/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: a(l(x1)) -> l(a(x1)) a(c(x1)) -> c(a(x1)) c(a(r(x1))) -> r(a(x1)) l(r(a(a(x1)))) -> a(a(l(c(c(c(r(x1))))))) Proof: DP Processor: DPs: a#(l(x1)) -> a#(x1) a#(l(x1)) -> l#(a(x1)) a#(c(x1)) -> a#(x1) a#(c(x1)) -> c#(a(x1)) c#(a(r(x1))) -> a#(x1) l#(r(a(a(x1)))) -> c#(r(x1)) l#(r(a(a(x1)))) -> c#(c(r(x1))) l#(r(a(a(x1)))) -> c#(c(c(r(x1)))) l#(r(a(a(x1)))) -> l#(c(c(c(r(x1))))) l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) TRS: a(l(x1)) -> l(a(x1)) a(c(x1)) -> c(a(x1)) c(a(r(x1))) -> r(a(x1)) l(r(a(a(x1)))) -> a(a(l(c(c(c(r(x1))))))) TDG Processor: DPs: a#(l(x1)) -> a#(x1) a#(l(x1)) -> l#(a(x1)) a#(c(x1)) -> a#(x1) a#(c(x1)) -> c#(a(x1)) c#(a(r(x1))) -> a#(x1) l#(r(a(a(x1)))) -> c#(r(x1)) l#(r(a(a(x1)))) -> c#(c(r(x1))) l#(r(a(a(x1)))) -> c#(c(c(r(x1)))) l#(r(a(a(x1)))) -> l#(c(c(c(r(x1))))) l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) TRS: a(l(x1)) -> l(a(x1)) a(c(x1)) -> c(a(x1)) c(a(r(x1))) -> r(a(x1)) l(r(a(a(x1)))) -> a(a(l(c(c(c(r(x1))))))) graph: c#(a(r(x1))) -> a#(x1) -> a#(c(x1)) -> c#(a(x1)) c#(a(r(x1))) -> a#(x1) -> a#(c(x1)) -> a#(x1) c#(a(r(x1))) -> a#(x1) -> a#(l(x1)) -> l#(a(x1)) c#(a(r(x1))) -> a#(x1) -> a#(l(x1)) -> a#(x1) l#(r(a(a(x1)))) -> c#(r(x1)) -> c#(a(r(x1))) -> a#(x1) l#(r(a(a(x1)))) -> c#(c(r(x1))) -> c#(a(r(x1))) -> a#(x1) l#(r(a(a(x1)))) -> c#(c(c(r(x1)))) -> c#(a(r(x1))) -> a#(x1) l#(r(a(a(x1)))) -> l#(c(c(c(r(x1))))) -> l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) l#(r(a(a(x1)))) -> l#(c(c(c(r(x1))))) -> l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) l#(r(a(a(x1)))) -> l#(c(c(c(r(x1))))) -> l#(r(a(a(x1)))) -> l#(c(c(c(r(x1))))) l#(r(a(a(x1)))) -> l#(c(c(c(r(x1))))) -> l#(r(a(a(x1)))) -> c#(c(c(r(x1)))) l#(r(a(a(x1)))) -> l#(c(c(c(r(x1))))) -> l#(r(a(a(x1)))) -> c#(c(r(x1))) l#(r(a(a(x1)))) -> l#(c(c(c(r(x1))))) -> l#(r(a(a(x1)))) -> c#(r(x1)) l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) -> a#(c(x1)) -> c#(a(x1)) l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) -> a#(c(x1)) -> a#(x1) l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) -> a#(l(x1)) -> l#(a(x1)) l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) -> a#(l(x1)) -> a#(x1) l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) -> a#(c(x1)) -> c#(a(x1)) l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) -> a#(c(x1)) -> a#(x1) l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) -> a#(l(x1)) -> l#(a(x1)) l