/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: active(first(0(),X)) -> mark(nil()) active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(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) Proof: Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [from](x0) = [0 1 1]x0 [1 0 1] , [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] [s](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [mark](x0) = [0 1 1]x0 [0 0 0] , [0] [nil] = [0] [0], [1 0 1] [active](x0) = [0 1 1]x0 [0 0 0] , [1 0 1] [1 0 1] [first](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 1 1] , [1] [0] = [0] [0] orientation: [1 1 2] [1] [0] active(first(0(),X)) = [0 1 1]X + [0] >= [0] = mark(nil()) [0 0 0] [0] [0] [1 0 1] [1 0 1] [1 1 1] [1 0 1] [1 0 1] [1 0 1] active(first(s(X),cons(Y,Z))) = [0 0 0]X + [0 0 0]Y + [0 1 1]Z >= [0 0 0]X + [0 0 0]Y + [0 1 1]Z = mark(cons(Y,first(X,Z))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [0 0 0] [2 0 2] [2 0 2] active(from(X)) = [1 1 2]X >= [1 0 1]X = mark(cons(X,from(s(X)))) [0 0 0] [0 0 0] [1 0 1] [1 1 2] [1 0 1] [1 1 2] mark(first(X1,X2)) = [0 0 0]X1 + [0 1 1]X2 >= [0 0 0]X1 + [0 1 1]X2 = active(first(mark(X1),mark(X2))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1] [1] mark(0()) = [0] >= [0] = active(0()) [0] [0] [0] [0] mark(nil()) = [0] >= [0] = active(nil()) [0] [0] [1 0 1] [1 0 1] mark(s(X)) = [0 0 0]X >= [0 0 0]X = active(s(mark(X))) [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] [2 0 2] mark(from(X)) = [1 1 2]X >= [1 1 2]X = active(from(mark(X))) [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] first(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = first(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] first(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = first(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] first(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = first(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] first(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = first(X1,X2) [0 0 0] [0 1 1] [0 0 0] [0 1 1] [1 0 1] [1 0 1] s(mark(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] [1 0 1] [1 0 1] s(active(X)) = [0 0 0]X >= [0 0 0]X = s(X) [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 0 1] from(mark(X)) = [0 1 1]X >= [0 1 1]X = from(X) [1 0 1] [1 0 1] [1 0 1] [1 0 1] from(active(X)) = [0 1 1]X >= [0 1 1]X = from(X) [1 0 1] [1 0 1] problem: active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(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) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [from](x0) = [0 0 0]x0 [1 0 1] , [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] [s](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [mark](x0) = [0 1 1]x0 [0 0 0] , [0] [nil] = [0] [0], [1 0 1] [active](x0) = [0 1 1]x0 [0 0 0] , [1 0 1] [1 0 1] [1] [first](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 1 1] [1], [0] [0] = [0] [0] orientation: [1 0 1] [1 0 1] [1 1 1] [2] [1 0 1] [1 0 1] [1 0 1] [1] active(first(s(X),cons(Y,Z))) = [0 0 0]X + [0 0 0]Y + [0 1 1]Z + [1] >= [0 0 0]X + [0 0 0]Y + [0 1 1]Z + [1] = mark(cons(Y,first(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] [2 0 2] active(from(X)) = [1 0 1]X >= [1 0 1]X = mark(cons(X,from(s(X)))) [0 0 0] [0 0 0] [1 0 1] [1 1 2] [2] [1 0 1] [1 1 2] [2] mark(first(X1,X2)) = [0 0 0]X1 + [0 1 1]X2 + [1] >= [0 0 0]X1 + [0 1 1]X2 + [1] = active(first(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] [0] [0] mark(nil()) = [0] >= [0] = active(nil()) [0] [0] [1 0 1] [1 0 1] mark(s(X)) = [0 0 0]X >= [0 0 0]X = active(s(mark(X))) [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] [2 0 2] mark(from(X)) = [1 0 1]X >= [1 0 1]X = active(from(mark(X))) [0 0 0] [0 0 0] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [1] first(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = first(X1,X2) [0 0 0] [0 1 1] [1] [0 0 0] [0 1 1] [1] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [1] first(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = first(X1,X2) [0 0 0] [0 1 1] [1] [0 0 0] [0 1 1] [1] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [1] first(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = first(X1,X2) [0 0 0] [0 1 1] [1] [0 0 0] [0 1 