/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(f(0())) -> mark(cons(0(),f(s(0())))) active(f(s(0()))) -> mark(f(p(s(0())))) active(p(s(0()))) -> mark(0()) mark(f(X)) -> active(f(mark(X))) mark(0()) -> active(0()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(p(X)) -> active(p(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) p(mark(X)) -> p(X) p(active(X)) -> p(X) Proof: Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [p](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [0] [mark](x0) = x0 + [1] [0], [1 0 0] [1 1 1] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [0] [s](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [0] [active](x0) = x0 + [1] [0], [1 0 1] [f](x0) = [0 0 0]x0 [0 0 0] , [0] [0] = [0] [1] orientation: [1] [1] active(f(0())) = [1] >= [1] = mark(cons(0(),f(s(0())))) [0] [0] [1] [1] active(f(s(0()))) = [1] >= [1] = mark(f(p(s(0())))) [0] [0] [0] [0] active(p(s(0()))) = [1] >= [1] = mark(0()) [1] [1] [1 0 1] [0] [1 0 1] [0] mark(f(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = active(f(mark(X))) [0 0 0] [0] [0 0 0] [0] [0] [0] mark(0()) = [1] >= [1] = active(0()) [1] [1] [1 0 0] [1 1 1] [0] [1 0 0] [1 1 1] [0] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = active(cons(mark(X1),X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] mark(s(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = active(s(mark(X))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] mark(p(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = active(p(mark(X))) [0 0 0] [1] [0 0 0] [1] [1 0 1] [1 0 1] f(mark(X)) = [0 0 0]X >= [0 0 0]X = f(X) [0 0 0] [0 0 0] [1 0 1] [1 0 1] f(active(X)) = [0 0 0]X >= [0 0 0]X = f(X) [0 0 0] [0 0 0] [1 0 0] [1 1 1] [1 0 0] [1 1 1] 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 1 1] [1] [1 0 0] [1 1 1] cons(X1,mark(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 1] [1 0 0] [1 1 1] 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 0] [1 1 1] [1] [1 0 0] [1 1 1] 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 0] [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 0 0] [0] [1 0 0] [0] p(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = p(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [0] [1 0 0] [0] p(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = p(X) [0 0 0] [1] [0 0 0] [1] problem: active(f(0())) -> mark(cons(0(),f(s(0())))) active(f(s(0()))) -> mark(f(p(s(0())))) active(p(s(0()))) -> mark(0()) mark(f(X)) -> active(f(mark(X))) mark(0()) -> active(0()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(p(X)) -> active(p(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) p(mark(X)) -> p(X) p(active(X)) -> p(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [p](x0) = [0 0 0]x0 [0 0 1] , [1 0 1] [mark](x0) = [0 0 0]x0 [1 0 1] , [1 0 0] [1 0 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 1] [0 0 0] , [1 0 0] [s](x0) = [0 0 0]x0 [0 0 1] , [1 1 0] [active](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [0] [f](x0) = [0 0 0]x0 + [1] [0 0 1] [1], [0] [0] = [0] [0] orientation: [1] [0] active(f(0())) = [0] >= [0] = mark(cons(0(),f(s(0())))) [1] [0] [1] [1] active(f(s(0()))) = [0] >= [0] = mark(f(p(s(0())))) [1] [1] [0] [0] active(p(s(0()))) = [0] >= [0] = mark(0()) [0] [0] [1 0 1] [1] [1 0 1] [1] mark(f(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(f(mark(X))) [1 0 1] [1] [1 0 1] [1] [0] [0] mark(0()) = [0] >= [0] = active(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)) [1 0 1] [1 0 0] [1 0 1] [0 0 0] [1 0 1] [1 0 1] mark(s(X)) = [0 0 0]X >= [0 0 0]X = active(s(mark(X))) [1 0 1] [1 0 1] [1 0 1] [1 0 1] mark(p(X)) = [0 0 0]X >= [0 0 0]X = active(p(mark(X))) [1 0 1] [1 0 1] [1 0 1] [0] [1 0 0] [0] f(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = f(X) [1 0 