/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(from(X)) -> mark(cons(X,from(s(X)))) active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) from(mark(X)) -> from(X) from(active(X)) -> from(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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Proof: Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [length1](x0) = [0 0 0]x0 [0 0 0] , [0] [0] = [0] [0], [1 0 0] [length](x0) = [0 0 0]x0 [0 0 0] , [0] [nil] = [0] [0], [1 1 0] [mark](x0) = [0 0 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] [1 1 0] , [1 1 0] [0] [s](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 1 0] [active](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [1] [from](x0) = [1 1 0]x0 + [1] [0 0 0] [0] orientation: [2 2 0] [2] [2 2 0] [1] active(from(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(cons(X,from(s(X)))) [0 0 0] [0] [0 0 0] [0] [0] [0] active(length(nil())) = [0] >= [0] = mark(0()) [0] [0] [1 1 0] [1 0 0] [1 0 0] active(length(cons(X,Y))) = [0 0 0]X + [0 0 0]Y >= [0 0 0]Y = mark(s(length1(Y))) [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] active(length1(X)) = [0 0 0]X >= [0 0 0]X = mark(length(X)) [0 0 0] [0 0 0] [2 2 0] [2] [2 2 0] [2] 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 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 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] mark(s(X)) = [0 0 0]X >= [0 0 0]X = active(s(mark(X))) [0 0 0] [0 0 0] [1 0 0] [1 0 0] mark(length(X)) = [0 0 0]X >= [0 0 0]X = active(length(X)) [0 0 0] [0 0 0] [0] [0] mark(nil()) = [0] >= [0] = active(nil()) [0] [0] [0] [0] mark(0()) = [0] >= [0] = active(0()) [0] [0] [1 0 0] [1 0 0] mark(length1(X)) = [0 0 0]X >= [0 0 0]X = active(length1(X)) [0 0 0] [0 0 0] [1 1 0] [1] [1 1 0] [1] from(mark(X)) = [1 1 0]X + [1] >= [1 1 0]X + [1] = from(X) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1] [1 1 0] [1] from(active(X)) = [1 1 0]X + [1] >= [1 1 0]X + [1] = from(X) [0 0 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] [1 1 0] [0 0 0] [1 1 0] [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] [1 1 0] [0 0 0] [1 1 0] [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] [1 1 0] [0 0 0] [1 1 0] [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] [1 1 0] [0 0 0] [1 1 0] [1 1 0] [0] [1 1 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 1 0] [0] [1 1 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 0] [1 0 0] length(mark(X)) = [0 0 0]X >= [0 0 0]X = length(X) [0 0 0] [0 0 0] [1 1 0] [1 0 0] length(active(X)) = [0 0 0]X >= [0 0 0]X = length(X) [0 0 0] [0 0 0] [1 1 0] [1 0 0] length1(mark(X)) = [0 0 0]X >= [0 0 0]X = length1(X) [0 0 0] [0 0 0] [1 1 0] [1 0 0] length1(active(X)) = [0 0 0]X >= [0 0 0]X = length1(X) [0 0 0] [0 0 0] problem: active(length(nil())) -> mark(0()) active(length(cons(X,Y))) -> mark(s(length1(Y))) active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) from(mark(X)) -> from(X) from(active(X)) -> from(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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Matrix Interpretation Processor: dim=1 interpretation: [length1](x0) = 4x0 + 3, [0] = 0, [length](x0) = 4x0 + 3, [nil] = 0, [mark](x0) = x0, [cons](x0, x1) = 4x0 + x1 + 1, [s](x0) = x0 + 3, [active](x0) = x0, [from](x0) = x0 + 4 orientation: active(length(nil())) = 3 >= 0 = mark(0()) active(length(cons(X,Y))) = 16X + 4Y + 7 >= 4Y + 6 = mark(s(length1(Y))) active(length1(X)) = 4X + 3 >= 4X + 3 = mark(length(X)) mark(from(X)) = X + 4 >= X + 4 = active(from(mark(X))) mark(cons(X1,X2)) = 4X1 + X2 + 1 >= 4X1 + X2 + 1 = active(cons(mark(X1),X2)) mark(s(X)) = X + 3 >= X + 3 = active(s(mark(X))) mark(length(X)) = 4X + 3 >= 4X + 3 = active(length(X)) mark(nil()) = 0 >= 0 = active(nil()) mark(0()) = 0 >= 0 = active(0()) mark(length1(X)) = 4X + 3 >= 4X + 3 = active(length1(X)) from(mark(X)) = X + 4 >= X + 4 = from(X) from(active(X)) = X + 4 >= X + 4 = from(X) cons(mark(X1),X2) = 4X1 + X2 + 1 >= 4X1 + X2 + 1 = cons(X1,X2) cons(X1,mark(X2)) = 4X1 + X2 + 1 >= 4X1 + X2 + 1 = cons(X1,X2) cons(active(X1),X2) = 4X1 + X2 + 1 >= 4X1 + X2 + 1 = cons(X1,X2) cons(X1,active(X2)) = 4X1 + X2 + 1 >= 4X1 + X2 + 1 = cons(X1,X2) s(mark(X)) = X + 3 >= X + 3 = s(X) s(active(X)) = X + 3 >= X + 3 = s(X) length(mark(X)) = 4X + 3 >= 4X + 3 = length(X) length(active(X)) = 4X + 3 >= 4X + 3 = length(X) length1(mark(X)) = 4X + 3 >= 4X + 3 = length1(X) length1(active(X)) = 4X + 3 >= 4X + 3 = length1(X) problem: active(length1(X)) -> mark(length(X)) mark(from(X)) -> active(from(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) mark(length1(X)) -> active(length1(X)) from(mark(X)) -> from(X) from(active(X)) -> from(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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Matrix Interpretation Processor: dim=1 interpretation: [length1](x0) = 6x0 + 4, [0] = 0, [length](x0) = 2x0, [nil] = 0, [mark](x0) = 2x0, [cons](x0, x1) = x0 + 4x1 + 4, [s](x0) = x0 + 3, [active](x0) = x0, [from](x0) = x0 orientation: active(length1(X)) = 6X + 4 >= 4X = mark(length(X)) mark(from(X)) = 2X >= 2X = active(from(mark(X))) mark(cons(X1,X2)) = 2X1 + 8X2 + 8 >= 2X1 + 4X2 + 4 = active(cons(mark(X1),X2)) mark(s(X)) = 2X + 6 >= 2X + 3 = active(s(mark(X))) mark(length(X)) = 4X >= 2X = active(length(X)) mark(nil()) = 0 >= 0 = active(nil()) mark(0()) = 0 >= 0 = active(0()) mark(length1(X)) = 12X + 8 >= 6X + 4 = active(length1(X)) from(mark(X)) = 2X >= X = from(X) from(active(X)) = X >= X = from(X) cons(mark(X1),X2) = 2X1 + 4X2 + 4 >= X1 + 4X2 + 4 = cons(X1,X2) cons(X1,mark(X2)) = X1 + 8X2 + 4 >= X1 + 4X2 + 4 = cons(X1,X2) cons(active(X1),X2) = X1 + 4X2 + 4 >= X1 + 4X2 + 4 = cons(X1,X2) cons(X1,active(X2)) = X1 + 4X2 + 4 >= X1 + 4X2 + 4 = cons(X1,X2) s(mark(X)) = 2X + 3 >= X + 3 = s(X) s(active(X)) = X + 3 >= X + 3 = s(X) length(mark(X)) = 4X >= 2X = length(X) length(active(X)) = 2X >= 2X = length(X) length1(mark(X)) = 12X + 4 >= 6X + 4 = length1(X) length1(active(X)) = 6X + 4 >= 6X + 4 = length1(X) problem: mark(from(X)) -> active(from(mark(X))) mark(length(X)) -> active(length(X)) mark(nil()) -> active(nil()) mark(0()) -> active(0()) from(mark(X)) -> from(X) from(active(X)) -> from(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) length(mark(X)) -> length(X) length(active(X)) -> length(X) length1(mark(X)) -> length1(X) length1(active(X)) -> length1(X) Matrix Interpretation Processor: dim=1 interpretation: [length1](x0) = 4x0 + 2, [0] = 0, [length](x0) = 7x0, [nil] = 0, [mark](x0) = 3x0 + 4, [cons](x0, x1) = 2x0 + 2x1, [s](x0) = 2x0, [active](x0) = x0 + 1, [from](x0) = x0 + 5 orientation: mark(from(X)) = 3X + 19 >= 3X + 10 = active(from(mark(X))) mark(length(X)) = 21X + 4 >= 7X + 1 = active(length(X)) mark(nil()) = 4 >= 1 = active(nil()) mark(0()) = 4 >= 1 = active(0()) from(mark(X)) = 3X + 9 >= X + 5 = from(X) from(active(X)) = X + 6 >= X + 5 = from(X) cons(mark(X1),X2) = 6X1 + 2X2 + 8 >= 2X1 + 2X2 = cons(X1,X2) cons(X1,mark(X2)) = 2X1 + 6X2 + 8 >= 2X1 + 2X2 = cons(X1,X2) cons(active(X1),X2) = 2X1 + 2X2 + 2 >= 2X1 + 2X2 = cons(X1,X2) cons(X1,active(X2)) = 2X1 + 2X2 + 2 >= 2X1 + 2X2 = cons(X1,X2) s(mark(X)) = 6X + 8 >= 2X = s(X) s(active(X)) = 2X + 2 >= 2X = s(X) length(mark(X)) = 21X + 28 >= 7X = length(X) length(active(X)) = 7X + 7 >= 7X = length(X) length1(mark(X)) = 12X + 18 >= 4X + 2 = length1(X) length1(active(X)) = 4X + 6 >= 4X + 2 = length1(X) problem: Qed