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())) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) __(mark(X1),X2) -> mark(__(X1,X2)) __(X1,mark(X2)) -> mark(__(X1,X2)) U11(mark(X)) -> mark(U11(X)) U12(mark(X)) -> mark(U12(X)) isNePal(mark(X)) -> mark(isNePal(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Proof: Matrix Interpretation Processor: dim=1 interpretation: [tt] = 0, [proper](x0) = x0, [active](x0) = x0, [nil] = 5, [U11](x0) = 4x0 + 7, [top](x0) = 2x0, [__](x0, x1) = 3x0 + x1 + 1, [isNePal](x0) = 5x0, [ok](x0) = x0, [U12](x0) = 4x0 + 5, [mark](x0) = x0 + 2 orientation: active(__(__(X,Y),Z)) = 9X + 3Y + Z + 4 >= 3X + 3Y + Z + 4 = mark(__(X,__(Y,Z))) active(__(X,nil())) = 3X + 6 >= X + 2 = mark(X) active(__(nil(),X)) = X + 16 >= X + 2 = mark(X) active(U11(tt())) = 7 >= 7 = mark(U12(tt())) active(U12(tt())) = 5 >= 2 = mark(tt()) active(isNePal(__(I,__(P,I)))) = 20I + 15P + 10 >= 9 = mark(U11(tt())) active(__(X1,X2)) = 3X1 + X2 + 1 >= 3X1 + X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = 3X1 + X2 + 1 >= 3X1 + X2 + 1 = __(X1,active(X2)) active(U11(X)) = 4X + 7 >= 4X + 7 = U11(active(X)) active(U12(X)) = 4X + 5 >= 4X + 5 = U12(active(X)) active(isNePal(X)) = 5X >= 5X = isNePal(active(X)) __(mark(X1),X2) = 3X1 + X2 + 7 >= 3X1 + X2 + 3 = mark(__(X1,X2)) __(X1,mark(X2)) = 3X1 + X2 + 3 >= 3X1 + X2 + 3 = mark(__(X1,X2)) U11(mark(X)) = 4X + 15 >= 4X + 9 = mark(U11(X)) U12(mark(X)) = 4X + 13 >= 4X + 7 = mark(U12(X)) isNePal(mark(X)) = 5X + 10 >= 5X + 2 = mark(isNePal(X)) proper(__(X1,X2)) = 3X1 + X2 + 1 >= 3X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 5 >= 5 = ok(nil()) proper(U11(X)) = 4X + 7 >= 4X + 7 = U11(proper(X)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = 4X + 5 >= 4X + 5 = U12(proper(X)) proper(isNePal(X)) = 5X >= 5X = isNePal(proper(X)) __(ok(X1),ok(X2)) = 3X1 + X2 + 1 >= 3X1 + X2 + 1 = ok(__(X1,X2)) U11(ok(X)) = 4X + 7 >= 4X + 7 = ok(U11(X)) U12(ok(X)) = 4X + 5 >= 4X + 5 = ok(U12(X)) isNePal(ok(X)) = 5X >= 5X = ok(isNePal(X)) top(mark(X)) = 2X + 4 >= 2X = top(proper(X)) top(ok(X)) = 2X >= 2X = top(active(X)) problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) active(U11(tt())) -> mark(U12(tt())) active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) __(X1,mark(X2)) -> mark(__(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=3 interpretation: [0] [tt] = [1] [0], [1 1 1] [proper](x0) = [0 1 0]x0 [0 0 1] , [1 0 1] [1] [active](x0) = [0 1 0]x0 + [0] [0 0 1] [0], [0] [nil] = [1] [0], [U11](x0) = x0 , [1 1 0] [top](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [__](x0, x1) = x0 + [0 0 0]x1 [0 1 1] , [isNePal](x0) = x0 , [1 1 1] [0] [ok](x0) = [0 0 0]x0 + [1] [0 0 0] [0], [U12](x0) = x0 , [1 0 0] [mark](x0) = [0 1 0]x0 [0 0 0] orientation: [1 0 1] [1 1 1] [1 1 1] [1] [1 