YES Problem: active(fst(0(),Z)) -> mark(nil()) active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) active(len(nil())) -> mark(0()) active(len(cons(X,Z))) -> mark(s(len(Z))) mark(fst(X1,X2)) -> active(fst(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(X)) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(add(X1,X2)) -> active(add(mark(X1),mark(X2))) mark(len(X)) -> active(len(mark(X))) fst(mark(X1),X2) -> fst(X1,X2) fst(X1,mark(X2)) -> fst(X1,X2) fst(active(X1),X2) -> fst(X1,X2) fst(X1,active(X2)) -> fst(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) add(mark(X1),X2) -> add(X1,X2) add(X1,mark(X2)) -> add(X1,X2) add(active(X1),X2) -> add(X1,X2) add(X1,active(X2)) -> add(X1,X2) len(mark(X)) -> len(X) len(active(X)) -> len(X) Proof: Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [0] [len](x0) = [0 1 1]x0 + [1] [0 0 0] [0], [1 1 0] [1 1 0] [add](x0, x1) = [0 1 1]x0 + [0 0 0]x1 [0 0 0] [0 1 1] , [1 1 0] [from](x0) = [1 1 0]x0 [0 0 0] , [1 1 0] [1 0 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 1]x1 [0 0 0] [0 1 1] , [1 0 0] [s](x0) = [0 0 0]x0 [0 1 1] , [1 1 0] [mark](x0) = [0 0 0]x0 [0 1 1] , [0] [nil] = [0] [0], [1 1 0] [active](x0) = [0 0 0]x0 [0 1 1] , [1 1 0] [1 1 0] [fst](x0, x1) = [0 1 1]x0 + [0 1 1]x1 [0 0 0] [0 0 0] , [0] [0] = [0] [0] orientation: [1 2 1] [0] active(fst(0(),Z)) = [0 0 0]Z >= [0] = mark(nil()) [0 1 1] [0] [1 1 1] [1 1 0] [1 1 3] [1 1 0] [1 1 0] [1 1 0] active(fst(s(X),cons(Y,Z))) = [0 0 0]X + [0 0 0]Y + [0 0 0]Z >= [0 0 0]X + [0 0 0]Y + [0 0 0]Z = mark(cons(Y,fst(X,Z))) [0 1 1] [0 0 0] [0 1 2] [0 1 1] [0 0 0] [0 1 1] [2 2 0] [2 1 0] active(from(X)) = [0 0 0]X >= [0 0 0]X = mark(cons(X,from(s(X)))) [1 1 0] [1 0 0] [1 1 0] [1 1 0] active(add(0(),X)) = [0 0 0]X >= [0 0 0]X = mark(X) [0 1 1] [0 1 1] [1 1 1] [1 1 0] [1 1 0] [1 1 0] active(add(s(X),Y)) = [0 0 0]X + [0 0 0]Y >= [0 0 0]X + [0 0 0]Y = mark(s(add(X,Y))) [0 1 1] [0 1 1] [0 1 1] [0 1 1] [1] [0] active(len(nil())) = [0] >= [0] = mark(0()) [1] [0] [1 1 0] [1 1 3] [1] [1 1 0] [0] active(len(cons(X,Z))) = [0 0 0]X + [0 0 0]Z + [0] >= [0 0 0]Z + [0] = mark(s(len(Z))) [0 0 0] [0 1 2] [1] [0 1 1] [1] [1 2 1] [1 2 1] [1 2 1] [1 2 1] mark(fst(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(fst(mark(X1),mark(X2))) [0 1 1] [0 1 1] [0 1 1] [0 1 1] [0] [0] mark(0()) = [0] >= [0] = active(0()) [0] [0] [0] [0] mark(nil()) = [0] >= [0] = active(nil()) [0] [0] [1 0 0] [1 0 0] mark(s(X)) = [0 0 0]X >= [0 0 0]X = active(s(X)) [0 1 1] [0 1 1] [1 1 0] [1 0 1] [1 1 0] [1 0 1] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(cons(mark(X1),X2)) [0 0 0] [0 1 2] [0 0 0] [0 1 2] [2 2 0] [2 2 0] mark(from(X)) = [0 0 0]X >= [0 0 0]X = active(from(mark(X))) [1 1 0] [1 1 0] [1 2 1] [1 1 0] [1 2 1] [1 1 0] mark(add(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(add(mark(X1),mark(X2))) [0 1 1] [0 1 1] [0 1 1] [0 1 1] [1 2 1] [1] [1 2 1] [1] mark(len(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(len(mark(X))) [0 1 1] [1] [0 1 1] [1] [1 1 0] [1 1 0] [1 1 0] [1 1 0] fst(mark(X1),X2) = [0 1 1]X1 + [0 1 1]X2 >= [0 1 1]X1 + [0 1 1]X2 = fst(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] fst(X1,mark(X2)) = [0 1 1]X1 + [0 1 1]X2 >= [0 1 1]X1 + [0 1 1]X2 = fst(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] fst(active(X1),X2) = [0 1 1]X1 + [0 1 1]X2 >= [0 1 1]X1 + [0 1 1]X2 = fst(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] fst(X1,active(X2)) = [0 1 1]X1 + [0 1 1]X2 >= [0 1 1]X1 + [0 1 1]X2 = fst(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 0 0] s(mark(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 1 1] [0 1 1] [1 1 0] [1 0 0] s(active(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 1 1] [0 1 1] [1 1 0] [1 0 0] [1 1 0] [1 0 0] cons(mark(X1),X2) = [0 0 0]X1 + [0 0 1]X2 >= [0 0 0]X1 + [0 0 1]X2 = cons(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 1 0] [1 1 0] [1 0 0] cons(X1,mark(X2)) = [0 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 0 1]X2 = cons(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 0 0] [1 1 0] [1 0 0] cons(active(X1),X2) = [0 0 0]X1 + [0 0 1]X2 >= [0 0 0]X1 + [0 0 1]X2 = cons(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 1 0] [1 1 0] [1 0 0] cons(X1,active(X2)) = [0 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 0 1]X2 = cons(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 1 0] from(mark(X)) = [1 1 0]X >= [1 1 0]X = from(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] from(active(X)) = [1 1 0]X >= [1 1 0]X = from(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] add(mark(X1),X2) = [0 1 1]X1 + [0 0 0]X2 >= [0 1 1]X1 + [0 0 0]X2 = add(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 1 0] [1 1 0] [1 1 0] add(X1,mark(X2)) = [0 1 1]X1 + [0 0 0]X2 >= [0 1 1]X1 + [0 0 0]X2 = add(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 1 0] [1 1 0] [1 1 0] add(active(X1),X2) = [0 1 1]X1 + [0 0 0]X2 >= [0 1 1]X1 + [0 0 0]X2 = add(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 1 0] [1 1 0] [1 1 0] add(X1,active(X2)) = [0 1 1]X1 + [0 0 0]X2 >= [0 1 1]X1 + [0 0 0]X2 = add(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [0] [1 1 0] [0] len(mark(X)) = [0 1 1]X + [1] >= [0 1 1]X + [1] = len(X) [0 0 0] [0] [0 0 0] [0] [1 1 0] [0] [1 1 0] [0] len(active(X)) = [0 1 1]X + [1] >= [0 1 1]X + [1] = len(X) [0 0 0] [0] [0 0 0] [0] problem: active(fst(0(),Z)) -> mark(nil()) active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) active(add(0(),X)) -> mark(X) active(add(s(X),Y)) -> mark(s(add(X,Y))) mark(fst(X1,X2)) -> active(fst(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(X)) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(add(X1,X2)) -> active(add(mark(X1),mark(X2))) mark(len(X)) -> active(len(mark(X))) fst(mark(X1),X2) -> fst(X1,X2) fst(X1,mark(X2)) -> fst(X1,X2) fst(active(X1),X2) -> fst(X1,X2) fst(X1,active(X2)) -> fst(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) add(mark(X1),X2) -> add(X1,X2) add(X1,mark(X2)) -> add(X1,X2) add(active(X1),X2) -> add(X1,X2) add(X1,active(X2)) -> add(X1,X2) len(mark(X)) -> len(X) len(active(X)) -> len(X) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [len](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [1 1 0] [add](x0, x1) = [0 1 1]x0 + [0 0 0]x1 [0 0 0] [0 1 1] , [1 1 0] [from](x0) = [1 1 0]x0 [0 0 0] , [1 1 0] [1 0 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 1 1] , [1 1 0] [s](x0) = [0 0 0]x0 [0 1 1] , [1 1 0] [mark](x0) = [0 0 0]x0 [0 1 1] , [0] [nil] = [0] [0], [1 1 0] [active](x0) = [0 0 0]x0 [0 1 1] , [1 1 0] [1 1 0] [fst](x0, x1) = [0 0 0]x0 + [0 1 1]x1 [0 0 0] [0 0 0] , [0] [0] = [0] [1] orientation: [1 2 1] [0] active(fst(0(),Z)) = [0 0 0]Z >= [0] = mark(nil()) [0 1 1] [0] [1 1 0] [1 1 0] [1 1 1] [1 1 0] [1 1 0] [1 1 0] active(fst(s(X),cons(Y,Z))) = [0 0 0]X + [0 0 0]Y + [0 0 0]Z >= [0 0 0]X + [0 0 0]Y + [0 0 0]Z = mark(cons(Y,fst(X,Z))) [0 0 0] [0 0 0] [0 1 1] [0 0 0] [0 0 0] [0 1 1] [2 2 0] [2 2 0] active(from(X)) = [0 0 0]X >= [0 0 0]X = mark(cons(X,from(s(X)))) [1 1 0] [1 1 0] [1 1 0] [1] [1 1 0] active(add(0(),X)) = [0 0 0]X + [0] >= [0 0 0]X = mark(X) [0 1 1] [1] [0 1 1] [1 2 1] [1 1 0] [1 2 1] [1 1 0] active(add(s(X),Y)) = [0 0 0]X + [0 0 0]Y >= [0 0 0]X + [0 0 0]Y = mark(s(add(X,Y))) [0 1 1] [0 1 1] [0 1 1] [0 1 1] [1 1 0] [1 2 1] [1 1 0] [1 2 1] mark(fst(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(fst(mark(X1),mark(X2))) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [0] [0] mark(0()) = [0] >= [0] = active(0()) [1] [1] [0] [0] mark(nil()) = [0] >= [0] = active(nil()) [0] [0] [1 1 0] [1 1 0] mark(s(X)) = [0 0 0]X >= [0 0 0]X = active(s(X)) [0 1 1] [0 1 1] [1 1 0] [1 0 0] [1 1 0] [1 0 0] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(cons(mark(X1),X2)) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [2 2 0] [2 2 0] mark(from(X)) = [0 0 0]X >= [0 0 0]X = active(from(mark(X))) [1 1 0] [1 1 0] [1 2 1] [1 1 0] [1 2 1] [1 1 0] mark(add(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(add(mark(X1),mark(X2))) [0 1 1] [0 1 1] [0 1 1] [0 1 1] [1 1 0] [1 1 0] mark(len(X)) = [0 0 0]X >= [0 0 0]X = active(len(mark(X))) [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] fst(mark(X1),X2) = [0 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 1 1]X2 = fst(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] fst(X1,mark(X2)) = [0 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 1 1]X2 = fst(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] fst(active(X1),X2) = [0 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 1 1]X2 = fst(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] fst(X1,active(X2)) = [0 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 1 1]X2 = fst(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] s(mark(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 1 1] [0 1 1] [1 1 0] [1 1 0] s(active(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 1 1] [0 1 1] [1 1 0] [1 0 0] [1 1 0] [1 0 0] cons(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 1 0] [1 1 0] [1 0 0] cons(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 0 0] [1 1 0] [1 0 0] cons(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 1 0] [1 1 0] [1 0 0] cons(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 1 0] from(mark(X)) = [1 1 0]X >= [1 1 0]X = from(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] from(active(X)) = [1 1 0]X >= [1 1 0]X = from(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] add(mark(X1),X2) = [0 1 1]X1 + [0 0 0]X2 >= [0 1 1]X1 + [0 0 0]X2 = add(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 1 0] [1 1 0] [1 1 