/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(a(x1)) -> x1 b(b(x1)) -> c(c(c(c(x1)))) c(c(x1)) -> a(c(b(x1))) Proof: DP Processor: DPs: b#(b(x1)) -> c#(x1) b#(b(x1)) -> c#(c(x1)) b#(b(x1)) -> c#(c(c(x1))) b#(b(x1)) -> c#(c(c(c(x1)))) c#(c(x1)) -> b#(x1) c#(c(x1)) -> c#(b(x1)) c#(c(x1)) -> a#(c(b(x1))) TRS: a(a(x1)) -> x1 b(b(x1)) -> c(c(c(c(x1)))) c(c(x1)) -> a(c(b(x1))) TDG Processor: DPs: b#(b(x1)) -> c#(x1) b#(b(x1)) -> c#(c(x1)) b#(b(x1)) -> c#(c(c(x1))) b#(b(x1)) -> c#(c(c(c(x1)))) c#(c(x1)) -> b#(x1) c#(c(x1)) -> c#(b(x1)) c#(c(x1)) -> a#(c(b(x1))) TRS: a(a(x1)) -> x1 b(b(x1)) -> c(c(c(c(x1)))) c(c(x1)) -> a(c(b(x1))) graph: c#(c(x1)) -> c#(b(x1)) -> c#(c(x1)) -> a#(c(b(x1))) c#(c(x1)) -> c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) c#(c(x1)) -> c#(b(x1)) -> c#(c(x1)) -> b#(x1) c#(c(x1)) -> b#(x1) -> b#(b(x1)) -> c#(c(c(c(x1)))) c#(c(x1)) -> b#(x1) -> b#(b(x1)) -> c#(c(c(x1))) c#(c(x1)) -> b#(x1) -> b#(b(x1)) -> c#(c(x1)) c#(c(x1)) -> b#(x1) -> b#(b(x1)) -> c#(x1) b#(b(x1)) -> c#(c(c(c(x1)))) -> c#(c(x1)) -> a#(c(b(x1))) b#(b(x1)) -> c#(c(c(c(x1)))) -> c#(c(x1)) -> c#(b(x1)) b#(b(x1)) -> c#(c(c(c(x1)))) -> c#(c(x1)) -> b#(x1) b#(b(x1)) -> c#(c(c(x1))) -> c#(c(x1)) -> a#(c(b(x1))) b#(b(x1)) -> c#(c(c(x1))) -> c#(c(x1)) -> c#(b(x1)) b#(b(x1)) -> c#(c(c(x1))) -> c#(c(x1)) -> b#(x1) b#(b(x1)) -> c#(c(x1)) -> c#(c(x1)) -> a#(c(b(x1))) b#(b(x1)) -> c#(c(x1)) -> c#(c(x1)) -> c#(b(x1)) b#(b(x1)) -> c#(c(x1)) -> c#(c(x1)) -> b#(x1) b#(b(x1)) -> c#(x1) -> c#(c(x1)) -> a#(c(b(x1))) b#(b(x1)) -> c#(x1) -> c#(c(x1)) -> c#(b(x1)) b#(b(x1)) -> c#(x1) -> c#(c(x1)) -> b#(x1) SCC Processor: #sccs: 1 #rules: 6 #arcs: 19/49 DPs: c#(c(x1)) -> c#(b(x1)) c#(c(x1)) -> b#(x1) b#(b(x1)) -> c#(x1) b#(b(x1)) -> c#(c(x1)) b#(b(x1)) -> c#(c(c(x1))) b#(b(x1)) -> c#(c(c(c(x1)))) TRS: a(a(x1)) -> x1 b(b(x1)) -> c(c(c(c(x1)))) c(c(x1)) -> a(c(b(x1))) Arctic Interpretation Processor: dimension: 3 usable rules: a(a(x1)) -> x1 b(b(x1)) -> c(c(c(c(x1)))) c(c(x1)) -> a(c(b(x1))) interpretation: [c#](x0) = [-& 0 0 ]x0 + [0], [b#](x0) = [-& 0 -&]x0 + [0], [-& 0 1 ] [0] [c](x0) = [-& -& -&]x0 + [0] [-& 1 0 ] [1], [0 1 0 ] [0] [b](x0) = [-& 1 0 ]x0 + [1] [-& 0 -&] [0], [-& 0 0 ] [0 ] [a](x0) = [-& 0 -&]x0 + [-&] [0 0 -&] [1 ] orientation: c#(c(x1)) = [-& 1 0 ]x1 + [1] >= [-& 1 0 ]x1 + [1] = c#(b(x1)) c#(c(x1)) = [-& 1 0 ]x1 + [1] >= [-& 0 -&]x1 + [0] = b#(x1) b#(b(x1)) = [-& 1 0 ]x1 + [1] >= [-& 0 0 ]x1 + [0] = c#(x1) b#(b(x1)) = [-& 1 0 ]x1 + [1] >= [-& 1 0 ]x1 + [1] = c#(c(x1)) b#(b(x1)) = [-& 1 0 ]x1 + [1] >= [-& 1 0 ]x1 + [1] = c#(c(c(x1))) b#(b(x1)) = [-& 1 0 ]x1 + [1] >= [-& 1 0 ]x1 + [1] = c#(c(c(c(x1)))) [0 0 -&] [1 ] a(a(x1)) = [-& 0 -&]x1 + [-&] >= x1 = x1 [-& 0 0 ] [1 ] [0 2 1 ] [2] [-& 2 1 ] [2] b(b(x1)) = [-& 2 1 ]x1 + [2] >= [-& -& -&]x1 + [0] = c(c(c(c(x1)))) [-& 1 0 ] [1] [-& 1 0 ] [1] [-& 2 1 ] [2] [-& 2 1 ] [2] c(c(x1)) = [-& -& -&]x1 + [0] >= [-& -& -&]x1 + [0] = a(c(b(x1))) [-& 1 0 ] [1] [-& 1 0 ] [1] problem: DPs: c#(c(x1)) -> c#(b(x1)) b#(b(x1)) -> c#(x1) b#(b(x1)) -> c#(c(x1)) b#(b(x1)) -> c#(c(c(x1))) b#(b(x1)) -> c#(c(c(c(x1)))) TRS: a(a(x1)) -> x1 b(b(x1)) -> c(c(c(c(x1)))) c(c(x1)) -> a(c(b(x1))) Restore Modifier: DPs: c#(c(x1)) -> c#(b(x1)) b#(b(x1)) -> c#(x1) b#(b(x1)) -> c#(c(x1)) b#(b(x1)) -> c#(c(c(x1))) b#(b(x1)) -> c#(c(c(c(x1)))) TRS: a(a(x1)) -> x1 b(b(x1)) -> c(c(c(c(x1)))) c(c(x1)) -> a(c(b(x1))) EDG Processor: DPs: c#(c(x1)) -> c#(b(x1)) b#(b(x1)) -> c#(x1) b#(b(x1)) -> c#(c(x1)) b#(b(x1)) -> c#(c(c(x1))) b#(b(x1)) -> c#(c(c(c(x1)))) TRS: a(a(x1)) -> x1 b(b(x1)) -> c(c(c(c(x1)))) c(c(x1)) -> a(c(b(x1))) graph: c#(c(x1)) -> c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) b#(b(x1)) -> c#(c(c(c(x1)))) -> c#(c(x1)) -> c#(b(x1)) b#(b(x1)) -> c#(c(c(x1))) -> c#(c(x1)) -> c#(b(x1)) b#(b(x1)) -> c#(c(x1)) -> c#(c(x1)) -> c#(b(x1)) b#(b(x1)) -> c#(x1) -> c#(c(x1)) -> c#(b(x1)) SCC Processor: #sccs: 1 #rules: 1 #arcs: 5/25 DPs: c#(c(x1)) -> c#(b(x1)) TRS: a(a(x1)) -> x1 b(b(x1)) -> c(c(c(c(x1)))) c(c(x1)) -> a(c(b(x1))) Matrix Interpretation Processor: dim=5 interpretation: [c#](x0) = [0 0 1 0 0]x0 + [1], [1 0 0 0 0] [0] [0 1 0 0 0] [0] [c](x0) = [1 1 0 0 0]x0 + [1] [0 1 1 0 0] [1] [0 0 1 0 0] [0], [1 1 0 0 0] [1] [0 1 0 0 0] [0] [b](x0) = [1 0 0 0 0]x0 + [0] [1 0 0 0 1] [0] [0 1 1 0 0] [1], [0 0 0 0 1] [0 1 0 0 0] [a](x0) = [0 0 0 1 0]x0 [0 0 1 0 0] [1 0 0 0 0] orientation: c#(c(x1)) = [1 1 0 0 0]x1 + [2] >= [1 0 0 0 0]x1 + [1] = c#(b(x1)) a(a(x1)) = x1 >= x1 = x1 [1 2 0 0 0] [2] [1 0 0 0 0] [0] [0 1 0 0 0] [0] [0 1 0 0 0] [0] b(b(x1)) = [1 1 0 0 0]x1 + [1] >= [1 1 0 0 0]x1 + [1] = c(c(c(c(x1)))) [1 2 1 0 0] [2] [1 2 0 0 0] [2] [1 1 0 0 0] [1] [1 1 0 0 0] [1] [1 0 0 0 0] [0] [1 0 0 0 0] [0] [0 1 0 0 0] [0] [0 1 0 0 0] [0] c(c(x1)) = [1 1 0 0 0]x1 + [1] >= [1 1 0 0 0]x1 + [1] = a(c(b(x1))) [1 2 0 0 0] [2] [1 2 0 0 0] [2] [1 1 0 0 0] [1] [1 1 0 0 0] [1] problem: DPs: TRS: a(a(x1)) -> x1 b(b(x1)) -> c(c(c(c(x1)))) c(c(x1)) -> a(c(b(x1))) Qed