/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)) c(b(x1)) -> b(a(x1)) L(a(a(x1))) -> L(a(b(c(x1)))) c(R(x1)) -> b(a(R(x1))) Proof: DP Processor: DPs: b#(a(a(x1))) -> c#(x1) b#(a(a(x1))) -> b#(c(x1)) c#(a(x1)) -> c#(x1) c#(b(x1)) -> b#(a(x1)) L#(a(a(x1))) -> c#(x1) L#(a(a(x1))) -> b#(c(x1)) L#(a(a(x1))) -> L#(a(b(c(x1)))) c#(R(x1)) -> b#(a(R(x1))) TRS: b(a(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) c(b(x1)) -> b(a(x1)) L(a(a(x1))) -> L(a(b(c(x1)))) c(R(x1)) -> b(a(R(x1))) TDG Processor: DPs: b#(a(a(x1))) -> c#(x1) b#(a(a(x1))) -> b#(c(x1)) c#(a(x1)) -> c#(x1) c#(b(x1)) -> b#(a(x1)) L#(a(a(x1))) -> c#(x1) L#(a(a(x1))) -> b#(c(x1)) L#(a(a(x1))) -> L#(a(b(c(x1)))) c#(R(x1)) -> b#(a(R(x1))) TRS: b(a(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) c(b(x1)) -> b(a(x1)) L(a(a(x1))) -> L(a(b(c(x1)))) c(R(x1)) -> b(a(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))) -> b#(c(x1)) L#(a(a(x1))) -> L#(a(b(c(x1)))) -> L#(a(a(x1))) -> c#(x1) L#(a(a(x1))) -> c#(x1) -> c#(R(x1)) -> b#(a(R(x1))) L#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> b#(a(x1)) L#(a(a(x1))) -> c#(x1) -> c#(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))) -> c#(x1) c#(R(x1)) -> b#(a(R(x1))) -> b#(a(a(x1))) -> b#(c(x1)) c#(R(x1)) -> b#(a(R(x1))) -> b#(a(a(x1))) -> c#(x1) c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(c(x1)) c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1) c#(a(x1)) -> c#(x1) -> c#(R(x1)) -> b#(a(R(x1))) c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> b#(a(x1)) c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1) b#(a(a(x1))) -> c#(x1) -> c#(R(x1)) -> b#(a(R(x1))) b#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> b#(a(x1)) b#(a(a(x1))) -> c#(x1) -> c#(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))) -> c#(x1) EDG Processor: DPs: b#(a(a(x1))) -> c#(x1) b#(a(a(x1))) -> b#(c(x1)) c#(a(x1)) -> c#(x1) c#(b(x1)) -> b#(a(x1)) L#(a(a(x1))) -> c#(x1) L#(a(a(x1))) -> b#(c(x1)) L#(a(a(x1))) -> L#(a(b(c(x1)))) c#(R(x1)) -> b#(a(R(x1))) TRS: b(a(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) c(b(x1)) -> b(a(x1)) L(a(a(x1))) -> L(a(b(c(x1)))) c(R(x1)) -> b(a(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))) -> L#(a(b(c(x1)))) L#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1) L#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> b#(a(x1)) L#(a(a(x1))) -> c#(x1) -> c#(R(x1)) -> b#(a(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)) c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> c#(x1) c#(b(x1)) -> b#(a(x1)) -> b#(a(a(x1))) -> b#(c(x1)) c#(a(x1)) -> c#(x1) -> c#(a(x1)) -> c#(x1) c#(a(x1)) -> c#(x1) -> c#(b(x1)) -> b#(a(x1)) c#(a(x1)) -> c#(x1) -> c#(R(x1)) -> b#(a(R(x1))) b#(a(a(x1))) -> c#(x1) -> c#(a(x1)) -> c#(x1) b#(a(a(x1))) -> c#(x1) -> c#(b(x1)) -> b#(a(x1)) b#(a(a(x1))) -> c#(x1) -> c#(R(x1)) -> b#(a(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)) SCC