0] add(X1,mark(X2)) = [0 1 1]X1 + [0 0 0]X2 >= [0 1 1]X1 + [0 0 0]X2 = add(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 1 0] [1 1 0] [1 1 0] add(active(X1),X2) = [0 1 1]X1 + [0 0 0]X2 >= [0 1 1]X1 + [0 0 0]X2 = add(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 1 0] [1 1 0] [1 1 0] add(X1,active(X2)) = [0 1 1]X1 + [0 0 0]X2 >= [0 1 1]X1 + [0 0 0]X2 = add(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 1 0] len(mark(X)) = [0 0 0]X >= [0 0 0]X = len(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] len(active(X)) = [0 0 0]X >= [0 0 0]X = len(X) [0 0 0] [0 0 0] problem: active(fst(0(),Z)) -> mark(nil()) active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) active(add(s(X),Y)) -> mark(s(add(X,Y))) mark(fst(X1,X2)) -> active(fst(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(X)) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(add(X1,X2)) -> active(add(mark(X1),mark(X2))) mark(len(X)) -> active(len(mark(X))) fst(mark(X1),X2) -> fst(X1,X2) fst(X1,mark(X2)) -> fst(X1,X2) fst(active(X1),X2) -> fst(X1,X2) fst(X1,active(X2)) -> fst(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) add(mark(X1),X2) -> add(X1,X2) add(X1,mark(X2)) -> add(X1,X2) add(active(X1),X2) -> add(X1,X2) add(X1,active(X2)) -> add(X1,X2) len(mark(X)) -> len(X) len(active(X)) -> len(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [0] [len](x0) = [0 0 0]x0 + [0] [1 0 1] [1], [1 0 1] [1 0 1] [0] [add](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 1 1] [0 0 0] [1], [1 0 1] [1] [from](x0) = [0 0 0]x0 + [0] [1 0 1] [0], [1 0 1] [1 0 0] [cons](x0, x1) = [0 0 0]x0 + [0 1 1]x1 [0 0 0] [0 0 0] , [1 0 1] [0] [s](x0) = [0 1 1]x0 + [1] [0 0 0] [0], [1 0 1] [mark](x0) = [0 1 1]x0 [0 0 0] , [0] [nil] = [1] [0], [1 0 1] [active](x0) = [0 1 1]x0 [0 0 0] , [1 0 1] [1 0 1] [fst](x0, x1) = [0 1 1]x0 + [0 0 0]x1 [0 0 0] [0 1 1] , [0] [0] = [1] [0] orientation: [1 1 2] [0] [0] active(fst(0(),Z)) = [0 1 1]Z + [1] >= [1] = mark(nil()) [0 0 0] [0] [0] [1 0 1] [1 0 1] [1 1 1] [0] [1 0 1] [1 0 1] [1 0 1] active(fst(s(X),cons(Y,Z))) = [0 1 1]X + [0 0 0]Y + [0 1 1]Z + [1] >= [0 1 1]X + [0 0 0]Y + [0 1 1]Z = mark(cons(Y,fst(X,Z))) [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] [2 0 2] [1] [2 0 2] [1] active(from(X)) = [1 0 1]X + [0] >= [1 0 1]X + [0] = mark(cons(X,from(s(X)))) [0 0 0] [0] [0 0 0] [0] [1 1 2] [1 0 1] [2] [1 1 2] [1 0 1] [1] active(add(s(X),Y)) = [0 1 1]X + [0 0 0]Y + [3] >= [0 1 1]X + [0 0 0]Y + [3] = mark(s(add(X,Y))) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 1 2] [1 0 1] [1 1 2] mark(fst(X1,X2)) = [0 1 1]X1 + [0 1 1]X2 >= [0 1 1]X1 + [0 1 1]X2 = active(fst(mark(X1),mark(X2))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0] [0] mark(0()) = [1] >= [1] = active(0()) [0] [0] [0] [0] mark(nil()) = [1] >= [1] = active(nil()) [0] [0] [1 0 1] [0] [1 0 1] [0] mark(s(X)) = [0 1 1]X + [1] >= [0 1 1]X + [1] = active(s(X)) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1 0 0] [1 0 1] [1 0 0] mark(cons(X1,X2)) = [0 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 1 1]X2 = active(cons(mark(X1),X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [2 0 2] [1] [2 0 2] [1] mark(from(X)) = [1 0 1]X + [0] >= [1 0 1]X + [0] = active(from(mark(X))) [0 0 0] [0] [0 0 0] [0] [1 1 2] [1 0 1] [1] [1 1 2] [1 0 1] [1] mark(add(X1,X2)) = [0 1 1]X1 + [0 0 0]X2 + [2] >= [0 1 1]X1 + [0 0 0]X2 + [2] = active(add(mark(X1),mark(X2))) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [2 0 2] [1] [2 0 2] [1] mark(len(X)) = [1 0 1]X + [1] >= [1 0 1]X + [1] = active(len(mark(X))) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] fst(mark(X1),X2) = [0 1 1]X1 + [0 0 0]X2 >= [0 1 1]X1 + [0 0 0]X2 = fst(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 0 1] [1 0 1] [1 0 1] [1 0 1] fst(X1,mark(X2)) = [0 1 1]X1 + [0 0 0]X2 >= [0 1 1]X1 + [0 0 0]X2 = fst(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 0 1] [1 0 1] [1 0 1] [1 0 1] fst(active(X1),X2) = [0 1 1]X1 + [0 0 0]X2 >= [0 1 1]X1 + [0 0 0]X2 = fst(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 0 1] [1 0 1] [1 0 1] [1 0 1] fst(X1,active(X2)) = [0 1 1]X1 + [0 0 0]X2 >= [0 1 1]X1 + [0 0 0]X2 = fst(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 0 1] [0] [1 0 1] [0] s(mark(X)) = [0 1 1]X + [1] >= [0 1 1]X + [1] = s(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [0] [1 0 1] [0] s(active(X)) = [0 1 1]X + [1] >= [0 1 1]X + [1] = s(X) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1 0 0] [1 0 1] [1 0 0] cons(mark(X1),X2) = [0 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 1 1]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1 0 1] [1 0 0] cons(X1,mark(X2)) = [0 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 1 1]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 0] [1 0 1] [1 0 0] cons(active(X1),X2) = [0 