/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- 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: [top](x0) = 2x0, [ok](x0) = x0, [proper](x0) = x0, [isNePal](x0) = 4x0 + 1, [U12](x0) = x0, [U11](x0) = 4x0, [tt] = 0, [nil] = 0, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = x0 + x1 orientation: active(__(__(X,Y),Z)) = X + Y + Z >= X + Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = X >= X = mark(X) active(__(nil(),X)) = X >= X = mark(X) active(U11(tt())) = 0 >= 0 = mark(U12(tt())) active(U12(tt())) = 0 >= 0 = mark(tt()) active(isNePal(__(I,__(P,I)))) = 8I + 4P + 1 >= 0 = mark(U11(tt())) active(__(X1,X2)) = X1 + X2 >= X1 + X2 = __(active(X1),X2) active(__(X1,X2)) = X1 + X2 >= X1 + X2 = __(X1,active(X2)) active(U11(X)) = 4X >= 4X = U11(active(X)) active(U12(X)) = X >= X = U12(active(X)) active(isNePal(X)) = 4X + 1 >= 4X + 1 = isNePal(active(X)) __(mark(X1),X2) = X1 + X2 >= X1 + X2 = mark(__(X1,X2)) __(X1,mark(X2)) = X1 + X2 >= X1 + X2 = mark(__(X1,X2)) U11(mark(X)) = 4X >= 4X = mark(U11(X)) U12(mark(X)) = X >= X = mark(U12(X)) isNePal(mark(X)) = 4X + 1 >= 4X + 1 = mark(isNePal(X)) proper(__(X1,X2)) = X1 + X2 >= X1 + X2 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X)) = 4X >= 4X = U11(proper(X)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = X >= X = U12(proper(X)) proper(isNePal(X)) = 4X + 1 >= 4X + 1 = isNePal(proper(X)) __(ok(X1),ok(X2)) = X1 + X2 >= X1 + X2 = ok(__(X1,X2)) U11(ok(X)) = 4X >= 4X = ok(U11(X)) U12(ok(X)) = X >= X = ok(U12(X)) isNePal(ok(X)) = 4X + 1 >= 4X + 1 = ok(isNePal(X)) top(mark(X)) = 2X >= 2X = top(proper(X)) top(ok(X)) = 2X >= 2X = top(active(X)) 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(__(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)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = x0 + 4, [ok](x0) = x0, [proper](x0) = x0, [isNePal](x0) = 4x0 + 6, [U12](x0) = 7x0 + 2, [U11](x0) = 5x0 + 6, [tt] = 2, [nil] = 1, [mark](x0) = x0, [active](x0) = x0, [__](x0, x1) = 4x0 + x1 orientation: active(__(__(X,Y),Z)) = 16X + 4Y + Z >= 4X + 4Y + Z = mark(__(X,__(Y,Z))) active(__(X,nil())) = 4X + 1 >= X = mark(X) active(__(nil(),X)) = X + 4 >= X = mark(X) active(U11(tt())) = 16 >= 16 = mark(U12(tt())) active(U12(tt())) = 16 >= 2 = mark(tt()) active(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(active(X1),X2) active(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(X1,active(X2)) active(U11(X)) = 5X + 6 >= 5X + 6 = U11(active(X)) active(U12(X)) = 7X + 2 >= 7X + 2 = U12(active(X)) active(isNePal(X)) = 4X + 6 >= 4X + 6 = isNePal(active(X)) __(mark(X1),X2) = 4X1 + X2 >= 4X1 + X2 = mark(__(X1,X2)) __(X1,mark(X2)) = 4X1 + X2 >= 4X1 + X2 = mark(__(X1,X2)) U11(mark(X)) = 5X + 6 >= 5X + 6 = mark(U11(X)) U12(mark(X)) = 7X + 2 >= 7X + 2 = mark(U12(X)) isNePal(mark(X)) = 4X + 6 >= 4X + 6 = mark(isNePal(X)) proper(__(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X)) = 5X + 6 >= 5X + 6 = U11(proper(X)) proper(tt()) = 2 >= 2 = ok(tt()) proper(U12(X)) = 7X + 2 >= 7X + 2 = U12(proper(X)) proper(isNePal(X)) = 4X + 6 >= 4X + 6 = isNePal(proper(X)) __(ok(X1),ok(X2)) = 4X1 + X2 >= 4X1 + X2 = ok(__(X1,X2)) U11(ok(X)) = 