/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(2nd(cons(X,cons(Y,Z)))) -> mark(Y) active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) Proof: Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [s](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [1] [from](x0) = [0 0 0]x0 + [0] [1 0 1] [1], [1 0 1] [mark](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [active](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [2nd](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [1 0 0] [1] [cons](x0, x1) = [0 0 0]x0 + [1 0 0]x1 + [0] [0 0 0] [0 0 0] [0] orientation: [1 0 1] [1 0 1] [1 0 0] [2] [1 0 1] active(2nd(cons(X,cons(Y,Z)))) = [0 0 0]X + [0 0 0]Y + [0 0 0]Z + [0] >= [0 0 0]Y = mark(Y) [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [2 0 2] [2] [2 0 2] [2] 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] [1 0 1] [1 0 1] mark(2nd(X)) = [0 0 0]X >= [0 0 0]X = active(2nd(mark(X))) [0 0 0] [0 0 0] [1 0 1] [1 0 0] [1] [1 0 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 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [2 0 2] [2] [2 0 2] [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 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 1] 2nd(mark(X)) = [0 0 0]X >= [0 0 0]X = 2nd(X) [0 0 0] [0 0 0] [1 0 1] [1 0 1] 2nd(active(X)) = [0 0 0]X >= [0 0 0]X = 2nd(X) [0 0 0] [0 0 0] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [1] cons(mark(X1),X2) = [0 0 0]X1 + [1 0 0]X2 + [0] >= [0 0 0]X1 + [1 0 0]X2 + [0] = cons(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 0] [1] cons(X1,mark(X2)) = [0 0 0]X1 + [1 0 1]X2 + [0] >= [0 0 0]X1 + [1 0 0]X2 + [0] = cons(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [1] cons(active(X1),X2) = [0 0 0]X1 + [1 0 0]X2 + [0] >= [0 0 0]X1 + [1 0 0]X2 + [0] = cons(X1,X2) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 0] [1] cons(X1,active(X2)) = [0 0 0]X1 + [1 0 1]X2 + [0] >= [0 0 0]X1 + [1 0 0]X2 + [0] = cons(X1,X2) [0 0 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] [1] [1 0 1] [1] [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] [1] [1 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] problem: active(from(X)) -> mark(cons(X,from(s(X)))) mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [s](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [1] [from](x0) = [1 1 0]x0 + [1] [0 0 0] [0], [1 1 0] [mark](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [active](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [2nd](x0) = [0 0 0]x0 [0 0 0] , [1 1 0] [1 0 0] [0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [1 0 0] [0 0 0] [1] 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] [1 1 0] [1 1 0] mark(2nd(X)) = [0 0 0]X >= [0 0 0]X = active(2nd(mark(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 0 0] [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 1 0] mark(s(X)) = [0 0 0]X >= [0 0 0]X = active(s(mark(X))) [0 0 0] [0 0 0] [1 1 0] [1 1 0] 2nd(mark(X)) = [0 0 0]X >= [0 0 0]X = 2nd(X) [0 0 0] [0 0 0] [1 1 0] [1 1 0] 2nd(active(X)) = [0 0 0]X >= [0 0 0]X = 2nd(X) [0 0 0] [0 0 0] [1 1 0] [1 0 0] [0] [1 1 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) [1 1 0] [0 0 0] [1] [1 0 0] [0 0 0] [1] [1 1 0] [1 1 0] [0] [1 1 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) [1 0 0] [0 0 0] [1] [1 0 0] [0 0 0] [1] [1 1 0] [1 0 0] [0] [1 1 0] [1 0 