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 1 1]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1 0 1] [1 0 0] cons(X1,active(X2)) = [0 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 1 1]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1] [1 0 1] [1] from(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = from(X) [1 0 1] [0] [1 0 1] [0] [1 0 1] [1] [1 0 1] [1] from(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = from(X) [1 0 1] [0] [1 0 1] [0] [1 0 1] [1 0 1] [0] [1 0 1] [1 0 1] [0] add(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = add(X1,X2) [0 1 1] [0 0 0] [1] [0 1 1] [0 0 0] [1] [1 0 1] [1 0 1] [0] [1 0 1] [1 0 1] [0] add(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = add(X1,X2) [0 1 1] [0 0 0] [1] [0 1 1] [0 0 0] [1] [1 0 1] [1 0 1] [0] [1 0 1] [1 0 1] [0] add(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = add(X1,X2) [0 1 1] [0 0 0] [1] [0 1 1] [0 0 0] [1] [1 0 1] [1 0 1] [0] [1 0 1] [1 0 1] [0] add(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = add(X1,X2) [0 1 1] [0 0 0] [1] [0 1 1] [0 0 0] [1] [1 0 1] [0] [1 0 1] [0] len(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = len(X) [1 0 1] [1] [1 0 1] [1] [1 0 1] [0] [1 0 1] [0] len(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = len(X) [1 0 1] [1] [1 0 1] [1] problem: active(fst(0(),Z)) -> mark(nil()) active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(fst(X1,X2)) -> active(fst(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(X)) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(add(X1,X2)) -> active(add(mark(X1),mark(X2))) mark(len(X)) -> active(len(mark(X))) fst(mark(X1),X2) -> fst(X1,X2) fst(X1,mark(X2)) -> fst(X1,X2) fst(active(X1),X2) -> fst(X1,X2) fst(X1,active(X2)) -> fst(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) add(mark(X1),X2) -> add(X1,X2) add(X1,mark(X2)) -> add(X1,X2) add(active(X1),X2) -> add(X1,X2) add(X1,active(X2)) -> add(X1,X2) len(mark(X)) -> len(X) len(active(X)) -> len(X) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [len](x0) = [0 1 1]x0 [0 0 0] , [1 1 0] [1 1 0] [add](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 1 1] , [1 1 0] [from](x0) = [1 1 0]x0 [0 0 0] , [1 1 0] [1 0 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 1 1] , [1 1 0] [s](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [mark](x0) = [0 0 0]x0 [0 1 1] , [0] [nil] = [0] [0], [1 1 0] [active](x0) = [0 0 0]x0 [0 1 1] , [1 1 0] [1 1 0] [fst](x0, x1) = [0 0 0]x0 + [0 1 1]x1 [0 0 0] [0 0 0] , [1] [0] = [1] [0] orientation: [1 2 1] [2] [0] active(fst(0(),Z)) = [0 0 0]Z + [0] >= [0] = mark(nil()) [0 1 1] [0] [0] [1 1 0] [1 1 0] [1 1 1] [1 1 0] [1 1 0] [1 1 0] active(fst(s(X),cons(Y,Z))) = [0 0 0]X + [0 0 0]Y + [0 0 0]Z >= [0 0 0]X + [0 0 0]Y + [0 0 0]Z = mark(cons(Y,fst(X,Z))) [0 0 0] [0 0 0] [0 1 1] [0 0 0] [0 0 0] [0 1 1] [2 2 0] [2 2 0] active(from(X)) = [0 0 0]X >= [0 0 0]X = mark(cons(X,from(s(X)))) [1 1 0] [1 1 0] [1 1 0] [1 2 1] [1 1 0] [1 2 1] mark(fst(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(fst(mark(X1),mark(X2))) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [2] [2] mark(0()) = [0] >= [0] = active(0()) [1] [1] [0] [0] mark(nil()) = [0] >= [0] = active(nil()) [0] [0] [1 1 0] [1 1 0] mark(s(X)) = [0 0 0]X >= [0 0 0]X = active(s(X)) [0 0 0] [0 0 0] [1 1 0] [1 0 0] [1 1 0] [1 0 0] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(cons(mark(X1),X2)) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [2 2 0] [2 2 0] mark(from(X)) = [0 0 0]X >= [0 0 0]X = active(from(mark(X))) [1 1 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] mark(add(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(add(mark(X1),mark(X2))) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 2 1] [1 2 1] mark(len(X)) = [0 0 0]X >= [0 0 0]X = active(len(mark(X))) [0 1 1] [0 1 1] [1 1 0] [1 1 0] [1 1 0] [1 1 0] fst(mark(X1),X2) = [0 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 1 1]X2 = fst(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] fst(X1,mark(X2)) = [0 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 1 1]X2 = fst(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] fst(active(X1),X2) = [0 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 1 1]X2 = fst(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] fst(X1,active(X2)) = [0 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 1 1]X2 = fst(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] s(mark(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] s(active(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] [1 1 0] [1 0 0] [1 1 0] [1 0 0] cons(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 1 0] [1 1 0] [1 0 0] cons(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 0 0] [1 1 0] [1 0 0] cons(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 