/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: strict: p(s(x1)) -> s(x1) n(s(x1)) -> s(x1) o(s(x1)) -> s(x1) o(n(x1)) -> n(o(x1)) o(m(x1)) -> n(o(x1)) n(o(p(x1))) -> o(n(x1)) weak: t(x1) -> t(c(n(x1))) p(n(x1)) -> m(p(x1)) p(m(x1)) -> m(p(x1)) n(p(x1)) -> p(n(x1)) c(p(x1)) -> p(c(x1)) c(m(x1)) -> m(c(x1)) c(n(x1)) -> n(c(x1)) c(o(x1)) -> o(c(x1)) c(o(x1)) -> o(x1) Proof: String Reversal Processor: strict: s(p(x1)) -> s(x1) s(n(x1)) -> s(x1) s(o(x1)) -> s(x1) n(o(x1)) -> o(n(x1)) m(o(x1)) -> o(n(x1)) p(o(n(x1))) -> n(o(x1)) weak: t(x1) -> n(c(t(x1))) n(p(x1)) -> p(m(x1)) m(p(x1)) -> p(m(x1)) p(n(x1)) -> n(p(x1)) p(c(x1)) -> c(p(x1)) m(c(x1)) -> c(m(x1)) n(c(x1)) -> c(n(x1)) o(c(x1)) -> c(o(x1)) o(c(x1)) -> o(x1) Arctic Interpretation Processor: dimension: 1 interpretation: [c](x0) = x0, [t](x0) = x0, [m](x0) = x0, [o](x0) = x0, [n](x0) = x0, [p](x0) = 8x0, [s](x0) = x0 orientation: s(p(x1)) = 8x1 >= x1 = s(x1) s(n(x1)) = x1 >= x1 = s(x1) s(o(x1)) = x1 >= x1 = s(x1) n(o(x1)) = x1 >= x1 = o(n(x1)) m(o(x1)) = x1 >= x1 = o(n(x1)) p(o(n(x1))) = 8x1 >= x1 = n(o(x1)) t(x1) = x1 >= x1 = n(c(t(x1))) n(p(x1)) = 8x1 >= 8x1 = p(m(x1)) m(p(x1)) = 8x1 >= 8x1 = p(m(x1)) p(n(x1)) = 8x1 >= 8x1 = n(p(x1)) p(c(x1)) = 8x1 >= 8x1 = c(p(x1)) m(c(x1)) = x1 >= x1 = c(m(x1)) n(c(x1)) = x1 >= x1 = c(n(x1)) o(c(x1)) = x1 >= x1 = c(o(x1)) o(c(x1)) = x1 >= x1 = o(x1) problem: strict: s(n(x1)) -> s(x1) s(o(x1)) -> s(x1) n(o(x1)) -> o(n(x1)) m(o(x1)) -> o(n(x1)) weak: t(x1) -> n(c(t(x1))) n(p(x1)) -> p(m(x1)) m(p(x1)) -> p(m(x1)) p(n(x1)) -> n(p(x1)) p(c(x1)) -> c(p(x1)) m(c(x1)) -> c(m(x1)) n(c(x1)) -> c(n(x1)) o(c(x1)) -> c(o(x1)) o(c(x1)) -> o(x1) String Reversal Processor: strict: n(s(x1)) -> s(x1) o(s(x1)) -> s(x1) o(n(x1)) -> n(o(x1)) o(m(x1)) -> n(o(x1)) weak: t(x1) -> t(c(n(x1))) p(n(x1)) -> m(p(x1)) p(m(x1)) -> m(p(x1)) n(p(x1)) -> p(n(x1)) c(p(x1)) -> p(c(x1)) c(m(x1)) -> m(c(x1)) c(n(x1)) -> n(c(x1)) c(o(x1)) -> o(c(x1)) c(o(x1)) -> o(x1) Arctic Interpretation Processor: dimension: 1 interpretation: [c](x0) = x0, [t](x0) = 1x0, [m](x0) = x0, [o](x0) = 3x0, [n](x0) = x0, [p](x0) = x0, [s](x0) = 5x0 orientation: n(s(x1)) = 5x1 >= 5x1 = s(x1) o(s(x1)) = 8x1 >= 5x1 = s(x1) o(n(x1)) = 3x1 >= 3x1 = n(o(x1)) o(m(x1)) = 3x1 >= 3x1 = n(o(x1)) t(x1) = 1x1 >= 1x1 = t(c(n(x1))) p(n(x1)) = x1 >= x1 = m(p(x1)) p(m(x1)) = x1 >= x1 = m(p(x1)) n(p(x1)) = x1 >= x1 = p(n(x1)) c(p(x1)) = x1 >= x1 = p(c(x1)) c(m(x1)) = x1 >= x1 = m(c(x1)) c(n(x1)) = x1 >= x1 = n(c(x1)) c(o(x1)) = 3x1 >= 3x1 = o(c(x1)) c(o(x1)) = 3x1 >= 3x1 = o(x1) problem: strict: n(s(x1)) -> s(x1) o(n(x1)) -> n(o(x1)) o(m(x1)) -> n(o(x1)) weak: t(x1) -> t(c(n(x1))) p(n(x1)) -> m(p(x1)) p(m(x1)) -> m(p(x1)) n(p(x1)) -> p(n(x1)) c(p(x1)) -> p(c(x1)) c(m(x1)) -> m(c(x1)) c(n(x1)) -> n(c(x1)) c(o(x1)) -> o(c(x1)) c(o(x1)) -> o(x1) String