/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: a(a(b(b(x1)))) -> b(b(c(c(a(a(x1)))))) b(b(c(c(x1)))) -> c(c(b(b(b(b(x1)))))) b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) Proof: DP Processor: DPs: a#(a(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> a#(a(x1)) a#(a(b(b(x1)))) -> b#(c(c(a(a(x1))))) a#(a(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) b#(b(c(c(x1)))) -> b#(x1) b#(b(c(c(x1)))) -> b#(b(x1)) b#(b(c(c(x1)))) -> b#(b(b(x1))) b#(b(c(c(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> a#(c(c(b(b(x1))))) b#(b(a(a(x1)))) -> a#(a(c(c(b(b(x1)))))) TRS: a(a(b(b(x1)))) -> b(b(c(c(a(a(x1)))))) b(b(c(c(x1)))) -> c(c(b(b(b(b(x1)))))) b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) TDG Processor: DPs: a#(a(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> a#(a(x1)) a#(a(b(b(x1)))) -> b#(c(c(a(a(x1))))) a#(a(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) b#(b(c(c(x1)))) -> b#(x1) b#(b(c(c(x1)))) -> b#(b(x1)) b#(b(c(c(x1)))) -> b#(b(b(x1))) b#(b(c(c(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> a#(c(c(b(b(x1))))) b#(b(a(a(x1)))) -> a#(a(c(c(b(b(x1)))))) TRS: a(a(b(b(x1)))) -> b(b(c(c(a(a(x1)))))) b(b(c(c(x1)))) -> c(c(b(b(b(b(x1)))))) b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) graph: b#(b(c(c(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> a#(a(c(c(b(b(x1)))))) b#(b(c(c(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> a#(c(c(b(b(x1))))) b#(b(c(c(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(c(c(x1)))) -> b#(b(b(b(x1)))) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(c(c(x1)))) -> b#(b(b(b(x1)))) -> b#(b(c(c(x1)))) -> b#(b(b(b(x1)))) b#(b(c(c(x1)))) -> b#(b(b(b(x1)))) -> b#(b(c(c(x1)))) -> b#(b(b(x1))) b#(b(c(c(x1)))) -> b#(b(b(b(x1)))) -> b#(b(c(c(x1)))) -> b#(b(x1)) b#(b(c(c(x1)))) -> b#(b(b(b(x1)))) -> b#(b(c(c(x1)))) -> b#(x1) b#(b(c(c(x1)))) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> a#(a(c(c(b(b(x1)))))) b#(b(c(c(x1)))) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> a#(c(c(b(b(x1))))) b#(b(c(c(x1)))) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(c(c(x1)))) -> b#(b(b(x1))) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(c(c(x1)))) -> b#(b(b(x1))) -> b#(b(c(c(x1)))) -> b#(b(b(b(x1)))) b#(b(c(c(x1)))) -> b#(b(b(x1))) -> b#(b(c(c(x1)))) -> b#(b(b(x1))) b#(b(c(c(x1)))) -> b#(b(b(x1))) -> b#(b(c(c(x1)))) -> b#(b(x1)) b#(b(c(c(x1)))) -> b#(b(b(x1))) -> b#(b(c(c(x1)))) -> b#(x1) b#(b(c(c(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(a(c(c(b(b(x1)))))) b#(b(c(c(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(c(c(b(b(x1))))) b#(b(c(c(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(c(c(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(c(c(x1)))) -> b#(b(x1)) -> b#(b(c(c(x1)))) -> b#(b(b(b(x1)))) b#(b(c(c(x1)))) -> b#(b(x1)) -> b#(b(c(c(x1)))) -> b#(b(b(x1))) b#(b(c(c(x1)))) -> b#(b(x1)) -> b#(b(c(c(x1)))) -> b#(b(x1)) b#(b(c(c(x1)))) -> b#(b(x1)) -> b#(b(c(c(x1)))) -> b#(x1) b#(b(c(c(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> a#(a(c(c(b(b(x1)))))) b#(b(c(c(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> a#(c(c(b(b(x1))))) b#(b(c(c(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(c(c(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(c(c(x1)))) -> b#(x1) -> b#(b(c(c(x1)))) -> b#(b(b(b(x1)))) b#(b(c(c(x1)))) -> b#(x1) -> b#(b(c(c(x1)))) -> b#(b(b(x1))) b#(b(c(c(x1)))) -> b#(x1) -> b#(b(c(c(x1)))) -> b#(b(x1)) b#(b(c(c(x1)))) -> b#(x1) -> b#(b(c(c(