5X + 6 >= 5X + 6 = ok(U11(X)) U12(ok(X)) = 7X + 2 >= 7X + 2 = ok(U12(X)) isNePal(ok(X)) = 4X + 6 >= 4X + 6 = ok(isNePal(X)) top(mark(X)) = X + 4 >= X + 4 = top(proper(X)) top(ok(X)) = X + 4 >= X + 4 = 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)) __(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)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [top](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [ok](x0) = [0 0 0]x0 [0 0 1] , [proper](x0) = x0 , [1 0 0] [isNePal](x0) = [0 1 0]x0 [1 0 0] , [1 0 0] [U12](x0) = [0 0 0]x0 [0 0 1] , [1 0 1] [U11](x0) = [0 1 0]x0 [0 0 1] , [0] [tt] = [0] [1], [0] [nil] = [0] [1], [1 0 0] [mark](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [active](x0) = [1 1 0]x0 [0 0 1] , [1 0 1] [1 0 1] [0] [__](x0, x1) = [0 1 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [1] orientation: [1 0 1] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [1 0 1] [1] active(__(__(X,Y),Z)) = [1 1 1]X + [1 0 1]Y + [1 0 1]Z + [1] >= [0 0 0]X + [0 0 0]Y + [0 0 0]Z + [0] = mark(__(X,__(Y,Z))) [0 0 0] [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0 0 0] [1] [1] [0] active(U11(tt())) = [1] >= [0] = mark(U12(tt())) [1] [1] [1 0 1] [1 0 1] [0] [1 0 1] [1 0 1] [0] active(__(X1,X2)) = [1 1 1]X1 + [1 0 1]X2 + [0] >= [1 1 0]X1 + [0 0 0]X2 + [0] = __(active(X1),X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 1] [1 0 1] [0] [1 0 1] [1 0 1] [0] active(__(X1,X2)) = [1 1 1]X1 + [1 0 1]X2 + [0] >= [0 1 0]X1 + [0 0 0]X2 + [0] = __(X1,active(X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 1] [1 0 1] active(U11(X)) = [1 1 1]X >= [1 1 0]X = U11(active(X)) [0 0 1] [0 0 1] [1 0 0] [1 0 0] active(U12(X)) = [1 0 0]X >= [0 0 0]X = U12(active(X)) [0 0 1] [0 0 1] [1 0 0] [1 0 0] active(isNePal(X)) = [1 1 0]X >= [1 1 0]X = isNePal(active(X)) [1 0 0] [1 0 0] [1 0 1] [1 0 1] [0] [1 0 1] [1 0 1] [0] __(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = mark(__(X1,X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 1] [1 0 1] [0] [1 0 1] [1 0 1] [0] __(X1,mark(X2)) = [0 1 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = mark(__(X1,X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 1] [1 0 1] U11(mark(X)) = [0 0 0]X >= [0 0 0]X = mark(U11(X)) [0 0 1] [0 0 1] [1 0 0] [1 0 0] U12(mark(X)) = [0 0 0]X >= [0 0 0]X = mark(U12(X)) [0 0 1] [0 0 1] [1 0 0] [1 0 0] isNePal(mark(X)) = [0 0 0]X >= [0 0 0]X = mark(isNePal(X)) [1 0 0] [1 0 0] [1 0 1] [1 0 1] [0] [1 0 1] [1 0 1] [0] proper(__(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 + [0] >= [0 1 0]X1 + [0 0 0]X2 + [0] = __(proper(X1),proper(X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [0] [0] proper(nil()) = [0] >= [0] = ok(nil()) [1] [1] [1 0 1] [1 0 1] proper(U11(X)) = [0 1 0]X >= [0 1 0]X = U11(proper(X)) [0 0 1] [0 0 1] [0] [0] proper(tt()) = [0] >= [0] = ok(tt()) [1] [1] [1 0 0] [1 0 0] proper(U12(X)) = [0 0 0]X >= [0 0 0]X = U12(proper(X)) [0 0 1] [0 0 1] [1 0 0] [1 0 0] proper(isNePal(X)) = [0 1 0]X >= [0 1 0]X = isNePal(proper(X)) [1 0 0] [1 0 0] [1 0 1] [1 0 1] [0] [1 0 1] [1 0 1] [0] __(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = ok(__(X1,X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 