/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(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)))) active(first(X1,X2)) -> first(active(X1),X2) active(first(X1,X2)) -> first(X1,active(X2)) active(s(X)) -> s(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(from(X)) -> from(active(X)) first(mark(X1),X2) -> mark(first(X1,X2)) first(X1,mark(X2)) -> mark(first(X1,X2)) s(mark(X)) -> mark(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) from(mark(X)) -> mark(from(X)) proper(first(X1,X2)) -> first(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) proper(s(X)) -> s(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(from(X)) -> from(proper(X)) first(ok(X1),ok(X2)) -> ok(first(X1,X2)) s(ok(X)) -> ok(s(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) from(ok(X)) -> ok(from(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Proof: Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [top](x0) = [1 1 0]x0 [0 0 1] , [1 0 1] [ok](x0) = [0 1 0]x0 [1 0 1] , [proper](x0) = x0 , [1 0 1] [0] [from](x0) = [0 1 0]x0 + [1] [1 0 1] [0], [1 0 0] [cons](x0, x1) = x0 + [0 0 0]x1 [0 0 1] , [0] [s](x0) = x0 + [1] [0], [0] [mark](x0) = x0 + [1] [0], [0] [nil] = [0] [0], [1 0 1] [active](x0) = [0 1 0]x0 [1 0 1] , [first](x0, x1) = x0 + x1 , [0] [0] = [1] [0] orientation: [1 0 1] [0] [0] active(first(0(),X)) = [0 1 0]X + [1] >= [1] = mark(nil()) [1 0 1] [0] [0] [1 0 1] [1 0 1] [1 0 1] [0] [1 0 0] [1 0 0] [0] active(first(s(X),cons(Y,Z))) = [0 1 0]X + [0 1 0]Y + [0 0 0]Z + [1] >= [0 0 0]X + Y + [0 0 0]Z + [1] = mark(cons(Y,first(X,Z))) [1 0 1] [1 0 1] [1 0 1] [0] [0 0 1] [0 0 1] [0] [2 0 2] [0] [2 0 1] [0] active(from(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = mark(cons(X,from(s(X)))) [2 0 2] [0] [1 0 2] [0] [1 0 1] [1 0 1] [1 0 1] active(first(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 >= [0 1 0]X1 + X2 = first(active(X1),X2) [1 0 1] [1 0 1] [1 0 1] [1 0 1] [1 0 1] [1 0 1] active(first(X1,X2)) = [0 1 0]X1 + [0 1 0]X2 >= X1 + [0 1 0]X2 = first(X1,active(X2)) [1 0 1] [1 0 1] [1 0 1] [1 0 1] [0] [1 0 1] [0] active(s(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = s(active(X)) [1 0 1] [0] [1 0 1] [0] [1 0 1] [1 0 1] [1 0 1] [1 0 0] active(cons(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = cons(active(X1),X2) [1 0 1] [1 0 1] [1 0 1] [0 0 1] [2 0 2] [0] [2 0 2] [0] active(from(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = from(active(X)) [2 0 2] [0] [2 0 2] [0] [0] [0] first(mark(X1),X2) = X1 + X2 + [1] >= X1 + X2 + [1] = mark(first(X1,X2)) [0] [0] [0] [0] first(X1,mark(X2)) = X1 + X2 + [1] >= X1 + X2 + [1] = mark(first(X1,X2)) [0] [0] [0] [0] s(mark(X)) = X + [2] >= X + [2] = mark(s(X)) [0] [0] [1 0 0] [0] [1 0 0] [0] cons(mark(X1),X2) = X1 + [0 0 0]X2 + [1] >= X1 + [0 0 0]X2 + [1] = mark(cons(X1,X2)) [0 0 1] [0] [0 0 1] [0] [1 0 1] [0] [1 0 1] [0] from(mark(X)) = [0 1 0]X + [2] >= [0 1 0]X + [2] = mark(from(X)) [1 0 1] [0] [1 0 1] [0] proper(first(X1,X2)) = X1 + X2 >= X1 + X2 = first(proper(X1),proper(X2)) [0] [0] proper(0()) = [1] >= [1] = ok(0()) [0] [0] [0] [0] proper(nil()) = [0] >= [0] = ok(nil()) [0] [0] [0] [0] proper(s(X)) = X + [1] >= X + [1] = s(proper(X)) [0] [0] [1 0 0] [1 0 0] proper(cons(X1,X2)) = X1 + [0 0 0]X2 >= X1 + [0 0 0]X2 = cons(proper(X1),proper(X2)) [0 0 1] [0 0 1] [1 0 1] [0] [1 0 1] [0] proper(from(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = from(proper(X)) [1 0 1] [0] [1 0 1] [0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] first(ok(X1),ok(X2)) = [0 1 0]X1 + [0 1 0]X2 >= [0 1 0]X1 + [0 1 0]X2 = ok(first(X1,X2)) [1 0 1] [1 0 1] [1 0 1] [1 0 1] [1 0 1] [0] [1 0 1] [0] s(ok(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = ok(s(X)) [1 0 1] [0] [1 0 1] [0] [1 0 1] [1 0 1] [1 0 1] [1 0 1] cons(ok(X1),ok(X2)) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = ok(cons(X1,X2)) [1 0 1] [1 0 1] [1 0 1] [1 0 1] [2 0 2] [0] [2 0 2] [0] from(ok(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = ok(from(X)) [2 0 2] [0] [2 0 2] [0] [1 1 0] [1] [1 1 0] top(mark(X)) = [1 1 0]X + [1] >= [1 1 0]X = top(proper(X)) [0 0 1] [0] [0 0 1] [1 1 1] [1 1 1] top(ok(X)) = [1 1 1]X >= [1 1 1]X = top(active(X)) [1 0 1] [1 0 1] 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)))) active(first(X1,X2)) -> first(active(X1),X2) active(first(X1,X2)) -> first(X1,active(X2)) active(s(X)) -> s(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(from(X)) -> from(active(X)) first(mark(X1),X2) -> mark(first(X1,X2)) first(X1,mark(X2)) -> mark(first(X1,X2)) s(mark(X)) -> mark(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) from(mark(X)) -> mark(from(X)) proper(first(X1,X2)) -> first(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) proper(s(X)) -> s(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(from(X)) -> from(proper(X)) first(ok(X1),ok(X2)) -> ok(first(X1,X2)) s(ok(X)) -> ok(s(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) from(ok(X)) -> ok(from(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dim=1 interpretation: [top](x0) = x0 + 4, [ok](x0) = 4x0 + 4, [proper](x0) = 6x0 + 2, [from](x0) = 2x0 + 1, [cons](x0, x1) = x0 + x1 + 1, [s](x0) = x0, [mark](x0) = x0, [nil] = 1, [active](x0) = 4x0 + 2, [first](x0, x1) = 2x0 + 4x1 + 2, [0] = 1 orientation: active(first(0(),X)) = 16X + 18 >= 1 = mark(nil()) active(first(s(X),cons(Y,Z))) = 8X + 16Y + 16Z + 26 >= 2X + Y + 4Z + 3 = mark(cons(Y,first(X,Z))) active(from(X)) = 8X + 6 >= 3X + 2 = mark(cons(X,from(s(X)))) active(first(X1,X2)) = 8X1 + 16X2 + 10 >= 8X1 + 4X2 + 6 = first(active(X1),X2) active(first(X1,X2)) = 8X1 + 16X2 + 10 >= 2X1 + 16X2 + 10 = first(X1,active(X2)) active(s(X)) = 4X + 2 >= 4X + 2 = s(active(X)) active(cons(X1,X2)) = 4X1 + 4X2 + 6 >= 4X1 + X2 + 3 = cons(active(X1),X2) active(from(X)) = 8X + 6 >= 8X + 5 = from(active(X)) first(mark(X1),X2) = 2X1 + 4X2 + 2 >= 2X1 + 4X2 + 2 = mark(first(X1,X2)) first(X1,mark(X2)) = 2X1 + 4X2 + 2 >= 2X1 + 4X2 + 2 = mark(first(X1,X2)) s(mark(X)) = X >= X = mark(s(X)) cons(mark(X1),X2) = X1 + X2 + 1 >= X1 + X2 + 1 = mark(cons(X1,X2)) from(mark(X)) = 2X + 1 >= 2X + 1 = mark(from(X)) proper(first(X1,X2)) = 12X1 + 24X2 + 14 >= 12X1 + 24X2 + 14 = first(proper(X1),proper(X2)) proper(0()) = 8 >= 8 = ok(0()) proper(nil()) = 8 >= 8 = ok(nil()) proper(s(X)) = 6X + 2 >= 6X + 2 = s(proper(X)) proper(cons(X1,X2)) = 6X1 + 6X2 + 8 >= 6X1 + 6X2 + 5 = cons(proper(X1),proper(X2)) proper(from(X)) = 12X + 8 >= 12X + 5 = from(proper(X)) first(ok(X1),ok(X2)) = 8X1 + 16X2 + 26 >= 8X1 + 16X2 + 12 = ok(first(X1,X2)) s(ok(X)) = 4X + 4 >= 4X + 4 = ok(s(X)) cons(ok(X1),ok(X2)) = 4X1 + 4X2 + 9 >= 4X1 + 4X2 + 8 = ok(cons(X1,X2)) from(ok(X)) = 8X + 9 >= 8X + 8 = ok(from(X)) top(ok(X)) = 4X + 8 >= 4X + 6 = top(active(X)) problem: active(first(X1,X2)) -> first(X1,active(X2)) active(s(X)) -> s(active(X)) first(mark(X1),X2) -> mark(first(X1,X2)) first(X1,mark(X2)) -> mark(first(X1,X2)) s(mark(X)) -> mark(s(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) from(mark(X)) -> mark(from(X)) proper(first(X1,X2)) -> first(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) proper(s(X)) -> s(proper(X)) s(ok(X)) -> ok(s(X)) Matrix Interpretation Processor: dim=1 interpretation: [ok](x0) = x0, [proper](x0) = 4x0, [from](x0) = x0 + 4, [cons](x0, x1) = x0 + 4x1 + 4, [s](x0) = 2x0, [mark](x0) = x0 + 3, [nil] = 1, [active](x0) = x0, [first](x0, x1) = x0 + 4x1 + 1, [0] = 1 orientation: active(first(X1,X2)) = X1 + 4X2 + 1 >= X1 + 4X2 + 1 = first(X1,active(X2)) active(s(X)) = 2X >= 2X = s(active(X)) first(mark(X1),X2) = X1 + 4X2 + 4 >= X1 + 4X2 + 4 = mark(first(X1,X2)) first(X1,mark(X2)) = X1 + 4X2 + 13 >= X1 + 4X2 + 4 = mark(first(X1,X2)) s(mark(X)) = 2X + 6 >= 2X + 3 = mark(s(X)) cons(mark(X1),X2) = X1 + 4X2 + 7 >= X1 + 4X2 + 7 = mark(cons(X1,X2)) from(mark(X)) = X + 7 >= X + 7 = mark(from(X)) proper(first(X1,X2)) = 4X1 + 16X2 + 4 >= 4X1 + 16X2 + 1 = first(proper(X1),proper(X2)) proper(0()) = 4 >= 1 = ok(0()) proper(nil()) = 4 >= 1 = ok(nil()) proper(s(X)) = 8X >= 8X = s(proper(X)) s(ok(X)) = 2X >= 2X = ok(s(X)) problem: active(first(X1,X2)) -> first(X1,active(X2)) active(s(X)) -> s(active(X)) first(mark(X1),X2) -> mark(first(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) from(mark(X)) -> mark(from(X)) proper(s(X)) -> s(proper(X)) s(ok(X)) -> ok(s(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1] [ok](x0) = [0 0 0]x0 + [0] [0 0 1] [0], [1 1 0] [proper](x0) = [1 1 0]x0 [0 0 1] , [1 0 0] [from](x0) = [0 0 0]x0 [0 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 1] [0] [s](x0) = [0 1 0]x0 + [1] [0 0 0] [0], [1 0 0] [1] [mark](x0) = [0 1 0]x0 + [0] [0 0 0] [1], [1 1 0] [0] [active](x0) = [0 1 0]x0 + [0] [0 0 0] [1], [1 0 0] [1 0 0] [0] [first](x0, x1) = [0 0 0]x0 + [0 1 0]x1 + [1] [0 0 0] [0 0 0] [1] orientation: [1 0 0] [1 1 0] [1] [1 0 0] [1 1 0] [0] active(first(X1,X2)) = [0 0 0]X1 + [0 1 0]X2 + [1] >= [0 0 0]X1 + [0 1 0]X2 + [1] = first(X1,active(X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 1 1] [1] [1 1 0] [1] active(s(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = s(active(X)) [0 0 0] [1] [0 0 0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] first(mark(X1),X2) = [0 0 0]X1 + [0 1 0]X2 + [1] >= [0 0 0]X1 + [0 1 0]X2 + [1] = mark(first(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] [1] cons(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = mark(cons(X1,X2)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1] [1 0 0] [1] from(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(from(X)) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1] [1 1 1] [0] proper(s(X)) = [1 1 1]X + [1] >= [1 1 0]X + [1] = s(proper(X)) [0 0 0] [0] [0 0 0] [0] [1 0 1] [1] [1 0 1] [1] s(ok(X)) = [0 0 0]X + [1] >= [0 0 0]X + [0] = ok(s(X)) [0 0 0] [0] [0 0 0] [0] problem: active(s(X)) -> s(active(X)) first(mark(X1),X2) -> mark(first(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) from(mark(X)) -> mark(from(X)) s(ok(X)) -> ok(s(X)) Matrix Interpretation Processor: dim=1 interpretation: [ok](x0) = 4x0 + 4, [from](x0) = x0 + 2, [cons](x0, x1) = x0 + 4x1, [s](x0) = 6x0 + 3, [mark](x0) = x0, [active](x0) = x0, [first](x0, x1) = x0 + x1 + 6 orientation: active(s(X)) = 6X + 3 >= 6X + 3 = s(active(X)) first(mark(X1),X2) = X1 + X2 + 6 >= X1 + X2 + 6 = mark(first(X1,X2)) cons(mark(X1),X2) = X1 + 4X2 >= X1 + 4X2 = mark(cons(X1,X2)) from(mark(X)) = X + 2 >= X + 2 = mark(from(X)) s(ok(X)) = 24X + 27 >= 24X + 16 = ok(s(X)) problem: active(s(X)) -> s(active(X)) first(mark(X1),X2) -> mark(first(X1,X2)) cons(mark(X1),X2) -> mark(cons(X1,X2)) from(mark(X)) -> mark(from(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [from](x0) = [1 1 0]x0 + [0] [1 0 0] [1], [1 0 0] [1 1 1] [0] [cons](x0, x1) = [1 1 0]x0 + [0 1 0]x1 + [0] [0 0 1] [1 1 1] [1], [1 1 1] [s](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [0] [mark](x0) = [0 1 0]x0 + [1] [1 0 0] [0], [1 0 1] [active](x0) = [0 1 0]x0 [0 0 0] , [1 1 0] [1 0 1] [first](x0, x1) = [0 1 0]x0 + [0 1 0]x1 [0 1 1] [1 0 1] orientation: [1 1 1] [1 1 1] active(s(X)) = [0 0 0]X >= [0 0 0]X = s(active(X)) [0 0 0] [0 0 0] [1 1 0] [1 0 1] [1] [1 1 0] [1 0 1] [0] first(mark(X1),X2) = [0 1 0]X1 + [0 1 0]X2 + [1] >= [0 1 0]X1 + [0 1 0]X2 + [1] = mark(first(X1,X2)) [1 1 0] [1 0 1] [1] [1 1 0] [1 0 1] [0] [1 0 0] [1 1 1] [0] [1 0 0] [1 1 1] [0] cons(mark(X1),X2) = [1 1 0]X1 + [0 1 0]X2 + [1] >= [1 1 0]X1 + [0 1 0]X2 + [1] = mark(cons(X1,X2)) [1 0 0] [1 1 1] [1] [1 0 0] [1 1 1] [0] [1 0 0] [0] [1 0 0] [0] from(mark(X)) = [1 1 0]X + [1] >= [1 1 0]X + [1] = mark(from(X)) [1 0 0] [1] [1 0 0] [0] problem: active(s(X)) -> s(active(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) from(mark(X)) -> mark(from(X)) Matrix Interpretation Processor: dim=1 interpretation: [from](x0) = x0, [cons](x0, x1) = 4x0 + x1 + 4, [s](x0) = 3x0 + 6, [mark](x0) = x0 + 1, [active](x0) = 4x0 + 7 orientation: active(s(X)) = 12X + 31 >= 12X + 27 = s(active(X)) cons(mark(X1),X2) = 4X1 + X2 + 8 >= 4X1 + X2 + 5 = mark(cons(X1,X2)) from(mark(X)) = X + 1 >= X + 1 = mark(from(X)) problem: from(mark(X)) -> mark(from(X)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [from](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [0] [mark](x0) = [0 0 0]x0 + [0] [0 0 1] [1] orientation: [1 0 1] [1] [1 0 1] [0] from(mark(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = mark(from(X)) [0 0 1] [1] [0 0 1] [1] problem: Qed