/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: b(a(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) b(c(a(x1))) -> a(b(c(x1))) c(b(x1)) -> d(x1) d(x1) -> b(a(x1)) a(d(x1)) -> d(a(x1)) a(a(x1)) -> a(b(a(x1))) Proof: DP Processor: DPs: b#(a(a(x1))) -> c#(x1) b#(a(a(x1))) -> b#(c(x1)) b#(a(a(x1))) -> a#(b(c(x1))) c#(a(x1)) -> c#(x1) c#(a(x1)) -> a#(c(x1)) b#(c(a(x1))) -> c#(x1) b#(c(a(x1))) -> b#(c(x1)) b#(c(a(x1))) -> a#(b(c(x1))) c#(b(x1)) -> d#(x1) d#(x1) -> a#(x1) d#(x1) -> b#(a(x1)) a#(d(x1)) -> a#(x1) a#(d(x1)) -> d#(a(x1)) a#(a(x1)) -> b#(a(x1)) a#(a(x1)) -> a#(b(a(x1))) TRS: b(a(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) b(c(a(x1))) -> a(b(c(x1))) c(b(x1)) -> d(x1) d(x1) -> b(a(x1)) a(d(x1)) -> d(a(x1)) a(a(x1)) -> a(b(a(x1))) TDG Processor: DPs: b#(a(a(x1))) -> c#(x1) b#(a(a(x1))) -> b#(c(x1)) b#(a(a(x1))) -> a#(b(c(x1))) c#(a(x1)) -> c#(x1) c#(a(x1)) -> a#(c(x1)) b#(c(a(x1))) -> c#(x1) b#(c(a(x1))) -> b#(c(x1)) b#(c(a(x1))) -> a#(b(c(x1))) c#(b(x1)) -> d#(x1) d#(x1) -> a#(x1) d#(x1) -> b#(a(x1)) a#(d(x1)) -> a#(x1) a#(d(x1)) -> d#(a(x1)) a#(a(x1)) -> b#(a(x1)) a#(a(x1)) -> a#(b(a(x1))) TRS: b(a(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) b(c(a(x1))) -> a(b(c(x1))) c(b(x1)) -> d(x1) d(x1) -> b(a(x1)) a(d(x1)) -> d(a(x1)) a(a(x1)) -> a(b(a(x1))) graph: d#(x1) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1))) d#(x1) -> a#(x1) -> a#(a(x1)) -> b#(a(x1)) d#(x1) -> a#(x1) -> a#(d(x1)) -> d#(a(x1)) d#(x1) -> a#(x1) -> a#(d(x1)) -> a#(x1) d#(x1) -> b#(a(x1)) -> b#(c(a(x1))) -> a#(b(c(x1))) d#(x1) -> b#(a(x1)) -> b#(c(a(x1))) -> b#(c(x1)) d#(x1) -> b#(a(x1)) -> b#(c(a(x1))) -> c#(x1) d#(x1) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(c(x1))) d#(x1) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(c(x1)) d#(x1) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1) a#(d(x1)) -> d#(a(x1)) -> d#(x1) -> b#(a(x1)) a#(d(x1)) -> d#(a(x1)) -> d#(x1) -> a#(x1) a#(d(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1))) a#(d(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1)) a#(d(x1)) -> a#(x1) -> a#(d(x1)) -> d#(a(x1)) a#(d(x1)) -> a#(x1) -> a#(d(x1)) -> a#(x1) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1))) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1)) a#(a(x1)) -> a#(b(a(x1))) -> a#(d(x1)) -> d#(a(x1)) a#(a(x1)) -> a#(b(a(x1))) -> a#(d(x1)) -> a#(x1) a#(a(x1)) -> b#(a(x1)) -> b#(c(a(x1))) -> a#(b(c(x1))) a#(a(x1)) -> b#(a(x1)) -> b#(c(a(x1))) -> b#(c(x1)) a#(a(x1)) -> b#(a(x1)) -> b#(c(a(x1))) -> c#(x1) a#(a(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(c(x1))) a#(a(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(c(x1)) a#(a(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1) c#(b(x1)) -> d#(x1) -> d#(x1) -> b#(a(x1)) c#(b(x1)) -> d#(x1) -> d#(x1) -> a#(x1) c#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(a(x1))) c#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(a(x1)) c#(a(x1)) -> a#(c(x1)) -> a#(d(x1)) -> d#(a(x1)) c#(a(x1)) -> a#(c(x1)) -> a#(d(x1)) -> a#(x1) c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> d#(x1) c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(x1)) c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1) b#(c(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(a(x1))) b#(c(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(a(x1)) b#(c(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> d#(a(x1)) b#(c(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> a#(x1) b#(c(a(x1))) -> c#(x1) -> c#(b(x1)) -> d#(x1) b#(c(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(c(x1)) b#(c(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1) b#(c(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> a#(b(c(x1))) b#(c(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> b#(c(x1)) b#(c(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> c#(x1) b#(c(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> a#(b(c(x1))) b#(c(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> b#(c(x1)) b#(c(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> c#(x1) b#(a(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(a(x1))) b#(a(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(a(x1)) b#(a(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> d#(a(x1)) b#(a(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> a#(x1) b#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> d#(x1) b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(c(x1)) b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1) b#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> a#(b(c(x1))) b#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> b#(c(x1)) b#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> c#(x1) b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> a#(b(c(x1))) b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> b#(c(x1)) b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> c#(x1) EDG Processor: DPs: b#(a(a(x1))) -> c#(x1) b#(a(a(x1))) -> b#(c(x1)) b#(a(a(x1))) -> a#(b(c(x1))) c#(a(x1)) -> c#(x1) c#(a(x1)) -> a#(c(x1)) b#(c(a(x1))) -> c#(x1) b#(c(a(x1))) -> b#(c(x1)) b#(c(a(x1))) -> a#(b(c(x1))) c#(b(x1)) -> d#(x1) d#(x1) -> a#(x1) d#(x1) -> b#(a(x1)) a#(d(x1)) -> a#(x1) a#(d(x1)) -> d#(a(x1)) a#(a(x1)) -> b#(a(x1)) a#(a(x1)) -> a#(b(a(x1))) TRS: b(a(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) b(c(a(x1))) -> a(b(c(x1))) c(b(x1)) -> d(x1) d(x1) -> b(a(x1)) a(d(x1)) -> d(a(x1)) a(a(x1)) -> a(b(a(x1))) graph: d#(x1) -> a#(x1) -> a#(d(x1)) -> a#(x1) d#(x1) -> a#(x1) -> a#(d(x1)) -> d#(a(x1)) d#(x1) -> a#(x1) -> a#(a(x1)) -> b#(a(x1)) d#(x1) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1))) d#(x1) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1) d#(x1) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(c(x1)) d#(x1) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(c(x1))) a#(d(x1)) -> d#(a(x1)) -> d#(x1) -> a#(x1) a#(d(x1)) -> d#(a(x1)) -> d#(x1) -> b#(a(x1)) a#(d(x1)) -> a#(x1) -> a#(d(x1)) -> a#(x1) a#(d(x1)) -> a#(x1) -> a#(d(x1)) -> d#(a(x1)) a#(d(