/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: a(b(b(a(x1)))) -> b(a(a(b(x1)))) a(b(b(b(x1)))) -> a(a(a(b(x1)))) b(b(a(a(x1)))) -> b(b(b(a(x1)))) Proof: DP Processor: DPs: a#(b(b(a(x1)))) -> b#(x1) a#(b(b(a(x1)))) -> a#(b(x1)) a#(b(b(a(x1)))) -> a#(a(b(x1))) a#(b(b(a(x1)))) -> b#(a(a(b(x1)))) a#(b(b(b(x1)))) -> a#(b(x1)) a#(b(b(b(x1)))) -> a#(a(b(x1))) a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) b#(b(a(a(x1)))) -> b#(a(x1)) b#(b(a(a(x1)))) -> b#(b(a(x1))) b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) TRS: a(b(b(a(x1)))) -> b(a(a(b(x1)))) a(b(b(b(x1)))) -> a(a(a(b(x1)))) b(b(a(a(x1)))) -> b(b(b(a(x1)))) TDG Processor: DPs: a#(b(b(a(x1)))) -> b#(x1) a#(b(b(a(x1)))) -> a#(b(x1)) a#(b(b(a(x1)))) -> a#(a(b(x1))) a#(b(b(a(x1)))) -> b#(a(a(b(x1)))) a#(b(b(b(x1)))) -> a#(b(x1)) a#(b(b(b(x1)))) -> a#(a(b(x1))) a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) b#(b(a(a(x1)))) -> b#(a(x1)) b#(b(a(a(x1)))) -> b#(b(a(x1))) b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) TRS: a(b(b(a(x1)))) -> b(a(a(b(x1)))) a(b(b(b(x1)))) -> a(a(a(b(x1)))) b(b(a(a(x1)))) -> b(b(b(a(x1)))) graph: b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) -> b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) -> b#(b(a(a(x1)))) -> b#(b(a(x1))) b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) -> b#(b(a(a(x1)))) -> b#(a(x1)) b#(b(a(a(x1)))) -> b#(b(a(x1))) -> b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) b#(b(a(a(x1)))) -> b#(b(a(x1))) -> b#(b(a(a(x1)))) -> b#(b(a(x1))) b#(b(a(a(x1)))) -> b#(b(a(x1))) -> b#(b(a(a(x1)))) -> b#(a(x1)) b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(a(x1)))) -> b#(b(a(x1))) b#(b(a(a(x1)))) -> b#(a(x1)) -> b#(b(a(a(x1)))) -> b#(a(x1)) a#(b(b(b(x1)))) -> a#(b(x1)) -> a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) a#(b(b(b(x1)))) -> a#(b(x1)) -> a#(b(b(b(x1)))) -> a#(a(b(x1))) a#(b(b(b(x1)))) -> a#(b(x1)) -> a#(b(b(b(x1)))) -> a#(b(x1)) a#(b(b(b(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> b#(a(a(b(x1)))) a#(b(b(b(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> a#(a(b(x1))) a#(b(b(b(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> a#(b(x1)) a#(b(b(b(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> b#(x1) a#(b(b(b(x1)))) -> a#(a(b(x1))) -> a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) a#(b(b(b(x1)))) -> a#(a(b(x1))) -> a#(b(b(b(x1)))) -> a#(a(b(x1))) a#(b(b(b(x1)))) -> a#(a(b(x1))) -> a#(b(b(b(x1)))) -> a#(b(x1)) a#(b(b(b(x1)))) -> a#(a(b(x1))) -> a#(b(b(a(x1)))) -> b#(a(a(b(x1)))) a#(b(b(b(x1)))) -> a#(a(b(x1))) -> a#(b(b(a(x1)))) -> a#(a(b(x1))) a#(b(b(b(x1)))) -> a#(a(b(x1))) -> a#(b(b(a(x1)))) -> a#(b(x1)) a#(b(b(b(x1)))) -> a#(a(b(x1))) -> a#(b(b(a(x1)))) -> b#(x1) a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> a#(b(b(b(x1)))) -> a#(a(b(x1))) a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> a#(b(b(b(x1)))) -> a#(b(x1)) a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> a#(b(b(a(x1)))) -> b#(a(a(b(x1)))) a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> a#(b(b(a(x1)))) -> a#(a(b(x1))) a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> a#(b(b(a(x1)))) -> a#(b(x1)) a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) -> a#(b(b(a(x1)))) -> b#(x1) a#(b(b(a(x1)))) -> b#(a(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) a#(b(b(a(x1)))) -> b#(a(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(a(x1))) a#(b(b(a(x1)))) -> b#(a(a(b(x1)))) -> b#(b(a(a(x1)))) -> b#(a(x1)) a#(b(b(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) a#(b(b(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(a(x1))) a#(b(b(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(a(x1)) a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(b(x1)))) -> a#(a(b(x1))) a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(b(x1)))) -> a#(b(x1)) a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> b#(a(a(b(x1)))) a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> a#(a(b(x1))) a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> a#(b(x1)) a#(b(b(a(x1)))) -> a#(b(x1)) -> a#(b(b(a(x1)))) -> b#(x1) a#(b(b(a(x1)))) -> a#(a(b(x1))) -> a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) a#(b(b(a(x1)))) -> a#(a(b(x1))) -> a#(b(b(b(x1)))) -> a#(a(b(x1))) a#(b(b(a(x1)))) -> a#(a(b(x1))) -> a#(b(b(b(x1)))) -> a#(b(x1)) a#(b(b(a(x1)))) -> a#(a(b(x1))) -> a#(b(b(a(x1)))) -> b#(a(a(b(x1)))) a#(b(b(a(x1)))) -> a#(a(b(x1))) -> a#(b(b(a(x1)))) -> a#(a(b(x1))) a#(b(b(a(x1)))) -> a#(a(b(x1))) -> a#(b(b(a(x1)))) -> a#(b(x1)) a#(b(b(a(x1)))) -> a#(a(b(x1))) -> a#(b(b(a(x1)))) -> b#(x1) SCC Processor: #sccs: 2 #rules: 8 #arcs: 50/100 DPs: a#(b(b(b(x1)))) -> a#(b(x1)) a#(b(b(a(x1)))) -> a#(b(x1)) a#(b(b(a(x1)))) -> a#(a(b(x1))) a#(b(b(b(x1)))) -> a#(a(b(x1))) a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) TRS: a(b(b(a(x1)))) -> b(a(a(b(x1)))) a(b(b(b(x1)))) -> a(a(a(b(x1)))) b(b(a(a(x1)))) -> b(b(b(a(x1)))) Polynomial Interpretation Processor: dimension: 1 usable rules: a(b(b(a(x1)))) -> b(a(a(b(x1)))) a(b(b(b(x1)))) -> a(a(a(b(x1)))) b(b(a(a(x1)))) -> b(b(b(a(x1)))) interpretation: [b](x0) = x0 + 1, [a](x0) = x0 + 1, [a#](x0) = x0 orientation: a#(b(b(b(x1)))) = x1 + 3 >= x1 + 1 = a#(b(x1)) a#(b(b(a(x1)))) = x1 + 3 >= x1 + 1 = a#(b(x1)) a#(b(b(a(x1)))) = x1 + 3 >= x1 + 2 = a#(a(b(x1))) a#(b(b(b(x1)))) = x1 + 3 >= x1 + 2 = a#(a(b(x1))) a#(b(b(b(x1)))) = x1 + 3 >= x1 + 3 = a#(a(a(b(x1)))) a(b(b(a(x1)))) = x1 + 4 >= x1 + 4 = b(a(a(b(x1)))) a(b(b(b(x1)))) = x1 + 4 >= x1 + 4 = a(a(a(b(x1)))) b(b(a(a(x1)))) = x1 + 4 >= x1 + 4 = b(b(b(a(x1)))) problem: DPs: a#(b(b(b(x1)))) -> a#(a(a(b(x1)))) TRS: