/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(x1)) -> a(b(a(c(c(x1))))) c(a(x1)) -> x1 c(b(x1)) -> a(x1) Proof: DP Processor: DPs: a#(a(x1)) -> c#(x1) a#(a(x1)) -> c#(c(x1)) a#(a(x1)) -> a#(c(c(x1))) a#(a(x1)) -> a#(b(a(c(c(x1))))) c#(b(x1)) -> a#(x1) TRS: a(a(x1)) -> a(b(a(c(c(x1))))) c(a(x1)) -> x1 c(b(x1)) -> a(x1) TDG Processor: DPs: a#(a(x1)) -> c#(x1) a#(a(x1)) -> c#(c(x1)) a#(a(x1)) -> a#(c(c(x1))) a#(a(x1)) -> a#(b(a(c(c(x1))))) c#(b(x1)) -> a#(x1) TRS: a(a(x1)) -> a(b(a(c(c(x1))))) c(a(x1)) -> x1 c(b(x1)) -> a(x1) graph: c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(c(c(x1))))) c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(c(x1))) c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(c(x1)) c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(x1) a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(x1) a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(x1) a#(a(x1)) -> a#(b(a(c(c(x1))))) -> a#(a(x1)) -> a#(b(a(c(c(x1))))) a#(a(x1)) -> a#(b(a(c(c(x1))))) -> a#(a(x1)) -> a#(c(c(x1))) a#(a(x1)) -> a#(b(a(c(c(x1))))) -> a#(a(x1)) -> c#(c(x1)) a#(a(x1)) -> a#(b(a(c(c(x1))))) -> a#(a(x1)) -> c#(x1) a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> a#(b(a(c(c(x1))))) a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> a#(c(c(x1))) a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> c#(c(x1)) a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> c#(x1) EDG Processor: DPs: a#(a(x1)) -> c#(x1) a#(a(x1)) -> c#(c(x1)) a#(a(x1)) -> a#(c(c(x1))) a#(a(x1)) -> a#(b(a(c(c(x1))))) c#(b(x1)) -> a#(x1) TRS: a(a(x1)) -> a(b(a(c(c(x1))))) c(a(x1)) -> x1 c(b(x1)) -> a(x1) graph: c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(x1) c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(c(x1)) c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(c(c(x1))) c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> a#(b(a(c(c(x1))))) a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(x1) a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(x1) a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> c#(x1) a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> c#(c(x1)) a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> a#(c(c(x1))) a#(a(x1)) -> a#(c(c(x1))) -> a#(a(x1)) -> a#(b(a(c(c(x1))))) SCC Processor: #sccs: 1 #rules: 4 #arcs: 10/25 DPs: c#(b(x1)) -> a#(x1) a#(a(x1)) -> a#(c(c(x1))) a#(a(x1)) -> c#(c(x1)) a#(a(x1)) -> c#(x1) TRS: a(a(x1)) -> a(b(a(c(c(x1))))) c(a(x1)) -> x1 c(b(x1)) -> a(x1) Arctic Interpretation Processor: dimension: 2 usable rules: a(a(x1)) -> a(b(a(c(c(x1))))) c(a(x1)) -> x1 c(b(x1)) -> a(x1) interpretation: [c#](x0) = [-& 0 ]x0 + [1], [a#](x0) = [-& 0 ]x0 + [0], [0 1] [2] [b](x0) = [0 0]x0 + [0], [-& 0 ] [0] [c](x0) = [0 -&]x0 + [0], [-& 0 ] [0] [a](x0) = [0 1 ]x0 + [1] orientation: c#(b(x1)) = [0 0]x1 + [1] >= [-& 0 ]x1 + [0] = a#(x1) a#(a(x1)) = [0 1]x1 + [1] >= [-& 0 ]x1 + [0] = a#(c(c(x1))) a#(a(x1)) = [0 1]x1 + [1] >= [0 -&]x1 + [1] = c#(c(x1)) a#(a(x1)) = [0 1]x1 + [1] >= [-& 0 ]x1 + [1] = c#(x1) [0 1] [1] [0 1] [1] a(a(x1)) = [1 2]x1 + [2] >= [1 2]x1 + [2] = a(b(a(c(c(x1))))) [0 1 ] [1] c(a(x1)) = [-& 0 ]x1 + [0] >= x1 = x1 [0 0] [0] [-& 0 ] [0] c(b(x1)) = [0 1]x1 + [2] >= [0 1 ]x1 + [1] = a(x1) problem: DPs: c#(b(x1)) -> a#(x1) a#(a(x1)) -> c#(c(x1)) a#(a(x1)) -> c#(x1) TRS: a(a(x1)) -> a(b(a(c(c(x1))))) c(a(x1)) -> x1 c(b(x1)) -> a(x1) Restore Modifier: DPs: c#(b(x1)) -> a#(x1) a#(a(x1)) -> c#(c(x1)) a#(a(x1)) -> c#(x1) TRS: a(a(x1)) -> a(b(a(c(c(x1))))) c(a(x1)) -> x1 c(b(x1)) -> a(x1) EDG Processor: DPs: c#(b(x1)) -> a#(x1) a#(a(x1)) -> c#(c(x1)) a#(a(x1)) -> c#(x1) TRS: a(a(x1)) -> a(b(a(c(c(x1))))) c(a(x1)) -> x1 c(b(x1)) -> a(x1) graph: c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(c(x1)) c#(b(x1)) -> a#(x1) -> a#(a(x1)) -> c#(x1) a#(a(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(x1) a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(x1) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {1} transitions: c{#,0}(9) -> 10* c{#,0}(18) -> 19* c0(45) -> 46* c0(31) -> 32* c0(8) -> 9* a0(32) -> 33* a0(27) -> 28* a0(34) -> 35* f50() -> 2* b0(33) -> 34* a{#,0}(2) -> 1* 1 -> 10,19 2 -> 27,9,18,8 9 -> 31* 10 -> 1* 19 -> 1* 27 -> 32* 28 -> 32,9 32 -> 46,31,45 33 -> 28* 34 -> 32* 35 -> 9* 46 -> 31* problem: DPs: a#(a(x1)) -> c#(c(x1)) a#(a(x1)) -> c#(x1) TRS: a(a(x1)) -> a(b(a(c(c(x1))))) c(a(x1)) -> x1 c(b(x1)) -> a(x1) Restore Modifier: DPs: a#(a(x1)) -> c#(c(x1)) a#(a(x1)) -> c#(x1) TRS: a(a(x1)) -> a(b(a(c(c(x1))))) c(a(x1)) -> x1 c(b(x1)) -> a(x1) EDG Processor: DPs: a#(a(x1)) -> c#(c(x1)) a#(a(x1)) -> c#(x1) TRS: a(a(x1)) -> a(b(a(c(c(x1))))) c(a(x1)) -> x1 c(b(x1)) -> a(x1) graph: SCC Processor: #sccs: 0 #rules: 0 #arcs: 0/4