/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(x1) -> b(b(x1)) c(b(x1)) -> d(x1) e(b(x1)) -> c(c(x1)) d(b(x1)) -> b(f(x1)) f(x1) -> a(e(x1)) c(x1) -> x1 a(a(x1)) -> f(x1) Proof: DP Processor: DPs: c#(b(x1)) -> d#(x1) e#(b(x1)) -> c#(x1) e#(b(x1)) -> c#(c(x1)) d#(b(x1)) -> f#(x1) f#(x1) -> e#(x1) f#(x1) -> a#(e(x1)) a#(a(x1)) -> f#(x1) TRS: a(x1) -> b(b(x1)) c(b(x1)) -> d(x1) e(b(x1)) -> c(c(x1)) d(b(x1)) -> b(f(x1)) f(x1) -> a(e(x1)) c(x1) -> x1 a(a(x1)) -> f(x1) TDG Processor: DPs: c#(b(x1)) -> d#(x1) e#(b(x1)) -> c#(x1) e#(b(x1)) -> c#(c(x1)) d#(b(x1)) -> f#(x1) f#(x1) -> e#(x1) f#(x1) -> a#(e(x1)) a#(a(x1)) -> f#(x1) TRS: a(x1) -> b(b(x1)) c(b(x1)) -> d(x1) e(b(x1)) -> c(c(x1)) d(b(x1)) -> b(f(x1)) f(x1) -> a(e(x1)) c(x1) -> x1 a(a(x1)) -> f(x1) graph: f#(x1) -> e#(x1) -> e#(b(x1)) -> c#(c(x1)) f#(x1) -> e#(x1) -> e#(b(x1)) -> c#(x1) f#(x1) -> a#(e(x1)) -> a#(a(x1)) -> f#(x1) e#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> d#(x1) e#(b(x1)) -> c#(x1) -> c#(b(x1)) -> d#(x1) d#(b(x1)) -> f#(x1) -> f#(x1) -> a#(e(x1)) d#(b(x1)) -> f#(x1) -> f#(x1) -> e#(x1) c#(b(x1)) -> d#(x1) -> d#(b(x1)) -> f#(x1) a#(a(x1)) -> f#(x1) -> f#(x1) -> a#(e(x1)) a#(a(x1)) -> f#(x1) -> f#(x1) -> e#(x1) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {15} transitions: a{#,0}(31) -> 32* e0(237) -> 238* e0(30) -> 31* e0(196) -> 197* e0(318) -> 319* d0(129) -> 130* d0(215) -> 216* b0(172) -> 173* b0(199) -> 200* b0(200) -> 201* f110() -> 16* f0(227) -> 228* f0(171) -> 172* d{#,0}(293) -> 294* d{#,0}(115) -> 116* c{#,0}(326) -> 327* c{#,0}(74) -> 75* c{#,0}(51) -> 52* c0(87) -> 88* c0(251) -> 252* c0(73) -> 74* c0(250) -> 251* f{#,0}(16) -> 15* f{#,0}(295) -> 296* a0(197) -> 198* e{#,0}(28) -> 29* e{#,0}(307) -> 308* 15 -> 116,75,52,32 16 -> 171,129,115,73,51,30,28 29 -> 15* 32 -> 296,294,15 52 -> 29,15 73 -> 74* 74 -> 87* 75 -> 29,15 87 -> 88,31 88 -> 252,319,31 116 -> 75,52 130 -> 74,87,88 171 -> 196* 172 -> 198,228,293,215 173 -> 130,74,216,87,31 197 -> 199* 198 -> 228,172 199 -> 326,250 200 -> 295,227 201 -> 198* 216 -> 88,31 227 -> 237* 228 -> 