/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: r1(a(x1)) -> a(a(a(r1(x1)))) r2(a(x1)) -> a(a(a(r2(x1)))) a(l1(x1)) -> l1(a(a(a(x1)))) a(a(l2(x1))) -> l2(a(a(x1))) r1(b(x1)) -> l1(b(x1)) r2(b(x1)) -> l2(a(b(x1))) b(l1(x1)) -> b(r2(x1)) b(l2(x1)) -> b(r1(x1)) a(a(x1)) -> x1 Proof: String Reversal Processor: a(r1(x1)) -> r1(a(a(a(x1)))) a(r2(x1)) -> r2(a(a(a(x1)))) l1(a(x1)) -> a(a(a(l1(x1)))) l2(a(a(x1))) -> a(a(l2(x1))) b(r1(x1)) -> b(l1(x1)) b(r2(x1)) -> b(a(l2(x1))) l1(b(x1)) -> r2(b(x1)) l2(b(x1)) -> r1(b(x1)) a(a(x1)) -> x1 Matrix Interpretation Processor: dim=3 interpretation: [1 1 0] [0] [b](x0) = [1 1 0]x0 + [1] [0 0 0] [0], [1 1 0] [l2](x0) = [1 1 0]x0 [0 0 0] , [l1](x0) = x0 , [r2](x0) = x0 , [r1](x0) = x0 , [1 0 0] [a](x0) = [0 0 1]x0 [0 1 0] orientation: [1 0 0] [1 0 0] a(r1(x1)) = [0 0 1]x1 >= [0 0 1]x1 = r1(a(a(a(x1)))) [0 1 0] [0 1 0] [1 0 0] [1 0 0] a(r2(x1)) = [0 0 1]x1 >= [0 0 1]x1 = r2(a(a(a(x1)))) [0 1 0] [0 1 0] [1 0 0] [1 0 0] l1(a(x1)) = [0 0 1]x1 >= [0 0 1]x1 = a(a(a(l1(x1)))) [0 1 0] [0 1 0] [1 1 0] [1 1 0] l2(a(a(x1))) = [1 1 0]x1 >= [1 1 0]x1 = a(a(l2(x1))) [0 0 0] [0 0 0] [1 1 0] [0] [1 1 0] [0] b(r1(x1)) = [1 1 0]x1 + [1] >= [1 1 0]x1 + [1] = b(l1(x1)) [0 0 0] [0] [0 0 0] [0] [1 1 0] [0] [1 1 0] [0] b(r2(x1)) = [1 1 0]x1 + [1] >= [1 1 0]x1 + [1] = b(a(l2(x1))) [0 0 0] [0] [0 0 0] [0] [1 1 0] [0] [1 1 0] [0] l1(b(x1)) = [1 1 0]x1 + [1] >= [1 1 0]x1 + [1] = r2(b(x1)) [0 0 0] [0] [0 0 0] [0] [2 2 0] [1] [1 1 0] [0] l2(b(x1)) = [2 2 0]x1 + [1] >= [1 1 0]x1 + [1] = r1(b(x1)) [0 0 0] [0] [0 0 0] [0] a(a(x1)) = x1 >= x1 = x1 problem: a(r1(x1)) -> r1(a(a(a(x1)))) a(r2(x1)) -> r2(a(a(a(x1)))) l1(a(x1)) -> a(a(a(l1(x1)))) l2(a(a(x1))) -> a(a(l2(x1))) b(r1(x1)) -> b(l1(x1)) b(r2(x1)) -> b(a(l2(x1))) l1(b(x1)) -> r2(b(x1)) a(a(x1)) -> x1 String Reversal Processor: r1(a(x1)) -> a(a(a(r1(x1)))) r2(a(x1)) -> a(a(a(r2(x1)))) a(l1(x1)) -> l1(a(a(a(x1)))) a(a(l2(x1))) -> l2(a(a(x1))) r1(b(x1)) -> l1(b(x1)) r2(b(x1)) -> l2(a(b(x1))) b(l1(x1)) -> b(r2(x1)) a(a(x1)) -> x1 Matrix Interpretation Processor: dim=1 interpretation: [b](x0) = 8x0 + 2, [l2](x0) = 2x0, [l1](x0) = 2x0 + 2, [r2](x0) = 2x0 + 1, [r1](x0) = 3x0, [a](x0) = x0 orientation: r1(a(x1)) = 3x1 >= 3x1 = a(a(a(r1(x1)))) r2(a(x1)) = 2x1 + 1 >= 2x1 + 1 = a(a(a(r2(x1)))) a(l1(x1)) = 2x1 + 2 >= 2x1 + 2 = l1(a(a(a(x1)))) a(a(l2(x1))) = 2x1 >= 2x1 = l2(a(a(x1))) r1(b(x1)) = 24x1 + 6 >= 16x1 + 6 = l1(b(x1)) r2(b(x1)) = 16x1 + 5 >= 16x1 + 4 = l2(a(b(x1))) b(l1(x1)) = 16x1 + 18 >= 16x1 + 10 = b(r2(x1)) a(a(x1)) = x1 >= x1 = x1 problem: r1(a(x1)) -> a(a(a(r1(x1)))) r2(a(x1)) -> a(a(a(r2(x1)))) a(l1(x1)) -> l1(a(a(a(x1)))) a(a(l2(x1))) -> l2(a(a(x1))) r1(b(x1)) -> l1(b(x1)) a(a(x1)) -> x1 