/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem: strict: c(a(c(x1))) -> a(b(b(x1))) c(c(c(x1))) -> a(a(a(x1))) weak: b(b(c(x1))) -> c(a(c(x1))) a(a(c(x1))) -> c(a(c(x1))) a(b(c(x1))) -> a(c(b(x1))) c(c(b(x1))) -> b(b(c(x1))) Proof: Arctic Interpretation Processor: dimension: 2 interpretation: [0 -&] [a](x0) = [-& -&]x0, [0 0 ] [c](x0) = [-& 2 ]x0, [0 -&] [b](x0) = [0 0 ]x0 orientation: [0 0 ] [0 -&] c(a(c(x1))) = [-& -&]x1 >= [-& -&]x1 = a(b(b(x1))) [0 4 ] [0 -&] c(c(c(x1))) = [-& 6 ]x1 >= [-& -&]x1 = a(a(a(x1))) [0 0] [0 0 ] b(b(c(x1))) = [0 2]x1 >= [-& -&]x1 = c(a(c(x1))) [0 0 ] [0 0 ] a(a(c(x1))) = [-& -&]x1 >= [-& -&]x1 = c(a(c(x1))) [0 0 ] [0 0 ] a(b(c(x1))) = [-& -&]x1 >= [-& -&]x1 = a(c(b(x1))) [2 2] [0 0] c(c(b(x1))) = [4 4]x1 >= [0 2]x1 = b(b(c(x1))) problem: strict: c(a(c(x1))) -> a(b(b(x1))) c(c(c(x1))) -> a(a(a(x1))) weak: b(b(c(x1))) -> c(a(c(x1))) a(a(c(x1))) -> c(a(c(x1))) a(b(c(x1))) -> a(c(b(x1))) RT Transformation Processor: c(a(c(x1))) -> a(b(b(x1))) c(c(c(x1))) -> a(a(a(x1))) b(b(c(x1))) -> c(a(c(x1))) a(a(c(x1))) -> c(a(c(x1))) a(b(c(x1))) -> a(c(b(x1))) DP Processor: DPs: c#(a(c(x1))) -> b#(x1) c#(a(c(x1))) -> b#(b(x1)) c#(a(c(x1))) -> a#(b(b(x1))) c#(c(c(x1))) -> a#(x1) c#(c(c(x1))) -> a#(a(x1)) c#(c(c(x1))) -> a#(a(a(x1))) b#(b(c(x1))) -> a#(c(x1)) b#(b(c(x1))) -> c#(a(c(x1))) a#(a(c(x1))) -> c#(a(c(x1))) a#(b(c(x1))) -> b#(x1) a#(b(c(x1))) -> c#(b(x1)) a#(b(c(x1))) -> a#(c(b(x1))) TRS: c(a(c(x1))) -> a(b(b(x1))) c(c(c(x1))) -> a(a(a(x1))) b(b(c(x1))) -> c(a(c(x1))) a(a(c(x1))) -> c(a(c(x1))) a(b(c(x1))) -> a(c(b(x1))) TDG Processor: DPs: c#(a(c(x1))) -> b#(x1) c#(a(c(x1))) -> b#(b(x1)) c#(a(c(x1))) -> a#(b(b(x1))) c#(c(c(x1))) -> a#(x1) c#(c(c(x1))) -> a#(a(x1)) c#(c(c(x1))) -> a#(a(a(x1))) b#(b(c(x1))) -> a#(c(x1)) b#(b(c(x1))) -> c#(a(c(x1))) a#(a(c(x1))) -> c#(a(c(x1))) a#(b(c(x1))) -> b#(x1) a#(b(c(x1))) -> c#(b(x1)) a#(b(c(x1))) -> a#(c(b(x1))) TRS: c(a(c(x1))) -> a(b(b(x1))) c(c(c(x1))) -> a(a(a(x1))) b(b(c(x1))) -> c(a(c(x1))) a(a(c(x1))) -> c(a(c(x1))) a(b(c(x1))) -> a(c(b(x1))) graph: a#(b(c(x1))) -> a#(c(b(x1))) -> a#(b(c(x1))) -> a#(c(b(x1))) a#(b(c(x1))) -> a#(c(b(x1))) -> a#(b(c(x1))) -> c#(b(x1)) a#(b(c(x1))) -> a#(c(b(x1))) -> a#(b(c(x1))) -> b#(x1) a#(b(c(x1))) -> a#(c(b(x1))) -> a#(a(c(x1))) -> c#(a(c(x1))) a#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> c#(a(c(x1))) a#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> a#(c(x1)) a#(b(c(x1))) -> c#(b(x1)) -> c#(c(c(x1))) -> a#(a(a(x1))) a#(b(c(x1))) -> c#(b(x1)) -> c#(c(c(x1))) -> a#(a(x1)) a#(b(c(x1))) -> c#(b(x1)) -> c#(c(c(x1))) -> a#(x1) a#(b(c(x1))) -> c#(b(x1)) -> c#(a(c(x1))) -> a#(b(b(x1))) a#(b(c(x1))) -> c#(b(x1)) -> c#(a(c(x1))) -> b#(b(x1)) a#(b(c(x1))) -> c#(b(x1)) -> c#(a(c(x1))) -> b#(x1) a#(a(c(x1))) -> c#(a(c(x1))) -> c#(c(c(x1))) -> a#(a(a(x1))) a#(a(c(x1))) -> c#(a(c(x1))) -> c#(c(c(x1))) -> a#(a(x1)) a#(a(c(x1))) -> c#(a(c(x1))) -> c#(c(c(x1))) -> a#(x1) a#(a(c(x1))) -> c#(a(c(x1))) -> c#(a(c(x1))) -> a#(b(b(x1))) a#(a(c(x1))) -> c#(a(c(x1))) -> c#(a(c(x1))) -> b#(b(x1)) a#(a(c(x1))) -> c#(a(c(x1))) -> c#(a(c(x1))) -> b#(x1) b#(b(c(x1))) -> a#(c(x1)) -> a#(b(c(x1))) -> a#(c(b(x1))) b#(b(c(x1))) -> a#(c(x1)) -> a#(b(c(x1))) -> c#(b(x1)) b#(b(c(x1))) -> a#(c(x1)) -> a#(b(c(x1))) -> b#(x1) b#(b(c(x1))) -> a#(c(x1)) -> a#(a(c(x1))) -> c#(a(c(x1))) b#(b(c(x1))) -> c#(a(c(x1))) -> c#(c(c(x1))) -> a#(a(a(x1))) b#(b(c(x1))) -> c#(a(c(x1))) -> c#(c(c(x1))) -> a#(a(x1)) b#(b(c(x1))) -> c#(a(c(x1))) -> c#(c(c(x1))) -> a#(x1) b#(b(c(x1))) -> c#(a(c(x1))) -> c#(a(c(x1))) -> a#(b(b(x1))) b#(b(c(x1))) -> c#(a(c(x1))) -> c#(a(c(x1))) -> b#(b(x1)) b#(b(c(x1))) -> c#(a(c(x1))) -> c#(a(c(x1))) -> b#(x1) c#(a(c(x1))) -> a#(b(b(x1))) -> a#(b(c(x1))) -> a#(c(b(x1))) c#(a(c(x1))) -> a#(b(b(x1))) -> a#(b(c(x1))) -> c#(b(x1)) c#(a(c(x1))) -> a#(b(b(x1))) -> a#(b(c(x1))) -> b#(x1) c#(a(c(x1))) -> a#(b(b(x1))) -> a#(a(c(x1))) -> c#(a(c(x1))) c#(a(c(x1))) -> b#(b(x1)) -> b#(b(c(x1))) -> c#(a(c(x1))) c#(a(c(x1))) -> b#(b(x1)) -> b#(b(c(x1))) -> a#(c(x1)) c#(a(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> c#(a(c(x1))) c#(a(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> a#(c(x1)) c#(c(c(x1))) -> a#(a(a(x1))) -> a#(b(c(x1))) -> a#(c(b(x1))) c#(c(c(x1))) -> a#(a(a(x1))) -> a#(b(c(x1))) -> c#(b(x1)) c#(c(c(x1))) -> a#(a(a(x1))) -> a#(b(c(x1))) -> b#(x1) c#(c(c(x1))) -> a#(a(a(x1))) -> a#(a(c(x1))) -> c#(a(c(x1))) c#(c(c(x1))) -> a#(a(