0 0] [1 0 0] [1 0 0] active(__(__(X,Y),Z)) = [0 1 0]X + [0 0 0]Y + [0 0 0]Z + [0] >= [0 1 0]X + [0 0 0]Y + [0 0 0]Z = mark(__(X,__(Y,Z))) [0 0 1] [0 1 1] [0 1 1] [0] [0 0 0] [0 0 0] [0 0 0] [1] [0] active(U11(tt())) = [1] >= [1] = mark(U12(tt())) [0] [0] [1 0 1] [1 1 1] [1] [1 0 1] [1 0 0] [1] active(__(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 + [0] >= [0 1 0]X1 + [0 0 0]X2 + [0] = __(active(X1),X2) [0 0 1] [0 1 1] [0] [0 0 1] [0 1 1] [0] [1 0 1] [1 1 1] [1] [1 0 1] [1] active(__(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 + [0] >= X1 + [0 0 0]X2 + [0] = __(X1,active(X2)) [0 0 1] [0 1 1] [0] [0 1 1] [0] [1 0 1] [1] [1 0 1] [1] active(U11(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = U11(active(X)) [0 0 1] [0] [0 0 1] [0] [1 0 1] [1] [1 0 1] [1] active(U12(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = U12(active(X)) [0 0 1] [0] [0 0 1] [0] [1 0 1] [1] [1 0 1] [1] active(isNePal(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = isNePal(active(X)) [0 0 1] [0] [0 0 1] [0] [1 0 0] [1 0 0] [1 0 0] __(X1,mark(X2)) = X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = mark(__(X1,X2)) [0 1 0] [0 0 0] [0 0 0] [1 1 1] [1 1 1] [1 1 1] [1 1 1] proper(__(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = __(proper(X1),proper(X2)) [0 0 1] [0 1 1] [0 0 1] [0 1 1] [1] [1] proper(nil()) = [1] >= [1] = ok(nil()) [0] [0] [1 1 1] [1 1 1] proper(U11(X)) = [0 1 0]X >= [0 1 0]X = U11(proper(X)) [0 0 1] [0 0 1] [1] [1] proper(tt()) = [1] >= [1] = ok(tt()) [0] [0] [1 1 1] [1 1 1] proper(U12(X)) = [0 1 0]X >= [0 1 0]X = U12(proper(X)) [0 0 1] [0 0 1] [1 1 1] [1 1 1] proper(isNePal(X)) = [0 1 0]X >= [0 1 0]X = isNePal(proper(X)) [0 0 1] [0 0 1] [1 1 1] [1 1 1] [0] [1 1 1] [1 1 1] [0] __(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = ok(__(X1,X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0] [1 1 1] [0] [1 1 1] [0] U11(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(U11(X)) [0 0 0] [0] [0 0 0] [0] [1 1 1] [0] [1 1 1] [0] U12(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(U12(X)) [0 0 0] [0] [0 0 0] [0] [1 1 1] [0] [1 1 1] [0] isNePal(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(isNePal(X)) [0 0 0] [0] [0 0 0] [0] [1 1 1] [1] [1 1 1] [1] top(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = top(active(X)) [0 0 0] [0] [0 0 0] [0] problem: active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) __(X1,mark(X2)) -> mark(__(X1,X2)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) proper(isNePal(X)) -> isNePal(proper(X)) __(ok(X1),ok(X2)) -> ok(__(X1,X2)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [tt] = 0, [proper](x0) = 6x0 + 1, [active](x0) = x0, [nil] = 0, [U11](x0) = x0, [top](x0) = x0, [__](x0, x1) = 4x0 + 2x1 + 1, [isNePal](x0) = 4x0 + 1, [ok](x0) = 