/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: top(sent(x)) -> top(check(rest(x))) rest(nil()) -> sent(nil()) rest(cons(x,y)) -> sent(y) check(sent(x)) -> sent(check(x)) check(rest(x)) -> rest(check(x)) check(cons(x,y)) -> cons(check(x),y) check(cons(x,y)) -> cons(x,check(y)) check(cons(x,y)) -> cons(x,y) Proof: Matrix Interpretation Processor: dim=3 interpretation: [0] [nil] = [0] [1], [1 1 0] [top](x0) = [1 1 0]x0 [0 0 0] , [check](x0) = x0 , [1 0 0] [1 0 1] [0] [cons](x0, x1) = [0 0 1]x0 + [0 0 0]x1 + [0] [0 0 0] [0 1 0] [1], [1 0 1] [0] [sent](x0) = [0 1 0]x0 + [1] [0 0 0] [0], [1 0 0] [1] [rest](x0) = [0 0 1]x0 + [0] [0 0 0] [0] orientation: [1 1 1] [1] [1 0 1] [1] top(sent(x)) = [1 1 1]x + [1] >= [1 0 1]x + [1] = top(check(rest(x))) [0 0 0] [0] [0 0 0] [0] [1] [1] rest(nil()) = [1] >= [1] = sent(nil()) [0] [0] [1 0 0] [1 0 1] [1] [1 0 1] [0] rest(cons(x,y)) = [0 0 0]x + [0 1 0]y + [1] >= [0 1 0]y + [1] = sent(y) [0 0 0] [0 0 0] [0] [0 0 0] [0] [1 0 1] [0] [1 0 1] [0] check(sent(x)) = [0 1 0]x + [1] >= [0 1 0]x + [1] = sent(check(x)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1] [1 0 0] [1] check(rest(x)) = [0 0 1]x + [0] >= [0 0 1]x + [0] = rest(check(x)) [0 0 0] [0] [0 0 0] [0] [1 0 0] [1 0 1] [0] [1 0 0] [1 0 1] [0] check(cons(x,y)) = [0 0 1]x + [0 0 0]y + [0] >= [0 0 1]x + [0 0 0]y + [0] = cons(check(x),y) [0 0 0] [0 1 0] [1] [0 0 0] [0 1 0] [1] [1 0 0] [1 0 1] [0] [1 0 0] [1 0 1] [0] check(cons(x,y)) = [0 0 1]x + [0 0 0]y + [0] >= [0 0 1]x + [0 0 0]y + [0] = cons(x,check(y)) [0 0 0] [0 1 0] [1] [0 0 0] [0 1 0] [1] [1 0 0] [1 0 1] [0] [1 0 0] [1 0 1] [0] check(cons(x,y)) = [0 0 1]x + [0 0 0]y + [0] >= [0 0 1]x + [0 0 0]y + [0] = cons(x,y) [0 0 0] [0 1 0] [1] [0 0 0] [0 1 0] [1] problem: top(sent(x)) -> top(check(rest(x))) rest(nil()) -> sent(nil()) check(sent(x)) -> sent(check(x)) check(rest(x)) -> rest(check(x)) check(cons(x,y)) -> cons(check(x),y) check(cons(x,y)) -> cons(x,check(y)) check(cons(x,y)) -> cons(x,y) Matrix Interpretation Processor: dim=3 interpretation: [0] [nil] = [1] [1], [1 1 1] [top](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [check](x0) = [0 1 0]x0 [0 0 0] , [1 1 0] [1 1 0] [cons](x0, x1) = [0 1 0]x0 + [0 0 1]x1 [0 0 0] [0 0 0] , [1 1 0] [0] [sent](x0) = [0 0 0]x0 + [1] [0 0 1] [0], [1 1 0] [rest](x0) = [0 0 1]x0 [0 0 1] orientation: [1 1 1] [1] [1 1 1] top(sent(x)) = [0 0 0]x + [0] >= [0 0 0]x = top(check(rest(x))) [0 0 0] [0] [0 0 0] [1] [1] rest(nil()) = [1] >= [1] = sent(nil()) [1] [1] [1 1 0] [0] [1 1 0] [0] check(sent(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = sent(check(x)) [0 0 0] [0] [0 0 0] [0] [1 1 0] [1 1 0] check(rest(x)) = [0 0 1]x >= [0 0 0]x = rest(check(x)) [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] check(cons(x,y)) = [0 1 0]x + [0 0 1]y >= [0 1 0]x + [0 0 1]y = cons(check(x),y) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] check(cons(x,y)) = [0 1 0]x + [0 0 1]y >= [0 1 0]x + [0 0 0]y = cons(x,check(y)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] check(cons(x,y)) = [0 1 0]x + [0 0 1]y >= [0 1 0]x + [0 0 1]y = cons(x,y) [0 0 0] [0 0 0] [0 0 0] [0 0 0] problem: rest(nil()) -> sent(nil()) check(sent(x)) -> sent(check(x)) check(rest(x)) -> rest(check(x)) check(cons(x,y)) -> cons(check(x),y) check(cons(x,y)) -> cons(x,check(y)) check(cons(x,y)) -> cons(x,y) Matrix Interpretation Processor: dim=3 interpretation: [0] [nil] = [0] [1], [1 1 0] [check](x0) = [0 1 0]x0 [0 0 0] , [1 0 0] [1 0 0] [0] [cons](x0, x1) = [0 1 1]x0 + [0 1 1]x1 + [1] [0 0 0] [0 0 0] [0], [1 0 0] [0] [sent](x0) = [0 1 0]x0 + [1] [0 0 0] [0], [1 0 1] [0] [rest](x0) = [0 1 0]x0 + [1] [0 0 0] [0] orientation: [1] [0] rest(nil()) = [1] >= [1] = sent(nil()) [0] [0] [1 1 0] [1] [1 1 0] [0] check(sent(x)) = [0 1 0]x + [1] >= [0 1 0]x + [1] = sent(check(x)) [0 0 0] [0] [0 0 0] [0] [1 1 1] [1] [1 1 0] [0] check(rest(x)) = [0 1 0]x + [1] >= [0 1 0]x + [1] = rest(check(x)) [0 0 0] [0] [0 0 0] [0] [1 1 1] [1 1 1] [1] [1 1 0] [1 0 0] [0] check(cons(x,y)) = [0 1 1]x + [0 1 1]y + [1] >= [0 1 0]x + [0 1 1]y + [1] = cons(check(x),y) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 1] [1 1 1] [1] [1 0 0] [1 1 0] [0] check(cons(x,y)) = [0 1 1]x + [0 1 1]y + [1] >= [0 1 1]x + [0 1 0]y + [1] = cons(x,check(y)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] [1 1 1] [1 1 1] [1] [1 0 0] [1 0 0] [0] check(cons(x,y)) = [0 1 1]x + [0 1 1]y + [1] >= [0 1 1]x + [0 1 1]y + [1] = cons(x,y) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0] problem: Qed