Processor: #sccs: 2 #rules: 5 #arcs: 18/64 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)) c(b(x1)) -> b(a(x1)) L(a(a(x1))) -> L(a(b(c(x1)))) c(R(x1)) -> b(a(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)) -> b(a(x1)) c(R(x1)) -> b(a(R(x1))) b(a(a(x1))) -> a(b(c(x1))) Arctic Interpretation Processor: dimension: 1 usable rules: c(a(x1)) -> a(c(x1)) c(b(x1)) -> b(a(x1)) c(R(x1)) -> b(a(R(x1))) b(a(a(x1))) -> a(b(c(x1))) interpretation: [L#](x0) = x0 + 0, [R](x0) = 0, [c](x0) = 1x0 + 1, [b](x0) = -1x0 + 0, [a](x0) = 1x0 + 1 orientation: L#(a(a(x1))) = 2x1 + 2 >= 1x1 + 1 = L#(a(b(c(x1)))) c(a(x1)) = 2x1 + 2 >= 2x1 + 2 = a(c(x1)) c(b(x1)) = x1 + 1 >= x1 + 0 = b(a(x1)) c(R(x1)) = 1 >= 0 = b(a(R(x1))) b(a(a(x1))) = 1x1 + 1 >= 1x1 + 1 = a(b(c(x1))) problem: DPs: TRS: c(a(x1)) -> a(c(x1)) c(b(x1)) -> b(a(x1)) c(R(x1)) -> b(a(R(x1))) b(a(a(x1))) -> a(b(c(x1))) Qed DPs: b#(a(a(x1))) -> b#(c(x1)) b#(a(a(x1))) -> c#(x1) c#(b(x1)) -> b#(a(x1)) c#(a(x1)) -> c#(x1) TRS: b(a(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) c(b(x1)) -> b(a(x1)) L(a(a(x1))) -> L(a(b(c(x1)))) c(R(x1)) -> b(a(R(x1))) Usable Rule Processor: DPs: b#(a(a(x1))) -> b#(c(x1)) b#(a(a(x1))) -> c#(x1) c#(b(x1)) -> b#(a(x1)) c#(a(x1)) -> c#(x1) TRS: c(a(x1)) -> a(c(x1)) c(b(x1)) -> b(a(x1)) c(R(x1)) -> b(a(R(x1))) b(a(a(x1))) -> a(b(c(x1))) Arctic Interpretation Processor: dimension: 1 usable rules: c(a(x1)) -> a(c(x1)) c(b(x1)) -> b(a(x1)) c(R(x1)) -> b(a(R(x1))) b(a(a(x1))) -> a(b(c(x1))) interpretation: [c#](x0) = 2x0, [b#](x0) = x0, [R](x0) = x0, [c](x0) = 1x0, [b](x0) = x0, [a](x0) = 1x0 orientation: b#(a(a(x1))) = 2x1 >= 1x1 = b#(c(x1)) b#(a(a(x1))) = 2x1 >= 2x1 = c#(x1) c#(b(x1)) = 2x1 >= 1x1 = b#(a(x1)) c#(a(x1)) = 3x1 >= 2x1 = c#(x1) c(a(x1)) = 2x1 >= 2x1 = a(c(x1)) c(b(x1)) = 1x1 >= 1x1 = b(a(x1)) c(R(x1)) = 1x1 >= 1x1 = b(a(R(x1))) b(a(a(x1))) = 2x1 >= 2x1 = a(b(c(x1))) problem: DPs: b#(a(a(x1))) -> c#(x1) TRS: c(a(x1)) -> a(c(x1)) c(b(x1)) -> b(a(x1)) c(R(x1)) -> b(a(R(x1))) b(a(a(x1))) -> a(b(c(x1))) Restore Modifier: DPs: b#(a(a(x1))) -> c#(x1) TRS: b(a(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) c(b(x1)) -> b(a(x1)) L(a(a(x1))) -> L(a(b(c(x1)))) c(R(x1)) -> b(a(R(x1))) EDG Processor: DPs: b#(a(a(x1))) -> c#(x1) TRS: b(a(a(x1))) -> a(b(c(x1))) c(a(x1)) -> a(c(x1)) c(b(x1)) -> b(a(x1)) L(a(a(x1))) -> L(a(b(c(x1)))) c(R(x1)) -> b(a(R(x1))) graph: SCC Processor: #sccs: 0 #rules: 0 #arcs: 0/1