4x0 + 1, [U12](x0) = x0, [mark](x0) = x0 + 2 orientation: active(__(X1,X2)) = 4X1 + 2X2 + 1 >= 4X1 + 2X2 + 1 = __(active(X1),X2) active(__(X1,X2)) = 4X1 + 2X2 + 1 >= 4X1 + 2X2 + 1 = __(X1,active(X2)) active(U11(X)) = X >= X = U11(active(X)) active(U12(X)) = X >= X = U12(active(X)) active(isNePal(X)) = 4X + 1 >= 4X + 1 = isNePal(active(X)) __(X1,mark(X2)) = 4X1 + 2X2 + 5 >= 4X1 + 2X2 + 3 = mark(__(X1,X2)) proper(__(X1,X2)) = 24X1 + 12X2 + 7 >= 24X1 + 12X2 + 7 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X)) = 6X + 1 >= 6X + 1 = U11(proper(X)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = 6X + 1 >= 6X + 1 = U12(proper(X)) proper(isNePal(X)) = 24X + 7 >= 24X + 5 = isNePal(proper(X)) __(ok(X1),ok(X2)) = 16X1 + 8X2 + 7 >= 16X1 + 8X2 + 5 = ok(__(X1,X2)) U11(ok(X)) = 4X + 1 >= 4X + 1 = ok(U11(X)) U12(ok(X)) = 4X + 1 >= 4X + 1 = ok(U12(X)) isNePal(ok(X)) = 16X + 5 >= 16X + 5 = ok(isNePal(X)) top(ok(X)) = 4X + 1 >= X = top(active(X)) problem: active(__(X1,X2)) -> __(active(X1),X2) active(__(X1,X2)) -> __(X1,active(X2)) active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) Matrix Interpretation Processor: dim=3 interpretation: [0] [tt] = [1] [1], [1 0 0] [proper](x0) = [1 1 0]x0 [0 1 0] , [1 1 1] [active](x0) = [0 1 0]x0 [1 1 1] , [1] [nil] = [0] [0], [1] [U11](x0) = x0 + [0] [0], [0] [__](x0, x1) = x0 + x1 + [1] [0], [0] [isNePal](x0) = x0 + [0] [1], [1 0 0] [0] [ok](x0) = [0 0 0]x0 + [1] [0 0 1] [0], [1] [U12](x0) = x0 + [0] [0] orientation: [1 1 1] [1 1 1] [1] [1 1 1] [0] active(__(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + X2 + [1] = __(active(X1),X2) [1 1 1] [1 1 1] [1] [1 1 1] [0] [1 1 1] [1 1 1] [1] [1 1 1] [0] active(__(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 + [1] >= X1 + [0 1 0]X2 + [1] = __(X1,active(X2)) [1 1 1] [1 1 1] [1] [1 1 1] [0] [1 1 1] [1] [1 1 1] [1] active(U11(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = U11(active(X)) [1 1 1] [1] [1 1 1] [0] [1 1 1] [1] [1 1 1] [1] active(U12(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = U12(active(X)) [1 1 1] [1] [1 1 1] [0] [1 1 1] [1] [1 1 1] [0] active(isNePal(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = isNePal(active(X)) [1 1 1] [1] [1 1 1] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] proper(__(X1,X2)) = [1 1 0]X1 + [1 1 0]X2 + [1] >= [1 1 0]X1 + [1 1 0]X2 + [1] = __(proper(X1),proper(X2)) [0 1 0] [0 1 0] [1] [0 1 0] [0 1 0] [0] [1] [1] proper(nil()) = [1] >= [1] = ok(nil()) [0] [0] [1 0 0] [1] [1 0 0] [1] proper(U11(X)) = [1 1 0]X + [1] >= [1 1 0]X + [0] = U11(proper(X)) [0 1 0] [0] [0 1 0] [0] [0] [0] proper(tt()) = [1] >= [1] = ok(tt()) [1] [1] [1 0 0] [1] [1 0 0] [1] proper(U12(X)) = [1 1 0]X + [1] >= [1 1 0]X + [0] = U12(proper(X)) [0 1 0] [0] [0 1 0] [0] [1 0 0] [1] [1 0 