/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(x1) -> x1 a(a(x1)) -> a(b(a(b(c(a(x1)))))) c(b(x1)) -> a(x1) Proof: String Reversal Processor: a(x1) -> x1 a(a(x1)) -> a(c(b(a(b(a(x1)))))) b(c(x1)) -> a(x1) DP Processor: DPs: a#(a(x1)) -> b#(a(x1)) a#(a(x1)) -> a#(b(a(x1))) a#(a(x1)) -> b#(a(b(a(x1)))) a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) b#(c(x1)) -> a#(x1) TRS: a(x1) -> x1 a(a(x1)) -> a(c(b(a(b(a(x1)))))) b(c(x1)) -> a(x1) TDG Processor: DPs: a#(a(x1)) -> b#(a(x1)) a#(a(x1)) -> a#(b(a(x1))) a#(a(x1)) -> b#(a(b(a(x1)))) a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) b#(c(x1)) -> a#(x1) TRS: a(x1) -> x1 a(a(x1)) -> a(c(b(a(b(a(x1)))))) b(c(x1)) -> a(x1) graph: b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(b(a(x1)))) b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1))) b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1)) a#(a(x1)) -> b#(a(b(a(x1)))) -> b#(c(x1)) -> a#(x1) a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(x1) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(b(a(x1)))) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1))) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1)) a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) -> a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) -> a#(a(x1)) -> b#(a(b(a(x1)))) a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) -> a#(a(x1)) -> a#(b(a(x1))) a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) -> a#(a(x1)) -> b#(a(x1)) EDG Processor: DPs: a#(a(x1)) -> b#(a(x1)) a#(a(x1)) -> a#(b(a(x1))) a#(a(x1)) -> b#(a(b(a(x1)))) a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) b#(c(x1)) -> a#(x1) TRS: a(x1) -> x1 a(a(x1)) -> a(c(b(a(b(a(x1)))))) b(c(x1)) -> a(x1) graph: b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1)) b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(x1))) b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(b(a(x1)))) b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) a#(a(x1)) -> b#(a(b(a(x1)))) -> b#(c(x1)) -> a#(x1) a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(x1) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(x1)) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(b(a(x1))) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> b#(a(b(a(x1)))) a#(a(x1)) -> a#(b(a(x1))) -> a#(a(x1)) -> a#(c(b(a(b(a(x1)))))) SCC Processor: #sccs: 1 #rules: 4 #arcs: 10/25 DPs: b#(c(x1)) -> a#(x1) a#(a(x1)) -> b#(a(b(a(x1)))) a#(a(x1)) -> a#(b(a(x1))) a#(a(x1)) -> b#(a(x1)) TRS: a(x1) -> x1 a(a(x1)) -> a(c(b(a(b(a(x1)))))) b(c(x1)) -> a(x1) Arctic Interpretation Processor: dimension: 2 usable rules: a(x1) -> x1 a(a(x1)) -> a(c(b(a(b(a(x1)))))) b(c(x1)) -> a(x1) interpretation: [b#](x0) = [-& 3 ]x0 + [0], [a#](x0) = [0 3]x0 + [0], [0 -&] [b](x0) = [0 -&]x0, [1 1] [1] [c](x0) = [0 0]x0 + [0], [0 0] [-&] [a](x0) = [1 1]x0 + [1 ] orientation: b#(c(x1)) = [3 3]x1 + [3] >= [0 3]x1 + [0] = a#(x1) a#(a(x1)) = [4 4]x1 + [4] >= [4 4]x1 + [4] = b#(a(b(a(x1)))) a#(a(x1)) = [4 4]x1 + [4] >= [3 3]x1 + [0] = a#(b(a(x1))) a#(a(x1)) = [4 4]x1 + [4] >= [4 4]x1 + [4] = b#(a(x1)) [0 0] [-&] a(x1) = [1 1]x1 + [1 ] >= x1 = x1 [1 1] [1] [1 1] [1] a(a(x1)) = [2 2]x1 + [2] >= [2 2]x1 + [2] = a(c(b(a(b(a(x1)))))) [1 1] [1] [0 0] [-&] b(c(x1)) = [1 1]x1 + [1] >= [1 1]x1 + [1 ] = a(x1) problem: DPs: b#(c(x1)) -> a#(x1) a#(a(x1)) -> b#(a(b(a(x1)))) a#(a(x1)) -> b#(a(x1)) TRS: a(x1) -> x1 a(a(x1)) -> a(c(b(a(b(a(x1)))))) b(c(x1)) -> a(x1) Restore Modifier: DPs: b#(c(x1)) -> a#(x1) a#(a(x1)) -> b#(a(b(a(x1)))) a#(a(x1)) -> b#(a(x1)) TRS: a(x1) -> x1 a(a(x1)) -> a(c(b(a(b(a(x1)))))) b(c(x1)) -> a(x1) EDG Processor: DPs: b#(c(x1)) -> a#(x1) a#(a(x1)) -> b#(a(b(a(x1)))) a#(a(x1)) -> b#(a(x1)) TRS: a(x1) -> x1 a(a(x1)) -> a(c(b(a(b(a(x1)))))) b(c(x1)) -> a(x1) graph: b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(b(a(x1)))) b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(a(x1)) a#(a(x1)) -> b#(a(b(a(x1)))) -> b#(c(x1)) -> a#(x1) a#(a(x1)) -> b#(a(x1)) -> b#(c(x1)) -> a#(x1) Arctic Interpretation Processor: dimension: 2 usable rules: a(x1) -> x1 a(a(x1)) -> a(c(b(a(b(a(x1)))))) b(c(x1)) -> a(x1) interpretation: [b#](x0) = [0 2]x0 + [0], [a#](x0) = [0 2]x0, [-& 0 ] [0] [b](x0) = [-& 0 ]x0 + [0], [0 0] [1] [c](x0) = [2 2]x0 + [2], [2 2] [2 ] [a](x0) = [0 0]x0 + [-&] orientation: b#(c(x1)) = [4 4]x1 + [4] >= [0 2]x1 = a#(x1) a#(a(x1)) = [2 2]x1 + [2] >= [2 2]x1 + [2] = b#(a(b(a(x1)))) a#(a(x1)) = [2 2]x1 + [2] >= [2 2]x1 + [2] = b#(a(x1)) [2 2] [2 ] a(x1) = [0 0]x1 + [-&] >= x1 = x1 [4 4] [4] [4 4] [4] a(a(x1)) = [2 2]x1 + [2] >= [2 2]x1 + [2] = a(c(b(a(b(a(x1)))))) [2 2] [2] [2 2] [2 ] b(c(x1)) = [2 2]x1 + [2] >= [0 0]x1 + [-&] = a(x1) problem: DPs: a#(a(x1)) -> b#(a(b(a(x1)))) a#(a(x1)) -> b#(a(x1)) TRS: a(x1) -> x1 a(a(x1)) -> a(c(b(a(b(a(x1)))))) b(c(x1)) -> a(x1) Restore Modifier: DPs: a#(a(x1)) -> b#(a(b(a(x1)))) a#(a(x1)) -> b#(a(x1)) TRS: a(x1) -> x1 a(a(x1)) -> a(c(b(a(b(a(x1)))))) b(c(x1)) -> a(x1) EDG Processor: DPs: a#(a(x1)) -> b#(a(b(a(x1)))) a#(a(x1)) -> b#(a(x1)) TRS: a(x1) -> x1 a(a(x1)) -> a(c(b(a(b(a(x1)))))) b(c(x1)) -> a(x1) graph: SCC Processor: #sccs: 0 #rules: 0 #arcs: 0/4