1] [1 0 1] U11(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(U11(X)) [0 0 1] [0 0 1] [1 0 0] [1 0 0] U12(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(U12(X)) [0 0 1] [0 0 1] [1 0 0] [1 0 0] isNePal(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isNePal(X)) [1 0 0] [1 0 0] [1 0 1] [1 0 1] top(mark(X)) = [0 0 0]X >= [0 0 0]X = top(proper(X)) [0 0 0] [0 0 0] [1 0 1] [1 0 1] top(ok(X)) = [0 0 0]X >= [0 0 0]X = top(active(X)) [0 0 0] [0 0 0] problem: active(__(__(X,Y),Z)) -> mark(__(X,__(Y,Z))) 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)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = 2x0, [ok](x0) = x0, [proper](x0) = x0, [isNePal](x0) = x0, [U12](x0) = x0, [U11](x0) = x0, [tt] = 0, [nil] = 0, [mark](x0) = x0 + 1, [active](x0) = x0, [__](x0, x1) = 3x0 + x1 + 1 orientation: active(__(__(X,Y),Z)) = 9X + 3Y + Z + 4 >= 3X + 3Y + Z + 3 = mark(__(X,__(Y,Z))) 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)) = X >= X = U11(active(X)) active(U12(X)) = X >= X = U12(active(X)) active(isNePal(X)) = X >= X = isNePal(active(X)) __(mark(X1),X2) = 3X1 + X2 + 4 >= 3X1 + X2 + 2 = mark(__(X1,X2)) __(X1,mark(X2)) = 3X1 + X2 + 2 >= 3X1 + X2 + 2 = mark(__(X1,X2)) U11(mark(X)) = X + 1 >= X + 1 = mark(U11(X)) U12(mark(X)) = X + 1 >= X + 1 = mark(U12(X)) isNePal(mark(X)) = X + 1 >= X + 1 = mark(isNePal(X)) proper(__(X1,X2)) = 3X1 + X2 + 1 >= 3X1 + X2 + 1 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X)) = X >= X = U11(proper(X)) proper(tt()) = 0 >= 0 = ok(tt()) proper(U12(X)) = X >= X = U12(proper(X)) proper(isNePal(X)) = X >= X = isNePal(proper(X)) __(ok(X1),ok(X2)) = 3X1 + X2 + 1 >= 3X1 + X2 + 1 = ok(__(X1,X2)) U11(ok(X)) = X >= X = ok(U11(X)) U12(ok(X)) = X >= X = ok(U12(X)) isNePal(ok(X)) = X >= X = ok(isNePal(X)) top(mark(X)) = 2X + 2 >= 2X = top(proper(X)) top(ok(X)) = 2X >= 2X = 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)) __(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(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [top](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [ok](x0) = [0 1 0]x0 [1 0 0] , [proper](x0) = x0 , [1 0 0] [isNePal](x0) = [0 1 0]x0 [1 0 0] , [1] [U12](x0) = x0 + [0] [1], [1 0 0] [U11](x0) = [0 1 0]x0 [1 0 0] , [1] [tt] = [1] [1], [1] [nil] = [1] [1], [1 0 0] [0] [mark](x0) = [0 1 0]x0 + [1] [0 0 0] [0], [active](x0) = x0 , [1 0 0] [1 1 0] [__](x0, x1) = [0 0 0]x0 + [0 1 0]x1 [1 0 0] [0 1 1] orientation: [1 0 0] [1 1 0] [1 0 0] [1 1 0] active(__(X1,X2)) = [0 0 0]X1 + [0 1 0]X2 >= [0 0 0]X1 + [0 1 0]X2 = __(active(X1),X2) [1 0 0] [0 1 1] [1 0 0] [0 1 1] [1 0 0] [1 1 0] [1 0 0] [1 1 0] active(__(X1,X2)) = [0 0 0]X1 + [0 1 0]X2 >= [0 0 0]X1 + [0 1 0]X2 = __(X1,active(X2)) [1 0 0] [0 1 1] [1 0 0] [0 1 1] [1 0 0] [1 0 0] active(U11(X)) = [0 1 0]X >= [0 1 0]X = U11(active(X)) [1 0 0] [1 0 0] [1] [1] active(U12(X)) = X + [0] >= X + [0] = U12(active(X)) [1] [1] [1 0 0] [1 0 0] active(isNePal(X)) = [0 1 0]X >= [0 1 0]X = isNePal(active(X)) [1 0 0] [1 0 0] [1 0 0] [1 1 0] [1] [1 0 0] [1 1 0] [0] __(X1,mark(X2)) = [0 0 0]X1 + [0 1 0]X2 + [1] >= [0 0 0]X1 + [0 