) -> active(U12(mark(X))) 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) U11(mark(X)) -> U11(X) U11(active(X)) -> U11(X) U12(mark(X)) -> U12(X) U12(active(X)) -> U12(X) isNePal(mark(X)) -> isNePal(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [isNePal](x0) = [1 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [0] [U12](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 0] , [0] [tt] = [0] [0], [1 0 0] [1] [mark](x0) = [1 0 1]x0 + [0] [0 0 1] [0], [1 0 0] [active](x0) = [1 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [__](x0, x1) = [1 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [1] [0] mark(tt()) = [0] >= [0] = active(tt()) [0] [0] [1 0 0] [1] [1 0 0] [1] mark(U12(X)) = [1 0 0]X + [1] >= [1 0 0]X + [1] = active(U12(mark(X))) [0 0 0] [1] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] mark(isNePal(X)) = [1 0 0]X + [1] >= [1 0 0]X + [1] = active(isNePal(mark(X))) [0 0 0] [1] [0 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] __(mark(X1),X2) = [1 0 0]X1 + [0 0 0]X2 + [1] >= [1 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] __(X1,mark(X2)) = [1 0 0]X1 + [0 0 0]X2 + [0] >= [1 0 0]X1 + [0 0 0]X2 = __(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(active(X1),X2) = [1 0 0]X1 + [0 0 0]X2 >= [1 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 0 0] [1 0 0] [1 0 0] __(X1,active(X2)) = [1 0 0]X1 + [0 0 0]X2 >= [1 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 0 0] U11(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = U11(X) [0 0 0] [0] [0 0 0] [1 0 0] [1 0 0] U11(active(X)) = [0 0 0]X >= [0 0 0]X = U11(X) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [0] U12(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U12(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] U12(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U12(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [0] isNePal(mark(X)) = [1 0 0]X + [1] >= [1 0 0]X + [0] = isNePal(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] isNePal(active(X)) = [1 0 0]X + [0] >= [1 0 0]X + [0] = isNePal(X) [0 0 0] [1] [0 0 0] [1] problem: mark(U12(X)) -> active(U12(mark(X))) mark(isNePal(X)) -> active(isNePal(mark(X))) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(active(X)) -> U11(X) U12(active(X)) -> U12(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=3 interpretation: [isNePal](x0) = x0 , [1 1 0] [0] [U12](x0) = [0 0 1]x0 + [1] [1 1 0] [1], [1 0 0] [U11](x0) = [0 0 0]x0 [1 0 0] , [1 1 0] [mark](x0) = [0 0 1]x0 [1 1 0] , [active](x0) = x0 , [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 1 1] [1] [1 1 1] [0] mark(U12(X)) = [1 1 0]X + [1] >= [1 1 0]X + [1] = active(U12(mark(X))) [1 1 1] [1] [1 1 1] [1] [1 1 0] [1 1 0] mark(isNePal(X)) = [0 0 1]X >= [0 0 1]X = active(isNePal(mark(X))) [1 1 0] [1 1 0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] __(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = __(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] __(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = __(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] U11(active(X)) = [0 0 0]X >= [0 0 0]X = U11(X) [1 0 0] [1 0 0] [1 1 0] [0] [1 1 0] [0] U12(active(X)) = [0 0 1]X + [1] >= [0 0 1]X + [1] = U12(X) [1 1 0] [1] [1 1 0] [1] isNePal(active(X)) = X >= X = isNePal(X) problem: mark(isNePal(X)) -> active(isNePal(mark(X))) __(active(X1),X2) -> __(X1,X2) __(X1,active(X2)) -> __(X1,X2) U11(active(X)) -> U11(X) U12(active(X)) -> U12(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1] [isNePal](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [1 