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) -> a#(l(x1)) -> a#(x1) a#(c(x1)) -> c#(a(x1)) -> c#(a(r(x1))) -> a#(x1) a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> c#(a(x1)) a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> a#(x1) a#(c(x1)) -> a#(x1) -> a#(l(x1)) -> l#(a(x1)) a#(c(x1)) -> a#(x1) -> a#(l(x1)) -> a#(x1) a#(l(x1)) -> l#(a(x1)) -> l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) a#(l(x1)) -> l#(a(x1)) -> l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) a#(l(x1)) -> l#(a(x1)) -> l#(r(a(a(x1)))) -> l#(c(c(c(r(x1))))) a#(l(x1)) -> l#(a(x1)) -> l#(r(a(a(x1)))) -> c#(c(c(r(x1)))) a#(l(x1)) -> l#(a(x1)) -> l#(r(a(a(x1)))) -> c#(c(r(x1))) a#(l(x1)) -> l#(a(x1)) -> l#(r(a(a(x1)))) -> c#(r(x1)) a#(l(x1)) -> a#(x1) -> a#(c(x1)) -> c#(a(x1)) a#(l(x1)) -> a#(x1) -> a#(c(x1)) -> a#(x1) a#(l(x1)) -> a#(x1) -> a#(l(x1)) -> l#(a(x1)) a#(l(x1)) -> a#(x1) -> a#(l(x1)) -> a#(x1) EDG Processor: DPs: a#(l(x1)) -> a#(x1) a#(l(x1)) -> l#(a(x1)) a#(c(x1)) -> a#(x1) a#(c(x1)) -> c#(a(x1)) c#(a(r(x1))) -> a#(x1) l#(r(a(a(x1)))) -> c#(r(x1)) l#(r(a(a(x1)))) -> c#(c(r(x1))) l#(r(a(a(x1)))) -> c#(c(c(r(x1)))) l#(r(a(a(x1)))) -> l#(c(c(c(r(x1))))) l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) TRS: a(l(x1)) -> l(a(x1)) a(c(x1)) -> c(a(x1)) c(a(r(x1))) -> r(a(x1)) l(r(a(a(x1)))) -> a(a(l(c(c(c(r(x1))))))) graph: c#(a(r(x1))) -> a#(x1) -> a#(l(x1)) -> a#(x1) c#(a(r(x1))) -> a#(x1) -> a#(l(x1)) -> l#(a(x1)) c#(a(r(x1))) -> a#(x1) -> a#(c(x1)) -> a#(x1) c#(a(r(x1))) -> a#(x1) -> a#(c(x1)) -> c#(a(x1)) l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) -> a#(l(x1)) -> a#(x1) l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) -> a#(l(x1)) -> l#(a(x1)) l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) -> a#(c(x1)) -> a#(x1) l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) -> a#(c(x1)) -> c#(a(x1)) l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) -> a#(l(x1)) -> a#(x1) l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) -> a#(l(x1)) -> l#(a(x1)) a#(c(x1)) -> c#(a(x1)) -> c#(a(r(x1))) -> a#(x1) a#(c(x1)) -> a#(x1) -> a#(l(x1)) -> a#(x1) a#(c(x1)) -> a#(x1) -> a#(l(x1)) -> l#(a(x1)) a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> a#(x1) a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> c#(a(x1)) a#(l(x1)) -> l#(a(x1)) -> l#(r(a(a(x1)))) -> c#(r(x1)) a#(l(x1)) -> l#(a(x1)) -> l#(r(a(a(x1)))) -> c#(c(r(x1))) a#(l(x1)) -> l#(a(x1)) -> l#(r(a(a(x1)))) -> c#(c(c(r(x1)))) a#(l(x1)) -> l#(a(x1)) -> l#(r(a(a(