0] [0] cons(active(X1),X2) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = cons(X1,X2) [1 1 0] [0 0 0] [1] [1 0 0] [0 0 0] [1] [1 1 0] [1 1 0] [0] [1 1 0] [1 0 0] [0] cons(X1,active(X2)) = [0 0 0]X1 + [0 0 0]X2 + [0] >= [0 0 0]X1 + [0 0 0]X2 + [0] = cons(X1,X2) [1 0 0] [0 0 0] [1] [1 0 0] [0 0 0] [1] [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 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] problem: mark(2nd(X)) -> active(2nd(mark(X))) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(from(X)) -> active(from(mark(X))) mark(s(X)) -> active(s(mark(X))) 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) Matrix Interpretation Processor: dim=3 interpretation: [0] [s](x0) = x0 + [1] [0], [0] [from](x0) = x0 + [1] [0], [1 1 0] [0] [mark](x0) = [0 1 0]x0 + [0] [0 0 1] [1], [active](x0) = x0 , [0] [2nd](x0) = x0 + [1] [0], [1 0 0] [0] [cons](x0, x1) = x0 + [0 0 0]x1 + [1] [0 0 0] [0] orientation: [1 1 0] [1] [1 1 0] [0] mark(2nd(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = active(2nd(mark(X))) [0 0 1] [1] [0 0 1] [1] [1 1 0] [1 0 0] [1] [1 1 0] [1 0 0] [0] mark(cons(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 + [1] >= [0 1 0]X1 + [0 0 0]X2 + [1] = active(cons(mark(X1),X2)) [0 0 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] [1 1 0] [1] [1 1 0] [0] mark(from(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = active(from(mark(X))) [0 0 1] [1] [0 0 1] [1] [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))) [0 0 1] [1] [0 0 1] [1] [1 1 0] [0] [0] 2nd(mark(X)) = [0 1 0]X + [1] >= X + [1] = 2nd(X) [0 0 1] [1] [0] [0] [0] 2nd(active(X)) = X + [1] >= X + [1] = 2nd(X) [0] [0] [1 1 0] [1 0 0] [0] [1 0 0] [0] cons(mark(X1),X2) = [0 1 0]X1 + [0 0 0]X2 + [1] >= X1 + [0 0 0]X2 + [1] = cons(X1,X2) [0 0 1] [0 0 0] [1] [0 0 0] [0] [1 1 0] [0] [1 0 0] [0] cons(X1,mark(X2)) = X1 + [0 0 0]X2 + [1] >= X1 + [0 0 0]X2 + [1] = cons(X1,X2) [0 0 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] cons(active(X1),X2) = X1 + [0 0 0]X2 + [1] >= X1 + [0 0 0]X2 + [1] = cons(X1,X2) [0 0 0] [0] [0 0 0] [0] [1 0 0] [0] [1 0 0] [0] cons(X1,active(X2)) = X1 + [0 0 0]X2 + [1] >= X1 + [0 0 0]X2 + [1] = cons(X1,X2) [0 0 0] [0] [0 0 0] [0] [1 1 0] [0] [0] from(mark(X)) = [0 1 0]X + [1] >= X + [1] = from(X) [0 0 1] [1] [0] [0] [0] from(active(X)) = X + [1] >= X + [1] = from(X) [0] [0] [1 1 0] [0] [0] s(mark(X)) = [0 1 0]X + [1] >= X + [1] = s(X) [0 0 1] [1] [0] [0] [0] s(active(X)) = X + [1] >= X + [1] = s(X) [0] [0] problem: 2nd(mark(X)) -> 2nd(X) 2nd(active(X)) -> 2nd(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) s(mark(X)) -> s(X) s(active(X)) -> s(X) Matrix Interpretation Processor: dim=1 interpretation: [s](x0) = x0 + 1, [from](x0) = 4x0, [mark](x0) = 6x0 + 3, [active](x0) = 6x0 + 2, [2nd](x0) = 5x0 + 3, [cons](x0, x1) = 4x0 + 2x1 + 2 orientation: 2nd(mark(X)) = 30X + 18 >= 5X + 3 = 2nd(X) 2nd(active(X)) = 30X + 13 >= 5X + 3 = 2nd(X) cons(mark(X1),X2) = 24X1 + 2X2 + 14 >= 4X1 + 2X2 + 2 = cons(X1,X2) cons(X1,mark(X2)) = 4X1 + 12X2 + 8 >= 4X1 + 2X2 + 2 = cons(X1,X2) cons(active(X1),X2) = 24X1 + 2X2 + 10 >= 4X1 + 2X2 + 2 = cons(X1,X2) cons(X1,active(X2)) = 4X1 + 12X2 + 6 >= 4X1 + 2X2 + 2 = cons(X1,X2) from(mark(X)) = 24X + 12 >= 4X = from(X) from(active(X)) = 24X + 8 >= 4X = from(X) s(mark(X)) = 6X + 4 >= X + 1 = s(X) s(active(X)) = 6X + 3 >= X + 1 = s(X) problem: Qed