1 0] [1 1 0] [1 0 0] cons(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 1 0] from(mark(X)) = [1 1 0]X >= [1 1 0]X = from(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] from(active(X)) = [1 1 0]X >= [1 1 0]X = from(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] add(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = add(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 1 0] [1 1 0] [1 1 0] add(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = add(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 1 0] [1 1 0] [1 1 0] add(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = add(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 1 0] [1 1 0] [1 1 0] add(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = add(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 1 0] [1 1 0] len(mark(X)) = [0 1 1]X >= [0 1 1]X = len(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] len(active(X)) = [0 1 1]X >= [0 1 1]X = len(X) [0 0 0] [0 0 0] problem: active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(fst(X1,X2)) -> active(fst(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(X)) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(add(X1,X2)) -> active(add(mark(X1),mark(X2))) mark(len(X)) -> active(len(mark(X))) fst(mark(X1),X2) -> fst(X1,X2) fst(X1,mark(X2)) -> fst(X1,X2) fst(active(X1),X2) -> fst(X1,X2) fst(X1,active(X2)) -> fst(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) add(mark(X1),X2) -> add(X1,X2) add(X1,mark(X2)) -> add(X1,X2) add(active(X1),X2) -> add(X1,X2) add(X1,active(X2)) -> add(X1,X2) len(mark(X)) -> len(X) len(active(X)) -> len(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [len](x0) = [1 0 1]x0 [1 0 1] , [1 0 1] [1 0 1] [add](x0, x1) = [0 0 0]x0 + [1 0 1]x1 [0 0 0] [0 0 0] , [1 0 1] [1] [from](x0) = [0 0 0]x0 + [0] [1 0 1] [0], [1 0 1] [1 1 0] [cons](x0, x1) = [0 0 0]x0 + [0 1 1]x1 [0 0 0] [0 0 0] , [1 0 1] [s](x0) = [0 1 0]x0 [0 0 0] , [1 0 1] [mark](x0) = [0 1 1]x0 [0 0 0] , [1] [nil] = [0] [1], [1 0 1] [active](x0) = [0 1 1]x0 [0 0 0] , [1 0 1] [1 0 1] [1] [fst](x0, x1) = [1 0 1]x0 + [0 0 0]x1 + [0] [1 0 1] [0 1 1] [1], [0] [0] = [0] [0] orientation: [2 0 2] [1 0 1] [1 2 1] [2] [2 0 2] [1 0 1] [1 0 1] [1] active(fst(s(X),cons(Y,Z))) = [2 0 2]X + [0 0 0]Y + [0 1 1]Z + [1] >= [2 0 2]X + [0 0 0]Y + [0 1 1]Z + [1] = mark(cons(Y,fst(X,Z))) [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] [0] [2 0 2] [1] [2 0 2] [1] active(from(X)) = [1 0 1]X + [0] >= [1 0 1]X + [0] = mark(cons(X,from(s(X)))) [0 0 0] [0] [0 0 0] [0] [2 0 2] [1 1 2] [2] [2 0 2] [1 1 2] [2] mark(fst(X1,X2)) = [2 0 2]X1 + [0 1 1]X2 + [1] >= [2 0 2]X1 + [0 1 1]X2 + [1] = active(fst(mark(X1),mark(X2))) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [0] [0] mark(0()) = [0] >= [0] = active(0()) [0] [0] [2] [2] mark(nil()) = [1] >= [1] = active(nil()) [0] [0] [1 0 1] [1 0 1] mark(s(X)) = [0 1 0]X >= [0 1 0]X = active(s(X)) [0 0 0] [0 0 0] [1 0 1] [1 1 0] [1 0 1] [1 1 0] mark(cons(X1,X2)) = [0 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 1 1]X2 = active(cons(mark(X1),X2)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [2 0 2] [1] [2 0 2] [1] mark(from(X)) = [1 0 1]X + [0] >= [1 0 1]X + [0] = active(from(mark(X))) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] mark(add(X1,X2)) = [0 0 0]X1 + [1 0 1]X2 >= [0 0 0]X1 + [1 0 1]X2 = active(add(mark(X1),mark(X2))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [2 0 2] [2 0 2] mark(len(X)) = [2 0 2]X >= [2 0 2]X = active(len(mark(X))) [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [1] fst(mark(X1),X2) = [1 0 1]X1 + [0 0 0]X2 + [0] >= [1 0 1]X1 + [0 0 0]X2 + [0] = fst(X1,X2) [1 0 1] [0 1 1] [1] [1 0 1] [0 1 1] [1] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [1] fst(X1,mark(X2)) = [1 0 1]X1 + [0 0 0]X2 + [0] >= [1 0 1]X1 + [0 0 0]X2 + [0] = fst(X1,X2) [1 0 1] [0 1 1] [1] [1 0 1] [0 1 1] [1] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [1] fst(active(X1),X2) = [1 0 1]X1 + [0 0 0]X2 + [0] >= [1 0 1]X1 + [0 0 0]X2 + [0] = fst(X1,X2) [1 0 1] [0 1 1] [1] [1 0 1] [0 1 1] [1] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [1] fst(X1,active(X2)) = [1 0 1]X1 + [0 0 0]X2 + [0] >= [1 0 1]X1 + [0 0 0]X2 + [0] = fst(X1,X2) [1 0 1] [0 1 1] [1] [1 0 1] [0 1 1] [1] [1 0 1] [1 0 1] s(mark(X)) = [0 1 1]X >= [0 1 0]X = s(X) [0 0 0] [0 0 0] [1 0 1] [1 0 1] s(active(X)) = [0 1 1]X >= [0 1 0]X = s(X) [0 0 0] [0 0 0] [1 0 1] [1 1 0] [1 0 1] [1 1 0] cons(mark(X1),X2) = [0 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 1 1]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 1 2] [1 0 1] [1 1 0] cons(X1,mark(X2)) = [0 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 1 1]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 1 0] [1 0 1] [1 1 0] cons(active(X1),X2) = [0 