Reversal Processor: strict: s(n(x1)) -> s(x1) n(o(x1)) -> o(n(x1)) m(o(x1)) -> o(n(x1)) weak: t(x1) -> n(c(t(x1))) n(p(x1)) -> p(m(x1)) m(p(x1)) -> p(m(x1)) p(n(x1)) -> n(p(x1)) p(c(x1)) -> c(p(x1)) m(c(x1)) -> c(m(x1)) n(c(x1)) -> c(n(x1)) o(c(x1)) -> c(o(x1)) o(c(x1)) -> o(x1) Matrix Interpretation Processor: dim=2 interpretation: [1 0] [c](x0) = [0 0]x0, [1 0] [0] [t](x0) = [0 0]x0 + [2], [1 0] [0] [m](x0) = [0 0]x0 + [1], [1 0] [0] [o](x0) = [0 0]x0 + [1], [0] [n](x0) = x0 + [1], [2 0] [p](x0) = [0 1]x0, [2 1] [2] [s](x0) = [0 0]x0 + [0] orientation: [2 1] [3] [2 1] [2] s(n(x1)) = [0 0]x1 + [0] >= [0 0]x1 + [0] = s(x1) [1 0] [0] [1 0] [0] n(o(x1)) = [0 0]x1 + [2] >= [0 0]x1 + [1] = o(n(x1)) [1 0] [0] [1 0] [0] m(o(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = o(n(x1)) [1 0] [0] [1 0] [0] t(x1) = [0 0]x1 + [2] >= [0 0]x1 + [1] = n(c(t(x1))) [2 0] [0] [2 0] [0] n(p(x1)) = [0 1]x1 + [1] >= [0 0]x1 + [1] = p(m(x1)) [2 0] [0] [2 0] [0] m(p(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = p(m(x1)) [2 0] [0] [2 0] [0] p(n(x1)) = [0 1]x1 + [1] >= [0 1]x1 + [1] = n(p(x1)) [2 0] [2 0] p(c(x1)) = [0 0]x1 >= [0 0]x1 = c(p(x1)) [1 0] [0] [1 0] m(c(x1)) = [0 0]x1 + [1] >= [0 0]x1 = c(m(x1)) [1 0] [0] [1 0] n(c(x1)) = [0 0]x1 + [1] >= [0 0]x1 = c(n(x1)) [1 0] [0] [1 0] o(c(x1)) = [0 0]x1 + [1] >= [0 0]x1 = c(o(x1)) [1 0] [0] [1 0] [0] o(c(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [1] = o(x1) problem: strict: n(o(x1)) -> o(n(x1)) m(o(x1)) -> o(n(x1)) weak: t(x1) -> n(c(t(x1))) n(p(x1)) -> p(m(x1)) m(p(x1)) -> p(m(x1)) p(n(x1)) -> n(p(x1)) p(c(x1)) -> c(p(x1)) m(c(x1)) -> c(m(x1)) n(c(x1)) -> c(n(x1)) o(c(x1)) -> c(o(x1)) o(c(x1)) -> o(x1) Matrix Interpretation Processor: dim=2 interpretation: [c](x0) = x0, [1 1] [t](x0) = [0 0]x0, [1 1] [m](x0) = [0 1]x0, [0] [o](x0) = x0 + [2], [1 1] [n](x0) = [0 1]x0, [2 0] [p](x0) = [0 2]x0 orientation: [1 1] [2] [1 1] [0] n(o(x1)) = [0 1]x1 + [2] >= [0 1]x1 + [2] = o(n(x1)) [1 1] [2] [1 1] [0] m(o(x1)) = [0 1]x1 + [2] >= [0 1]x1 + [2] = o(n(x1)) [1 1] [1 1] t(x1) = [0 0]x1 >= [0 0]x1 = n(c(t(x1))) [2 2] [2 2] n(p(x1)) = [0 2]x1 >= [0 2]x1 = p(m(x1)) [2 2] [2 2] m(p(x1)) = [0 2]x1 >= [0 2]x1 = p(m(x1)) [2 2] [2 2] p(n(x1)) = [0 2]x1 >= [0 2]x1 = n(p(x1)) [2 0] [2 0] p(c(x1)) = [0 2]x1 >= [0 2]x1 = c(p(x1)) [1 1] [1 1] m(c(x1)) = [0 1]x1 >= [0 1]x1 = c(m(x1)) [1 1] [1 1] n(c(x1)) = [0 1]x1 >= [0 1]x1 = c(n(x1)) [0] [0] o(c(x1)) = x1 + [2] >= x1 + [2] = c(o(x1)) [0] [0] o(c(x1)) = x1 + [2] >= x1 + [2] = o(x1) problem: strict: weak: t(x1) -> n(c(t(x1))) n(p(x1)) -> p(m(x1)) m(p(x1)) -> p(m(x1)) p(n(x1)) -> n(p(x1)) p(c(x1)) -> c(p(x1)) m(c(x1)) -> c(m(x1)) n(c(x1)) -> c(n(x1)) o(c(x1)) -> c(o(x1)) o(c(x1)) -> o(x1) Qed