x1)) -> a#(b(c(x1))) -> a#(c(b(x1))) c#(c(c(x1))) -> a#(a(x1)) -> a#(b(c(x1))) -> c#(b(x1)) c#(c(c(x1))) -> a#(a(x1)) -> a#(b(c(x1))) -> b#(x1) c#(c(c(x1))) -> a#(a(x1)) -> a#(a(c(x1))) -> c#(a(c(x1))) c#(c(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> a#(c(b(x1))) c#(c(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> c#(b(x1)) c#(c(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> b#(x1) c#(c(c(x1))) -> a#(x1) -> a#(a(c(x1))) -> c#(a(c(x1))) EDG Processor: DPs: c#(a(c(x1))) -> b#(x1) c#(a(c(x1))) -> b#(b(x1)) c#(a(c(x1))) -> a#(b(b(x1))) c#(c(c(x1))) -> a#(x1) c#(c(c(x1))) -> a#(a(x1)) c#(c(c(x1))) -> a#(a(a(x1))) b#(b(c(x1))) -> a#(c(x1)) b#(b(c(x1))) -> c#(a(c(x1))) a#(a(c(x1))) -> c#(a(c(x1))) a#(b(c(x1))) -> b#(x1) a#(b(c(x1))) -> c#(b(x1)) a#(b(c(x1))) -> a#(c(b(x1))) TRS: c(a(c(x1))) -> a(b(b(x1))) c(c(c(x1))) -> a(a(a(x1))) b(b(c(x1))) -> c(a(c(x1))) a(a(c(x1))) -> c(a(c(x1))) a(b(c(x1))) -> a(c(b(x1))) graph: a#(b(c(x1))) -> a#(c(b(x1))) -> a#(a(c(x1))) -> c#(a(c(x1))) a#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> a#(c(x1)) a#(b(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> c#(a(c(x1))) a#(b(c(x1))) -> c#(b(x1)) -> c#(a(c(x1))) -> b#(x1) a#(b(c(x1))) -> c#(b(x1)) -> c#(a(c(x1))) -> b#(b(x1)) a#(b(c(x1))) -> c#(b(x1)) -> c#(a(c(x1))) -> a#(b(b(x1))) a#(b(c(x1))) -> c#(b(x1)) -> c#(c(c(x1))) -> a#(x1) a#(b(c(x1))) -> c#(b(x1)) -> c#(c(c(x1))) -> a#(a(x1)) a#(b(c(x1))) -> c#(b(x1)) -> c#(c(c(x1))) -> a#(a(a(x1))) a#(a(c(x1))) -> c#(a(c(x1))) -> c#(a(c(x1))) -> b#(x1) a#(a(c(x1))) -> c#(a(c(x1))) -> c#(a(c(x1))) -> b#(b(x1)) a#(a(c(x1))) -> c#(a(c(x1))) -> c#(a(c(x1))) -> a#(b(b(x1))) a#(a(c(x1))) -> c#(a(c(x1))) -> c#(c(c(x1))) -> a#(x1) a#(a(c(x1))) -> c#(a(c(x1))) -> c#(c(c(x1))) -> a#(a(x1)) a#(a(c(x1))) -> c#(a(c(x1))) -> c#(c(c(x1))) -> a#(a(a(x1))) b#(b(c(x1))) -> a#(c(x1)) -> a#(a(c(x1))) -> c#(a(c(x1))) b#(b(c(x1))) -> c#(a(c(x1))) -> c#(a(c(x1))) -> b#(x1) b#(b(c(x1))) -> c#(a(c(x1))) -> c#(a(c(x1))) -> b#(b(x1)) b#(b(c(x1))) -> c#(a(c(x1))) -> c#(a(c(x1))) -> a#(b(b(x1))) b#(b(c(x1))) -> c#(a(c(x1))) -> c#(c(c(x1))) -> a#(x1) b#(b(c(x1))) -> c#(a(c(x1))) -> c#(c(c(x1))) -> a#(a(x1)) b#(b(c(x1))) -> c#(a(c(x1))) -> c#(c(c(