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1)) a#(d(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1))) a#(a(x1)) -> a#(b(a(x1))) -> a#(d(x1)) -> a#(x1) a#(a(x1)) -> a#(b(a(x1))) -> a#(d(x1)) -> d#(a(x1)) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1)) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1))) a#(a(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1) a#(a(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(c(x1)) a#(a(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(c(x1))) c#(b(x1)) -> d#(x1) -> d#(x1) -> a#(x1) c#(b(x1)) -> d#(x1) -> d#(x1) -> b#(a(x1)) c#(a(x1)) -> a#(c(x1)) -> a#(d(x1)) -> a#(x1) c#(a(x1)) -> a#(c(x1)) -> a#(d(x1)) -> d#(a(x1)) c#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(a(x1)) c#(a(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(a(x1))) c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1) c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> a#(c(x1)) c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> d#(x1) b#(c(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> a#(x1) b#(c(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> d#(a(x1)) b#(c(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(a(x1)) b#(c(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(a(x1))) b#(c(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1) b#(c(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(c(x1)) b#(c(a(x1))) -> c#(x1) -> c#(b(x1)) -> d#(x1) b#(c(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> c#(x1) b#(c(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> b#(c(x1)) b#(c(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> a#(b(c(x1))) b#(c(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> c#(x1) b#(c(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> b#(c(x1)) b#(c(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> a#(b(c(x1))) b#(a(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> a#(x1) b#(a(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> d#(a(x1)) b#(a(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(a(x1)) b#(a(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(a(x1))) b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1) b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(c(x1)) b#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> d#(x1) b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> c#(x1) b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> b#(c(x1)) b#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> a#(b(c(x1))) b#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> c#(x1) b#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> b#(c(x1)) b#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> a#(b(c(x1))) Arctic Interpretation Processor: dimension: 1 usable rules: b(a(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) b(c(a(x1))) -> a(b(c(x1))) c(b(x1)) -> d(x1) d(x1) -> b(a(x1)) a(d(x1)) -> d(a(x1)) a(a(x1)) -> a(b(a(x1))) interpretation: [d#](x0) = 1x0, [a#](x0) = 1x0, [c#](x0) = 