1 0]X2 + [1] = mark(__(X1,X2)) [1 0 0] [0 1 0] [1] [0 0 0] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] U11(mark(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = mark(U11(X)) [1 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] U12(mark(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = mark(U12(X)) [0 0 0] [1] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] isNePal(mark(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = mark(isNePal(X)) [1 0 0] [0] [0 0 0] [0] [1 0 0] [1 1 0] [1 0 0] [1 1 0] proper(__(X1,X2)) = [0 0 0]X1 + [0 1 0]X2 >= [0 0 0]X1 + [0 1 0]X2 = __(proper(X1),proper(X2)) [1 0 0] [0 1 1] [1 0 0] [0 1 1] [1] [1] proper(nil()) = [1] >= [1] = ok(nil()) [1] [1] [1 0 0] [1 0 0] proper(U11(X)) = [0 1 0]X >= [0 1 0]X = U11(proper(X)) [1 0 0] [1 0 0] [1] [1] proper(tt()) = [1] >= [1] = ok(tt()) [1] [1] [1] [1] proper(U12(X)) = X + [0] >= X + [0] = U12(proper(X)) [1] [1] [1 0 0] [1 0 0] proper(isNePal(X)) = [0 1 0]X >= [0 1 0]X = isNePal(proper(X)) [1 0 0] [1 0 0] [1 0 0] [1 1 0] [1 0 0] [1 1 0] __(ok(X1),ok(X2)) = [0 0 0]X1 + [0 1 0]X2 >= [0 0 0]X1 + [0 1 0]X2 = ok(__(X1,X2)) [1 0 0] [1 1 0] [1 0 0] [1 1 0] [1 0 0] [1 0 0] U11(ok(X)) = [0 1 0]X >= [0 1 0]X = ok(U11(X)) [1 0 0] [1 0 0] [1 0 0] [1] [1 0 0] [1] U12(ok(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = ok(U12(X)) [1 0 0] [1] [1 0 0] [1] [1 0 0] [1 0 0] isNePal(ok(X)) = [0 1 0]X >= [0 1 0]X = ok(isNePal(X)) [1 0 0] [1 0 0] [1 0 0] [1 0 0] top(ok(X)) = [0 0 0]X >= [0 0 0]X = top(active(X)) [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)) 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(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [top](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [0] [ok](x0) = [0 0 0]x0 + [0] [0 0 1] [1], [1 1 0] [0] [proper](x0) = [0 1 0]x0 + [0] [0 0 0] [1], [isNePal](x0) = x0 , [U12](x0) = x0 , [U11](x0) = x0 , [0] [tt] = [0] [0], [1] [nil] = [0] [0], [1 0 0] [0] [mark](x0) = [0 1 0]x0 + [0] [0 0 0] [1], [1 1 0] [active](x0) = [0 1 0]x0 [0 0 1] , [1 0 1] [1 0 0] [0] [__](x0, x1) = [0 1 0]x0 + [0 1 0]x1 + [1] [0 0 1] [0 0 0] [0] orientation: [1 1 1] [1 1 0] [1] [1 1 1] [1 0 0] [0] active(__(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [1] = __(active(X1),X2) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [1 1 1] [1 1 0] [1] [1 0 1] [1 1 0] [0] active(__(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [1] = __(X1,active(X2)) [0 0 1] [0 0 0] [0] [0 0 1] [0 0 0] [0] [1 1 0] [1 1 0] active(U11(X)) = [0 1 0]X >= [0 1 0]X = U11(active(X)) [0 0 1] [0 0 1] [1 1 0] [1 1 0] active(U12(X)) = [0 1 0]X >= [0 1 0]X = U12(active(X)) [0 0 1] [0 0 1] [1 1 0] [1 1 0] active(isNePal(X)) = [0 1 0]X >= [0 1 0]X = isNePal(active(X)) [0 0 1] [0 0 1] [1 0 0] [0] [1 0 0] [0] U11(mark(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = mark(U11(X)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] U12(mark(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = mark(U12(X)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] isNePal(mark(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = mark(isNePal(X)) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1 