1] [1] [0 0 1] [1] [1 1 0] [0] [1 0 0] [0] f(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = f(X) [0 0 1] [1] [0 0 1] [1] [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) [1 0 1] [0 0 0] [0 0 1] [0 0 0] [1 1 0] [1 0 0] [1 0 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 1] [0 0 0] [0 0 1] [0 0 0] [1 0 1] [1 0 0] s(mark(X)) = [0 0 0]X >= [0 0 0]X = s(X) [1 0 1] [0 0 1] [1 1 0] [1 0 0] s(active(X)) = [0 0 0]X >= [0 0 0]X = s(X) [0 0 1] [0 0 1] [1 0 1] [1 0 0] p(mark(X)) = [0 0 0]X >= [0 0 0]X = p(X) [1 0 1] [0 0 1] [1 1 0] [1 0 0] p(active(X)) = [0 0 0]X >= [0 0 0]X = p(X) [0 0 1] [0 0 1] problem: active(f(s(0()))) -> mark(f(p(s(0())))) active(p(s(0()))) -> mark(0()) mark(f(X)) -> active(f(mark(X))) mark(0()) -> active(0()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(p(X)) -> active(p(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) p(mark(X)) -> p(X) p(active(X)) -> p(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [p](x0) = [1 0 0]x0 [0 0 0] , [1 0 0] [mark](x0) = [1 0 0]x0 [1 0 1] , [1 0 0] [1 1 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1] [s](x0) = [0 0 0]x0 + [0] [0 0 1] [0], [1 0 0] [active](x0) = [1 0 0]x0 [0 1 1] , [1 0 0] [f](x0) = [0 0 0]x0 [0 0 1] , [0] [0] = [0] [1] orientation: [1] [1] active(f(s(0()))) = [1] >= [1] = mark(f(p(s(0())))) [1] [1] [1] [0] active(p(s(0()))) = [1] >= [0] = mark(0()) [1] [1] [1 0 0] [1 0 0] mark(f(X)) = [1 0 0]X >= [1 0 0]X = active(f(mark(X))) [1 0 1] [1 0 1] [0] [0] mark(0()) = [0] >= [0] = active(0()) [1] [1] [1 0 0] [1 1 0] [1 0 0] [1 1 0] mark(cons(X1,X2)) = [1 0 0]X1 + [1 1 0]X2 >= [1 0 0]X1 + [1 1 0]X2 = active(cons(mark(X1),X2)) [1 0 0] [1 1 0] [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] mark(s(X)) = [1 0 0]X + [1] >= [1 0 0]X + [1] = active(s(mark(X))) [1 0 1] [1] [1 0 1] [0] [1 0 0] [1 0 0] mark(p(X)) = [1 0 0]X >= [1 0 0]X = active(p(mark(X))) [1 0 0] [1 0 0] [1 0 0] [1 0 0] f(mark(X)) = [0 0 0]X >= [0 0 0]X = f(X) [1 0 1] [0 0 1] [1 0 0] [1 0 0] f(active(X)) = [0 0 0]X >= [0 0 0]X = f(X) [0 1 1] [0 0 1] [1 0 0] [1 1 0] [1 0 0] [1 1 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 1 0] [1 0 0] [1 1 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 0] [1] [1 0 0] [1] s(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = s(X) [1 0 1] [0] [0 0 1] [0] [1 0 0] [1] [1 0 0] [1] s(active(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = s(X) [0 1 1] [0] [0 0 1] [0] [1 0 0] [1 0 0] p(mark(X)) = [1 0 0]X >= [1 0 0]X = p(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] p(active(X)) = [1 0 0]X >= [1 0 0]X = p(X) [0 0 0] [0 0 0] problem: active(f(s(0()))) -> mark(f(p(s(0())))) mark(f(X)) -> active(f(mark(X))) mark(0()) -> active(0()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(p(X)) -> active(p(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) p(mark(X)) -> p(X) p(active(X)) -> p(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [p](x0) = [0 1 0]x0 [0 0 0] , [mark](x0) = x0 , [1 0 0] [1 1 0] [0] [cons](x0, x1) = [0 0 0]x0 + [0 1 1]x1 + [1] [0 0 0] [0 0 0] [0], [1 1 0] [0] [s](x0) = [1 0 1]x0 + [0] [0 0 0] [1], [active](x0) = x0 , [1 0 1] [0] [f](x0) = [0 0 0]x0 + [1] [0 1 0] [0], [0] [0] = [0] [1] orientation: [1] [0] active(f(s(0()))) = [1] >= [1] = mark(f(p(s(0())))) [1] [1] [1 0 1] [0] [1 0 1] [0] mark(f(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = active(f(mark(X))) [0 1 0] [0] [0 1 0] [0] [0] [0] mark(0()) = [0] >= [0] = active(0()) [1] [1] [1 0 0] [1 1 0] [0] [1 0 0] [1 1 0] [0] mark(cons(X1,X2)) = [0 0 0]X1 + [0 1 1]X2 + [1] >= [0 0 0]X1 + [0 1 1]X2 + [1] = active(cons(mark(X1),X2)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [0] [1 1 0] [0] mark(s(X)) = [1 0 1]X + [0] >= [1 0 1]X + [0] = active(s(mark(X))) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 