/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: a(b(b(a(x1)))) -> b(a(b(a(x1)))) a(b(b(b(x1)))) -> a(a(b(a(x1)))) a(a(a(a(x1)))) -> b(b(b(a(x1)))) Proof: DP Processor: DPs: a#(b(b(a(x1)))) -> a#(b(a(x1))) a#(b(b(b(x1)))) -> a#(x1) a#(b(b(b(x1)))) -> a#(b(a(x1))) a#(b(b(b(x1)))) -> a#(a(b(a(x1)))) TRS: a(b(b(a(x1)))) -> b(a(b(a(x1)))) a(b(b(b(x1)))) -> a(a(b(a(x1)))) a(a(a(a(x1)))) -> b(b(b(a(x1)))) Polynomial Interpretation Processor: dimension: 1 usable rules: a(b(b(a(x1)))) -> b(a(b(a(x1)))) a(b(b(b(x1)))) -> a(a(b(a(x1)))) a(a(a(a(x1)))) -> b(b(b(a(x1)))) interpretation: [b](x0) = x0 + 1, [a](x0) = x0 + 1, [a#](x0) = x0 orientation: a#(b(b(a(x1)))) = x1 + 3 >= x1 + 2 = a#(b(a(x1))) a#(b(b(b(x1)))) = x1 + 3 >= x1 = a#(x1) a#(b(b(b(x1)))) = x1 + 3 >= x1 + 2 = a#(b(a(x1))) a#(b(b(b(x1)))) = x1 + 3 >= x1 + 3 = a#(a(b(a(x1)))) a(b(b(a(x1)))) = x1 + 4 >= x1 + 4 = b(a(b(a(x1)))) a(b(b(b(x1)))) = x1 + 4 >= x1 + 4 = a(a(b(a(x1)))) a(a(a(a(x1)))) = x1 + 4 >= x1 + 4 = b(b(b(a(x1)))) problem: DPs: a#(b(b(b(x1)))) -> a#(a(b(a(x1)))) TRS: a(b(b(a(x1)))) -> b(a(b(a(x1)))) a(b(b(b(x1)))) -> a(a(b(a(x1)))) a(a(a(a(x1)))) -> b(b(b(a(x1)))) Root-Labeling Processor: DPs: a{#,(f3)}(f3(b)(b(b)(b(b)(b(f3)(x1))))) -> a{#,(f3)}(f3(a)(a(b)(b(a)(a(f3)(x1))))) a{#,(f3)}(f3(b)(b(b)(b(b)(b(a)(x1))))) -> a{#,(f3)}(f3(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f3)}(f3(b)(b(b)(b(b)(b(b)(x1))))) -> a{#,(f3)}(f3(a)(a(b)(b(a)(a(b)(x1))))) TRS: f3(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) f3(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(a)(x1))))) f3(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) b(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(b)(b(b)(b(b)(b(f3)(x1)))) -> a(a)(a(b)(b(a)(a(f3)(x1)))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(a(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(a)(a(b)(x1)))) f3(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) f3(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(a)(x1))))) f3(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(b)(x1))))) a(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) a(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(b)(x1))))) b(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) b(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(a)(x1))))) b(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(b)(x1))))) Polynomial Interpretation Processor: dimension: 1 interpretation: [a{#,(f3)}](x0) = x0, [f3(a)](x0) = x0, [f3(b)](x0) = x0, [b(a)](x0) = x0, [b(f3)](x0) = x0 + 1, [a(a)](x0) = x0, [a(f3)](x0) = x0, [a(b)](x0) = x0, [b(b)](x0) = x0 orientation: a{#,(f3)}(f3(b)(b(b)(b(b)(b(f3)(x1))))) = x1 + 1 >= x1 = a{#,(f3)}(f3(a)(a(b)(b(a)(a(f3)(x1))))) a{#,(f3)}(f3(b)(b(b)(b(b)(b(a)(x1))))) = x1 >= x1 = a{#,(f3)}(f3(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f3)}(f3(b)(b(b)(b(b)(b(b)(x1))))) = x1 >= x1 = a{#,(f3)}(f3(a)(a(b)(b(a)(a(b)(x1))))) f3(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) = x1 >= x1 = f3(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) f3(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 >= x1 = f3(b)(b(a)(a(b)(b(a)(a(a)(x1))))) f3(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 >= x1 = f3(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) = x1 >= x1 = a(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 >= x1 = a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 >= x1 = a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) b(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) = x1 >= x1 = b(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 >= x1 = b(b)(b(a)(a(b)(b(a)(a(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 >= x1 = b(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(b)(b(b)(b(b)(b(f3)(x1)))) = x1 + 1 >= x1 = a(a)(a(b)(b(a)(a(f3)(x1)))) a(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = a(a)(a(b)(b(a)(a(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = a(a)(a(b)(b(a)(a(b)(x1)))) f3(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) = x1 >= x1 = f3(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) f3(a)(a(a)(a(a)(a(a)(a(a)(x1))))) = x1 >= x1 = f3(b)(b(b)(b(b)(b(a)(a(a)(x1))))) f3(a)(a(a)(a(a)(a(a)(a(b)(x1))))) = x1 >= x1 = f3(b)(b(b)(b(b)(b(a)(a(b)(x1))))) a(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) = x1 >= x1 = a(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) a(a)(a(a)(a(a)(a(a)(a(a)(x1))))) = x1 >= x1 = a(b)(b(b)(b(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(a)(a(a)(a(b)(x1))))) = x1 >= x1 = a(b)(b(b)(b(b)(b(a)(a(b)(x1))))) b(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) = x1 >= x1 = b(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) b(a)(a(a)(a(a)(a(a)(a(a)(x1))))) = x1 >= x1 = b(b)(b(b)(b(b)(b(a)(a(a)(x1))))) b(a)(a(a)(a(a)(a(a)(a(b)(x1))))) = x1 >= x1 = b(b)(b(b)(b(b)(b(a)(a(b)(x1))))) problem: DPs: a{#,(f3)}(f3(b)(b(b)(b(b)(b(a)(x1))))) -> a{#,(f3)}(f3(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f3)}(f3(b)(b(b)(b(b)(b(b)(x1))))) -> a{#,(f3)}(f3(a)(a(b)(b(a)(a(b)(x1))))) TRS: f3(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) f3(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(a)(x1))))) f3(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) b(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(a(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(a)(a(b)(x1)))) f3(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) f3(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(a)(x1))))) f3(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(b)(x1))))) a(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) a(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(b)(x1))))) b(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) b(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(a)(x1))))) b(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(b)(x1))))) Polynomial Interpretation Processor: dimension: 1 usable rules: f3(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) f3(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(a)(x1))))) f3(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) b(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(a(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(a)(a(b)(x1)))) f3(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) f3(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(a)(x1))))) f3(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(b)(x1))))) a(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) a(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(b)(x1))))) b(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) b(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(a)(x1))))) b(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(b)(x1))))) interpretation: [a{#,(f3)}](x0) = x0 + 1, [f3(a)](x0) = x0 + 1, [f3(b)](x0) = x0 + 1, [b(a)](x0) = x0, [a(a)](x0) = x0 + 1, [a(f3)](x0) = 0, [a(b)](x0) = x0 + 1, [b(b)](x0) = x0 + 1 orientation: a{#,(f3)}(f3(b)(b(b)(b(b)(b(a)(x1))))) = x1 + 4 >= x1 + 4 = a{#,(f3)}(f3(a)(a(b)(b(a)(a(a)(x1))))) a{#,(f3)}(f3(b)(b(b)(b(b)(b(b)(x1))))) = x1 + 5 >= x1 + 4 = a{#,(f3)}(f3(a)(a(b)(b(a)(a(b)(x1))))) f3(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) = 3 >= 2 = f3(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) f3(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 + 4 >= x1 + 3 = f3(b)(b(a)(a(b)(b(a)(a(a)(x1))))) f3(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 + 4 >= x1 + 3 = f3(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) = 3 >= 2 = a(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 + 4 >= x1 + 3 = a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 + 4 >= x1 + 3 = a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) b(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) = 2 >= 2 = b(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 + 3 >= x1 + 3 = b(b)(b(a)(a(b)(b(a)(a(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 + 3 >= x1 + 3 = b(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(b)(b(b)(b(b)(b(a)(x1)))) = x1 + 3 >= x1 + 3 = a(a)(a(b)(b(a)(a(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 4 >= x1 + 3 = a(a)(a(b)(b(a)(a(b)(x1)))) f3(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) = 4 >= 3 = f3(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) f3(a)(a(a)(a(a)(a(a)(a(a)(x1))))) = x1 + 5 >= x1 + 4 = f3(b)(b(b)(b(b)(b(a)(a(a)(x1))))) f3(a)(a(a)(a(a)(a(a)(a(b)(x1))))) = x1 + 5 >= x1 + 4 = f3(b)(b(b)(b(b)(b(a)(a(b)(x1))))) a(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) = 4 >= 3 = a(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) a(a)(a(a)(a(a)(a(a)(a(a)(x1))))) = x1 + 5 >= x1 + 4 = a(b)(b(b)(b(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(a)(a(a)(a(b)(x1))))) = x1 + 5 >= x1 + 4 = a(b)(b(b)(b(b)(b(a)(a(b)(x1))))) b(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) = 3 >= 3 = b(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) b(a)(a(a)(a(a)(a(a)(a(a)(x1))))) = x1 + 4 >= x1 + 4 = b(b)(b(b)(b(b)(b(a)(a(a)(x1))))) b(a)(a(a)(a(a)(a(a)(a(b)(x1))))) = x1 + 4 >= x1 + 4 = b(b)(b(b)(b(b)(b(a)(a(b)(x1))))) problem: DPs: a{#,(f3)}(f3(b)(b(b)(b(b)(b(a)(x1))))) -> a{#,(f3)}(f3(a)(a(b)(b(a)(a(a)(x1))))) TRS: f3(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) f3(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(a)(x1))))) f3(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) b(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(a(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(a)(a(b)(x1)))) f3(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) f3(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(a)(x1))))) f3(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(b)(x1))))) a(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) a(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(b)(x1))))) b(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) b(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(a)(x1))))) b(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(b)(x1))))) Polynomial Interpretation Processor: dimension: 1 usable rules: f3(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) f3(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(a)(x1))))) f3(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) b(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(a(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(a)(a(b)(x1)))) f3(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) f3(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(a)(x1))))) f3(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(b)(x1))))) a(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) a(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(b)(x1))))) b(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) b(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(a)(x1))))) b(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(b)(x1))))) interpretation: [a{#,(f3)}](x0) = x0, [f3(a)](x0) = x0, [f3(b)](x0) = x0, [b(a)](x0) = x0 + 1, [a(a)](x0) = x0 + 1, [a(f3)](x0) = 0, [a(b)](x0) = x0, [b(b)](x0) = x0 + 1 orientation: a{#,(f3)}(f3(b)(b(b)(b(b)(b(a)(x1))))) = x1 + 3 >= x1 + 2 = a{#,(f3)}(f3(a)(a(b)(b(a)(a(a)(x1))))) f3(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) = 2 >= 2 = f3(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) f3(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 + 3 >= x1 + 3 = f3(b)(b(a)(a(b)(b(a)(a(a)(x1))))) f3(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 + 2 >= x1 + 2 = f3(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) = 3 >= 2 = a(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 + 4 >= x1 + 3 = a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 + 3 >= x1 + 2 = a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) b(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) = 3 >= 3 = b(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 + 4 >= x1 + 4 = b(b)(b(a)(a(b)(b(a)(a(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 + 3 >= x1 + 3 = b(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(b)(b(b)(b(b)(b(a)(x1)))) = x1 + 3 >= x1 + 3 = a(a)(a(b)(b(a)(a(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) = x1 + 3 >= x1 + 2 = a(a)(a(b)(b(a)(a(b)(x1)))) f3(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) = 3 >= 3 = f3(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) f3(a)(a(a)(a(a)(a(a)(a(a)(x1))))) = x1 + 4 >= x1 + 4 = f3(b)(b(b)(b(b)(b(a)(a(a)(x1))))) f3(a)(a(a)(a(a)(a(a)(a(b)(x1))))) = x1 + 3 >= x1 + 3 = f3(b)(b(b)(b(b)(b(a)(a(b)(x1))))) a(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) = 4 >= 3 = a(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) a(a)(a(a)(a(a)(a(a)(a(a)(x1))))) = x1 + 5 >= x1 + 4 = a(b)(b(b)(b(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(a)(a(a)(a(b)(x1))))) = x1 + 4 >= x1 + 3 = a(b)(b(b)(b(b)(b(a)(a(b)(x1))))) b(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) = 4 >= 4 = b(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) b(a)(a(a)(a(a)(a(a)(a(a)(x1))))) = x1 + 5 >= x1 + 5 = b(b)(b(b)(b(b)(b(a)(a(a)(x1))))) b(a)(a(a)(a(a)(a(a)(a(b)(x1))))) = x1 + 4 >= x1 + 4 = b(b)(b(b)(b(b)(b(a)(a(b)(x1))))) problem: DPs: TRS: f3(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) f3(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(a)(x1))))) f3(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f3(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(b)(b(a)(a(b)(x1))))) b(a)(a(b)(b(b)(b(a)(a(f3)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(f3)(x1))))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(b)(b(a)(a(b)(x1))))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(b)(b(a)(a(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(b)(b(a)(a(b)(x1)))) f3(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) f3(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(a)(x1))))) f3(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> f3(b)(b(b)(b(b)(b(a)(a(b)(x1))))) a(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) a(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(a)(x1))))) a(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> a(b)(b(b)(b(b)(b(a)(a(b)(x1))))) b(a)(a(a)(a(a)(a(a)(a(f3)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(f3)(x1))))) b(a)(a(a)(a(a)(a(a)(a(a)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(a)(x1))))) b(a)(a(a)(a(a)(a(a)(a(b)(x1))))) -> b(b)(b(b)(b(b)(b(a)(a(b)(x1))))) Qed