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