0] mark(p(X)) = [0 1 0]X >= [0 1 0]X = active(p(mark(X))) [0 0 0] [0 0 0] [1 0 1] [0] [1 0 1] [0] f(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = f(X) [0 1 0] [0] [0 1 0] [0] [1 0 1] [0] [1 0 1] [0] f(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = f(X) [0 1 0] [0] [0 1 0] [0] [1 0 0] [1 1 0] [0] [1 0 0] [1 1 0] [0] cons(mark(X1),X2) = [0 0 0]X1 + [0 1 1]X2 + [1] >= [0 0 0]X1 + [0 1 1]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 1 0] [0] cons(active(X1),X2) = [0 0 0]X1 + [0 1 1]X2 + [1] >= [0 0 0]X1 + [0 1 1]X2 + [1] = cons(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 0] [0] [1 1 0] [0] s(mark(X)) = [1 0 1]X + [0] >= [1 0 1]X + [0] = s(X) [0 0 0] [1] [0 0 0] [1] [1 1 0] [0] [1 1 0] [0] s(active(X)) = [1 0 1]X + [0] >= [1 0 1]X + [0] = s(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1 0 0] p(mark(X)) = [0 1 0]X >= [0 1 0]X = p(X) [0 0 0] [0 0 0] [1 0 0] [1 0 0] p(active(X)) = [0 1 0]X >= [0 1 0]X = p(X) [0 0 0] [0 0 0] problem: mark(f(X)) -> active(f(mark(X))) mark(0()) -> active(0()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(p(X)) -> active(p(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) p(mark(X)) -> p(X) p(active(X)) -> p(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [p](x0) = [0 1 0]x0 [0 1 0] , [1 1 0] [mark](x0) = [0 1 0]x0 [1 1 0] , [1 0 0] [1 0 0] [cons](x0, x1) = [0 1 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [0] [s](x0) = [0 1 0]x0 + [1] [0 0 0] [0], [1 0 0] [active](x0) = [0 1 0]x0 [1 0 0] , [1 0 0] [1] [f](x0) = [0 1 0]x0 + [0] [0 0 0] [0], [1] [0] = [0] [0] orientation: [1 1 0] [1] [1 1 0] [1] mark(f(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = active(f(mark(X))) [1 1 0] [1] [1 1 0] [1] [1] [1] mark(0()) = [0] >= [0] = active(0()) [1] [1] [1 1 0] [1 0 0] [1 1 0] [1 0 0] mark(cons(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = active(cons(mark(X1),X2)) [1 1 0] [1 0 0] [1 1 0] [1 0 0] [1 1 0] [1] [1 1 0] [0] mark(s(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = active(s(mark(X))) [1 1 0] [1] [1 1 0] [0] [1 1 0] [1 1 0] mark(p(X)) = [0 1 0]X >= [0 1 0]X = active(p(mark(X))) [1 1 0] [1 1 0] [1 1 0] [1] [1 0 0] [1] f(mark(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = f(X) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] f(active(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = f(X) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1 0 0] [1 0 0] [1 0 0] cons(mark(X1),X2) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 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 0] [1 0 0] [1 0 0] cons(active(X1),X2) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = cons(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 0]X + [1] >= [0 1 0]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 0]X + [1] >= [0 1 0]X + [1] = s(X) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1 0 0] p(mark(X)) = [0 1 0]X >= [0 1 0]X = p(X) [0 1 0] [0 1 0] [1 0 0] [1 0 0] p(active(X)) = [0 1 0]X >= [0 1 0]X = p(X) [0 1 0] [0 1 0] problem: mark(f(X)) -> active(f(mark(X))) mark(0()) -> active(0()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(p(X)) -> active(p(mark(X))) f(mark(X)) -> f(X) f(active(X)) -> f(X) cons(mark(X1),X2) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) p(mark(X)) -> p(X) p(active(X)) -> p(X) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [p](x0) = [0 1 1]x0 + [0] [0 0 0] [1], [1 1 1] [mark](x0) = [0 0 0]x0 [0 1 1] , [1 0 0] [1 0 0] [0] [cons](x0, x1) = [0 1 1]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 1] [1], [1 0 0] [s](x0) = [0 0 0]x0 [1 0 0] , [1 0 0] [1] [active](x0) = [0 0 0]x0 + [0] [0 1 1] [0], [1 0 0] [0] [f](x0) = [0 0 0]x0 + [1] [0 1 1] [0], [0] [0] = [0] [1] orientation: [1 1 1] [1] [1 1 