x1)))) -> l#(c(c(c(r(x1))))) a#(l(x1)) -> l#(a(x1)) -> l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) a#(l(x1)) -> l#(a(x1)) -> l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) a#(l(x1)) -> a#(x1) -> a#(l(x1)) -> a#(x1) a#(l(x1)) -> a#(x1) -> a#(l(x1)) -> l#(a(x1)) a#(l(x1)) -> a#(x1) -> a#(c(x1)) -> a#(x1) a#(l(x1)) -> a#(x1) -> a#(c(x1)) -> c#(a(x1)) SCC Processor: #sccs: 1 #rules: 7 #arcs: 25/121 DPs: c#(a(r(x1))) -> a#(x1) a#(c(x1)) -> c#(a(x1)) a#(c(x1)) -> a#(x1) a#(l(x1)) -> l#(a(x1)) l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) a#(l(x1)) -> a#(x1) l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) TRS: a(l(x1)) -> l(a(x1)) a(c(x1)) -> c(a(x1)) c(a(r(x1))) -> r(a(x1)) l(r(a(a(x1)))) -> a(a(l(c(c(c(r(x1))))))) Arctic Interpretation Processor: dimension: 1 usable rules: a(l(x1)) -> l(a(x1)) a(c(x1)) -> c(a(x1)) c(a(r(x1))) -> r(a(x1)) l(r(a(a(x1)))) -> a(a(l(c(c(c(r(x1))))))) interpretation: [c#](x0) = x0 + 0, [l#](x0) = 1x0 + 10, [a#](x0) = x0 + 0, [r](x0) = 8x0, [c](x0) = x0, [a](x0) = x0, [l](x0) = 1x0 + 10 orientation: c#(a(r(x1))) = 8x1 + 0 >= x1 + 0 = a#(x1) a#(c(x1)) = x1 + 0 >= x1 + 0 = c#(a(x1)) a#(c(x1)) = x1 + 0 >= x1 + 0 = a#(x1) a#(l(x1)) = 1x1 + 10 >= 1x1 + 10 = l#(a(x1)) l#(r(a(a(x1)))) = 9x1 + 10 >= 9x1 + 10 = a#(a(l(c(c(c(r(x1))))))) a#(l(x1)) = 1x1 + 10 >= x1 + 0 = a#(x1) l#(r(a(a(x1)))) = 9x1 + 10 >= 9x1 + 10 = a#(l(c(c(c(r(x1)))))) a(l(x1)) = 1x1 + 10 >= 1x1 + 10 = l(a(x1)) a(c(x1)) = x1 >= x1 = c(a(x1)) c(a(r(x1))) = 8x1 >= 8x1 = r(a(x1)) l(r(a(a(x1)))) = 9x1 + 10 >= 9x1 + 10 = a(a(l(c(c(c(r(x1))))))) problem: DPs: c#(a(r(x1))) -> a#(x1) a#(c(x1)) -> c#(a(x1)) a#(c(x1)) -> a#(x1) a#(l(x1)) -> l#(a(x1)) l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) TRS: a(l(x1)) -> l(a(x1)) a(c(x1)) -> c(a(x1)) c(a(r(x1))) -> r(a(x1)) l(r(a(a(x1)))) -> a(a(l(c(c(c(r(x1))))))) Restore Modifier: DPs: c#(a(r(x1))) -> a#(x1) a#(c(x1)) -> c#(a(x1)) a#(c(x1)) -> a#(x1) a#(l(x1)) -> l#(a(x1)) l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) TRS: a(l(x1)) -> l(a(x1)) a(c(x1)) -> c(a(x1)) c(a(r(x1))) -> r(a(x1)) l(r(a(a(x1)))) -> a(a(l(c(c(c(r(x1))))))) EDG Processor: DPs: c#(a(r(x1))) -> a#(x1) a#(c(x1)) -> c#(a(x1)) a#(c(x1)) -> a#(x1) a#(l(x1)) -> l#(a(x1)) l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) TRS: a(l(x1)) -> l(a(x1)) a(c(x1)) -> c(a(x1)) c(a(r(x1))) -> r(a(x1)) l(r(a(a(x1)))) -> a(a(l(c(c(c(r(x1))))))) graph: c#(a(r(x1))) -> a#(x1) -> a#(c(x1)) -> c#(a(x1)) c#(a(r(x1))) -> a#(x1) -> a#(c(x1)) -> a#(x1) c#(a(r(x1))) -> a#(x1) -> a#(l(x1)) -> l#(a(x1)) l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) -> a#(c(x1)) -> c#(a(x1)) l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) -> a#(c(x1)) -> a#(x1) l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) -> a#(l(x1)) -> l#(a(x1)) l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) -> a#(l(x1)) -> l#(a(x1)) a#(c(x1)) -> c#(a(x1)) -> c#(a(r(x1))) -> a#(x1) a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> c#(a(x1)) a#(c(x1)) -> a#(x1) -> a#(c(x1)) -> a#(x1) a#(c(x1)) -> a#(x1) -> a#(l(x1)) -> l#(a(x1)) a#(l(x1)) -> l#(a(x1)) -> l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) a#(l(x1)) -> l#(a(x1)) -> l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) Arctic Interpretation Processor: dimension: 1 usable rules: a(l(x1)) -> l(a(x1)) a(c(x1)) -> c(a(x1)) c(a(r(x1))) -> r(a(x1)) l(r(a(a(x1)))) -> a(a(l(c(c(c(r(x1))))))) interpretation: [c#](x0) = x0 + 1, [l#](x0) = 5, [a#](x0) = 1x0 + 0, [r](x0) = 2x0, [c](x0) = 2x0 + 0, [a](x0) = x0, [l](x0) = 4 orientation: c#(a(r(x1))) = 2x1 + 1 >= 1x1 + 0 = a#(x1) a#(c(x1)) = 3x1 + 1 >= x1 + 1 = c#(a(x1)) a#(c(x1)) = 3x1 + 1 >= 1x1 + 0 = a#(x1) a#(l(x1)) = 5 >= 5 = l#(a(x1)) l#(r(a(a(x1)))) = 5 >= 5 = a#(a(l(c(c(c(r(x1))))))) l#(r(a(a(x1)))) = 5 >= 5 = a#(l(c(c(c(r(x1)))))) a(l(x1)) = 4 >= 4 = l(a(x1)) a(c(x1)) = 2x1 + 0 >= 2x1 + 0 = c(a(x1)) c(a(r(x1))) = 4x1 + 0 >= 2x1 = r(a(x1)) l(r(a(a(x1)))) = 4 >= 4 = a(a(l(c(c(c(r(x1))))))) problem: DPs: a#(c(x1)) -> c#(a(x1)) a#(l(x1)) -> l#(a(x1)) l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) TRS: a(l(x1)) -> l(a(x1)) a(c(x1)) -> c(a(x1)) c(a(r(x1))) -> r(a(x1)) l(r(a(a(x1)))) -> a(a(l(c(c(c(r(x1))))))) Restore Modifier: DPs: a#(c(x1)) -> c#(a(x1)) a#(l(x1)) -> l#(a(x1)) l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) TRS: a(l(x1)) -> l(a(x1)) a(c(x1)) -> c(a(x1)) c(a(r(x1))) -> r(a(x1)) l(r(a(a(x1)))) -> a(a(l(c(c(c(r(x1))))))) EDG Processor: DPs: a#(c(x1)) -> c#(a(x1)) a#(l(x1)) -> l#(a(x1)) l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) TRS: a(l(x1)) -> l(a(x1)) a(c(x1)) -> c(a(x1)) c(a(r(x1))) -> r(a(x1)) l(r(a(a(x1)))) -> a(a(l(c(c(c(r(x1))))))) graph: l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) -> a#(l(x1)) -> l#(a(x1)) l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) -> a#(c(x1)) -> c#(a(x1)) l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) -> a#(l(x1)) -> l#(a(x1)) a#(l(x1)) -> l#(a(x1)) -> l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) a#(l(x1)) -> l#(a(x1)) -> l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) SCC