1] [1] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [1] first(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = first(X1,X2) [0 0 0] [0 1 1] [1] [0 0 0] [0 1 1] [1] [1 0 1] [1 0 1] s(mark(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] [1 0 1] [1 0 1] s(active(X)) = [0 0 0]X >= [0 0 0]X = s(X) [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 0 1] from(mark(X)) = [0 0 0]X >= [0 0 0]X = from(X) [1 0 1] [1 0 1] [1 0 1] [1 0 1] from(active(X)) = [0 0 0]X >= [0 0 0]X = from(X) [1 0 1] [1 0 1] problem: active(from(X)) -> mark(cons(X,from(s(X)))) mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(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) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [0] [from](x0) = [0 0 0]x0 + [0] [1 0 1] [1], [1 0 1] [1 0 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 1] [s](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [mark](x0) = [0 0 0]x0 [0 0 0] , [1] [nil] = [0] [0], [1 0 1] [active](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [1 0 1] [first](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [0] = [0] [1] orientation: [2 0 2] [1] [2 0 2] active(from(X)) = [0 0 0]X + [0] >= [0 0 0]X = mark(cons(X,from(s(X)))) [0 0 0] [0] [0 0 0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] mark(first(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(first(mark(X1),mark(X2))) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1] [1] mark(0()) = [0] >= [0] = active(0()) [0] [0] [1] [1] mark(nil()) = [0] >= [0] = active(nil()) [0] [0] [1 0 1] [1 0 1] mark(s(X)) = [0 0 0]X >= [0 0 0]X = active(s(mark(X))) [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 0 0]X2 >= [0 0 0]X1 + [0 0 0]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)) = [0 0 0]X + [0] >= [0 0 0]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] first(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = first(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] first(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = first(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] first(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = first(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] first(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = first(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 1] [1 0 1] s(mark(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 0] [0 0 0] [1 0 1] [1 0 1] s(active(X)) = [0 0 0]X >= [0 0 0]X = s(X) [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 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 1] [1 0 1] [1 0 1] [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 0 1] [1 0 0] [1 0 1] [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 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 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 1] [0] [1 0 1] [0] from(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = from(X) [1 0 1] [1] [1 0 1] [1] [1 0 1] [0] [1 0 1] [0] from(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = from(X) [1 0 1] [1] [1 0 1] [1] problem: mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(nil()) -> active(nil()) mark(s(X)) -> active(s(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(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) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1] [from](x0) = [0 1 1]x0 + [0] [0 0 0] [0], [1 0 0] [1 0 0] [0] [cons](x0, x1) = [0 1 1]x0 + [0 0 0]x1 + [1] [0 0 0] [0 0 0] [0], [1 0 0] [0] [s](x0) = [0 1 1]x0 + [1] [0 0 0] [0], [1 1 0] [mark](x0) = [0 0 0]x0 [0 1 1] , [0] [nil] = [1] [0], [1 0 0] [active](x0) = [0 0 1]x0 [0 1 0] , [1 0 0] [1 0 0] [first](x0, x1) = [0 1 1]x0 + [0 1 1]x1 [0 0 0] [0 0 0] , [1] [0] = [0] [0] orientation: [1 1 1] [1 1 1] [1 1 0] [1 1 0] mark(first(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = active(first(mark(X1),mark(X2))) [0 1 1] [0 1 1] [0 1 1] [0 1 1] [1] [1] mark(0()) = [0] >= [0] = active(0()) [0] [0] [1] [0] mark(nil()) = [0] >= [0] = active(nil()) [1] [1] [1 1 1] [1] [1 1 0] [0] mark(s(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(s(mark(X))) [0 1 1] [1] [0 1 1] [1] [1 1 1] [1 0 0] [1] [1 1 0] [1 0 0] [0] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = active(cons(mark(X1),X2)) [0 1 1] [0 0 0] [1] [0 1 1] [0 0 0] [1] [1 1 1] [1] [1 1 0] [1] mark(from(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(from(mark(X))) [0 