1 0] [1] [1 1 0] [1 1 0] [1] proper(__(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [1] = __(proper(X1),proper(X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1] [1] proper(nil()) = [0] >= [0] = ok(nil()) [1] [1] [1 1 0] [0] [1 1 0] [0] proper(U11(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = U11(proper(X)) [0 0 0] [1] [0 0 0] [1] [0] [0] proper(tt()) = [0] >= [0] = ok(tt()) [1] [1] [1 1 0] [0] [1 1 0] [0] proper(U12(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = U12(proper(X)) [0 0 0] [1] [0 0 0] [1] [1 1 0] [0] [1 1 0] [0] proper(isNePal(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = isNePal(proper(X)) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1 1 0] [1] [1 1 1] [1 1 0] [1] __(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [0] = ok(__(X1,X2)) [0 0 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] [1 1 0] [0] [1 1 0] [0] U11(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(U11(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [0] [1 1 0] [0] U12(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(U12(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [0] [1 1 0] [0] isNePal(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(isNePal(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [1 1 0] top(ok(X)) = [0 0 0]X >= [0 0 0]X = top(active(X)) [0 0 0] [0 0 0] problem: active(U11(X)) -> U11(active(X)) active(U12(X)) -> U12(active(X)) active(isNePal(X)) -> isNePal(active(X)) 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(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [top](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [0] [ok](x0) = [0 1 1]x0 + [0] [0 0 1] [1], [1 1 0] [0] [proper](x0) = [0 1 0]x0 + [0] [0 0 0] [1], [isNePal](x0) = x0 , [1 0 1] [0] [U12](x0) = [0 1 0]x0 + [1] [0 0 1] [0], [1 0 1] [0] [U11](x0) = [0 1 0]x0 + [1] [0 0 1] [0], [0] [tt] = [0] [0], [0] [nil] = [0] [0], [1 0 0] [1] [mark](x0) = [0 0 0]x0 + [0] [0 0 1] [0], [1 1 0] [active](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [__](x0, x1) = [0 1 0]x0 + x1 [0 0 0] orientation: [1 1 1] [1] [1 1 0] [0] active(U11(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = U11(active(X)) [0 0 0] [0] [0 0 0] [0] [1 1 1] [1] [1 1 0] [0] active(U12(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = U12(active(X)) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1 1 0] active(isNePal(X)) = [0 1 0]X >= [0 1 0]X = isNePal(active(X)) [0 0 0] [0 0 0] [1 0 1] [1] [1 0 1] [1] U11(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = mark(U11(X)) [0 0 1] [0] [0 0 1] [0] [1 0 1] [1] [1 0 1] [1] U12(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = mark(U12(X)) [0 0 1] [0] [0 0 1] [0] [1 0 0] [1] [1 0 0] [1] isNePal(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(isNePal(X)) [0 0 1] [0] [0 0 1] [0] [1 1 0] [1 1 0] [0] [1 1 0] [1 1 0] [0] proper(__(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 + [0] >= [0 1 0]X1 + [0 1 0]X2 + [0] = __(proper(X1),proper(X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [0] [0] proper(nil()) = [0] >= [0] = ok(nil()) [1] [1] [1 1 1] [1] [1 