2x0, [b#](x0) = x0, [d](x0) = 1x0, [c](x0) = 1x0, [b](x0) = x0, [a](x0) = 1x0 orientation: b#(a(a(x1))) = 2x1 >= 2x1 = c#(x1) b#(a(a(x1))) = 2x1 >= 1x1 = b#(c(x1)) b#(a(a(x1))) = 2x1 >= 2x1 = a#(b(c(x1))) c#(a(x1)) = 3x1 >= 2x1 = c#(x1) c#(a(x1)) = 3x1 >= 2x1 = a#(c(x1)) b#(c(a(x1))) = 2x1 >= 2x1 = c#(x1) b#(c(a(x1))) = 2x1 >= 1x1 = b#(c(x1)) b#(c(a(x1))) = 2x1 >= 2x1 = a#(b(c(x1))) c#(b(x1)) = 2x1 >= 1x1 = d#(x1) d#(x1) = 1x1 >= 1x1 = a#(x1) d#(x1) = 1x1 >= 1x1 = b#(a(x1)) a#(d(x1)) = 2x1 >= 1x1 = a#(x1) a#(d(x1)) = 2x1 >= 2x1 = d#(a(x1)) a#(a(x1)) = 2x1 >= 1x1 = b#(a(x1)) a#(a(x1)) = 2x1 >= 2x1 = a#(b(a(x1))) b(a(a(x1))) = 2x1 >= 2x1 = a(b(c(x1))) c(a(x1)) = 2x1 >= 2x1 = a(c(x1)) b(c(a(x1))) = 2x1 >= 2x1 = a(b(c(x1))) c(b(x1)) = 1x1 >= 1x1 = d(x1) d(x1) = 1x1 >= 1x1 = b(a(x1)) a(d(x1)) = 2x1 >= 2x1 = d(a(x1)) a(a(x1)) = 2x1 >= 2x1 = a(b(a(x1))) problem: DPs: b#(a(a(x1))) -> c#(x1) b#(a(a(x1))) -> a#(b(c(x1))) b#(c(a(x1))) -> c#(x1) b#(c(a(x1))) -> a#(b(c(x1))) d#(x1) -> a#(x1) d#(x1) -> b#(a(x1)) a#(d(x1)) -> d#(a(x1)) a#(a(x1)) -> a#(b(a(x1))) TRS: b(a(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) b(c(a(x1))) -> a(b(c(x1))) c(b(x1)) -> d(x1) d(x1) -> b(a(x1)) a(d(x1)) -> d(a(x1)) a(a(x1)) -> a(b(a(x1))) Restore Modifier: DPs: b#(a(a(x1))) -> c#(x1) b#(a(a(x1))) -> a#(b(c(x1))) b#(c(a(x1))) -> c#(x1) b#(c(a(x1))) -> a#(b(c(x1))) d#(x1) -> a#(x1) d#(x1) -> b#(a(x1)) a#(d(x1)) -> d#(a(x1)) a#(a(x1)) -> a#(b(a(x1))) TRS: b(a(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) b(c(a(x1))) -> a(b(c(x1))) c(b(x1)) -> d(x1) d(x1) -> b(a(x1)) a(d(x1)) -> d(a(x1)) a(a(x1)) -> a(b(a(x1))) EDG Processor: DPs: b#(a(a(x1))) -> c#(x1) b#(a(a(x1))) -> a#(b(c(x1))) b#(c(a(x1))) -> c#(x1) b#(c(a(x1))) -> a#(b(c(x1))) d#(x1) -> a#(x1) d#(x1) -> b#(a(x1)) a#(d(x1)) -> d#(a(x1)) a#(a(x1)) -> a#(b(a(x1))) TRS: b(a(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) b(c(a(x1))) -> a(b(c(x1))) c(b(x1)) -> d(x1) d(x1) -> b(a(x1)) a(d(x1)) -> d(a(x1)) a(a(x1)) -> a(b(a(x1))) graph: d#(x1) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1))) d#(x1) -> a#(x1) -> a#(d(x1)) -> d#(a(x1)) d#(x1) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(c(x1))) d#(x1) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1) a#(d(x1)) -> d#(a(x1)) -> d#(x1) -> b#(a(x1)) a#(d(x1)) -> d#(a(x1)) -> d#(x1) -> a#(x1) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1))) a#(a(x1)) -> a#(b(a(x1))) -> a#(d(x1)) -> d#(a(x1)) b#(c(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(a(x1))) b#(c(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> d#(a(x1)) b#(a(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(a(x1))) b#(a(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> d#(a(x1)) SCC Processor: #sccs: 1 #rules: 5 #arcs: 12/64 DPs: d#(x1) -> a#(x1) a#(d(x1)) -> d#(a(x1)) d#(x1) -> b#(a(x1)) b#(a(a(x1))) -> a#(b(c(x1))) a#(a(x1)) -> a#(b(a(x1))) TRS: b(a(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) b(c(a(x1))) -> a(b(c(x1))) c(b(x1)) -> d(x1) d(x1) -> b(a(x1)) a(d(x1)) -> d(a(x1)) a(a(x1)) -> a(b(a(x1))) Arctic