1 1] [0] [0 1 1] [0] [1 1 0] [1 0 0] [1 0 0] [1 0 0] first(mark(X1),X2) = [0 1 1]X1 + [0 1 1]X2 >= [0 1 1]X1 + [0 1 1]X2 = first(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 1 0] [1 0 0] [1 0 0] first(X1,mark(X2)) = [0 1 1]X1 + [0 1 1]X2 >= [0 1 1]X1 + [0 1 1]X2 = first(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] first(active(X1),X2) = [0 1 1]X1 + [0 1 1]X2 >= [0 1 1]X1 + [0 1 1]X2 = first(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] first(X1,active(X2)) = [0 1 1]X1 + [0 1 1]X2 >= [0 1 1]X1 + [0 1 1]X2 = first(X1,X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [0] [1 0 0] [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 0] [0] [1 0 0] [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 1 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] cons(mark(X1),X2) = [0 1 1]X1 + [0 0 0]X2 + [1] >= [0 1 1]X1 + [0 0 0]X2 + [1] = cons(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 1 0] [0] [1 0 0] [1 0 0] [0] cons(X1,mark(X2)) = [0 1 1]X1 + [0 0 0]X2 + [1] >= [0 1 1]X1 + [0 0 0]X2 + [1] = cons(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] cons(active(X1),X2) = [0 1 1]X1 + [0 0 0]X2 + [1] >= [0 1 1]X1 + [0 0 0]X2 + [1] = cons(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] cons(X1,active(X2)) = [0 1 1]X1 + [0 0 0]X2 + [1] >= [0 1 1]X1 + [0 0 0]X2 + [1] = cons(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [1] [1 0 0] [1] from(mark(X)) = [0 1 1]X + [0] >= [0 1 1]X + [0] = from(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] from(active(X)) = [0 1 1]X + [0] >= [0 1 1]X + [0] = from(X) [0 0 0] [0] [0 0 0] [0] problem: mark(first(X1,X2)) -> active(first(mark(X1),mark(X2))) mark(0()) -> active(0()) mark(from(X)) -> active(from(mark(X))) first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(X1,X2) first(active(X1),X2) -> first(X1,X2) first(X1,active(X2)) -> first(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) Matrix Interpretation Processor: dim=1 interpretation: [from](x0) = 4x0 + 1, [cons](x0, x1) = 4x0 + 4x1, [s](x0) = 2x0, [mark](x0) = 4x0, [active](x0) = x0 + 1, [first](x0, x1) = x0 + 2x1 + 4, [0] = 3 orientation: mark(first(X1,X2)) = 4X1 + 8X2 + 16 >= 4X1 + 8X2 + 5 = active(first(mark(X1),mark(X2))) mark(0()) = 12 >= 4 = active(0()) mark(from(X)) = 16X + 4 >= 16X + 2 = active(from(mark(X))) first(mark(X1),X2) = 4X1 + 2X2 + 4 >= X1 + 2X2 + 4 = first(X1,X2) first(X1,mark(X2)) = X1 + 8X2 + 4 >= X1 + 2X2 + 4 = first(X1,X2) first(active(X1),X2) = X1 + 2X2 + 5 >= X1 + 2X2 + 4 = first(X1,X2) first(X1,active(X2)) = X1 + 2X2 + 6 >= X1 + 2X2 + 4 = first(X1,X2) s(mark(X)) = 8X >= 2X = s(X) s(active(X)) = 2X + 2 >= 2X = s(X) cons(mark(X1),X2) = 16X1 + 4X2 >= 4X1 + 4X2 = cons(X1,X2) cons(X1,mark(X2)) = 4X1 + 16X2 >= 4X1 + 4X2 = cons(X1,X2) cons(active(X1),X2) = 4X1 + 4X2 + 4 >= 4X1 + 4X2 = cons(X1,X2) cons(X1,active(X2)) = 4X1 + 4X2 + 4 >= 4X1 + 4X2 = cons(X1,X2) from(mark(X)) = 16X + 1 >= 4X + 1 = from(X) from(active(X)) = 4X + 5 >= 4X + 1 = from(X) problem: first(mark(X1),X2) -> first(X1,X2) first(X1,mark(X2)) -> first(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) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [from](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 0 0] [0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [1], [1 0 0] [s](x0) = [0 0 0]x0 [0 0 0] , [1] [mark](x0) = x0 + [0] [0], [1 0 0] [1 0 0] [first](x0, x1) = [0 0 0]x0 + [0 1 0]x1 [0 0 0] [0 0 0] orientation: [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] first(mark(X1),X2) = [0 0 0]X1 + [0 1 0]X2 + [0] >= [0 0 0]X1 + [0 1 0]X2 = first(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] first(X1,mark(X2)) = [0 0 0]X1 + [0 1 0]X2 + [0] >= [0 0 0]X1 + [0 1 0]X2 = first(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] s(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = s(X) [0 0 0] [0] [0 0 0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [0] cons(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = cons(X1,X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [0] cons(X1,mark(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = cons(X1,X2) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 1] [1] [1 0 1] from(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = from(X) [0 0 0] [0] [0 0 0] problem: Qed