0] [1] U11(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(U11(X)) [0 0 1] [0] [0 0 1] [0] [1 0 0] [1] [1 0 0] [1] U12(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(U12(X)) [0 0 1] [0] [0 0 1] [0] [1 0 0] [0] [1 0 0] [0] isNePal(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(isNePal(X)) [0 0 1] [1] [0 0 1] [1] problem: active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) Matrix Interpretation Processor: dim=3 interpretation: [0] [tt] = [0] [0], [1 0 0] [proper](x0) = [0 0 0]x0 [0 0 1] , [1 0 1] [active](x0) = [0 0 0]x0 [0 0 1] , [0] [nil] = [0] [0], [1 0 0] [U11](x0) = [0 0 0]x0 [0 0 1] , [1 1 0] [1 0 0] [1] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [0], [1 0 0] [1] [isNePal](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [ok](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [U12](x0) = [0 0 0]x0 + [0] [0 0 1] [1] orientation: [1 0 1] [1 0 1] active(U11(X)) = [0 0 0]X >= [0 0 0]X = U11(active(X)) [0 0 1] [0 0 1] [1 0 1] [1] [1 0 1] [0] active(U12(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U12(active(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] proper(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = __(proper(X1),proper(X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [0] [0] proper(nil()) = [0] >= [0] = ok(nil()) [0] [0] [1 0 0] [1 0 0] proper(U11(X)) = [0 0 0]X >= [0 0 0]X = U11(proper(X)) [0 0 1] [0 0 1] [0] [0] proper(tt()) = [0] >= [0] = ok(tt()) [0] [0] [1 0 0] [0] [1 0 0] [0] proper(U12(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U12(proper(X)) [0 0 1] [1] [0 0 1] [1] [1 0 0] [1 0 0] U11(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(U11(X)) [0 0 0] [0 0 0] [1 0 0] [0] [1 0 0] U12(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X = ok(U12(X)) [0 0 0] [1] [0 0 0] [1 0 0] [1] [1 0 0] [1] isNePal(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(isNePal(X)) [0 0 0] [0] [0 0 0] [0] problem: active(U11(X)) -> U11(active(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) isNePal(ok(X)) -> ok(isNePal(X)) Matrix Interpretation Processor: dim=1 interpretation: [tt] = 0, [proper](x0) = 4x0 + 1, [active](x0) = 4x0 + 1, [nil] = 0, [U11](x0) = x0, [__](x0, x1) = 6x0 + 4x1 + 3, [isNePal](x0) = 2x0 + 1, [ok](x0) = x0 + 1, [U12](x0) = x0 orientation: active(U11(X)) = 4X + 1 >= 4X + 1 = U11(active(X)) proper(__(X1,X2)) = 24X1 + 16X2 + 13 >= 24X1 + 16X2 + 13 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X)) = 4X + 1 >= 4X + 1 = U11(proper(X)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = 4X + 1 >= 4X + 1 = U12(proper(X)) U11(ok(X)) = X + 1 >= X + 1 = ok(U11(X)) U12(ok(X)) = X + 1 >= X + 1 = ok(U12(X)) isNePal(ok(X)) = 2X + 3 >= 2X + 2 = ok(isNePal(X)) problem: active(U11(X)) -> U11(active(X)) proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) Matrix