/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: r(r(x1)) -> s(r(x1)) r(s(x1)) -> s(r(x1)) r(n(x1)) -> s(r(x1)) r(b(x1)) -> u(s(b(x1))) r(u(x1)) -> u(r(x1)) s(u(x1)) -> u(s(x1)) n(u(x1)) -> u(n(x1)) t(r(u(x1))) -> t(c(r(x1))) t(s(u(x1))) -> t(c(r(x1))) t(n(u(x1))) -> t(c(r(x1))) c(u(x1)) -> u(c(x1)) c(s(x1)) -> s(c(x1)) c(r(x1)) -> r(c(x1)) c(n(x1)) -> n(c(x1)) c(n(x1)) -> n(x1) Proof: String Reversal Processor: r(r(x1)) -> r(s(x1)) s(r(x1)) -> r(s(x1)) n(r(x1)) -> r(s(x1)) b(r(x1)) -> b(s(u(x1))) u(r(x1)) -> r(u(x1)) u(s(x1)) -> s(u(x1)) u(n(x1)) -> n(u(x1)) u(r(t(x1))) -> r(c(t(x1))) u(s(t(x1))) -> r(c(t(x1))) u(n(t(x1))) -> r(c(t(x1))) u(c(x1)) -> c(u(x1)) s(c(x1)) -> c(s(x1)) r(c(x1)) -> c(r(x1)) n(c(x1)) -> c(n(x1)) n(c(x1)) -> n(x1) Matrix Interpretation Processor: dim=1 interpretation: [c](x0) = x0, [t](x0) = x0 + 2, [u](x0) = 2x0, [b](x0) = x0, [n](x0) = 2x0, [s](x0) = 2x0, [r](x0) = 4x0 orientation: r(r(x1)) = 16x1 >= 8x1 = r(s(x1)) s(r(x1)) = 8x1 >= 8x1 = r(s(x1)) n(r(x1)) = 8x1 >= 8x1 = r(s(x1)) b(r(x1)) = 4x1 >= 4x1 = b(s(u(x1))) u(r(x1)) = 8x1 >= 8x1 = r(u(x1)) u(s(x1)) = 4x1 >= 4x1 = s(u(x1)) u(n(x1)) = 4x1 >= 4x1 = n(u(x1)) u(r(t(x1))) = 8x1 + 16 >= 4x1 + 8 = r(c(t(x1))) u(s(t(x1))) = 4x1 + 8 >= 4x1 + 8 = r(c(t(x1))) u(n(t(x1))) = 4x1 + 8 >= 4x1 + 8 = r(c(t(x1))) u(c(x1)) = 2x1 >= 2x1 = c(u(x1)) s(c(x1)) = 2x1 >= 2x1 = c(s(x1)) r(c(x1)) = 4x1 >= 4x1 = c(r(x1)) n(c(x1)) = 2x1 >= 2x1 = c(n(x1)) n(c(x1)) = 2x1 >= 2x1 = n(x1) problem: r(r(x1)) -> r(s(x1)) s(r(x1)) -> r(s(x1)) n(r(x1)) -> r(s(x1)) b(r(x1)) -> b(s(u(x1))) u(r(x1)) -> r(u(x1)) u(s(x1)) -> s(u(x1)) u(n(x1)) -> n(u(x1)) u(s(t(x1))) -> r(c(t(x1))) u(n(t(x1))) -> r(c(t(x1))) u(c(x1)) -> c(u(x1)) s(c(x1)) -> c(s(x1)) r(c(x1)) -> c(r(x1)) n(c(x1)) -> c(n(x1)) n(c(x1)) -> n(x1) String Reversal Processor: r(r(x1)) -> s(r(x1)) r(s(x1)) -> s(r(x1)) r(n(x1)) -> s(r(x1)) r(b(x1)) -> u(s(b(x1))) r(u(x1)) -> u(r(x1)) s(u(x1)) -> u(s(x1)) n(u(x1)) -> u(n(x1)) t(s(u(x1))) -> t(c(r(x1))) t(n(u(x1))) -> t(c(r(x1))) c(u(x1)) -> u(c(x1)) c(s(x1)) -> s(c(x1)) c(r(x1)) -> r(c(x1)) c(n(x1)) -> n(c(x1)) c(n(x1)) -> n(x1) Matrix Interpretation Processor: dim=1 interpretation: [c](x0) = x0, [t](x0) = x0 + 5, [u](x0) = x0, [b](x0) = x0, [n](x0) = 8x0 + 4, [s](x0) = x0, [r](x0) = x0 orientation: r(r(x1)) = x1 >= x1 = s(r(x1)) r(s(x1)) = x1 >= x1 = s(r(x1)) r(n(x1)) = 8x1 + 4 >= x1 = s(r(x1)) r(b(x1)) = x1 >= x1 = u(s(b(x1))) r(u(x1)) = x1 >= x1 = u(r(x1)) s(u(x1)) = x1 >= x1 = u(s(x1)) n(u(x1)) = 8x1 + 4 >= 8x1 + 4 = u(n(x1)) t(s(u(x1))) = x1 + 5 >= x1 + 5 = t(c(r(x1))) t(n(u(x1))) = 8x1 + 9 >= x1 + 5 = t(c(r(x1))) c(u(x1)) = x1 >= x1 = u(c(x1)) c(s(x1)) = x1 >= x1 = s(c(x1)) c(r(x1)) = x1 >= x1 = r(c(x1)) c(n(x1)) = 8x1 + 4 >= 8x1 + 4 = n(c(x1)) c(n(x1)) = 