172* 238 -> 197* 250 -> 251* 251 -> 319,31,252,238,197,250 252 -> 238,197,199 294 -> 327,308,116 295 -> 318,307 296 -> 294,32 308 -> 296,294,29 319 -> 31* 327 -> 308,75 problem: DPs: c#(b(x1)) -> d#(x1) e#(b(x1)) -> c#(x1) e#(b(x1)) -> c#(c(x1)) d#(b(x1)) -> f#(x1) f#(x1) -> e#(x1) f#(x1) -> a#(e(x1)) TRS: a(x1) -> b(b(x1)) c(b(x1)) -> d(x1) e(b(x1)) -> c(c(x1)) d(b(x1)) -> b(f(x1)) f(x1) -> a(e(x1)) c(x1) -> x1 a(a(x1)) -> f(x1) Restore Modifier: DPs: c#(b(x1)) -> d#(x1) e#(b(x1)) -> c#(x1) e#(b(x1)) -> c#(c(x1)) d#(b(x1)) -> f#(x1) f#(x1) -> e#(x1) f#(x1) -> a#(e(x1)) TRS: a(x1) -> b(b(x1)) c(b(x1)) -> d(x1) e(b(x1)) -> c(c(x1)) d(b(x1)) -> b(f(x1)) f(x1) -> a(e(x1)) c(x1) -> x1 a(a(x1)) -> f(x1) EDG Processor: DPs: c#(b(x1)) -> d#(x1) e#(b(x1)) -> c#(x1) e#(b(x1)) -> c#(c(x1)) d#(b(x1)) -> f#(x1) f#(x1) -> e#(x1) f#(x1) -> a#(e(x1)) TRS: a(x1) -> b(b(x1)) c(b(x1)) -> d(x1) e(b(x1)) -> c(c(x1)) d(b(x1)) -> b(f(x1)) f(x1) -> a(e(x1)) c(x1) -> x1 a(a(x1)) -> f(x1) graph: f#(x1) -> e#(x1) -> e#(b(x1)) -> c#(x1) f#(x1) -> e#(x1) -> e#(b(x1)) -> c#(c(x1)) e#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> d#(x1) e#(b(x1)) -> c#(x1) -> c#(b(x1)) -> d#(x1) d#(b(x1)) -> f#(x1) -> f#(x1) -> e#(x1) d#(b(x1)) -> f#(x1) -> f#(x1) -> a#(e(x1)) c#(b(x1)) -> d#(x1) -> d#(b(x1)) -> f#(x1) SCC Processor: #sccs: 1 #rules: 5 #arcs: 7/36 DPs: f#(x1) -> e#(x1) e#(b(x1)) -> c#(c(x1)) c#(b(x1)) -> d#(x1) d#(b(x1)) -> f#(x1) e#(b(x1)) -> c#(x1) TRS: a(x1) -> b(b(x1)) c(b(x1)) -> d(x1) e(b(x1)) -> c(c(x1)) d(b(x1)) -> b(f(x1)) f(x1) -> a(e(x1)) c(x1) -> x1 a(a(x1)) -> f(x1) Arctic Interpretation Processor: dimension: 3 usable rules: a(x1) -> b(b(x1)) c(b(x1)) -> d(x1) e(b(x1)) -> c(c(x1)) d(b(x1)) -> b(f(x1)) f(x1) -> a(e(x1)) c(x1) -> x1 a(a(x1)) -> f(x1) interpretation: [f#](x0) = [0 0 1]x0 + [1], [e#](x0) = [-& -& 0 ]x0 + [0], [d#](x0) = [0 0 0]x0 + [0], [c#](x0) = [0 -& 0 ]x0 + [0], [0 0 1] [1] [f](x0) = [0 0 1]x0 + [1] [0 0 1] [0], [-& -& 0 ] [0] [e](x0) = [-& 0 1 ]x0 + [0] [-& -& 0 ] [0], [0 0 0 ] [d](x0) = [-& 1 1 ]x0 [0 0 0 ] , [0 -& 0 ] [-&] [c](x0) = [1 