a(b(b(a(x1)))) -> b(a(a(b(x1)))) a(b(b(b(x1)))) -> a(a(a(b(x1)))) b(b(a(a(x1)))) -> b(b(b(a(x1)))) Root-Labeling Processor: DPs: a{#,(f4)}(f4(b)(b(b)(b(b)(b(f4)(x1))))) -> a{#,(f4)}(f4(a)(a(a)(a(b)(b(f4)(x1))))) a{#,(f4)}(f4(b)(b(b)(b(b)(b(a)(x1))))) -> a{#,(f4)}(f4(a)(a(a)(a(b)(b(a)(x1))))) a{#,(f4)}(f4(b)(b(b)(b(b)(b(b)(x1))))) -> a{#,(f4)}(f4(a)(a(a)(a(b)(b(b)(x1))))) TRS: f4(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(f4)(x1))))) f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(a)(x1))))) f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(f4)(x1))))) a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) b(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(f4)(x1))))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(b)(b(b)(b(b)(b(f4)(x1)))) -> a(a)(a(a)(a(b)(b(f4)(x1)))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) b(b)(b(a)(a(a)(a(f4)(x1)))) -> b(b)(b(b)(b(a)(a(f4)(x1)))) b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) Polynomial Interpretation Processor: dimension: 1 interpretation: [b(f4)](x0) = x0, [a{#,(f4)}](x0) = x0, [a(a)](x0) = x0, [b(b)](x0) = x0, [b(a)](x0) = x0, [a(b)](x0) = x0, [f4(a)](x0) = x0, [a(f4)](x0) = x0 + 1, [f4(b)](x0) = x0 orientation: a{#,(f4)}(f4(b)(b(b)(b(b)(b(f4)(x1))))) = x1 >= x1 = a{#,(f4)}(f4(a)(a(a)(a(b)(b(f4)(x1))))) a{#,(f4)}(f4(b)(b(b)(b(b)(b(a)(x1))))) = x1 >= x1 = a{#,(f4)}(f4(a)(a(a)(a(b)(b(a)(x1))))) a{#,(f4)}(f4(b)(b(b)(b(b)(b(b)(x1))))) = x1 >= x1 = a{#,(f4)}(f4(a)(a(a)(a(b)(b(b)(x1))))) f4(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) = x1 + 1 >= x1 = f4(b)(b(a)(a(a)(a(b)(b(f4)(x1))))) f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 >= x1 = f4(b)(b(a)(a(a)(a(b)(b(a)(x1))))) f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 >= x1 = f4(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) = x1 + 1 >= x1 = a(b)(b(a)(a(a)(a(b)(b(f4)(x1))))) a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 >= x1 = a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 >= x1 = a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) b(a)(a(b)(b(b)(b(a)(a(f4)(x1))))) = x1 + 1 >= x1 = b(b)(b(a)(a(a)(a(b)(b(f4)(x1))))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 >= x1 = b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 >= x1 = b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(b)(b(b)(b(b)(b(f4)(x1)))) = x1 >= x1 = a(a)(a(a)(a(b)(b(f4)(x1)))) a(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = a(a)(a(a)(a(b)(b(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = a(a)(a(a)(a(b)(b(b)(x1)))) b(b)(b(a)(a(a)(a(f4)(x1)))) = x1 + 1 >= x1 + 1 = b(b)(b(b)(b(a)(a(f4)(x1)))) b(b)(b(a)(a(a)(a(a)(x1)))) = x1 >= x1 = b(b)(b(b)(b(a)(a(a)(x1)))) b(b)(b(a)(a(a)(a(b)(x1)))) = x1 >= x1 = b(b)(b(b)(b(a)(a(b)(x1)))) problem: DPs: a{#,(f4)}(f4(b)(b(b)(b(b)(b(f4)(x1))))) -> a{#,(f4)}(f4(a)(a(a)(a(b)(b(f4)(x1))))) a{#,(f4)}(f4(b)(b(b)(b(b)(b(a)(x1))))) -> a{#,(f4)}(f4(a)(a(a)(a(b)(b(a)(x1))))) a{#,(f4)}(f4(b)(b(b)(b(b)(b(b)(x1))))) -> a{#,(f4)}(f4(a)(a(a)(a(b)(b(b)(x1))))) TRS: f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(a)(x1))))) f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(b)(b(b)(b(b)(b(f4)(x1)))) -> a(a)(a(a)(a(b)(b(f4)(x1)))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) b(b)(b(a)(a(a)(a(f4)(x1)))) -> b(b)(b(b)(b(a)(a(f4)(x1)))) b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) Polynomial Interpretation Processor: dimension: 1 usable rules: f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(a)(x1))))) f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(b)(b(b)(b(b)(b(f4)(x1)))) -> a(a)(a(a)(a(b)(b(f4)(x1)))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) b(b)(b(a)(a(a)(a(f4)(x1)))) -> b(b)(b(b)(b(a)(a(f4)(x1)))) b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) interpretation: [b(f4)](x0) = 1, [a{#,(f4)}](x0) = x0, [a(a)](x0) = x0, [b(b)](x0) = x0, [b(a)](x0) = 0, [a(b)](x0) = 1, [f4(a)](x0) = 0, [a(f4)](x0) = 0, [f4(b)](x0) = x0 orientation: a{#,(f4)}(f4(b)(b(b)(b(b)(b(f4)(x1))))) = 1 >= 0 = a{#,(f4)}(f4(a)(a(a)(a(b)(b(f4)(x1))))) a{#,(f4)}(f4(b)(b(b)(b(b)(b(a)(x1))))) = 0 >= 0 = a{#,(f4)}(f4(a)(a(a)(a(b)(b(a)(x1))))) a{#,(f4)}(f4(b)(b(b)(b(b)(b(b)(x1))))) = x1 >= 0 = a{#,(f4)}(f4(a)(a(a)(a(b)(b(b)(x1))))) f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = 0 >= 0 = f4(b)(b(a)(a(a)(a(b)(b(a)(x1))))) f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 0 >= 0 = f4(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = 1 >= 1 = a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 1 >= 1 = a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = 0 >= 0 = b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 0 >= 0 = b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(b)(b(b)(b(b)(b(f4)(x1)))) = 1 >= 1 = a(a)(a(a)(a(b)(b(f4)(x1)))) a(b)(b(b)(b(b)(b(a)(x1)))) = 1 >= 1 = a(a)(a(a)(a(b)(b(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) = 1 >= 1 = a(a)(a(a)(a(b)(b(b)(x1)))) b(b)(b(a)(a(a)(a(f4)(x1)))) = 0 >= 0 = b(b)(b(b)(b(a)(a(f4)(x1)))) b(b)(b(a)(a(a)(a(a)(x1)))) = 0 >= 0 = b(b)(b(b)(b(a)(a(a)(x1)))) b(b)(b(a)(a(a)(a(b)(x1)))) = 0 >= 0 = b(b)(b(b)(b(a)(a(b)(x1)))) problem: DPs: a{#,(f4)}(f4(b)(b(b)(b(b)(b(a)(x1))))) -> a{#,(f4)}(f4(a)(a(a)(a(b)(b(a)(x1))))) a{#,(f4)}(f4(b)(b(b)(b(b)(b(b)(x1))))) -> a{#,(f4)}(f4(a)(a(a)(a(b)(b(b)(x1))))) TRS: f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(a)(x1))))) f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(b)(b(b)(b(b)(b(f4)(x1)))) -> a(a)(a(a)(a(b)(b(f4)(x1)))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) b(b)(b(a)(a(a)(a(f4)(x1)))) -> b(b)(b(b)(b(a)(a(f4)(x1)))) b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) Polynomial