Processor: #sccs: 1 #rules: 3 #arcs: 5/16 DPs: l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) a#(l(x1)) -> l#(a(x1)) l#(r(a(a(x1)))) -> a#(l(c(c(c(r(x1)))))) TRS: a(l(x1)) -> l(a(x1)) a(c(x1)) -> c(a(x1)) c(a(r(x1))) -> r(a(x1)) l(r(a(a(x1)))) -> a(a(l(c(c(c(r(x1))))))) Arctic Interpretation Processor: dimension: 1 usable rules: a(l(x1)) -> l(a(x1)) a(c(x1)) -> c(a(x1)) c(a(r(x1))) -> r(a(x1)) l(r(a(a(x1)))) -> a(a(l(c(c(c(r(x1))))))) interpretation: [l#](x0) = 3x0, [a#](x0) = 4x0, [r](x0) = x0, [c](x0) = x0, [a](x0) = 1x0, [l](x0) = x0 orientation: l#(r(a(a(x1)))) = 5x1 >= 5x1 = a#(a(l(c(c(c(r(x1))))))) a#(l(x1)) = 4x1 >= 4x1 = l#(a(x1)) l#(r(a(a(x1)))) = 5x1 >= 4x1 = a#(l(c(c(c(r(x1)))))) a(l(x1)) = 1x1 >= 1x1 = l(a(x1)) a(c(x1)) = 1x1 >= 1x1 = c(a(x1)) c(a(r(x1))) = 1x1 >= 1x1 = r(a(x1)) l(r(a(a(x1)))) = 2x1 >= 2x1 = a(a(l(c(c(c(r(x1))))))) problem: DPs: l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) a#(l(x1)) -> l#(a(x1)) TRS: a(l(x1)) -> l(a(x1)) a(c(x1)) -> c(a(x1)) c(a(r(x1))) -> r(a(x1)) l(r(a(a(x1)))) -> a(a(l(c(c(c(r(x1))))))) Restore Modifier: DPs: l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) a#(l(x1)) -> l#(a(x1)) TRS: a(l(x1)) -> l(a(x1)) a(c(x1)) -> c(a(x1)) c(a(r(x1))) -> r(a(x1)) l(r(a(a(x1)))) -> a(a(l(c(c(c(r(x1))))))) EDG Processor: DPs: l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) a#(l(x1)) -> l#(a(x1)) TRS: a(l(x1)) -> l(a(x1)) a(c(x1)) -> c(a(x1)) c(a(r(x1))) -> r(a(x1)) l(r(a(a(x1)))) -> a(a(l(c(c(c(r(x1))))))) graph: l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) -> a#(l(x1)) -> l#(a(x1)) a#(l(x1)) -> l#(a(x1)) -> l#(r(a(a(x1)))) -> a#(a(l(c(c(c(r(x1))))))) Matrix Interpretation Processor: dim=1 usable rules: a(l(x1)) -> l(a(x1)) a(c(x1)) -> c(a(x1)) c(a(r(x1))) -> r(a(x1)) l(r(a(a(x1)))) -> a(a(l(c(c(c(r(x1))))))) interpretation: [l#](x0) = 13/2x0 + 2, [a#](x0) = 9/2x0, [r](x0) = 1, [c](x0) = 1/2x0, [a](x0) = 2x0, [l](x0) = 7/2x0 + 1/2 orientation: l#(r(a(a(x1)))) = 17/2 >= 135/16 = a#(a(l(c(c(c(r(x1))))))) a#(l(x1)) = 63/4x1 + 9/4 >= 13x1 + 2 = l#(a(x1)) a(l(x1)) = 7x1 + 1 >= 7x1 + 1/2 = l(a(x1)) a(c(x1)) = x1 >= x1 = c(a(x1)) c(a(r(x1))) = 1 >= 1 = r(a(x1)) l(r(a(a(x1)))) = 4 >= 15/4 = a(a(l(c(c(c(r(x1))))))) problem: DPs: TRS: a(l(x1)) -> l(a(x1)) a(c(x1)) -> c(a(x1)) c(a(r(x1))) -> r(a(x1)) l(r(a(a(x1)))) -> a(a(l(c(c(c(r(x1))))))) Qed