0 0 ]x0 + [0 ] [0 -& 0 ] [0 ], [0 0 0 ] [-&] [b](x0) = [0 0 1 ]x0 + [1 ] [0 -& 0 ] [-&], [0 0 1] [1 ] [a](x0) = [1 0 1]x0 + [1 ] [0 0 0] [-&] orientation: f#(x1) = [0 0 1]x1 + [1] >= [-& -& 0 ]x1 + [0] = e#(x1) e#(b(x1)) = [0 -& 0 ]x1 + [0] >= [0 -& 0 ]x1 + [0] = c#(c(x1)) c#(b(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = d#(x1) d#(b(x1)) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = f#(x1) e#(b(x1)) = [0 -& 0 ]x1 + [0] >= [0 -& 0 ]x1 + [0] = c#(x1) [0 0 1] [1 ] [0 0 1] [1 ] a(x1) = [1 0 1]x1 + [1 ] >= [1 0 1]x1 + [1 ] = b(b(x1)) [0 0 0] [-&] [0 0 0] [-&] [0 0 0] [-&] [0 0 0 ] c(b(x1)) = [1 1 1]x1 + [1 ] >= [-& 1 1 ]x1 = d(x1) [0 0 0] [0 ] [0 0 0 ] [0 -& 0 ] [0] [0 -& 0 ] [0] e(b(x1)) = [1 0 1 ]x1 + [1] >= [1 0 1 ]x1 + [0] = c(c(x1)) [0 -& 0 ] [0] [0 -& 0 ] [0] [0 0 1] [1] [0 0 1] [1] d(b(x1)) = [1 1 2]x1 + [2] >= [1 1 2]x1 + [1] = b(f(x1)) [0 0 1] [1] [0 0 1] [1] [0 0 1] [1] [-& 0 1 ] [1] f(x1) = [0 0 1]x1 + [1] >= [-& 0 1 ]x1 + [1] = a(e(x1)) [0 0 1] [0] [-& 0 1 ] [0] [0 -& 0 ] [-&] c(x1) = [1 0 0 ]x1 + [0 ] >= x1 = x1 [0 -& 0 ] [0 ] [1 1 1] [1] [0 0 1] [1] a(a(x1)) = [1 1 2]x1 + [2] >= [0 0 1]x1 + [1] = f(x1) [1 0 1] [1] [0 0 1] [0] problem: DPs: e#(b(x1)) -> c#(c(x1)) c#(b(x1)) -> d#(x1) d#(b(x1)) -> f#(x1) e#(b(x1)) -> c#(x1) TRS: a(x1) -> b(b(x1)) c(b(x1)) -> d(x1) e(b(x1)) -> c(c(x1)) d(b(x1)) -> b(f(x1)) f(x1) -> a(e(x1)) c(x1) -> x1 a(a(x1)) -> f(x1) Restore Modifier: DPs: e#(b(x1)) -> c#(c(x1)) c#(b(x1)) -> d#(x1) d#(b(x1)) -> f#(x1) e#(b(x1)) -> c#(x1) TRS: a(x1) -> b(b(x1)) c(b(x1)) -> d(x1) e(b(x1)) -> c(c(x1)) d(b(x1)) -> b(f(x1)) f(x1) -> a(e(x1)) c(x1) -> x1 a(a(x1)) -> f(x1) EDG Processor: DPs: e#(b(x1)) -> c#(c(x1)) c#(b(x1)) -> d#(x1) d#(b(x1)) -> f#(x1) e#(b(x1)) -> c#(x1) TRS: a(x1) -> b(b(x1)) c(b(x1)) -> d(x1) e(b(x1)) -> c(c(x1)) d(b(x1)) -> b(f(x1)) f(x1) -> a(e(x1)) c(x1) -> x1 a(a(x1)) -> f(x1) graph: e#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> d#(x1) e#(b(x1)) -> c#(x1) -> c#(b(x1)) -> d#(x1) c#(b(x1)) -> d#(x1) -> d#(b(x1)) -> f#(x1) SCC Processor: #sccs: 0 #rules: 0 #arcs: 3/16