/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(a(a(x1)))) -> b(b(b(b(b(b(x1)))))) b(b(b(b(x1)))) -> c(c(c(c(c(c(x1)))))) c(c(c(c(x1)))) -> d(d(d(d(d(d(x1)))))) b(b(x1)) -> d(d(d(d(x1)))) c(c(d(d(d(d(x1)))))) -> a(a(x1)) Proof: DP Processor: DPs: a#(a(a(a(x1)))) -> b#(x1) a#(a(a(a(x1)))) -> b#(b(x1)) a#(a(a(a(x1)))) -> b#(b(b(x1))) a#(a(a(a(x1)))) -> b#(b(b(b(x1)))) a#(a(a(a(x1)))) -> b#(b(b(b(b(x1))))) a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) b#(b(b(b(x1)))) -> c#(x1) b#(b(b(b(x1)))) -> c#(c(x1)) b#(b(b(b(x1)))) -> c#(c(c(x1))) b#(b(b(b(x1)))) -> c#(c(c(c(x1)))) b#(b(b(b(x1)))) -> c#(c(c(c(c(x1))))) b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) c#(c(d(d(d(d(x1)))))) -> a#(x1) c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) TRS: a(a(a(a(x1)))) -> b(b(b(b(b(b(x1)))))) b(b(b(b(x1)))) -> c(c(c(c(c(c(x1)))))) c(c(c(c(x1)))) -> d(d(d(d(d(d(x1)))))) b(b(x1)) -> d(d(d(d(x1)))) c(c(d(d(d(d(x1)))))) -> a(a(x1)) TDG Processor: DPs: a#(a(a(a(x1)))) -> b#(x1) a#(a(a(a(x1)))) -> b#(b(x1)) a#(a(a(a(x1)))) -> b#(b(b(x1))) a#(a(a(a(x1)))) -> b#(b(b(b(x1)))) a#(a(a(a(x1)))) -> b#(b(b(b(b(x1))))) a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) b#(b(b(b(x1)))) -> c#(x1) b#(b(b(b(x1)))) -> c#(c(x1)) b#(b(b(b(x1)))) -> c#(c(c(x1))) b#(b(b(b(x1)))) -> c#(c(c(c(x1)))) b#(b(b(b(x1)))) -> c#(c(c(c(c(x1))))) b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) c#(c(d(d(d(d(x1)))))) -> a#(x1) c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) TRS: a(a(a(a(x1)))) -> b(b(b(b(b(b(x1)))))) b(b(b(b(x1)))) -> c(c(c(c(c(c(x1)))))) c(c(c(c(x1)))) -> d(d(d(d(d(d(x1)))))) b(b(x1)) -> d(d(d(d(x1)))) c(c(d(d(d(d(x1)))))) -> a(a(x1)) graph: c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(b(b(b(b(x1))))) c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(b(b(b(x1)))) c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(b(b(x1))) c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(b(x1)) c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) -> a#(a(a(a(x1)))) -> b#(x1) c#(c(d(d(d(d(x1)))))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) c#(c(d(d(d(d(x1)))))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(b(b(b(b(x1))))) c#(c(d(d(d(d(x1)))))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(b(b(b(x1)))) c#(c(d(d(d(d(x1)))))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(b(b(x1))) c#(c(d(d(d(d(x1)))))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(b(x1)) c#(c(d(d(d(d(x1)))))) -> a#(x1) -> a#(a(a(a(x1)))) -> b#(x1) b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) -> c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) -> c#(c(d(d(d(d(x1)))))) -> a#(x1) b#(b(b(b(x1)))) -> c#(c(c(c(c(x1))))) -> c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) b#(b(b(b(x1)))) -> c#(c(c(c(c(x1))))) -> c#(c(d(d(d(d(x1)))))) -> a#(x1) b#(b(b(b(x1)))) -> c#