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 1 1]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 1 2] [1 0 1] [1 1 0] cons(X1,active(X2)) = [0 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 1 1]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1] [1 0 1] [1] from(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = from(X) [1 0 1] [0] [1 0 1] [0] [1 0 1] [1] [1 0 1] [1] from(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = from(X) [1 0 1] [0] [1 0 1] [0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] add(mark(X1),X2) = [0 0 0]X1 + [1 0 1]X2 >= [0 0 0]X1 + [1 0 1]X2 = add(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] add(X1,mark(X2)) = [0 0 0]X1 + [1 0 1]X2 >= [0 0 0]X1 + [1 0 1]X2 = add(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] add(active(X1),X2) = [0 0 0]X1 + [1 0 1]X2 >= [0 0 0]X1 + [1 0 1]X2 = add(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] add(X1,active(X2)) = [0 0 0]X1 + [1 0 1]X2 >= [0 0 0]X1 + [1 0 1]X2 = add(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 1] len(mark(X)) = [1 0 1]X >= [1 0 1]X = len(X) [1 0 1] [1 0 1] [1 0 1] [1 0 1] len(active(X)) = [1 0 1]X >= [1 0 1]X = len(X) [1 0 1] [1 0 1] problem: active(from(X)) -> mark(cons(X,from(s(X)))) mark(fst(X1,X2)) -> active(fst(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(X)) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(add(X1,X2)) -> active(add(mark(X1),mark(X2))) mark(len(X)) -> active(len(mark(X))) fst(mark(X1),X2) -> fst(X1,X2) fst(X1,mark(X2)) -> fst(X1,X2) fst(active(X1),X2) -> fst(X1,X2) fst(X1,active(X2)) -> fst(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) add(mark(X1),X2) -> add(X1,X2) add(X1,mark(X2)) -> add(X1,X2) add(active(X1),X2) -> add(X1,X2) add(X1,active(X2)) -> add(X1,X2) len(mark(X)) -> len(X) len(active(X)) -> len(X) Matrix Interpretation Processor: dim=2 interpretation: [1 1] [2] [len](x0) = [1 1]x0 + [1], [1 1] [1 1] [add](x0, x1) = [0 0]x0 + [0 0]x1, [2 2] [1] [from](x0) = [2 2]x0 + [3], [1 1] [1 0] [2] [cons](x0, x1) = [0 0]x0 + [0 0]x1 + [0], [1 0] [s](x0) = [0 0]x0, [1 1] [mark](x0) = [0 0]x0, [1] [nil] = [1], [1 1] [active](x0) = [0 0]x0, [1 1] [1 1] [1] [fst](x0, x1) = [0 0]x0 + [0 0]x1 + [2], [0] [0] = [1] orientation: [4 4] [4] [3 1] [3] active(from(X)) = [0 0]X + [0] >= [0 0]X + [0] = mark(cons(X,from(s(X)))) [1 1] [1 1] [3] [1 1] [1 1] [3] mark(fst(X1,X2)) = [0 0]X1 + [0 0]X2 + [0] >= [0 0]X1 + [0 0]X2 + [0] = active(fst(mark(X1),mark(X2))) [1] [1] mark(0()) = [0] >= [0] = active(0()) [2] [2] mark(nil()) = [0] >= [0] = active(nil()) [1 0] [1 0] mark(s(X)) = [0 0]X >= [0 0]X = active(s(X)) [1 1] [1 0] [2] [1 1] [1 0] [2] mark(cons(X1,X2)) = [0 0]X1 + [0 0]X2 + [0] >= [0 0]X1 + [0 0]X2 + [0] = active(cons(mark(X1),X2)) [4 4] [4] [4 4] [4] mark(from(X)) = [0 0]X + [0] >= [0 0]X + [0] = active(from(mark(X))) [1 1] [1 1] [1 1] [1 1] mark(add(X1,X2)) = [0 0]X1 + [0 0]X2 >= [0 0]X1 + [0 0]X2 = active(add(mark(X1),mark(X2))) [2 2] [3] [2 2] [3] mark(len(X)) = [0 0]X + [0] >= [0 0]X + [0] = active(len(mark(X))) [1 1] [1 1] [1] [1 1] [1 1] [1] fst(mark(X1),X2) = [0 0]X1 + [0 0]X2 + [2] >= [0 0]X1 + [0 0]X2 + [2] = fst(X1,X2) [1 1] [1 1] [1] [1 1] [1 1] [1] fst(X1,mark(X2)) = [0 0]X1 + [0 0]X2 + [2] >= [0 0]X1 + [0 0]X2 + [2] = fst(X1,X2) [1 1] [1 1] [1] [1 1] [1 1] [1] fst(active(X1),X2) = [0 0]X1 + [0 0]X2 + [2] >= [0 0]X1 + [0 0]X2 + [2] = fst(X1,X2) [1 1] [1 1] [1] [1 1] [1 1] [1] fst(X1,active(X2)) = [0 0]X1 + [0 0]X2 + [2] >= [0 0]X1 + [0 0]X2 + [2] = fst(X1,X2) [1 1] [1 0] s(mark(X)) = [0 0]X >= [0 0]X = s(X) [1 1] [1 0] s(active(X)) = [0 0]X >= [0 0]X = s(X) [1 1] [1 0] [2] [1 1] [1 0] [2] cons(mark(X1),X2) = [0 0]X1 + [0 0]X2 + [0] >= [0 0]X1 + [0 0]X2 + [0] = cons(X1,X2) [1 1] [1 1] [2] [1 1] [1 0] [2] cons(X1,mark(X2)) = [0 0]X1 + [0 0]X2 + [0] >= [0 0]X1 + [0 0]X2 + [0] = cons(X1,X2) [1 1] [1 0] [2] [1 1] [1 0] [2] cons(active(X1),X2) = [0 0]X1 + [0 0]X2 + [0] >= [0 0]X1 + [0 0]X2 + [0] = cons(X1,X2) [1 1] [1 1] [2] [1 1] [1 0] [2] cons(X1,active(X2)) = [0 0]X1 + [0 0]X2 + [0] >= [0 0]X1 + [0 0]X2 + [0] = cons(X1,X2) [2 2] [1] [2 2] [1] from(mark(X)) = [2 2]X + [3] >= [2 2]X + [3] = from(X) [2 2] [1] [2 2] [1] from(active(X)) = [2 2]X + [3] >= [2 2]X + [3] = from(X) [1 1] [1 1] [1 1] [1 1] add(mark(X1),X2) = [0 0]X1 + [0 0]X2 >= [0 0]X1 + [0 0]X2 = add(X1,X2) [1 1] [1 1] [1 1] [1 1] add(X1,mark(X2)) = [0 0]X1 + [0 0]X2 >= [0 0]X1 + [0 0]X2 = add(X1,X2) [1 1] [1 1] [1 1] [1 1] add(active(X1),X2) = [0 0]X1 + [0 0]X2 >= [0 0]X1 + [0 0]X2 = add(X1,X2) [1 1] [1 1] [1 1] [1 1] add(X1,active(X2)) = [0 0]X1 + [0 0]X2 >= [0 0]X1 + [0 0]X2 = add(X1,X2) [1 1] [2] [1 1] [2] len(mark(X)) = [1 1]X + [1] >= [1 1]X + [1] = len(X) [1 1] [2] [1 1] [2] len(active(X)) = [1 1]X + [1] >= [1 1]X + [1] = len(X) problem: mark(fst(X1,X2)) -> active(fst(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(X)) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(add(X1,X2)) -> active(add(mark(X1),mark(X2))) mark(len(X)) -> active(len(mark(X))) fst(mark(X1),X2) -> fst(X1,X2) fst(X1,mark(X2)) -> fst(X1,X2) fst(active(X1),X2) -> fst(X1,X2) fst(X1,active(X2)) -> fst(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) add(mark(X1),X2) -> add(X1,X2) add(X1,mark(X2)) -> add(X1,X2) add(active(X1),X2) -> add(X1,X2) add(X1,active(X2)) -> add(X1,X2) len(mark(X)) -> len(X) len(active(X)) -> len(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [len](x0) = [0 0 1]x0 + [1] [0 1 0] [0], [1 0 0] [1 0 0] [add](x0, x1) = [0 0 1]x0 + [0 1 1]x1 [0 1 0] [0 0 0] , [1 0 0] [0] [from](x0) = [0 0 0]x0 + [0] [0 1 1] [1], [1 0 0] [1 0 0] [0] [cons](x0, x1) = [0 0 1]x0 + [0 0 0]x1 + [1] [0 1 0] [0 0 0] [0], [1 0 0] [0] [s](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 1 1] [mark](x0) = [0 1 0]x0 [0 0 1] , [0] [nil] = [0] [1], [active](x0) = x0 , [1 0 0] [0] [fst](x0, x1) = [0 0 0]x0 + x1 + [1] [0 1 1] [0], [0] [0] = [1] [0] orientation: [1 1 1] [1 1 1] [1] [1 1 1] [1 1 1] [0] mark(fst(X1,X2)) = [0 0 0]X1 + [0 1 0]X2 + [1] >= [0 0 0]X1 + [0 1 0]X2 + [1] = active(fst(mark(X1),mark(X2))) [0 1 1] [0 0 1] [0] [0 1 1] [0 0 1] [0] [1] [0] mark(0()) = [1] >= [1] = active(0()) [0] [0] [1] [0] mark(nil()) = [0] >= [0] = active(nil()) [1] [1] [1 0 0] [1] [1 0 0] [0] mark(s(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(s(X)) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1 0 0] [1] [1 1 1] [1 0 0] [0] mark(cons(X1,X2)) = [0 0 1]X1 + [0 0 0]X2 + [1] >= [0 0 1]X1 + [0 0 0]X2 + [1] = active(cons(mark(X1),X2)) [0 1 0] [0 0 0] [0] [0 1 0] [0 0 0] [0] [1 1 1] [1] [1 1 1] [0] mark(from(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(from(mark(X))) [0 1 1] [1] [0 1 1] [1] [1 1 1] [1 1 1] [1 1 1] [1 1 1] mark(add(X1,X2)) = [0 0 1]X1 + [0 1 1]X2 >= [0 0 1]X1 + [0 1 1]X2 = active(add(mark(X1),mark(X2))) [0 1 0] [0 0 0] [0 1 0] [0 0 0] [1 1 1] [1] [1 1 1] [0] mark(len(X)) = [0 0 1]X + [1] >= [0 0 1]X + [1] = active(len(mark(X))) [0 1 0] [0] [0 1 0] [0] [1 1 1] [0] [1 0 0] [0] fst(mark(X1),X2) = [0 0 0]X1 + X2 + [1] >= [0 0 0]X1 + X2 + [1] = fst(X1,X2) [0 1 1] [0] [0 1 1] [0] [1 0 0] [1 1 1] [0] [1 0 0] [0] fst(X1,mark(X2)) = [0 0 0]X1 + [0 1 0]X2 + [1] >= [0 0 0]X1 + X2 + [1] = fst(X1,X2) [0 1 1] [0 0 1] [0] [0 1 1] [0] [1 0 0] [0] [1 0 0] [0] fst(active(X1),X2) = [0 0 0]X1 + X2 + [1] >= [0 0 0]X1 + X2 + [1] = fst(X1,X2) [0 1 1] [0] [0 1 1] [0] [1 0 0] [0] [1 0 0] [0] fst(X1,active(X2)) = [0 0 0]X1 + X2 + [1] >= [0 0 0]X1 + X2 + [1] = fst(X1,X2) [0 1 1] [0] [0 1 1] [0] [1 1 1] [0] [1 0 0] [0] s(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = s(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] s(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = s(X) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1 0 0] [0] [1 0 0] [1 0 0] [0] cons(mark(X1),X2) = [0 0 1]X1 + [0 0 0]X2 + [1] >= [0 0 1]X1 + [0 0 0]X2 + [1] = cons(X1,X2) [0 1 0] [0 0 0] [0] [0 1 0] [0 0 0] [0] [1 0 0] [1 1 1] [0] [1 0 0] [1 0 0] [0] cons(X1,mark(X2)) = [0 0 1]X1 + [0 0 0]X2 + [1] >= [0 0 1]X1 + [0 0 0]X2 + [1] = cons(X1,X2) [0 1 0] [0 0 0] [0] [0 1 0] [0 0 0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] cons(active(X1),X2) = [0 0 1]X1 + [0 0 0]X2 + [1] >= [0 0 1]X1 + [0 0 0]X2 + [1] = cons(X1,X2) [0 1 0] [0 0 0] [0] [0 1 0] [0 0 0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] cons(X1,active(X2)) = [0 0 1]X1 + [0 0 0]X2 + [1] >= [0 0 1]X1 + [0 0 0]X2 + [1] = cons(X1,X2) [0 1 0] [0 0 0] [0] [0 1 0] [0 0 0] [0] [1 1 1] [0] [1 0 0] [0] from(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = from(X) [0 1 1] [1] [0 1 1] [1] [1 0 0] [0] [1 0 0] [0] from(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = from(X) [0 1 1] [1] [0 1 1] [1] [1 1 1] [1 0 0] [1 0 0] [1 0 0] add(mark(X1),X2) = [0 0 1]X1 + [0 1 1]X2 >= [0 0 1]X1 + [0 1 1]X2 = add(X1,X2) [0 1 0] [0 0 0] [0 1 0] [0 0 0] [1 0 0] [1 1 1] [1 0 0] [1 0 0] add(X1,mark(X2)) = [0 0 1]X1 + [0 1 1]X2 >= [0 0 1]X1 + [0 1 1]X2 = add(X1,X2) [0 1 0] [0 0 0] [0 1 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] add(active(X1),X2) = [0 0 1]X1 + [0 1 1]X2 >= [0 0 1]X1 + [0 1 1]X2 = add(X1,X2) [0 1 0] [0 0 0] [0 1 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1 0 0] add(X1,active(X2)) = [0 0 1]X1 + [0 1 1]X2 >= [0 0 1]X1 + [0 1 1]X2 = add(X1,X2) [0 1 0] [0 0 0] [0 1 0] [0 0 0] [1 1 1] [0] [1 0 0] [0] len(mark(X)) = [0 0 1]X + [1] >= [0 0 1]X + [1] = len(X) [0 1 0] [0] [0 1 0] [0] [1 0 0] [0] [1 0 0] [0] len(active(X)) = [0 0 1]X + [1] >= [0 0 1]X + [1] = len(X) [0 1 0] [0] [0 1 0] [0] problem: mark(add(X1,X2)) -> active(add(mark(X1),mark(X2))) fst(mark(X1),X2) -> fst(X1,X2) fst(X1,mark(X2)) -> fst(X1,X2) fst(active(X1),X2) -> fst(X1,X2) fst(X1,active(X2)) -> fst(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) from(active(X)) -> from(X) add(mark(X1),X2) -> add(X1,X2) add(X1,mark(X2)) -> add(X1,X2) add(active(X1),X2) -> add(X1,X2) add(X1,active(X2)) -> add(X1,X2) len(mark(X)) -> len(X) len(active(X)) -> len(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [len](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [0] [add](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 1] [0 0 1] [1], [1 0 0] [from](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [s](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [mark](x0) = [0 0 1]x0 [1 0 1] , [1 1 0] [1] [active](x0) = [0 0 0]x0 + [0] [0 0 1] [0], [1 0 0] [1 0 0] [fst](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] orientation: [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [1] mark(add(X1,X2)) = [0 0 1]X1 + [0 0 1]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(add(mark(X1),mark(X2))) [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 0] [1 0 0] [1 0 0] fst(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = fst(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] fst(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = fst(X1,X2) [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] fst(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = fst(X1,X2) [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] fst(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = fst(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 1] [1 0 0] s(mark(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] [1 1 0] [1] [1 0 0] s(active(X)) = [0 0 0]X + [0] >= [0 0 0]X = s(X) [0 0 0] [0] [0 0 0] [1 0 1] [1 0 0] [1 0 0] [1 0 0] cons(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(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] cons(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [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] cons(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [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] cons(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 = cons(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 1] [1 0 0] from(mark(X)) = [0 0 0]X >= [0 0 0]X = from(X) [0 0 0] [0 0 0] [1 1 0] [1] [1 0 0] from(active(X)) = [0 0 0]X + [0] >= [0 0 0]X = from(X) [0 0 0] [0] [0 0 0] [1 0 1] [1 0 0] [0] [1 0 0] [1 0 0] [0] add(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = add(X1,X2) [1 0 1] [0 0 1] [1] [0 0 1] [0 0 1] [1] [1 0 0] [1 0 1] [0] [1 0 0] [1 0 0] [0] add(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = add(X1,X2) [0 0 1] [1 0 1] [1] [0 0 1] [0 0 1] [1] [1 1 0] [1 0 0] [1] [1 0 0] [1 0 0] [0] add(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = add(X1,X2) [0 0 1] [0 0 1] [1] [0 0 1] [0 0 1] [1] [1 0 0] [1 1 0] [1] [1 0 0] [1 0 0] [0] add(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = add(X1,X2) [0 0 1] [0 0 1] [1] [0 0 1] [0 0 1] [1] [1 0 1] [1 0 0] len(mark(X)) = [0 0 0]X >= [0 0 0]X = len(X) [0 0 0] [0 0 0] [1 1 0] [1] [1 0 0] len(active(X)) = [0 0 0]X + [0] >= [0 0 0]X = len(X) [0 0 0] [0] [0 0 0] problem: mark(add(X1,X2)) -> active(add(mark(X1),mark(X2))) fst(mark(X1),X2) -> fst(X1,X2) fst(X1,mark(X2)) -> fst(X1,X2) s(mark(X)) -> s(X) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) from(mark(X)) -> from(X) add(mark(X1),X2) -> add(X1,X2) add(X1,mark(X2)) -> add(X1,X2) len(mark(X)) -> len(X) Matrix Interpretation Processor: dim=1 interpretation: [len](x0) = x0 + 1, [add](x0, x1) = x0 + 4x1 + 6, [from](x0) = x0, [cons](x0, x1) = x0 + x1 + 1, [s](x0) = 2x0, [mark](x0) = 4x0 + 4, [active](x0) = x0 + 2, [fst](x0, x1) = x0 + 4x1 + 2 orientation: mark(add(X1,X2)) = 4X1 + 16X2 + 28 >= 4X1 + 16X2 + 28 = active(add(mark(X1),mark(X2))) fst(mark(X1),X2) = 4X1 + 4X2 + 6 >= X1 + 4X2 + 2 = fst(X1,X2) fst(X1,mark(X2)) = X1 + 16X2 + 18 >= X1 + 4X2 + 2 = fst(X1,X2) s(mark(X)) = 8X + 8 >= 2X = s(X) cons(mark(X1),X2) = 4X1 + X2 + 5 >= X1 + X2 + 1 = cons(X1,X2) cons(X1,mark(X2)) = X1 + 4X2 + 5 >= X1 + X2 + 1 = cons(X1,X2) from(mark(X)) = 4X + 4 >= X = from(X) add(mark(X1),X2) = 4X1 + 4X2 + 10 >= X1 + 4X2 + 6 = add(X1,X2) add(X1,mark(X2)) = X1 + 16X2 + 22 >= X1 + 4X2 + 6 = add(X1,X2) len(mark(X)) = 4X + 5 >= X + 1 = len(X) problem: mark(add(X1,X2)) -> active(add(mark(X1),mark(X2))) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [0] [add](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [0 0 1] [0 1 1] [1], [1 0 1] [mark](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [active](x0) = [0 0 0]x0 [0 0 0] orientation: [1 0 1] [1 1 1] [1] [1 0 1] [1 0 1] mark(add(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 = active(add(mark(X1),mark(X2))) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] problem: Qed