/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: 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) a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) L(a(a(x1))) -> L(a(b(c(x1)))) c(R(x1)) -> c(b(R(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) a#(d(x1)) -> a#(x1) a#(d(x1)) -> d#(a(x1)) d#(x1) -> a#(x1) d#(x1) -> b#(a(x1)) L#(a(a(x1))) -> c#(x1) L#(a(a(x1))) -> b#(c(x1)) L#(a(a(x1))) -> a#(b(c(x1))) L#(a(a(x1))) -> L#(a(b(c(x1)))) c#(R(x1)) -> b#(R(x1)) c#(R(x1)) -> c#(b(R(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) a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) L(a(a(x1))) -> L(a(b(c(x1)))) c(R(x1)) -> c(b(R(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) a#(d(x1)) -> a#(x1) a#(d(x1)) -> d#(a(x1)) d#(x1) -> a#(x1) d#(x1) -> b#(a(x1)) L#(a(a(x1))) -> c#(x1) L#(a(a(x1))) -> b#(c(x1)) L#(a(a(x1))) -> a#(b(c(x1))) L#(a(a(x1))) -> L#(a(b(c(x1)))) c#(R(x1)) -> b#(R(x1)) c#(R(x1)) -> c#(b(R(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) a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) L(a(a(x1))) -> L(a(b(c(x1)))) c(R(x1)) -> c(b(R(x1))) graph: L#(a(a(x1))) -> L#(a(b(c(x1)))) -> L#(a(a(x1))) -> L#(a(b(c(x1)))) L#(a(a(x1))) -> L#(a(b(c(x1)))) -> L#(a(a(x1))) -> a#(b(c(x1))) L#(a(a(x1))) -> L#(a(b(c(x1)))) -> L#(a(a(x1))) -> b#(c(x1)) L#(a(a(x1))) -> L#(a(b(c(x1)))) -> L#(a(a(x1))) -> c#(x1) L#(a(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> d#(a(x1)) L#(a(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> a#(x1) L#(a(a(x1))) -> c#(x1) -> c#(R(x1)) -> c#(b(R(x1))) L#(a(a(x1))) -> c#(x1) -> c#(R(x1)) -> b#(R(x1)) L#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> d#(x1) L#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(c(x1)) L#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1) L#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> a#(b(c(x1))) L#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> b#(c(x1)) L#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> c#(x1) L#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> a#(b(c(x1))) L#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> b#(c(x1)) L#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> c#(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#(d(x1)) -> d#(a(x1)) a#(d(x1)) -> a#(x1) -> a#(d(x1)) -> a#(x1) c#(R(x1)) -> c#(b(R(x1))) -> c#(R(x1)) -> c#(b(R(x1))) c#(R(x1)) -> c#(b(R(x1))) -> c#(R(x1)) -> b#(R(x1)) c#(R(x1)) -> c#(b(R(x1))) -> c#(b(x1)) -> d#(x1) c#(R(x1)) -> c#(b(R(x1))) -> c#(a(x1)) -> a#(c(x1)) c#(R(x1)) -> c#(b(R(x1))) -> c#(a(x1)) -> c#(x1) c#(R(x1)) -> b#(R(x1)) -> b#(c(a(x1))) -> a#(b(c(x1))) c#(R(x1)) -> b#(R(x1)) -> b#(c(a(x1))) -> b#(c(x1)) c#(R(x1)) -> b#(R(x1)) -> b#(c(a(x1))) -> c#(x1) c#(R(x1)) -> b#(R(x1)) -> b#(a(a(x1))) -> a#(b(c(x1))) c#(R(x1)) -> b#(R(x1)) -> b#(a(a(x1))) -> b#(c(x1)) c#(R(x1)) -> b#(R(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#(d(x1)) -> d#(a(x1)) c#(a(x1)) -> a#(c(x1)) -> a#(d(x1)) -> a#(x1) c#(a(x1)) -> c#(x1) -> c#(R(x1)) -> c#(b(R(x1))) c#(a(x1)) -> c#(x1) -> c#(R(x1)) -> b#(R(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#(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#(R(x1)) -> c#(b(R(x1))) b#(c(a(x1))) -> c#(x1) -> c#(R(x1)) -> b#(R(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#(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#(R(x1)) -> c#(b(R(x1))) b#(a(a(x1))) -> c#(x1) -> c#(R(x1)) -> b#(R(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) a#(d(x1)) -> a#(x1) a#(d(x1)) -> d#(a(x1)) d#(x1) -> a#(x1) d#(x1) -> b#(a(x1)) L#(a(a(x1))) -> c#(x1) L#(a(a(x1))) -> b#(c(x1)) L#(a(a(x1))) -> a#(b(c(x1))) L#(a(a(x1))) -> L#(a(b(c(x1)))) c#(R(x1)) -> b#(R(x1)) c#(R(x1)) -> c#(b(R(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) a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) L(a(a(x1))) -> L(a(b(c(x1)))) c(R(x1)) -> c(b(R(x1))) graph: L#(a(a(x1))) -> L#(a(b(c(x1)))) -> L#(a(a(x1))) -> c#(x1) L#(a(a(x1))) -> L#(a(b(c(x1)))) -> L#(a(a(x1))) -> b#(c(x1)) L#(a(a(x1))) -> L#(a(b(c(x1)))) -> L#(a(a(x1))) -> a#(b(c(x1))) L#(a(a(x1))) -> L#(a(b(c(x1)))) -> L#(a(a(x1))) -> L#(a(b(c(x1)))) L#(a(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> a#(x1) L#(a(a(x1))) -> a#(b(c(x1))) -> a#(d(x1)) -> d#(a(x1)) L#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1) L#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> a#(c(x1)) L#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> d#(x1) L#(a(a(x1))) -> c#(x1) -> c#(R(x1)) -> b#(R(x1)) L#(a(a(x1))) -> c#(x1) -> c#(R(x1)) -> c#(b(R(x1))) L#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> c#(x1) L#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> b#(c(x1)) L#(a(a(x1))) -> b#(c(x1)) -> b#(a(a(x1))) -> a#(b(c(x1))) L#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> c#(x1) L#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> b#(c(x1)) L#(a(a(x1))) -> b#(c(x1)) -> b#(c(a(x1))) -> a#(b(c(x1))) d#(x1) -> a#(x1) -> a#(d(x1)) -> a#(x1) d#(x1) -> a#(x1) -> a#(d(x1)) -> d#(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)) c#(R(x1)) -> c#(b(R(x1))) -> c#(b(x1)) -> d#(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)) -> 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) c#(a(x1)) -> c#(x1) -> c#(R(x1)) -> b#(R(x1)) c#(a(x1)) -> c#(x1) -> c#(R(x1)) -> c#(b(R(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))) -> 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))) -> c#(x1) -> c#(R(x1)) -> b#(R(x1)) b#(c(a(x1))) -> c#(x1) -> c#(R(x1)) -> c#(b(R(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))) -> 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))) -> c#(x1) -> c#(R(x1)) -> b#(R(x1)) b#(a(a(x1))) -> c#(x1) -> c#(R(x1)) -> c#(b(R(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))) SCC Processor: #sccs: 2 #rules: 15 #arcs: 62/361 DPs: L#(a(a(x1))) -> L#(a(b(c(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) a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) L(a(a(x1))) -> L(a(b(c(x1)))) c(R(x1)) -> c(b(R(x1))) Usable