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(a(c(c(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> a#(c(c(b(b(x1))))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(c(c(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(c(c(x1)))) -> b#(b(b(x1))) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(c(c(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(b(x1)) -> b#(b(c(c(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> a#(a(c(c(b(b(x1)))))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> a#(c(c(b(b(x1))))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(a(a(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(c(c(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(c(c(x1)))) -> b#(b(b(x1))) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(c(c(x1)))) -> b#(b(x1)) b#(b(a(a(x1)))) -> b#(x1) -> b#(b(c(c(x1)))) -> b#(x1) b#(b(a(a(x1)))) -> a#(c(c(b(b(x1))))) -> a#(a(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) b#(b(a(a(x1)))) -> a#(c(c(b(b(x1))))) -> a#(a(b(b(x1)))) -> b#(c(c(a(a(x1))))) b#(b(a(a(x1)))) -> a#(c(c(b(b(x1))))) -> a#(a(b(b(x1)))) -> a#(a(x1)) b#(b(a(a(x1)))) -> a#(c(c(b(b(x1))))) -> a#(a(b(b(x1)))) -> a#(x1) b#(b(a(a(x1)))) -> a#(a(c(c(b(b(x1)))))) -> a#(a(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) b#(b(a(a(x1)))) -> a#(a(c(c(b(b(x1)))))) -> a#(a(b(b(x1)))) -> b#(c(c(a(a(x1))))) b#(b(a(a(x1)))) -> a#(a(c(c(b(b(x1)))))) -> a#(a(b(b(x1)))) -> a#(a(x1)) b#(b(a(a(x1)))) -> a#(a(c(c(b(b(x1)))))) -> a#(a(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> b#(c(c(a(a(x1))))) -> b#(b(a(a(x1)))) -> a#(a(c(c(b(b(x1)))))) a#(a(b(b(x1)))) -> b#(c(c(a(a(x1))))) -> b#(b(a(a(x1)))) -> a#(c(c(b(b(x1))))) a#(a(b(b(x1)))) -> b#(c(c(a(a(x1))))) -> b#(b(a(a(x1)))) -> b#(b(x1)) a#(a(b(b(x1)))) -> b#(c(c(a(a(x1))))) -> b#(b(a(a(x1)))) -> b#(x1) a#(a(b(b(x1)))) -> b#(c(c(a(a(x1))))) -> b#(b(c(c(x1)))) -> b#(b(b(b(x1)))) a#(a(b(b(x1)))) -> b#(c(c(a(a(x1))))) -> b#(b(c(c(x1)))) -> b#(b(b(x1))) a#(a(b(b(x1)))) -> b#(c(c(a(a(x1))))) -> b#(b(c(c(x1)))) -> b#(b(x1)) a#(a(b(b(x1)))) -> b#(c(c(a(a(x1))))) -> b#(b(c(c(x1)))) -> b#(x1) a#(a(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) -> b#(b(a(a(x1)))) -> a#(a(c(c(b(b(x1)))))) a#(a(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) -> b#(b(a(a(x1)))) -> a#(c(c(b(b(x1))))) a#(a(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) -> b#(b(a(a(x1)))) -> b#(b(x1)) a#(a(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) -> b#(b(a(a(x1)))) -> b#(x1) a#(a(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) -> b#(b(c(c(x1)))) -> b#(b(b(b(x1)))) a#(a(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) -> b#(b(c(c(x1)))) -> b#(b(b(x1))) a#(a(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) -> b#(b(c(c(x1)))) -> b#(b(x1)) a#(a(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) -> b#(b(c(c(x1)))) -> b#(x1) a#(a(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) a#(a(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> b#(c(c(a(a(x1))))) a#(a(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> a#(a(x1)) a#(a(b(b(x1)))) -> a#(a(x1)) -> a#(a(b(b(x1)))) -> a#(x1) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> b#(c(c(a(a(x1))))) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> a#(a(x1)) a#(a(b(b(x1)))) -> a#(x1) -> a#(a(b(b(x1)))) -> a#(x1) Polynomial Interpretation Processor: dimension: 1 interpretation: [b#](x0) = x0, [a#](x0) = x0 + 1, [c](x0) = x0, [a](x0) = x0 + 1, [b](x0) = x0 orientation: a#(a(b(b(x1)))) = x1 + 2 >= x1 + 1 = a#(x1) a#(a(b(b(x1)))) = x1 + 2 >= x1 + 2 = a#(a(x1)) a#(a(b(b(x1)))) = x1 + 2 >= x1 + 2 = b#(c(c(a(a(x1))))) a#(a(b(b(x1)))) = x1 + 2 >= x1 + 2 = b#(b(c(c(a(a(x1)))))) b#(b(c(c(x1)))) = x1 >= x1 = b#(x1) b#(b(c(c(x1)))) = x1 >= x1 = b#(b(x1)) b#(b(c(c(x1)))) = x1 >= x1 = b#(b(b(x1))) b#(b(c(c(x1)))) = x1 >= x1 = b#(b(b(b(x1)))) b#(b(a(a(x1)))) = x1 + 2 >= x1 = b#(x1) b#(b(a(a(x1)))) = x1 + 2 >= x1 = b#(b(x1)) b#(b(a(a(x1)))) = x1 + 2 >= x1 + 1 = a#(c(c(b(b(x1))))) b#(b(a(a(x1)))) = x1 + 2 >= x1 + 2 = a#(a(c(c(b(b(x1)))))) a(a(b(b(x1)))) = x1 + 2 >= x1 + 2 = b(b(c(c(a(a(x1)))))) b(b(c(c(x1)))) = x1 >= x1 = c(c(b(b(b(b(x1)))))) b(b(a(a(x1)))) = x1 + 2 >= x1 + 2 = a(a(c(c(b(b(x1)))))) problem: DPs: a#(a(b(b(x1)))) -> a#(a(x1)) a#(a(b(b(x1)))) -> b#(c(c(a(a(x1))))) a#(a(b(b(x1)))) -> b#(b(c(c(a(a(x1)))))) b#(b(c(c(x1)))) -> b#(x1) b#(b(c(c(x1)))) -> b#(b(x1)) b#(b(c(c(x1)))) -> b#(b(b(x1))) b#(b(c(c(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> a#(a(c(c(b(b(x1)))))) TRS: a(a(b(b(x1)))) -> b(b(c(c(a(a(x1)))))) b(b(c(c(x1)))) -> c(c(b(b(b(b(x1)))))) b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) Polynomial Interpretation Processor: dimension: 1 usable rules: a(a(b(b(x1)))) -> b(b(c(c(a(a(x1)))))) b(b(c(c(x1)))) -> c(c(b(b(b(b(x1)))))) b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) interpretation: [b#](x0) = 0, [a#](x0) = x0, [c](x0) = 0, [a](x0) = x0, [b](x0) = x0 + 1 orientation: a#(a(b(b(x1)))) = x1 + 2 >= x1 = a#(a(x1)) a#(a(b(b(x1)))) = x1 + 2 >= 0 = b#(c(c(a(a(x1))))) a#(a(b(b(x1)))) = x1 + 2 >= 0 = b#(b(c(c(a(a(x1)))))) b#(b(c(c(x1)))) = 0 >= 0 = b#(x1) b#(b(c(c(x1)))) = 0 >= 0 = b#(b(x1)) b#(b(c(c(x1)))) = 0 >= 0 = b#(b(b(x1))) b#(b(c(c(x1)))) = 0 >= 0 = b#(b(b(b(x1)))) b#(b(a(a(x1)))) = 0 >= 0 = a#(a(c(c(b(b(x1)))))) a(a(b(b(x1)))) = x1 + 2 >= 2 = b(b(c(c(a(a(x1)))))) b(b(c(c(x1)))) = 2 >= 0 = c(c(b(b(b(b(x1)))))) b(b(a(a(x1)))) = x1 + 2 >= 0 = a(a(c(c(b(b(x1)))))) problem: DPs: b#(b(c(c(x1)))) -> b#(x1) b#(b(c(c(x1)))) -> b#(b(x1)) b#(b(c(c(x1)))) -> b#(b(b(x1))) b#(b(c(c(x1)))) -> b#(b(b(b(x1)))) b#(b(a(a(x1)))) -> a#(a(c(c(b(b(x1)))))) TRS: a(a(b(b(x1)))) -> b(b(c(c(a(a(x1)))))) b(b(c(c(x1)))) -> c(c(b(b(b(b(x1)))))) b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) SCC Processor: #sccs: 1 #rules: 4 #arcs: 80/25 DPs: b#(b(c(c(x1)))) -> b#(b(b(b(x1)))) b#(b(c(c(x1)))) -> b#(x1) b#(b(c(c(x1)))) -> b#(b(x1)) b#(b(c(c(x1)))) -> b#(b(b(x1))) TRS: a(a(b(b(x1)))) -> b(b(c(c(a(a(x1)))))) b(b(c(c(x1)))) -> c(c(b(b(b(b(x1)))))) b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) Usable Rule Processor: DPs: b#(b(c(c(x1)))) -> b#(b(b(b(x1)))) b#(b(c(c(x1)))) -> b#(x1) b#(b(c(c(x1)))) -> b#(b(x1)) b#(b(c(c(x1)))) -> b#(b(b(x1))) TRS: b(b(c(c(x1)))) -> c(c(b(b(b(b(x1)))))) b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) Polynomial Interpretation Processor: dimension: 1 usable rules: b(b(c(c(x1)))) -> c(c(b(b(b(b(x1)))))) b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) interpretation: [b#](x0) = x0 + 1, [c](x0) = x0 + 1, [a](x0) = 1, [b](x0) = x0 orientation: b#(b(c(c(x1)))) = x1 + 3 >= x1 + 1 = b#(b(b(b(x1)))) b#(b(c(c(x1)))) = x1 + 3 >= x1 + 1 = b#(x1) b#(b(c(c(x1)))) = x1 + 3 >= x1 + 1 = b#(b(x1)) b#(b(c(c(x1)))) = x1 + 3 >= x1 + 1 = b#(b(b(x1))) b(b(c(c(x1)))) = x1 + 2 >= x1 + 2 = c(c(b(b(b(b(x1)))))) b(b(a(a(x1)))) = 1 >= 1 = a(a(c(c(b(b(x1)))))) problem: DPs: TRS: b(b(c(c(x1)))) -> c(c(b(b(b(b(x1)))))) b(b(a(a(x1)))) -> a(a(c(c(b(b(x1)))))) Qed