0 1] [U12](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1] [U11](x0) = [0 0 1]x0 + [1] [0 0 0] [0], [1 0 0] [0] [mark](x0) = [0 0 0]x0 + [1] [1 0 0] [0], [1 0 0] [0] [active](x0) = [0 0 0]x0 + [1] [0 1 1] [0], [1 0 0] [1 1 1] [__](x0, x1) = [0 1 1]x0 + [0 0 1]x1 [1 1 1] [1 0 0] orientation: [1 0 0] [1] [1 0 0] [1] mark(isNePal(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = active(isNePal(mark(X))) [1 0 0] [1] [0 0 0] [1] [1 0 0] [1 1 1] [0] [1 0 0] [1 1 1] __(active(X1),X2) = [0 1 1]X1 + [0 0 1]X2 + [1] >= [0 1 1]X1 + [0 0 1]X2 = __(X1,X2) [1 1 1] [1 0 0] [1] [1 1 1] [1 0 0] [1 0 0] [1 1 1] [1] [1 0 0] [1 1 1] __(X1,active(X2)) = [0 1 1]X1 + [0 1 1]X2 + [0] >= [0 1 1]X1 + [0 0 1]X2 = __(X1,X2) [1 1 1] [1 0 0] [0] [1 1 1] [1 0 0] [1 0 0] [1] [1 0 0] [1] U11(active(X)) = [0 1 1]X + [1] >= [0 0 1]X + [1] = U11(X) [0 0 0] [0] [0 0 0] [0] [1 1 1] [1 0 1] U12(active(X)) = [0 0 0]X >= [0 0 0]X = U12(X) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] isNePal(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = isNePal(X) [0 0 0] [0] [0 0 0] [0] problem: mark(isNePal(X)) -> active(isNePal(mark(X))) __(active(X1),X2) -> __(X1,X2) U11(active(X)) -> U11(X) U12(active(X)) -> U12(X) isNePal(active(X)) -> isNePal(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [0] [isNePal](x0) = [0 1 0]x0 + [1] [0 1 0] [0], [1 0 1] [0] [U12](x0) = [1 0 0]x0 + [1] [1 1 0] [0], [1 0 0] [1] [U11](x0) = [0 0 0]x0 + [1] [1 0 0] [1], [1 0 1] [1] [mark](x0) = [0 1 0]x0 + [0] [0 1 0] [0], [0] [active](x0) = x0 + [0] [1], [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 1] [0 0 0] orientation: [1 1 1] [1] [1 1 1] [1] mark(isNePal(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = active(isNePal(mark(X))) [0 1 0] [1] [0 1 0] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 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 1] [0 0 0] [1] [0 0 1] [0 0 0] [1 0 0] [1] [1 0 0] [1] U11(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = U11(X) [1 0 0] [1] [1 0 0] [1] [1 0 1] [1] [1 0 1] [0] U12(active(X)) = [1 0 0]X + [1] >= [1 0 0]X + [1] = U12(X) [1 1 0] [0] [1 1 0] [0] [1 0 1] [1] [1 0 1] [0] isNePal(active(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = isNePal(X) [0 1 0] [0] [0 1 0] [0] problem: mark(isNePal(X)) -> active(isNePal(mark(X))) __(active(X1),X2) -> __(X1,X2) U11(active(X)) -> U11(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [isNePal](x0) = [0 0 0]x0 + [0] [0 0 1] [1], [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [0] [mark](x0) = [1 0 0]x0 + [1] [0 0 0] [0], [1 1 0] [1] [active](x0) = [0 0 1]x0 + [0] [0 0 0] [0], [1 1 0] [1 0 0] [__](x0, x1) = [1 1 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [1 0 1] [1] [1 0 1] [1] mark(isNePal(X)) = [1 0 0]X + [1] >= [0 0 0]X + [1] = active(isNePal(mark(X))) [0 0 0] [0] [0 0 0] [0] [1 1 1] [1 0 0] [1] [1 1 0] [1 0 0] __(active(X1),X2) = [1 1 1]X1 + [0 0 0]X2 + [1] >= [1 1 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] [1 0 0] U11(active(X)) = [0 0 0]X + [0] >= [0 0 0]X = U11(X) [0 0 0] [0] [0 0 0] problem: mark(isNePal(X)) -> active(isNePal(mark(X))) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [0] [isNePal](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 1] [mark](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [active](x0) = [0 0 0]x0 [0 0 0] orientation: [1 0 1] [1] [1 0 1] mark(isNePal(X)) = [0 0 0]X + [0] >= [0 0 0]X = active(isNePal(mark(X))) [0 0 0] [0] [0 0 0] problem: Qed