x1))) -> a#(a(a(x1))) c#(a(c(x1))) -> a#(b(b(x1))) -> a#(a(c(x1))) -> c#(a(c(x1))) c#(a(c(x1))) -> a#(b(b(x1))) -> a#(b(c(x1))) -> b#(x1) c#(a(c(x1))) -> a#(b(b(x1))) -> a#(b(c(x1))) -> c#(b(x1)) c#(a(c(x1))) -> a#(b(b(x1))) -> a#(b(c(x1))) -> a#(c(b(x1))) c#(a(c(x1))) -> b#(b(x1)) -> b#(b(c(x1))) -> a#(c(x1)) c#(a(c(x1))) -> b#(b(x1)) -> b#(b(c(x1))) -> c#(a(c(x1))) c#(a(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> a#(c(x1)) c#(a(c(x1))) -> b#(x1) -> b#(b(c(x1))) -> c#(a(c(x1))) c#(c(c(x1))) -> a#(a(a(x1))) -> a#(a(c(x1))) -> c#(a(c(x1))) c#(c(c(x1))) -> a#(a(x1)) -> a#(a(c(x1))) -> c#(a(c(x1))) c#(c(c(x1))) -> a#(x1) -> a#(a(c(x1))) -> c#(a(c(x1))) c#(c(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> b#(x1) c#(c(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> c#(b(x1)) c#(c(c(x1))) -> a#(x1) -> a#(b(c(x1))) -> a#(c(b(x1))) Subterm Criterion Processor: simple projection: pi(c) = [0,0] pi(a) = [0,0] pi(b) = [0,0] pi(c#) = [0,0] pi(b#) = [0,0] pi(a#) = [0,0] problem: DPs: c#(a(c(x1))) -> a#(b(b(x1))) c#(c(c(x1))) -> a#(a(a(x1))) b#(b(c(x1))) -> c#(a(c(x1))) a#(a(c(x1))) -> c#(a(c(x1))) a#(b(c(x1))) -> a#(c(b(x1))) TRS: c(a(c(x1))) -> a(b(b(x1))) c(c(c(x1))) -> a(a(a(x1))) b(b(c(x1))) -> c(a(c(x1))) a(a(c(x1))) -> c(a(c(x1))) a(b(c(x1))) -> a(c(b(x1))) SCC Processor: #sccs: 1 #rules: 4 #arcs: 36/25 DPs: a#(b(c(x1))) -> a#(c(b(x1))) a#(a(c(x1))) -> c#(a(c(x1))) c#(c(c(x1))) -> a#(a(a(x1))) c#(a(c(x1))) -> a#(b(b(x1))) TRS: c(a(c(x1))) -> a(b(b(x1))) c(c(c(x1))) -> a(a(a(x1))) b(b(c(x1))) -> c(a(c(x1))) a(a(c(x1))) -> c(a(c(x1))) a(b(c(x1))) -> a(c(b(x1))) Arctic Interpretation Processor: dimension: 2 usable rules: c(a(c(x1))) -> a(b(b(x1))) c(c(c(x1))) -> a(a(a(x1))) b(b(c(x1))) -> c(a(c(x1))) a(a(c(x1))) -> c(a(c(x1))) a(b(c(x1))) -> a(c(b(x1))) interpretation: [-& 0 ] [0] [a](x0) = [0 -&]x0 + [0], [c#](x0) = [0 0]x0 + [0], [a#](x0) = [0 0]x0 + [0], [-& 0 ] [0] [c](x0) = [0 1 ]x0 + [1], [0 1 ] [0 ] [b](x0) = [-& 0 ]x0 + [-&] orientation: a#(b(c(x1))) = [1 2]x1 + [2] >= [0 1]x1 + [1] = a#(c(b(x1))) a#(a(c(x1))) = [0 1]x1 + [1] >= [0 1]x1 + [1] = c#(a(c(x1))) c#(c(c(x1))) = [1 2]x1 + [2] >= [0 0]x1 + [0] = a#(a(a(x1))) c#(a(c(x1))) = [0 1]x1 + [1] >= [0 1]x1 + [0] = a#(b(b(x1))) [-& 0 ] [0] [-& 0 ] [0] c(a(c(x1))) = [0 1 ]x1 + [1] >= [0 1 ]x1 + [0] = a(b(b(x1))) [1 2] [2] [-& 0 ] [0] c(c(c(x1))) = [2 3]x1 + [3] >= [0 -&]x1 + [0] = a(a(a(x1))) [1 2] [2] [-& 0 ] [0] b(b(c(x1))) = [0 1]x1 + [1] >= [0 1 ]x1 + [1] = c(a(c(x1))) [-& 0 ] [0] [-& 0 ] [0] a(a(c(x1))) = [0 1 ]x1 + [1] >= [0 1 ]x1 + [1] = c(a(c(x1))) [0 1] [1] [0 1 ] [1] a(b(c(x1))) = [1 2]x1 + [2] >= [-& 0 ]x1 + [0] = a(c(b(x1))) problem: DPs: a#(a(c(x1))) -> c#(a(c(x1))) c#(a(c(x1))) -> a#(b(b(x1))) TRS: c(a(c(x1))) -> a(b(b(x1))) c(c(c(x1))) -> a(a(a(x1))) b(b(c(x1))) -> c(a(c(x1))) a(a(c(x1))) -> c(a(c(x1))) a(b(c(x1))) -> a(c(b(x1))) Restore Modifier: DPs: a#(a(c(x1))) -> c#(a(c(x1))) c#(a(c(x1))) -> a#(b(b(x1))) TRS: c(a(c(x1))) -> a(b(b(x1))) c(c(c(x1))) -> a(a(a(x1))) b(b(c(x1))) -> c(a(c(x1))) a(a(c(x1))) -> c(a(c(x1))) a(b(c(x1))) -> a(c(b(x1))) Arctic Interpretation Processor: dimension: 2 usable rules: c(a(c(x1))) -> a(b(b(x1))) c(c(c(x1))) -> a(a(a(x1))) b(b(c(x1))) -> c(a(c(x1))) a(a(c(x1))) -> c(a(c(x1))) a(b(c(x1))) -> a(c(b(x1))) interpretation: [0 0 ] [0] [a](x0) = [0 -&]x0 + [0], [c#](x0) = [0 1]x0 + [0], [a#](x0) = [0 0]x0 + [0], [-& 0 ] [0] [c](x0) = [0 1 ]x0 + [1], [-& 0 ] [0] [b](x0) = [-& 0 ]x0 + [0] orientation: a#(a(c(x1))) = [0 1]x1 + [1] >= [0 1]x1 + [1] = c#(a(c(x1))) c#(a(c(x1))) = [0 1]x1 + [1] >= [-& 0 ]x1 + [0] = a#(b(b(x1))) [-& 0 ] [0] [-& 0 ] [0] c(a(c(x1))) = [0 1 ]x1 + [1] >= [-& 0 ]x1 + [0] = a(b(b(x1))) [1 2] [2] [0 0] [0] c(c(c(x1))) = [2 3]x1 + [3] >= [0 0]x1 + [0] = a(a(a(x1))) [0 1] [1] [-& 0 ] [0] b(b(c(x1))) = [0 1]x1 + [1] >= [0 1 ]x1 + [1] = c(a(c(x1))) [0 1] [1] [-& 0 ] [0] a(a(c(x1))) = [0 1]x1 + [1] >= [0 1 ]x1 + [1] = c(a(c(x1))) [0 1] [1] [-& 1 ] [1] a(b(c(x1))) = [0 1]x1 + [1] >= [-& 0 ]x1 + [0] = a(c(b(x1))) problem: DPs: a#(a(c(x1))) -> c#(a(c(x1))) TRS: c(a(c(x1))) -> a(b(b(x1))) c(c(c(x1))) -> a(a(a(x1))) b(b(c(x1))) -> c(a(c(x1))) a(a(c(x1))) -> c(a(c(x1))) a(b(c(x1))) -> a(c(b(x1))) Restore Modifier: DPs: a#(a(c(x1))) -> c#(a(c(x1))) TRS: c(a(c(x1))) -> a(b(b(x1))) c(c(c(x1))) -> a(a(a(x1))) b(b(c(x1))) -> c(a(c(x1))) a(a(c(x1))) -> c(a(c(x1))) a(b(c(x1))) -> a(c(b(x1))) SCC Processor: #sccs: 0 #rules: 0 #arcs: 6/1