Interpretation Processor: dim=3 interpretation: [0] [tt] = [0] [0], [1 0 1] [proper](x0) = [1 0 1]x0 [1 0 1] , [1 0 1] [active](x0) = [0 0 0]x0 [0 0 1] , [0] [nil] = [0] [1], [1 0 0] [0] [U11](x0) = [0 0 0]x0 + [0] [0 0 1] [1], [1 0 0] [1 0 0] [0] [__](x0, x1) = [1 0 0]x0 + [1 0 0]x1 + [1] [0 0 1] [0 0 1] [1], [1 1 0] [ok](x0) = [0 0 0]x0 [0 0 0] , [1] [U12](x0) = x0 + [0] [0] orientation: [1 0 1] [1] [1 0 1] [0] active(U11(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U11(active(X)) [0 0 1] [1] [0 0 1] [1] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [0] proper(__(X1,X2)) = [1 0 1]X1 + [1 0 1]X2 + [1] >= [1 0 1]X1 + [1 0 1]X2 + [1] = __(proper(X1),proper(X2)) [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [1] [1] [0] proper(nil()) = [1] >= [0] = ok(nil()) [1] [0] [1 0 1] [1] [1 0 1] [0] proper(U11(X)) = [1 0 1]X + [1] >= [0 0 0]X + [0] = U11(proper(X)) [1 0 1] [1] [1 0 1] [1] [0] [0] proper(tt()) = [0] >= [0] = ok(tt()) [0] [0] [1 0 1] [1] [1 0 1] [1] proper(U12(X)) = [1 0 1]X + [1] >= [1 0 1]X + [0] = U12(proper(X)) [1 0 1] [1] [1 0 1] [0] [1 1 0] [0] [1 0 0] U11(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X = ok(U11(X)) [0 0 0] [1] [0 0 0] [1 1 0] [1] [1 1 0] [1] U12(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(U12(X)) [0 0 0] [0] [0 0 0] [0] problem: proper(tt()) -> ok(tt()) proper(U12(X)) -> U12(proper(X)) U11(ok(X)) -> ok(U11(X)) U12(ok(X)) -> ok(U12(X)) Matrix Interpretation Processor: dim=3 interpretation: [0] [tt] = [0] [0], [1 0 0] [1] [proper](x0) = [0 0 1]x0 + [0] [0 1 0] [1], [1 1 1] [0] [U11](x0) = [0 0 1]x0 + [0] [0 1 0] [1], [1 0 0] [0] [ok](x0) = [0 0 1]x0 + [0] [0 1 0] [1], [1 0 0] [0] [U12](x0) = [0 0 1]x0 + [0] [0 1 0] [1] orientation: [1] [0] proper(tt()) = [0] >= [0] = ok(tt()) [1] [1] [1] [1] proper(U12(X)) = X + [1] >= X + [1] = U12(proper(X)) [1] [1] [1 1 1] [1] [1 1 1] [0] U11(ok(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = ok(U11(X)) [0 0 1] [1] [0 0 1] [1] [0] [0] U12(ok(X)) = X + [1] >= X + [1] = ok(U12(X)) [1] [1] problem: proper(U12(X)) -> U12(proper(X)) U12(ok(X)) -> ok(U12(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 1 1] [proper](x0) = [0 1 0]x0 [0 0 1] , [1 0 0] [0] [ok](x0) = [0 0 1]x0 + [1] [0 1 0] [0], [1 0 0] [0] [U12](x0) = [0 0 1]x0 + [1] [0 1 0] [0] orientation: [1 1 1] [1] [1 1 1] [0] proper(U12(X)) = [0 0 1]X + [1] >= [0 0 1]X + [1] = U12(proper(X)) [0 1 0] [0] [0 1 0] [0] [0] [0] U12(ok(X)) = X + [1] >= X + [1] = ok(U12(X)) [1] [1] problem: U12(ok(X)) -> ok(U12(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [ok](x0) = [0 1 0]x0 + [1] [0 0 0] [0], [1 1 0] [U12](x0) = [0 1 0]x0 [0 0 0] orientation: [1 1 0] [1] [1 1 0] [0] U12(ok(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = ok(U12(X)) [0 0 0] [0] [0 0 0] [0] problem: Qed