1] [1] mark(f(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(f(mark(X))) [0 1 1] [1] [0 1 1] [1] [1] [1] mark(0()) = [0] >= [0] = active(0()) [1] [1] [1 1 1] [1 0 1] [1] [1 1 1] [1 0 0] [1] 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 1] [1] [0 1 1] [0 0 1] [1] [1 1 1] [1] [1 1 1] [1] mark(p(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = active(p(mark(X))) [0 1 1] [1] [0 1 1] [1] [1 1 1] [0] [1 0 0] [0] f(mark(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = f(X) [0 1 1] [0] [0 1 1] [0] [1 0 0] [1] [1 0 0] [0] f(active(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = f(X) [0 1 1] [0] [0 1 1] [0] [1 1 1] [1 0 0] [0] [1 0 0] [1 0 0] [0] cons(mark(X1),X2) = [0 1 1]X1 + [0 0 0]X2 + [0] >= [0 1 1]X1 + [0 0 0]X2 + [0] = cons(X1,X2) [0 0 0] [0 0 1] [1] [0 0 0] [0 0 1] [1] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [0] cons(active(X1),X2) = [0 1 1]X1 + [0 0 0]X2 + [0] >= [0 1 1]X1 + [0 0 0]X2 + [0] = cons(X1,X2) [0 0 0] [0 0 1] [1] [0 0 0] [0 0 1] [1] [1 1 1] [1 0 0] s(mark(X)) = [0 0 0]X >= [0 0 0]X = s(X) [1 1 1] [1 0 0] [1 0 0] [1] [1 0 0] s(active(X)) = [0 0 0]X + [0] >= [0 0 0]X = s(X) [1 0 0] [1] [1 0 0] [1 1 1] [0] [1 0 0] [0] p(mark(X)) = [0 1 1]X + [0] >= [0 1 1]X + [0] = p(X) [0 0 0] [1] [0 0 0] [1] [1 0 0] [1] [1 0 0] [0] p(active(X)) = [0 1 1]X + [0] >= [0 1 1]X + [0] = p(X) [0 0 0] [1] [0 0 0] [1] problem: mark(f(X)) -> active(f(mark(X))) mark(0()) -> active(0()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(p(X)) -> active(p(mark(X))) f(mark(X)) -> f(X) cons(mark(X1),X2) -> cons(X1,X2) s(mark(X)) -> s(X) p(mark(X)) -> p(X) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [0] [p](x0) = [0 0 1]x0 + [1] [0 0 0] [0], [1 1 0] [mark](x0) = [0 0 1]x0 [0 0 1] , [1 1 0] [1 0 0] [0] [cons](x0, x1) = [0 0 1]x0 + [0 0 0]x1 + [1] [0 0 0] [0 0 0] [1], [1 1 0] [1] [s](x0) = [0 0 0]x0 + [0] [0 0 0] [0], [1 0 0] [active](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [0] [f](x0) = [0 0 1]x0 + [1] [0 0 0] [0], [0] [0] = [0] [0] orientation: [1 1 1] [1] [1 1 1] mark(f(X)) = [0 0 0]X + [0] >= [0 0 0]X = active(f(mark(X))) [0 0 0] [0] [0 0 0] [0] [0] mark(0()) = [0] >= [0] = active(0()) [0] [0] [1 1 1] [1 0 0] [1] [1 1 1] [1 0 0] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 = active(cons(mark(X1),X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1 1 1] [1] [1 1 1] mark(p(X)) = [0 0 0]X + [0] >= [0 0 0]X = active(p(mark(X))) [0 0 0] [0] [0 0 0] [1 1 1] [0] [1 1 0] [0] f(mark(X)) = [0 0 1]X + [1] >= [0 0 1]X + [1] = f(X) [0 0 0] [0] [0 0 0] [0] [1 1 1] [1 0 0] [0] [1 1 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 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 1 1] [1] [1 1 0] [1] s(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = s(X) [0 0 0] [0] [0 0 0] [0] [1 1 1] [0] [1 1 0] [0] p(mark(X)) = [0 0 1]X + [1] >= [0 0 1]X + [1] = p(X) [0 0 0] [0] [0 0 0] [0] problem: mark(0()) -> active(0()) f(mark(X)) -> f(X) cons(mark(X1),X2) -> cons(X1,X2) s(mark(X)) -> s(X) p(mark(X)) -> p(X) Matrix Interpretation Processor: dim=3 interpretation: [1 1 1] [p](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1] [mark](x0) = [0 1 1]x0 + [0] [0 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 0] [active](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [f](x0) = [0 0 0]x0 [0 0 0] , [0] [0] = [0] [0] orientation: [1] [0] mark(0()) = [0] >= [0] = active(0()) [0] [0] [1 0 0] [1] [1 0 0] f(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = f(X) [0 0 0] [0] [0 0 0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] cons(mark(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 0] s(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = s(X) [0 0 0] [0] [0 0 0] [1 1 1] [1] [1 1 1] p(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X = p(X) [0 0 0] [0] [0 0 0] problem: Qed