(c(c(c(x1)))) -> c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) b#(b(b(b(x1)))) -> c#(c(c(c(x1)))) -> c#(c(d(d(d(d(x1)))))) -> a#(x1) b#(b(b(b(x1)))) -> c#(c(c(x1))) -> c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) b#(b(b(b(x1)))) -> c#(c(c(x1))) -> c#(c(d(d(d(d(x1)))))) -> a#(x1) b#(b(b(b(x1)))) -> c#(c(x1)) -> c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) b#(b(b(b(x1)))) -> c#(c(x1)) -> c#(c(d(d(d(d(x1)))))) -> a#(x1) b#(b(b(b(x1)))) -> c#(x1) -> c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) b#(b(b(b(x1)))) -> c#(x1) -> c#(c(d(d(d(d(x1)))))) -> a#(x1) a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) -> b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) -> b#(b(b(b(x1)))) -> c#(c(c(c(c(x1))))) a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) -> b#(b(b(b(x1)))) -> c#(c(c(c(x1)))) a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) -> b#(b(b(b(x1)))) -> c#(c(c(x1))) a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) -> b#(b(b(b(x1)))) -> c#(c(x1)) a#(a(a(a(x1)))) -> b#(b(b(b(b(b(x1)))))) -> b#(b(b(b(x1)))) -> c#(x1) a#(a(a(a(x1)))) -> b#(b(b(b(b(x1))))) -> b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) a#(a(a(a(x1)))) -> b#(b(b(b(b(x1))))) -> b#(b(b(b(x1)))) -> c#(c(c(c(c(x1))))) a#(a(a(a(x1)))) -> b#(b(b(b(b(x1))))) -> b#(b(b(b(x1)))) -> c#(c(c(c(x1)))) a#(a(a(a(x1)))) -> b#(b(b(b(b(x1))))) -> b#(b(b(b(x1)))) -> c#(c(c(x1))) a#(a(a(a(x1)))) -> b#(b(b(b(b(x1))))) -> b#(b(b(b(x1)))) -> c#(c(x1)) a#(a(a(a(x1)))) -> b#(b(b(b(b(x1))))) -> b#(b(b(b(x1)))) -> c#(x1) a#(a(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) a#(a(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(b(b(x1)))) -> c#(c(c(c(c(x1))))) a#(a(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(b(b(x1)))) -> c#(c(c(c(x1)))) a#(a(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(b(b(x1)))) -> c#(c(c(x1))) a#(a(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(b(b(x1)))) -> c#(c(x1)) a#(a(a(a(x1)))) -> b#(b(b(b(x1)))) -> b#(b(b(b(x1)))) -> c#(x1) a#(a(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) a#(a(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(b(x1)))) -> c#(c(c(c(c(x1))))) a#(a(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(b(x1)))) -> c#(c(c(c(x1)))) a#(a(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(b(x1)))) -> c#(c(c(x1))) a#(a(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(b(x1)))) -> c#(c(x1)) a#(a(a(a(x1)))) -> b#(b(b(x1))) -> b#(b(b(b(x1)))) -> c#(x1) a#(a(a(a(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) a#(a(a(a(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> c#(c(c(c(c(x1))))) a#(a(a(a(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> c#(c(c(c(x1)))) a#(a(a(a(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> c#(c(c(x1))) a#(a(a(a(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