1 0] [1] proper(U11(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = U11(proper(X)) [0 0 0] [1] [0 0 0] [1] [0] [0] proper(tt()) = [0] >= [0] = ok(tt()) [1] [1] [1 1 1] [1] [1 1 0] [1] proper(U12(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = U12(proper(X)) [0 0 0] [1] [0 0 0] [1] [1 1 0] [0] [1 1 0] [0] proper(isNePal(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = isNePal(proper(X)) [0 0 0] [1] [0 0 0] [1] [1 1 0] [1 1 0] [0] [1 1 0] [1 1 0] [0] __(ok(X1),ok(X2)) = [0 1 1]X1 + [0 1 1]X2 + [0] >= [0 1 0]X1 + [0 1 1]X2 + [0] = ok(__(X1,X2)) [0 0 0] [0 0 1] [1] [0 0 0] [0 0 1] [1] [1 1 1] [1] [1 1 1] [1] U11(ok(X)) = [0 1 1]X + [1] >= [0 1 1]X + [1] = ok(U11(X)) [0 0 1] [1] [0 0 1] [1] [1 1 1] [1] [1 1 1] [1] U12(ok(X)) = [0 1 1]X + [1] >= [0 1 1]X + [1] = ok(U12(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [0] [1 1 0] [0] isNePal(ok(X)) = [0 1 1]X + [0] >= [0 1 1]X + [0] = ok(isNePal(X)) [0 0 1] [1] [0 0 1] [1] [1 1 0] [1 1 0] top(ok(X)) = [0 0 0]X >= [0 0 0]X = top(active(X)) [0 0 0] [0 0 0] problem: active(isNePal(X)) -> isNePal(active(X)) 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(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = x0 + 2, [ok](x0) = 2x0 + 1, [proper](x0) = 2x0 + 1, [isNePal](x0) = 2x0 + 1, [U12](x0) = 3x0 + 2, [U11](x0) = 6x0 + 5, [tt] = 0, [nil] = 0, [mark](x0) = 5x0 + 4, [active](x0) = x0, [__](x0, x1) = 4x0 + 4x1 + 7 orientation: active(isNePal(X)) = 2X + 1 >= 2X + 1 = isNePal(active(X)) U11(mark(X)) = 30X + 29 >= 30X + 29 = mark(U11(X)) U12(mark(X)) = 15X + 14 >= 15X + 14 = mark(U12(X)) isNePal(mark(X)) = 10X + 9 >= 10X + 9 = mark(isNePal(X)) proper(__(X1,X2)) = 8X1 + 8X2 + 15 >= 8X1 + 8X2 + 15 = __(proper(X1),proper(X2)) proper(nil()) = 1 >= 1 = ok(nil()) proper(U11(X)) = 12X + 11 >= 12X + 11 = U11(proper(X)) proper(tt()) = 1 >= 1 = ok(tt()) proper(U12(X)) = 6X + 5 >= 6X + 5 = U12(proper(X)) proper(isNePal(X)) = 4X + 3 >= 4X + 3 = isNePal(proper(X)) __(ok(X1),ok(X2)) = 8X1 + 8X2 + 15 >= 8X1 + 8X2 + 15 = ok(__(X1,X2)) U11(ok(X)) = 12X + 11 >= 12X + 11 = ok(U11(X)) U12(ok(X)) = 6X + 5 >= 6X + 5 = ok(U12(X)) isNePal(ok(X)) = 4X + 3 >= 4X + 3 = ok(isNePal(X)) top(ok(X)) = 2X + 3 >= X + 2 = top(active(X)) problem: active(isNePal(X)) -> isNePal(active(X)) 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)) Matrix Interpretation Processor: dim=1 interpretation: [ok](x0) = 4x0 + 4, [proper](x0) = 4x0 + 4, [isNePal](x0) = 4x0 + 4, [U12](x0) = 4x0 + 4, [U11](x0) = x0, [tt] = 0, [nil] = 2, [mark](x0) = x0, [active](x0) = 6x0 + 3, [__](x0, x1) = 3x0 + x1 + 4 orientation: active(isNePal(X)) = 24X + 27 >= 24X + 16 = isNePal(active(X)) U11(mark(X)) = X >= X = mark(U11(X)) U12(mark(X)) = 4X + 4 >= 4X + 4 = mark(U12(X)) isNePal(mark(X)) = 4X + 4 >= 4X + 4 = mark(isNePal(X)) proper(__(X1,X2)) = 12X1 + 4X2 + 20 >= 12X1 + 4X2 + 20 = __(proper(X1),proper(X2)) proper(nil()) = 12 >= 12 = ok(nil()) proper(U11(X)) = 4X + 4 >= 4X + 4 = U11(proper(X)) proper(tt()) = 4 >= 4 = ok(tt()) proper(U12(X)) = 16X + 20 >= 16X + 20 = U12(proper(X)) proper(isNePal(X)) = 16X + 20 >= 16X + 20 = isNePal(proper(X)) __(ok(X1),ok(X2)) = 12X1 + 4X2 + 20 >= 12X1 + 4X2 + 20 = ok(__(X1,X2)) U11(ok(X)) = 4X + 4 >= 4X + 4 = ok(U11(X)) U12(ok(X)) = 16X + 20 >= 16X + 20 = ok(U12(X)) isNePal(ok(X)) = 16X + 20 >= 16X + 20 = ok(isNePal(X)) problem: 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)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [ok](x0) = [0 1 0]x0 [0 0 0] , [1 0 1] [0] [proper](x0) = [0 0 0]x0 + [1] [0 0 1] [0], [1 0 0] [isNePal](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [1] [U12](x0) = [0 0 0]x0 + [0] [0 0 1] [0], [1 1 0] [0] [U11](x0) = [0 0 0]x0 + [1] [0 0 1] [1], [0] [tt] = [0] [1], [0] [nil] = [0] [0], [1 0 0] [mark](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [1 0 0] [__](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 1] [0 0 1] orientation: [1 1 0] [0] [1 1 0] [0] U11(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = mark(U11(X)) [0 0 0] [1] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] U12(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(U12(X)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 0] isNePal(mark(X)) = [0 0 0]X >= [0 0 0]X = mark(isNePal(X)) [0 0 0] [0 0 0] [1 0 1] [1 0 1] [0] [1 0 1] [1 0 1] proper(__(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 = __(proper(X1),proper(X2)) [0 0 1] [0 0 1] [0] [0 0 1] [0 0 1] [0] [0] proper(nil()) = [1] >= [0] = ok(nil()) [0] [0] [1 1 1] [1] [1 0 1] [1] proper(U11(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = U11(proper(X)) [0 0 1] [1] [0 0 1] [1] [1] [0] proper(tt()) = [1] >= [0] = ok(tt()) [1] [0] [1 0 1] [1] [1 0 1] [1] proper(U12(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = U12(proper(X)) [0 0 1] [0] [0 0 1] [0] [1 0 1] [0] [1 0 1] proper(isNePal(X)) = [0 0 0]X + [1] >= [0 0 0]X = isNePal(proper(X)) [0 0 1] [0] [0 0 1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] __(ok(X1),ok(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = ok(__(X1,X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [0] [1 1 0] [0] U11(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = ok(U11(X)) [0 0 0] [1] [0 0 0] [0] [1 0 0] [1] [1 0 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] [1 0 0] [1 0 0] isNePal(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isNePal(X)) [0 0 0] [0 0 0] problem: 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(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)) Matrix Interpretation Processor: dim=1 interpretation: [ok](x0) = 3x0 + 2, [proper](x0) = 4x0, [isNePal](x0) = 2x0 + 1, [U12](x0) = 2x0, [U11](x0) = 3x0, [nil] = 2, [mark](x0) = x0, [__](x0, x1) = 6x0 + 6x1 orientation: U11(mark(X)) = 3X >= 3X = mark(U11(X)) U12(mark(X)) = 2X >= 2X = mark(U12(X)) isNePal(mark(X)) = 2X + 1 >= 2X + 1 = mark(isNePal(X)) proper(__(X1,X2)) = 24X1 + 24X2 >= 24X1 + 24X2 = __(proper(X1),proper(X2)) proper(nil()) = 8 >= 8 = ok(nil()) proper(U11(X)) = 12X >= 12X = U11(proper(X)) proper(U12(X)) = 8X >= 8X = U12(proper(X)) proper(isNePal(X)) = 8X + 4 >= 8X + 1 = isNePal(proper(X)) __(ok(X1),ok(X2)) = 18X1 + 18X2 + 24 >= 18X1 + 18X2 + 2 = ok(__(X1,X2)) U11(ok(X)) = 9X + 6 >= 9X + 2 = ok(U11(X)) U12(ok(X)) = 6X + 4 >= 6X + 2 = ok(U12(X)) isNePal(ok(X)) = 6X + 5 >= 6X + 5 = ok(isNePal(X)) problem: 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(U12(X)) -> U12(proper(X)) isNePal(ok(X)) -> ok(isNePal(X)) Matrix Interpretation Processor: dim=1 interpretation: [ok](x0) = 2x0, [proper](x0) = x0, [isNePal](x0) = 2x0, [U12](x0) = 2x0, [U11](x0) = 2x0, [nil] = 0, [mark](x0) = 4x0 + 4, [__](x0, x1) = 4x0 + 2x1 + 2 orientation: U11(mark(X)) = 8X + 8 >= 8X + 4 = mark(U11(X)) U12(mark(X)) = 8X + 8 >= 8X + 4 = mark(U12(X)) isNePal(mark(X)) = 8X + 8 >= 8X + 4 = mark(isNePal(X)) proper(__(X1,X2)) = 4X1 + 2X2 + 2 >= 4X1 + 2X2 + 2 = __(proper(X1),proper(X2)) proper(nil()) = 0 >= 0 = ok(nil()) proper(U11(X)) = 2X >= 2X = U11(proper(X)) proper(U12(X)) = 2X >= 2X = U12(proper(X)) isNePal(ok(X)) = 4X >= 4X = ok(isNePal(X)) problem: proper(__(X1,X2)) -> __(proper(X1),proper(X2)) proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) proper(U12(X)) -> U12(proper(X)) isNePal(ok(X)) -> ok(isNePal(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 1 1] [ok](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [proper](x0) = [1 1 0]x0 [0 0 0] , [1 0 0] [isNePal](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [U12](x0) = [0 1 0]x0 + [1] [0 0 0] [0], [1 0 0] [1] [U11](x0) = [0 1 0]x0 + [0] [0 0 0] [0], [0] [nil] = [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 0] [0] proper(__(X1,X2)) = [1 1 0]X1 + [1 1 1]X2 + [1] >= [1 1 0]X1 + [1 1 0]X2 + [1] = __(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 1 0] [1] [1 1 0] [1] proper(U11(X)) = [1 1 0]X + [1] >= [1 1 0]X + [0] = U11(proper(X)) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1] [1 1 0] [0] proper(U12(X)) = [1 1 0]X + [1] >= [1 1 0]X + [1] = U12(proper(X)) [0 0 0] [0] [0 0 0] [0] [1 1 1] [1 0 0] isNePal(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(isNePal(X)) [0 0 0] [0 0 0] problem: proper(nil()) -> ok(nil()) proper(U11(X)) -> U11(proper(X)) isNePal(ok(X)) -> ok(isNePal(X)) Matrix Interpretation Processor: dim=3 interpretation: [ok](x0) = x0 , [1 0 1] [1] [proper](x0) = [0 1 0]x0 + [0] [0 0 0] [1], [1 0 0] [0] [isNePal](x0) = [1 0 0]x0 + [1] [0 1 1] [0], [U11](x0) = x0 , [0] [nil] = [0] [0] orientation: [1] [0] proper(nil()) = [0] >= [0] = ok(nil()) [1] [0] [1 0 1] [1] [1 0 1] [1] proper(U11(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = U11(proper(X)) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] isNePal(ok(X)) = [1 0 0]X + [1] >= [1 0 0]X + [1] = ok(isNePal(X)) [0 1 1] [0] [0 1 1] [0] problem: proper(U11(X)) -> U11(proper(X)) isNePal(ok(X)) -> ok(isNePal(X)) Matrix Interpretation Processor: dim=1 interpretation: [ok](x0) = 2x0 + 2, [proper](x0) = x0 + 1, [isNePal](x0) = 4x0 + 3, [U11](x0) = x0 + 1 orientation: proper(U11(X)) = X + 2 >= X + 2 = U11(proper(X)) isNePal(ok(X)) = 8X + 11 >= 8X + 8 = ok(isNePal(X)) problem: proper(U11(X)) -> U11(proper(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [proper](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [0] [U11](x0) = [0 0 0]x0 + [0] [0 0 1] [1] orientation: [1 0 1] [1] [1 0 1] [0] proper(U11(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = U11(proper(X)) [0 0 1] [1] [0 0 1] [1] problem: Qed