Interpretation Processor: dimension: 1 usable rules: b(a(a(x1))) -> a(b(c(x1))) b(c(a(x1))) -> a(b(c(x1))) d(x1) -> b(a(x1)) a(d(x1)) -> d(a(x1)) a(a(x1)) -> a(b(a(x1))) interpretation: [d#](x0) = 8x0 + 1, [a#](x0) = x0 + 0, [b#](x0) = x0 + 0, [d](x0) = 8x0 + 8, [c](x0) = 10, [b](x0) = 0, [a](x0) = x0 + 0 orientation: d#(x1) = 8x1 + 1 >= x1 + 0 = a#(x1) a#(d(x1)) = 8x1 + 8 >= 8x1 + 8 = d#(a(x1)) d#(x1) = 8x1 + 1 >= x1 + 0 = b#(a(x1)) b#(a(a(x1))) = x1 + 0 >= 0 = a#(b(c(x1))) a#(a(x1)) = x1 + 0 >= 0 = a#(b(a(x1))) b(a(a(x1))) = 0 >= 0 = a(b(c(x1))) c(a(x1)) = 10 >= 10 = a(c(x1)) b(c(a(x1))) = 0 >= 0 = a(b(c(x1))) c(b(x1)) = 10 >= 8x1 + 8 = d(x1) d(x1) = 8x1 + 8 >= 0 = b(a(x1)) a(d(x1)) = 8x1 + 8 >= 8x1 + 8 = d(a(x1)) a(a(x1)) = x1 + 0 >= 0 = a(b(a(x1))) problem: DPs: a#(d(x1)) -> d#(a(x1)) b#(a(a(x1))) -> a#(b(c(x1))) a#(a(x1)) -> a#(b(a(x1))) TRS: b(a(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) b(c(a(x1))) -> a(b(c(x1))) c(b(x1)) -> d(x1) d(x1) -> b(a(x1)) a(d(x1)) -> d(a(x1)) a(a(x1)) -> a(b(a(x1))) Restore Modifier: DPs: a#(d(x1)) -> d#(a(x1)) b#(a(a(x1))) -> a#(b(c(x1))) a#(a(x1)) -> a#(b(a(x1))) TRS: b(a(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) b(c(a(x1))) -> a(b(c(x1))) c(b(x1)) -> d(x1) d(x1) -> b(a(x1)) a(d(x1)) -> d(a(x1)) a(a(x1)) -> a(b(a(x1))) EDG Processor: DPs: a#(d(x1)) -> d#(a(x1)) b#(a(a(x1))) -> a#(b(c(x1))) a#(a(x1)) -> a#(b(a(x1))) TRS: b(a(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) b(c(a(x1))) -> a(b(c(x1))) c(b(x1)) -> d(x1) d(x1) -> b(a(x1)) a(d(x1)) -> d(a(x1)) a(a(x1)) -> a(b(a(x1))) graph: a#(a(x1)) -> a#(b(a(x1))) -> a#(d(x1)) -> d#(a(x1)) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1))) b#(a(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> d#(a(x1)) b#(a(a(x1))) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(a(x1))) SCC Processor: #sccs: 1 #rules: 1 #arcs: 4/9 DPs: a#(a(x1)) -> a#(b(a(x1))) TRS: b(a(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) b(c(a(x1))) -> a(b(c(x1))) c(b(x1)) -> d(x1) d(x1) -> b(a(x1)) a(d(x1)) -> d(a(x1)) a(a(x1)) -> a(b(a(x1))) Arctic Interpretation Processor: dimension: 1 usable rules: b(a(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) b(c(a(x1))) -> a(b(c(x1))) c(b(x1)) -> d(x1) d(x1) -> b(a(x1)) a(d(x1)) -> d(a(x1)) a(a(x1)) -> a(b(a(x1))) interpretation: [a#](x0) = 1x0 + 8, [d](x0) = 8x0 + 11, [c](x0) = 15x0, [b](x0) = -7x0 + 1, [a](x0) = 15x0 + 8 orientation: a#(a(x1)) = 16x1 + 9 >= 9x1 + 8 = a#(b(a(x1))) b(a(a(x1))) = 23x1 + 16 >= 23x1 + 16 = a(b(c(x1))) c(a(x1)) = 30x1 + 23 >= 30x1 + 8 = a(c(x1)) b(c(a(x1))) = 23x1 + 16 >= 23x1 + 16 = a(b(c(x1))) c(b(x1)) = 8x1 + 16 >= 8x1 + 11 = d(x1) d(x1) = 8x1 + 11 >= 8x1 + 1 = b(a(x1)) a(d(x1)) = 23x1 + 26 >= 23x1 + 16 = d(a(x1)) a(a(x1)) = 30x1 + 23 >= 23x1 + 16 = a(b(a(x1))) problem: DPs: TRS: b(a(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) b(c(a(x1))) -> a(b(c(x1))) c(b(x1)) -> d(x1) d(x1) -> b(a(x1)) a(d(x1)) -> d(a(x1)) a(a(x1)) -> a(b(a(x1))) Qed