String Reversal Processor: a(r1(x1)) -> r1(a(a(a(x1)))) a(r2(x1)) -> r2(a(a(a(x1)))) l1(a(x1)) -> a(a(a(l1(x1)))) l2(a(a(x1))) -> a(a(l2(x1))) b(r1(x1)) -> b(l1(x1)) a(a(x1)) -> x1 Matrix Interpretation Processor: dim=1 interpretation: [b](x0) = x0 + 2, [l2](x0) = 2x0 + 8, [l1](x0) = x0, [r2](x0) = x0, [r1](x0) = 2x0 + 8, [a](x0) = x0 orientation: a(r1(x1)) = 2x1 + 8 >= 2x1 + 8 = r1(a(a(a(x1)))) a(r2(x1)) = x1 >= x1 = r2(a(a(a(x1)))) l1(a(x1)) = x1 >= x1 = a(a(a(l1(x1)))) l2(a(a(x1))) = 2x1 + 8 >= 2x1 + 8 = a(a(l2(x1))) b(r1(x1)) = 2x1 + 10 >= x1 + 2 = b(l1(x1)) a(a(x1)) = x1 >= x1 = x1 problem: a(r1(x1)) -> r1(a(a(a(x1)))) a(r2(x1)) -> r2(a(a(a(x1)))) l1(a(x1)) -> a(a(a(l1(x1)))) l2(a(a(x1))) -> a(a(l2(x1))) a(a(x1)) -> x1 Matrix Interpretation Processor: dim=2 interpretation: [2 2] [1] [l2](x0) = [0 3]x0 + [0], [1 0] [0] [l1](x0) = [0 3]x0 + [3], [1 0] [3] [r2](x0) = [0 0]x0 + [3], [2 0] [r1](x0) = [0 0]x0, [0] [a](x0) = x0 + [1] orientation: [2 0] [0] [2 0] a(r1(x1)) = [0 0]x1 + [1] >= [0 0]x1 = r1(a(a(a(x1)))) [1 0] [3] [1 0] [3] a(r2(x1)) = [0 0]x1 + [4] >= [0 0]x1 + [3] = r2(a(a(a(x1)))) [1 0] [0] [1 0] [0] l1(a(x1)) = [0 3]x1 + [6] >= [0 3]x1 + [6] = a(a(a(l1(x1)))) [2 2] [5] [2 2] [1] l2(a(a(x1))) = [0 3]x1 + [6] >= [0 3]x1 + [2] = a(a(l2(x1))) [0] a(a(x1)) = x1 + [2] >= x1 = x1 problem: a(r1(x1)) -> r1(a(a(a(x1)))) a(r2(x1)) -> r2(a(a(a(x1)))) l1(a(x1)) -> a(a(a(l1(x1)))) a(a(x1)) -> x1 String Reversal Processor: r1(a(x1)) -> a(a(a(r1(x1)))) r2(a(x1)) -> a(a(a(r2(x1)))) a(l1(x1)) -> l1(a(a(a(x1)))) a(a(x1)) -> x1 Matrix Interpretation Processor: dim=2 interpretation: [2 0] [3] [l1](x0) = [0 0]x0 + [0], [1 1] [2] [r2](x0) = [0 3]x0 + [1], [1 0] [2] [r1](x0) = [0 3]x0 + [3], [0] [a](x0) = x0 + [1] orientation: [1 0] [2] [1 0] [2] r1(a(x1)) = [0 3]x1 + [6] >= [0 3]x1 + [6] = a(a(a(r1(x1)))) [1 1] [3] [1 1] [2] r2(a(x1)) = [0 3]x1 + [4] >= [0 3]x1 + [4] = a(a(a(r2(x1)))) [2 0] [3] [2 0] [3] a(l1(x1)) = [0 0]x1 + [1] >= [0 0]x1 + [0] = l1(a(a(a(x1)))) [0] a(a(x1)) = x1 + [2] >= x1 = x1 problem: r1(a(x1)) -> a(a(a(r1(x1)))) a(l1(x1)) -> l1(a(a(a(x1)))) a(a(x1)) -> x1 Matrix Interpretation Processor: dim=2 interpretation: [2 0] [1] [l1](x0) = [2 0]x0 + [1], [1 1] [2] [r1](x0) = [0 3]x0 + [1], [0] [a](x0) = x0 + [2] orientation: [1 1] [4] [1 1] [2] r1(a(x1)) = [0 3]x1 + [7] >= [0 3]x1 + [7] = a(a(a(r1(x1)))) [2 0] [1] [2 0] [1] a(l1(x1)) = [2 0]x1 + [3] >= [2 0]x1 + [1] = l1(a(a(a(x1)))) [0] a(a(x1)) = x1 + [4] >= x1 = x1 problem: a(l1(x1)) -> l1(a(a(a(x1)))) a(a(x1)) -> x1 KBO Processor: weight function: w0 = 1 w(l1) = 1 w(a) = 0 precedence: a > l1 problem: Qed