/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: p(0(x1)) -> s(s(0(s(s(p(x1)))))) p(s(0(x1))) -> 0(x1) p(s(s(x1))) -> s(p(s(x1))) f(s(x1)) -> g(q(i(x1))) g(x1) -> f(p(p(x1))) q(i(x1)) -> q(s(x1)) q(s(x1)) -> s(s(x1)) i(x1) -> s(x1) Proof: Matrix Interpretation Processor: dim=4 interpretation: [1 0 0 0] [0 1 1 0] [i](x0) = [0 0 0 0]x0 [1 0 0 0] , [1 0 0 1] [0] [1 0 0 0] [1] [p](x0) = [1 0 0 0]x0 + [1] [0 1 0 0] [0], [1 0 0 0] [0] [0 0 0 0] [0] [f](x0) = [0 0 0 0]x0 + [1] [1 0 0 0] [0], [1 0 0 0] [0 0 0 0] [q](x0) = [0 0 0 1]x0 [0 0 0 0] , [1 0 0 1] [0] [0 0 0 0] [0] [0](x0) = [0 0 0 0]x0 + [1] [0 0 0 0] [1], [1 1 0 1] [0] [0 0 0 0] [0] [g](x0) = [0 0 0 1]x0 + [1] [1 1 0 1] [0], [1 0 0 0] [0 0 1 0] [s](x0) = [0 0 0 0]x0 [0 0 0 0] orientation: [1 0 0 1] [1] [1 0 0 1] [1 0 0 1] [1] [0 0 0 0] p(0(x1)) = [1 0 0 1]x1 + [1] >= [0 0 0 0]x1 = s(s(0(s(s(p(x1)))))) [0 0 0 0] [0] [0 0 0 0] [1 0 0 1] [0] [1 0 0 1] [0] [1 0 0 1] [1] [0 0 0 0] [0] p(s(0(x1))) = [1 0 0 1]x1 + [1] >= [0 0 0 0]x1 + [1] = 0(x1) [0 0 0 0] [1] [0 0 0 0] [1] [1 0 0 0] [0] [1 0 0 0] [0] [1 0 0 0] [1] [1 0 0 0] [1] p(s(s(x1))) = [1 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [0] = s(p(s(x1))) [0 0 0 0] [0] [0 0 0 0] [0] [1 0 0 0] [0] [1 0 0 0] [0] [0 0 0 0] [0] [0 0 0 0] [0] f(s(x1)) = [0 0 0 0]x1 + [1] >= [0 0 0 0]x1 + [1] = g(q(i(x1))) [1 0 0 0] [0] [1 0 0 0] [0] [1 1 0 1] [0] [1 1 0 1] [0] [0 0 0 0] [0] [0 0 0 0] [0] g(x1) = [0 0 0 1]x1 + [1] >= [0 0 0 0]x1 + [1] = f(p(p(x1))) [1 1 0 1] [0] [1 1 0 1] [0] [1 0 0 0] [1 0 0 0] [0 0 0 0] [0 0 0 0] q(i(x1)) = [1 0 0 0]x1 >= [0 0 0 0]x1 = q(s(x1)) [0 0 0 0] [0 0 0 0] [1 0 0 0] [1 0 0 0] [0 0 0 0] [0 0 0 0] q(s(x1)) = [0 0 0 0]x1 >= [0 0 0 0]x1 = s(s(x1)) [0 0 0 0] [0 0 0 0] [1 0 0 0] [1 0 0 0] [0 1 1 0] [0 0 1 0] i(x1) = [0 0 0 0]x1 >= [0 0 0 0]x1 = s(x1) [1 0 0 0] [0 0 0 0] problem: p(s(0(x1))) -> 0(x1) p(s(s(x1))) -> s(p(s(x1))) f(s(x1)) -> g(q(i(x1))) g(x1) -> f(p(p(x1))) q(i(x1)) -> q(s(x1)) q(s(x1)) -> s(s(x1)) i(x1) -> s(x1) Matrix Interpretation