> c#(c(x1)) a#(a(a(a(x1)))) -> b#(b(x1)) -> b#(b(b(b(x1)))) -> c#(x1) a#(a(a(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> c#(c(c(c(c(c(x1)))))) a#(a(a(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> c#(c(c(c(c(x1))))) a#(a(a(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> c#(c(c(c(x1)))) a#(a(a(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> c#(c(c(x1))) a#(a(a(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> c#(c(x1)) a#(a(a(a(x1)))) -> b#(x1) -> b#(b(b(b(x1)))) -> c#(x1) Matrix Interpretation Processor: dim=1 usable rules: a(a(a(a(x1)))) -> b(b(b(b(b(b(x1)))))) b(b(b(b(x1)))) -> c(c(c(c(c(c(x1)))))) c(c(c(c(x1)))) -> d(d(d(d(d(d(x1)))))) b(b(x1)) -> d(d(d(d(x1)))) c(c(d(d(d(d(x1)))))) -> a(a(x1)) interpretation: [c#](x0) = 1/2x0 + 1/2, [b#](x0) = 1/2x0 + 3/2, [a#](x0) = 1/2x0 + 5/2, [d](x0) = x0 + 2, [c](x0) = x0 + 3, [b](x0) = x0 + 9/2, [a](x0) = x0 + 7 orientation: a#(a(a(a(x1)))) = 1/2x1 + 13 >= 1/2x1 + 3/2 = b#(x1) a#(a(a(a(x1)))) = 1/2x1 + 13 >= 1/2x1 + 15/4 = b#(b(x1)) a#(a(a(a(x1)))) = 1/2x1 + 13 >= 1/2x1 + 6 = b#(b(b(x1))) a#(a(a(a(x1)))) = 1/2x1 + 13 >= 1/2x1 + 33/4 = b#(b(b(b(x1)))) a#(a(a(a(x1)))) = 1/2x1 + 13 >= 1/2x1 + 21/2 = b#(b(b(b(b(x1))))) a#(a(a(a(x1)))) = 1/2x1 + 13 >= 1/2x1 + 51/4 = b#(b(b(b(b(b(x1)))))) b#(b(b(b(x1)))) = 1/2x1 + 33/4 >= 1/2x1 + 1/2 = c#(x1) b#(b(b(b(x1)))) = 1/2x1 + 33/4 >= 1/2x1 + 2 = c#(c(x1)) b#(b(b(b(x1)))) = 1/2x1 + 33/4 >= 1/2x1 + 7/2 = c#(c(c(x1))) b#(b(b(b(x1)))) = 1/2x1 + 33/4 >= 1/2x1 + 5 = c#(c(c(c(x1)))) b#(b(b(b(x1)))) = 1/2x1 + 33/4 >= 1/2x1 + 13/2 = c#(c(c(c(c(x1))))) b#(b(b(b(x1)))) = 1/2x1 + 33/4 >= 1/2x1 + 8 = c#(c(c(c(c(c(x1)))))) c#(c(d(d(d(d(x1)))))) = 1/2x1 + 6 >= 1/2x1 + 5/2 = a#(x1) c#(c(d(d(d(d(x1)))))) = 1/2x1 + 6 >= 1/2x1 + 6 = a#(a(x1)) a(a(a(a(x1)))) = x1 + 28 >= x1 + 27 = b(b(b(b(b(b(x1)))))) b(b(b(b(x1)))) = x1 + 18 >= x1 + 18 = c(c(c(c(c(c(x1)))))) c(c(c(c(x1)))) = x1 + 12 >= x1 + 12 = d(d(d(d(d(d(x1)))))) b(b(x1)) = x1 + 9 >= x1 + 8 = d(d(d(d(x1)))) c(c(d(d(d(d(x1)))))) = x1 + 14 >= x1 + 14 = a(a(x1)) problem: DPs: c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) TRS: a(a(a(a(x1)))) -> b(b(b(b(b(b(x1)))))) b(b(b(b(x1)))) -> c(c(c(c(c(c(x1)))))) c(c(c(c(x1)))) -> d(d(d(d(d(d(x1)))))) b(b(x1)) -> d(d(d(d(x1)))) c(c(d(d(d(d(x1)))))) -> a(a(x1)) Restore Modifier: DPs: c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) TRS: a(a(a(a(x1)))) -> b(b(b(b(b(b(x1)))))) b(b(b(b(x1)))) -> c(c(c(c(c(c(x1)))))) c(c(c(c(x1)))) -> d(d(d(d(d(d(x1)))))) b(b(x1)) -> d(d(d(d(x1)))) c(c(d(d(d(d(x1)))))) -> a(a(x1)) EDG Processor: DPs: c#(c(d(d(d(d(x1)))))) -> a#(a(x1)) TRS: a(a(a(a(x1)))) -> b(b(b(b(b(b(x1)))))) b(b(b(b(x1)))) -> c(c(c(c(c(c(x1)))))) c(c(c(c(x1)))) -> d(d(d(d(d(d(x1)))))) b(b(x1)) -> d(d(d(d(x1)))) c(c(d(d(d(d(x1)))))) -> a(a(x1)) graph: SCC Processor: #sccs: 0 #rules: 0 #arcs: 0/1