8x1 + 4 >= 8x1 + 4 = n(x1) problem: r(r(x1)) -> s(r(x1)) r(s(x1)) -> s(r(x1)) r(b(x1)) -> u(s(b(x1))) r(u(x1)) -> u(r(x1)) s(u(x1)) -> u(s(x1)) n(u(x1)) -> u(n(x1)) t(s(u(x1))) -> t(c(r(x1))) c(u(x1)) -> u(c(x1)) c(s(x1)) -> s(c(x1)) c(r(x1)) -> r(c(x1)) c(n(x1)) -> n(c(x1)) c(n(x1)) -> n(x1) Matrix Interpretation Processor: dim=1 interpretation: [c](x0) = x0, [t](x0) = 8x0 + 9, [u](x0) = 2x0 + 2, [b](x0) = 4x0, [n](x0) = 4x0 + 5, [s](x0) = x0, [r](x0) = 2x0 + 2 orientation: r(r(x1)) = 4x1 + 6 >= 2x1 + 2 = s(r(x1)) r(s(x1)) = 2x1 + 2 >= 2x1 + 2 = s(r(x1)) r(b(x1)) = 8x1 + 2 >= 8x1 + 2 = u(s(b(x1))) r(u(x1)) = 4x1 + 6 >= 4x1 + 6 = u(r(x1)) s(u(x1)) = 2x1 + 2 >= 2x1 + 2 = u(s(x1)) n(u(x1)) = 8x1 + 13 >= 8x1 + 12 = u(n(x1)) t(s(u(x1))) = 16x1 + 25 >= 16x1 + 25 = t(c(r(x1))) c(u(x1)) = 2x1 + 2 >= 2x1 + 2 = u(c(x1)) c(s(x1)) = x1 >= x1 = s(c(x1)) c(r(x1)) = 2x1 + 2 >= 2x1 + 2 = r(c(x1)) c(n(x1)) = 4x1 + 5 >= 4x1 + 5 = n(c(x1)) c(n(x1)) = 4x1 + 5 >= 4x1 + 5 = n(x1) problem: r(s(x1)) -> s(r(x1)) r(b(x1)) -> u(s(b(x1))) r(u(x1)) -> u(r(x1)) s(u(x1)) -> u(s(x1)) t(s(u(x1))) -> t(c(r(x1))) c(u(x1)) -> u(c(x1)) c(s(x1)) -> s(c(x1)) c(r(x1)) -> r(c(x1)) c(n(x1)) -> n(c(x1)) c(n(x1)) -> n(x1) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [c](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [t](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [u](x0) = [0 1 0]x0 [0 1 1] , [1 0 0] [0] [b](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [1 0 1] [n](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [s](x0) = [0 0 0]x0 [0 1 1] , [1 0 1] [r](x0) = [0 0 0]x0 [0 0 1] orientation: [1 1 1] [1 0 1] r(s(x1)) = [0 0 0]x1 >= [0 0 0]x1 = s(r(x1)) [0 1 1] [0 0 1] [1 0 0] [1] [1 0 0] [0] r(b(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = u(s(b(x1))) [0 0 0] [1] [0 0 0] [1] [1 1 1] [1 0 1] r(u(x1)) = [0 0 0]x1 >= [0 0 0]x1 = u(r(x1)) [0 1 1] [0 0 1] [1 0 0] [1 0 0] s(u(x1)) = [0 0 0]x1 >= [0 0 0]x1 = u(s(x1)) [0 2 1] [0 1 1] [1 2 1] [1 0 1] t(s(u(x1))) = [0 0 0]x1 >= [0 0 0]x1 = t(c(r(x1))) [0 0 0] [0 0 0] [1 0 0] [1 0 0] c(u(x1)) = [0 0 0]x1 >= [0 0 0]x1 = u(c(x1)) [0 0 0] [0 0 0] [1 0 0] [1 0 0] c(s(x1)) = [0 0 0]x1 >= [0 0 0]x1 = s(c(x1)) [0 0 0] [0 0 0] [1 0 1] [1 0 0] c(r(x1)) = [0 0 0]x1 >= [0 0 0]x1 = r(c(x1)) [0 0 0] [0 0 0] [1 0 1] [1 0 0] c(n(x1)) = [0 0 0]x1 >= [0 0 0]x1 = n(c(x1)) [0 0 0] [0 0 0] [1 0 1] [1 0 1] c(n(x1)) = [0 0 0]x1 >= [0 0 0]x1 = n(x1) [0 0 0] [0 0 0] problem: r(s(x1)) -> s(r(x1)) r(u(x1)) -> u(r(x1)) s(u(x1)) -> u(s(x1)) t(s(u(x1))) -> t(c(r(x1))) c(u(x1)) -> u(c(x1)) c(s(x1)) -> s(c(x1)) c(r(x1)) -> r(c(x1)) c(n(x1)) -> n(c(x1)) c(n(x1)) -> n(x1) KBO Processor: weight function: w0 = 1 w(t) = w(u) = w(n) = w(s) = w(r) = 1 w(c) = 0 precedence: c > r > s > t ~ u ~ n problem: Qed