Processor: dim=4 interpretation: [1 0 0 1] [0] [0 1 0 1] [1] [i](x0) = [1 0 0 1]x0 + [0] [0 1 0 0] [0], [1 0 0 0] [0 0 0 1] [p](x0) = [0 0 0 1]x0 [0 0 1 0] , [1 1 0 0] [0] [1 1 0 0] [1] [f](x0) = [0 0 0 0]x0 + [0] [0 1 0 0] [1], [1 0 0 0] [0] [0 1 0 1] [1] [q](x0) = [0 0 0 1]x0 + [0] [0 1 1 0] [0], [1 1 0 1] [1 1 0 0] [0](x0) = [0 0 0 0]x0 [0 0 0 0] , [1 0 1 0] [1] [1 0 1 0] [1] [g](x0) = [0 0 0 0]x0 + [0] [0 0 1 0] [1], [1 0 0 0] [0] [0 1 0 1] [1] [s](x0) = [0 0 0 1]x0 + [0] [0 1 0 0] [0] orientation: [1 1 0 1] [1 1 0 1] [1 1 0 0] [1 1 0 0] p(s(0(x1))) = [1 1 0 0]x1 >= [0 0 0 0]x1 = 0(x1) [0 0 0 0] [0 0 0 0] [1 0 0 0] [0] [1 0 0 0] [0] [0 1 0 1] [1] [0 1 0 1] [1] p(s(s(x1))) = [0 1 0 1]x1 + [1] >= [0 0 0 1]x1 + [0] = s(p(s(x1))) [0 1 0 0] [0] [0 1 0 0] [0] [1 1 0 1] [1] [1 1 0 1] [1] [1 1 0 1] [2] [1 1 0 1] [1] f(s(x1)) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = g(q(i(x1))) [0 1 0 1] [2] [0 1 0 0] [1] [1 0 1 0] [1] [1 0 1 0] [0] [1 0 1 0] [1] [1 0 1 0] [1] g(x1) = [0 0 0 0]x1 + [0] >= [0 0 0 0]x1 + [0] = f(p(p(x1))) [0 0 1 0] [1] [0 0 1 0] [1] [1 0 0 1] [0] [1 0 0 0] [0] [0 2 0 1] [2] [0 2 0 1] [2] q(i(x1)) = [0 1 0 0]x1 + [0] >= [0 1 0 0]x1 + [0] = q(s(x1)) [1 1 0 2] [1] [0 1 0 2] [1] [1 0 0 0] [0] [1 0 0 0] [0] [0 2 0 1] [2] [0 2 0 1] [2] q(s(x1)) = [0 1 0 0]x1 + [0] >= [0 1 0 0]x1 + [0] = s(s(x1)) [0 1 0 2] [1] [0 1 0 1] [1] [1 0 0 1] [0] [1 0 0 0] [0] [0 1 0 1] [1] [0 1 0 1] [1] i(x1) = [1 0 0 1]x1 + [0] >= [0 0 0 1]x1 + [0] = s(x1) [0 1 0 0] [0] [0 1 0 0] [0] problem: p(s(0(x1))) -> 0(x1) p(s(s(x1))) -> s(p(s(x1))) f(s(x1)) -> g(q(i(x1))) q(i(x1)) -> q(s(x1)) q(s(x1)) -> s(s(x1)) i(x1) -> s(x1) Bounds Processor: bound: 2 enrichment: match automaton: final states: {4,10,9,6,3,1} transitions: g0(8) -> 6* q1(15) -> 16* s1(14) -> 15* s1(17) -> 18* f70() -> 2* p0(4) -> 5* i0(2) -> 7* s0(2) -> 4* s0(4) -> 10* s0(5) -> 3* 00(2) -> 1* s2(25) -> 26* s2(24) -> 25* q0(4) -> 9* q0(7) -> 8* 14 -> 24* 16 -> 8* 2 -> 14* 26 -> 16,8 1 -> 5* 3 -> 5* 18 -> 8,9 15 -> 7,17 problem: Qed