Rule Processor: DPs: L#(a(a(x1))) -> L#(a(b(c(x1)))) TRS: c(a(x1)) -> a(c(x1)) c(b(x1)) -> d(x1) c(R(x1)) -> c(b(R(x1))) a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) b(a(a(x1))) -> a(b(c(x1))) b(c(a(x1))) -> a(b(c(x1))) Arctic Interpretation Processor: dimension: 1 usable rules: c(a(x1)) -> a(c(x1)) c(b(x1)) -> d(x1) c(R(x1)) -> c(b(R(x1))) a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) b(a(a(x1))) -> a(b(c(x1))) b(c(a(x1))) -> a(b(c(x1))) interpretation: [L#](x0) = x0 + 0, [R](x0) = 7x0 + 0, [d](x0) = x0 + 7, [c](x0) = 1x0 + 8, [b](x0) = -1x0 + 0, [a](x0) = 1x0 + 8 orientation: L#(a(a(x1))) = 2x1 + 9 >= 1x1 + 8 = L#(a(b(c(x1)))) c(a(x1)) = 2x1 + 9 >= 2x1 + 9 = a(c(x1)) c(b(x1)) = x1 + 8 >= x1 + 7 = d(x1) c(R(x1)) = 8x1 + 8 >= 7x1 + 8 = c(b(R(x1))) a(d(x1)) = 1x1 + 8 >= 1x1 + 8 = d(a(x1)) d(x1) = x1 + 7 >= x1 + 7 = b(a(x1)) b(a(a(x1))) = 1x1 + 8 >= 1x1 + 8 = a(b(c(x1))) b(c(a(x1))) = 1x1 + 8 >= 1x1 + 8 = a(b(c(x1))) problem: DPs: TRS: c(a(x1)) -> a(c(x1)) c(b(x1)) -> d(x1) c(R(x1)) -> c(b(R(x1))) a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) b(a(a(x1))) -> a(b(c(x1))) b(c(a(x1))) -> a(b(c(x1))) Qed DPs: a#(d(x1)) -> d#(a(x1)) d#(x1) -> b#(a(x1)) b#(a(a(x1))) -> a#(b(c(x1))) a#(d(x1)) -> a#(x1) b#(a(a(x1))) -> b#(c(x1)) b#(c(a(x1))) -> a#(b(c(x1))) b#(c(a(x1))) -> b#(c(x1)) b#(c(a(x1))) -> c#(x1) c#(R(x1)) -> c#(b(R(x1))) c#(b(x1)) -> d#(x1) d#(x1) -> a#(x1) c#(a(x1)) -> a#(c(x1)) c#(a(x1)) -> c#(x1) b#(a(a(x1))) -> c#(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) a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) L(a(a(x1))) -> L(a(b(c(x1)))) c(R(x1)) -> c(b(R(x1))) Usable Rule Processor: DPs: a#(d(x1)) -> d#(a(x1)) d#(x1) -> b#(a(x1)) b#(a(a(x1))) -> a#(b(c(x1))) a#(d(x1)) -> a#(x1) b#(a(a(x1))) -> b#(c(x1)) b#(c(a(x1))) -> a#(b(c(x1))) b#(c(a(x1))) -> b#(c(x1)) b#(c(a(x1))) -> c#(x1) c#(R(x1)) -> c#(b(R(x1))) c#(b(x1)) -> d#(x1) d#(x1) -> a#(x1) c#(a(x1)) -> a#(c(x1)) c#(a(x1)) -> c#(x1) b#(a(a(x1))) -> c#(x1) TRS: a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) b(a(a(x1))) -> a(b(c(x1))) b(c(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) c(b(x1)) -> d(x1) c(R(x1)) -> c(b(R(x1))) Arctic Interpretation Processor: dimension: 1 usable rules: a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) b(a(a(x1))) -> a(b(c(x1))) b(c(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) c(b(x1)) -> d(x1) c(R(x1)) -> c(b(R(x1))) interpretation: [d#](x0) = 2x0, [a#](x0) = 2x0, [c#](x0) = 2x0, [b#](x0) = x0, [R](x0) = 1x0, [d](x0) = 2x0, [c](x0) = 2x0, [b](x0) = x0, [a](x0) = 2x0 orientation: a#(d(x1)) = 4x1 >= 4x1 = d#(a(x1)) d#(x1) = 2x1 >= 2x1 = b#(a(x1)) b#(a(a(x1))) = 4x1 >= 4x1 = a#(b(c(x1))) a#(d(x1)) = 4x1 >= 2x1 = a#(x1) b#(a(a(x1))) = 4x1 >= 2x1 = b#(c(x1)) b#(c(a(x1))) = 4x1 >= 4x1 = a#(b(c(x1))) b#(c(a(x1))) = 4x1 >= 2x1 = b#(c(x1)) b#(c(a(x1))) = 4x1 >= 2x1 = c#(x1) c#(R(x1)) = 3x1 >= 3x1 = c#(b(R(x1))) c#(b(x1)) = 2x1 >= 2x1 = d#(x1) d#(x1) = 2x1 >= 2x1 = a#(x1) c#(a(x1)) = 4x1 >= 4x1 = a#(c(x1)) c#(a(x1)) = 4x1 >= 2x1 = c#(x1) b#(a(a(x1))) = 4x1 >= 2x1 = c#(x1) a(d(x1)) = 4x1 >= 4x1 = d(a(x1)) d(x1) = 2x1 >= 2x1 = b(a(x1)) b(a(a(x1))) = 4x1 >= 4x1 = a(b(c(x1))) b(c(a(x1))) = 4x1 >= 4x1 = a(b(c(x1))) c(a(x1)) = 4x1 >= 4x1 = a(c(x1)) c(b(x1)) = 2x1 >= 2x1 = d(x1) c(R(x1)) = 3x1 >= 3x1 = c(b(R(x1))) problem: DPs: a#(d(x1)) -> d#(a(x1)) d#(x1) -> b#(a(x1)) b#(a(a(x1))) -> a#(b(c(x1))) b#(c(a(x1))) -> a#(b(c(x1))) c#(R(x1)) -> c#(b(R(x1))) c#(b(x1)) -> d#(x1) d#(x1) -> a#(x1) c#(a(x1)) -> a#(c(x1)) TRS: a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) b(a(a(x1))) -> a(b(c(x1))) b(c(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) c(b(x1)) -> d(x1) c(R(x1)) -> c(b(R(x1))) Restore Modifier: DPs: a#(d(x1)) -> d#(a(x1)) d#(x1) -> b#(a(x1)) b#(a(a(x1))) -> a#(b(c(x1))) b#(c(a(x1))) -> a#(b(c(x1))) c#(R(x1)) -> c#(b(R(x1))) c#(b(x1)) -> d#(x1) d#(x1) -> a#(x1) c#(a(x1)) -> a#(c(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) a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) L(a(a(x1))) -> L(a(b(c(x1)))) c(R(x1)) -> c(b(R(x1))) EDG Processor: DPs: a#(d(x1)) -> d#(a(x1)) d#(x1) -> b#(a(x1)) b#(a(a(x1))) -> a#(b(c(x1))) b#(c(a(x1))) -> a#(b(c(x1))) c#(R(x1)) -> c#(b(R(x1))) c#(b(x1)) -> d#(x1) d#(x1) -> a#(x1) c#(a(x1)) -> a#(c(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) a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) L(a(a(x1))) -> L(a(b(c(x1)))) c(R(x1)) -> c(b(R(x1))) graph: d#(x1) -> a#(x1) -> a#(d(x1)) -> d#(a(x1)) d#(x1) -> b#(a(x1)) -> b#(a(a(x1))) -> a#(b(c(x1))) a#(d(x1)) -> d#(a(x1)) -> d#(x1) -> b#(a(x1)) a#(d(x1)) -> d#(a(x1)) -> d#(x1) -> a#(x1) c#(R(x1)) -> c#(b(R(x1))) -> c#(b(x1)) -> d#(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#(d(x1)) -> d#(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#(d(x1)) -> d#(a(x1)) SCC Processor: #sccs: 1 #rules: 4 #arcs: 10/64 DPs: d#(x1) -> a#(x1) a#(d(x1)) -> d#(a(x1)) d#(x1) -> b#(a(x1)) b#(a(a(x1))) -> a#(b(c(x1))) 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) a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) L(a(a(x1))) -> L(a(b(c(x1)))) c(R(x1)) -> c(b(R(x1))) Usable Rule Processor: DPs: d#(x1) -> a#(x1) a#(d(x1)) -> d#(a(x1)) d#(x1) -> b#(a(x1)) b#(a(a(x1))) -> a#(b(c(x1))) TRS: a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) b(a(a(x1))) -> a(b(c(x1))) b(c(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) c(b(x1)) -> d(x1) c(R(x1)) -> c(b(R(x1))) Arctic Interpretation Processor: dimension: 1 usable rules: a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) b(a(a(x1))) -> a(b(c(x1))) b(c(a(x1))) -> a(b(c(x1))) interpretation: [d#](x0) = x0 + 14, [a#](x0) = x0 + 0, [b#](x0) = x0 + 14, [R](x0) = x0 + 11, [d](x0) = x0 + 14, [c](x0) = 4x0 + 4, [b](x0) = 12, [a](x0) = x0 + 12 orientation: d#(x1) = x1 + 14 >= x1 + 0 = a#(x1) a#(d(x1)) = x1 + 14 >= x1 + 14 = d#(a(x1)) d#(x1) = x1 + 14 >= x1 + 14 = b#(a(x1)) b#(a(a(x1))) = x1 + 14 >= 12 = a#(b(c(x1))) a(d(x1)) = x1 + 14 >= x1 + 14 = d(a(x1)) d(x1) = x1 + 14 >= 12 = b(a(x1)) b(a(a(x1))) = 12 >= 12 = a(b(c(x1))) b(c(a(x1))) = 12 >= 12 = a(b(c(x1))) c(a(x1)) = 4x1 + 16 >= 4x1 + 12 = a(c(x1)) c(b(x1)) = 16 >= x1 + 14 = d(x1) c(R(x1)) = 4x1 + 15 >= 16 = c(b(R(x1))) problem: DPs: d#(x1) -> a#(x1) a#(d(x1)) -> d#(a(x1)) d#(x1) -> b#(a(x1)) TRS: a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) b(a(a(x1))) -> a(b(c(x1))) b(c(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) c(b(x1)) -> d(x1) c(R(x1)) -> c(b(R(x1))) Restore Modifier: DPs: d#(x1) -> a#(x1) a#(d(x1)) -> d#(a(x1)) d#(x1) -> 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) a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) L(a(a(x1))) -> L(a(b(c(x1)))) c(R(x1)) -> c(b(R(x1))) EDG Processor: DPs: d#(x1) -> a#(x1) a#(d(x1)) -> d#(a(x1)) d#(x1) -> 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) a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) L(a(a(x1))) -> L(a(b(c(x1)))) c(R(x1)) -> c(b(R(x1))) graph: d#(x1) -> a#(x1) -> a#(d(x1)) -> d#(a(x1)) a#(d(x1)) -> d#(a(x1)) -> d#(x1) -> a#(x1) a#(d(x1)) -> d#(a(x1)) -> d#(x1) -> b#(a(x1)) SCC Processor: #sccs: 1 #rules: 2 #arcs: 3/9 DPs: d#(x1) -> a#(x1) a#(d(x1)) -> d#(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) a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) L(a(a(x1))) -> L(a(b(c(x1)))) c(R(x1)) -> c(b(R(x1))) Usable Rule Processor: DPs: d#(x1) -> a#(x1) a#(d(x1)) -> d#(a(x1)) TRS: a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) b(a(a(x1))) -> a(b(c(x1))) b(c(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) c(b(x1)) -> d(x1) c(R(x1)) -> c(b(R(x1))) Arctic Interpretation Processor: dimension: 1 usable rules: a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) b(a(a(x1))) -> a(b(c(x1))) b(c(a(x1))) -> a(b(c(x1))) interpretation: [d#](x0) = 8x0 + 0, [a#](x0) = x0, [R](x0) = x0, [d](x0) = 8x0 + 0, [c](x0) = 2x0 + 8, [b](x0) = 0, [a](x0) = x0 orientation: d#(x1) = 8x1 + 0 >= x1 = a#(x1) a#(d(x1)) = 8x1 + 0 >= 8x1 + 0 = d#(a(x1)) a(d(x1)) = 8x1 + 0 >= 8x1 + 0 = d(a(x1)) d(x1) = 8x1 + 0 >= 0 = b(a(x1)) b(a(a(x1))) = 0 >= 0 = a(b(c(x1))) b(c(a(x1))) = 0 >= 0 = a(b(c(x1))) c(a(x1)) = 2x1 + 8 >= 2x1 + 8 = a(c(x1)) c(b(x1)) = 8 >= 8x1 + 0 = d(x1) c(R(x1)) = 2x1 + 8 >= 8 = c(b(R(x1))) problem: DPs: a#(d(x1)) -> d#(a(x1)) TRS: a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) b(a(a(x1))) -> a(b(c(x1))) b(c(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) c(b(x1)) -> d(x1) c(R(x1)) -> c(b(R(x1))) Restore Modifier: DPs: a#(d(x1)) -> d#(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) a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) L(a(a(x1))) -> L(a(b(c(x1)))) c(R(x1)) -> c(b(R(x1))) EDG Processor: DPs: a#(d(x1)) -> d#(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) a(d(x1)) -> d(a(x1)) d(x1) -> b(a(x1)) L(a(a(x1))) -> L(a(b(c(x1)))) c(R(x1)) -> c(b(R(x1))) graph: SCC Processor: #sccs: 0 #rules: 0 #arcs: 0/1