Interpretation Processor: dimension: 1 usable rules: f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(a)(x1))))) f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(b)(b(b)(b(b)(b(f4)(x1)))) -> a(a)(a(a)(a(b)(b(f4)(x1)))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) b(b)(b(a)(a(a)(a(f4)(x1)))) -> b(b)(b(b)(b(a)(a(f4)(x1)))) b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) interpretation: [b(f4)](x0) = 0, [a{#,(f4)}](x0) = x0, [a(a)](x0) = 0, [b(b)](x0) = 1, [b(a)](x0) = x0, [a(b)](x0) = x0, [f4(a)](x0) = 0, [a(f4)](x0) = 0, [f4(b)](x0) = x0 orientation: a{#,(f4)}(f4(b)(b(b)(b(b)(b(a)(x1))))) = 1 >= 0 = a{#,(f4)}(f4(a)(a(a)(a(b)(b(a)(x1))))) a{#,(f4)}(f4(b)(b(b)(b(b)(b(b)(x1))))) = 1 >= 0 = a{#,(f4)}(f4(a)(a(a)(a(b)(b(b)(x1))))) f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = 0 >= 0 = f4(b)(b(a)(a(a)(a(b)(b(a)(x1))))) f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 0 >= 0 = f4(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = 0 >= 0 = a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 0 >= 0 = a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = 1 >= 1 = b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 1 >= 1 = b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(b)(b(b)(b(b)(b(f4)(x1)))) = 1 >= 0 = a(a)(a(a)(a(b)(b(f4)(x1)))) a(b)(b(b)(b(b)(b(a)(x1)))) = 1 >= 0 = a(a)(a(a)(a(b)(b(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) = 1 >= 0 = a(a)(a(a)(a(b)(b(b)(x1)))) b(b)(b(a)(a(a)(a(f4)(x1)))) = 1 >= 1 = b(b)(b(b)(b(a)(a(f4)(x1)))) b(b)(b(a)(a(a)(a(a)(x1)))) = 1 >= 1 = b(b)(b(b)(b(a)(a(a)(x1)))) b(b)(b(a)(a(a)(a(b)(x1)))) = 1 >= 1 = b(b)(b(b)(b(a)(a(b)(x1)))) problem: DPs: TRS: f4(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(a)(x1))))) f4(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f4(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(b)(b(b)(b(b)(b(f4)(x1)))) -> a(a)(a(a)(a(b)(b(f4)(x1)))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) b(b)(b(a)(a(a)(a(f4)(x1)))) -> b(b)(b(b)(b(a)(a(f4)(x1)))) b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) Qed DPs: b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) b#(b(a(a(x1)))) -> b#(a(x1)) b#(b(a(a(x1)))) -> b#(b(a(x1))) TRS: a(b(b(a(x1)))) -> b(a(a(b(x1)))) a(b(b(b(x1)))) -> a(a(a(b(x1)))) b(b(a(a(x1)))) -> b(b(b(a(x1)))) Polynomial Interpretation Processor: dimension: 1 usable rules: a(b(b(a(x1)))) -> b(a(a(b(x1)))) a(b(b(b(x1)))) -> a(a(a(b(x1)))) b(b(a(a(x1)))) -> b(b(b(a(x1)))) interpretation: [b](x0) = x0 + 1, [b#](x0) = x0, [a](x0) = x0 + 1 orientation: b#(b(a(a(x1)))) = x1 + 3 >= x1 + 3 = b#(b(b(a(x1)))) b#(b(a(a(x1)))) = x1 + 3 >= x1 + 1 = b#(a(x1)) b#(b(a(a(x1)))) = x1 + 3 >= x1 + 2 = b#(b(a(x1))) a(b(b(a(x1)))) = x1 + 4 >= x1 + 4 = b(a(a(b(x1)))) a(b(b(b(x1)))) = x1 + 4 >= x1 + 4 = a(a(a(b(x1)))) b(b(a(a(x1)))) = x1 + 4 >= x1 + 4 = b(b(b(a(x1)))) problem: DPs: b#(b(a(a(x1)))) -> b#(b(b(a(x1)))) TRS: a(b(b(a(x1)))) -> b(a(a(b(x1)))) a(b(b(b(x1)))) -> a(a(a(b(x1)))) b(b(a(a(x1)))) -> b(b(b(a(x1)))) Root-Labeling Processor: DPs: b{#,(f14)}(f14(b)(b(a)(a(a)(a(f14)(x1))))) -> b{#,(f14)}(f14(b)(b(b)(b(a)(a(f14)(x1))))) b{#,(f14)}(f14(b)(b(a)(a(a)(a(a)(x1))))) -> b{#,(f14)}(f14(b)(b(b)(b(a)(a(a)(x1))))) b{#,(f14)}(f14(b)(b(a)(a(a)(a(b)(x1))))) -> b{#,(f14)}(f14(b)(b(b)(b(a)(a(b)(x1))))) TRS: f14(a)(a(b)(b(b)(b(a)(a(f14)(x1))))) -> f14(b)(b(a)(a(a)(a(b)(b(f14)(x1))))) f14(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> f14(b)(b(a)(a(a)(a(b)(b(a)(x1))))) f14(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> f14(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(a)(a(b)(b(b)(b(a)(a(f14)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(f14)(x1))))) a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) b(a)(a(b)(b(b)(b(a)(a(f14)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(f14)(x1))))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(b)(b(b)(b(b)(b(f14)(x1)))) -> a(a)(a(a)(a(b)(b(f14)(x1)))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) b(b)(b(a)(a(a)(a(f14)(x1)))) -> b(b)(b(b)(b(a)(a(f14)(x1)))) b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) Usable Rule Processor: DPs: b{#,(f14)}(f14(b)(b(a)(a(a)(a(f14)(x1))))) -> b{#,(f14)}(f14(b)(b(b)(b(a)(a(f14)(x1))))) b{#,(f14)}(f14(b)(b(a)(a(a)(a(a)(x1))))) -> b{#,(f14)}(f14(b)(b(b)(b(a)(a(a)(x1))))) b{#,(f14)}(f14(b)(b(a)(a(a)(a(b)(x1))))) -> b{#,(f14)}(f14(b)(b(b)(b(a)(a(b)(x1))))) TRS: a(a)(a(b)(b(b)(b(a)(a(f14)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(f14)(x1))))) a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(b)(b(b)(b(b)(b(f14)(x1)))) -> a(a)(a(a)(a(b)(b(f14)(x1)))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) b(a)(a(b)(b(b)(b(a)(a(f14)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(f14)(x1))))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) b(b)(b(a)(a(a)(a(f14)(x1)))) -> b(b)(b(b)(b(a)(a(f14)(x1)))) b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) Polynomial Interpretation Processor: dimension: 1 interpretation: [b{#,(f14)}](x0) = x0, [f14(b)](x0) = x0 + 1, [b(f14)](x0) = x0, [a(f14)](x0) = x0 + 1, [a(a)](x0) = x0, [b(b)](x0) = x0, [b(a)](x0) = x0, [a(b)](x0) = x0 orientation: b{#,(f14)}(f14(b)(b(a)(a(a)(a(f14)(x1))))) = x1 + 2 >= x1 + 2 = b{#,(f14)}(f14(b)(b(b)(b(a)(a(f14)(x1))))) b{#,(f14)}(f14(b)(b(a)(a(a)(a(a)(x1))))) = x1 + 1 >= x1 + 1 = b{#,(f14)}(f14(b)(b(b)(b(a)(a(a)(x1))))) b{#,(f14)}(f14(b)(b(a)(a(a)(a(b)(x1))))) = x1 + 1 >= x1 + 1 = b{#,(f14)}(f14(b)(b(b)(b(a)(a(b)(x1))))) a(a)(a(b)(b(b)(b(a)(a(f14)(x1))))) = x1 + 1 >= x1 = a(b)(b(a)(a(a)(a(b)(b(f14)(x1))))) a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 >= x1 = a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 >= x1 = a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(b)(b(b)(b(b)(b(f14)(x1)))) = x1 >= x1 = a(a)(a(a)(a(b)(b(f14)(x1)))) a(b)(b(b)(b(b)(b(a)(x1)))) = x1 >= x1 = a(a)(a(a)(a(b)(b(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) = x1 >= x1 = a(a)(a(a)(a(b)(b(b)(x1)))) b(a)(a(b)(b(b)(b(a)(a(f14)(x1))))) = x1 + 1 >= x1 = b(b)(b(a)(a(a)(a(b)(b(f14)(x1))))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = x1 >= x1 = b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = x1 >= x1 = b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) b(b)(b(a)(a(a)(a(b)(x1)))) = x1 >= x1 = b(b)(b(b)(b(a)(a(b)(x1)))) b(b)(b(a)(a(a)(a(f14)(x1)))) = x1 + 1 >= x1 + 1 = b(b)(b(b)(b(a)(a(f14)(x1)))) b(b)(b(a)(a(a)(a(a)(x1)))) = x1 >= x1 = b(b)(b(b)(b(a)(a(a)(x1)))) problem: DPs: b{#,(f14)}(f14(b)(b(a)(a(a)(a(f14)(x1))))) -> b{#,(f14)}(f14(b)(b(b)(b(a)(a(f14)(x1))))) b{#,(f14)}(f14(b)(b(a)(a(a)(a(a)(x1))))) -> b{#,(f14)}(f14(b)(b(b)(b(a)(a(a)(x1))))) b{#,(f14)}(f14(b)(b(a)(a(a)(a(b)(x1))))) -> b{#,(f14)}(f14(b)(b(b)(b(a)(a(b)(x1))))) TRS: a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(b)(b(b)(b(b)(b(f14)(x1)))) -> a(a)(a(a)(a(b)(b(f14)(x1)))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) b(b)(b(a)(a(a)(a(f14)(x1)))) -> b(b)(b(b)(b(a)(a(f14)(x1)))) b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) Polynomial Interpretation Processor: dimension: 1 usable rules: a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(b)(b(b)(b(b)(b(f14)(x1)))) -> a(a)(a(a)(a(b)(b(f14)(x1)))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) b(b)(b(a)(a(a)(a(f14)(x1)))) -> b(b)(b(b)(b(a)(a(f14)(x1)))) b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) interpretation: [b{#,(f14)}](x0) = x0, [f14(b)](x0) = x0, [b(f14)](x0) = 0, [a(f14)](x0) = 0, [a(a)](x0) = x0, [b(b)](x0) = 0, [b(a)](x0) = x0, [a(b)](x0) = 1 orientation: b{#,(f14)}(f14(b)(b(a)(a(a)(a(f14)(x1))))) = 0 >= 0 = b{#,(f14)}(f14(b)(b(b)(b(a)(a(f14)(x1))))) b{#,(f14)}(f14(b)(b(a)(a(a)(a(a)(x1))))) = x1 >= 0 = b{#,(f14)}(f14(b)(b(b)(b(a)(a(a)(x1))))) b{#,(f14)}(f14(b)(b(a)(a(a)(a(b)(x1))))) = 1 >= 0 = b{#,(f14)}(f14(b)(b(b)(b(a)(a(b)(x1))))) a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = 1 >= 1 = a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 1 >= 1 = a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(b)(b(b)(b(b)(b(f14)(x1)))) = 1 >= 1 = a(a)(a(a)(a(b)(b(f14)(x1)))) a(b)(b(b)(b(b)(b(a)(x1)))) = 1 >= 1 = a(a)(a(a)(a(b)(b(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) = 1 >= 1 = a(a)(a(a)(a(b)(b(b)(x1)))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = 1 >= 0 = b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 1 >= 0 = b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) b(b)(b(a)(a(a)(a(b)(x1)))) = 0 >= 0 = b(b)(b(b)(b(a)(a(b)(x1)))) b(b)(b(a)(a(a)(a(f14)(x1)))) = 0 >= 0 = b(b)(b(b)(b(a)(a(f14)(x1)))) b(b)(b(a)(a(a)(a(a)(x1)))) = 0 >= 0 = b(b)(b(b)(b(a)(a(a)(x1)))) problem: DPs: b{#,(f14)}(f14(b)(b(a)(a(a)(a(f14)(x1))))) -> b{#,(f14)}(f14(b)(b(b)(b(a)(a(f14)(x1))))) b{#,(f14)}(f14(b)(b(a)(a(a)(a(a)(x1))))) -> b{#,(f14)}(f14(b)(b(b)(b(a)(a(a)(x1))))) TRS: a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(b)(b(b)(b(b)(b(f14)(x1)))) -> a(a)(a(a)(a(b)(b(f14)(x1)))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) b(b)(b(a)(a(a)(a(f14)(x1)))) -> b(b)(b(b)(b(a)(a(f14)(x1)))) b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) Polynomial Interpretation Processor: dimension: 1 usable rules: b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) b(b)(b(a)(a(a)(a(f14)(x1)))) -> b(b)(b(b)(b(a)(a(f14)(x1)))) b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) interpretation: [b{#,(f14)}](x0) = x0, [f14(b)](x0) = x0, [b(f14)](x0) = 0, [a(f14)](x0) = 1, [a(a)](x0) = x0 + 1, [b(b)](x0) = 0, [b(a)](x0) = x0, [a(b)](x0) = 0 orientation: b{#,(f14)}(f14(b)(b(a)(a(a)(a(f14)(x1))))) = 2 >= 0 = b{#,(f14)}(f14(b)(b(b)(b(a)(a(f14)(x1))))) b{#,(f14)}(f14(b)(b(a)(a(a)(a(a)(x1))))) = x1 + 2 >= 0 = b{#,(f14)}(f14(b)(b(b)(b(a)(a(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = 1 >= 0 = a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 1 >= 0 = a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(b)(b(b)(b(b)(b(f14)(x1)))) = 0 >= 2 = a(a)(a(a)(a(b)(b(f14)(x1)))) a(b)(b(b)(b(b)(b(a)(x1)))) = 0 >= 2 = a(a)(a(a)(a(b)(b(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) = 0 >= 2 = a(a)(a(a)(a(b)(b(b)(x1)))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) = 0 >= 0 = b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) = 0 >= 0 = b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) b(b)(b(a)(a(a)(a(b)(x1)))) = 0 >= 0 = b(b)(b(b)(b(a)(a(b)(x1)))) b(b)(b(a)(a(a)(a(f14)(x1)))) = 0 >= 0 = b(b)(b(b)(b(a)(a(f14)(x1)))) b(b)(b(a)(a(a)(a(a)(x1)))) = 0 >= 0 = b(b)(b(b)(b(a)(a(a)(x1)))) problem: DPs: TRS: a(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(a)(x1))))) a(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> a(b)(b(a)(a(a)(a(b)(b(b)(x1))))) a(b)(b(b)(b(b)(b(f14)(x1)))) -> a(a)(a(a)(a(b)(b(f14)(x1)))) a(b)(b(b)(b(b)(b(a)(x1)))) -> a(a)(a(a)(a(b)(b(a)(x1)))) a(b)(b(b)(b(b)(b(b)(x1)))) -> a(a)(a(a)(a(b)(b(b)(x1)))) b(a)(a(b)(b(b)(b(a)(a(a)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(a)(x1))))) b(a)(a(b)(b(b)(b(a)(a(b)(x1))))) -> b(b)(b(a)(a(a)(a(b)(b(b)(x1))))) b(b)(b(a)(a(a)(a(b)(x1)))) -> b(b)(b(b)(b(a)(a(b)(x1)))) b(b)(b(a)(a(a)(a(f14)(x1)))) -> b(b)(b(b)(b(a)(a(f14)(x1)))) b(b)(b(a)(a(a)(a(a)(x1)))) -> b(b)(b(b)(b(a)(a(a)(x1)))) Qed