/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: strict: a(a(c(x1))) -> a(a(a(x1))) c(a(c(x1))) -> a(a(a(x1))) weak: b(b(a(x1))) -> c(c(c(x1))) c(b(a(x1))) -> a(c(b(x1))) b(b(b(x1))) -> b(c(b(x1))) c(a(a(x1))) -> c(c(a(x1))) Proof: String Reversal Processor: strict: c(a(a(x1))) -> a(a(a(x1))) c(a(c(x1))) -> a(a(a(x1))) weak: a(b(b(x1))) -> c(c(c(x1))) a(b(c(x1))) -> b(c(a(x1))) b(b(b(x1))) -> b(c(b(x1))) a(a(c(x1))) -> a(c(c(x1))) Arctic Interpretation Processor: dimension: 1 interpretation: [a](x0) = 4x0, [c](x0) = 4x0, [b](x0) = 9x0 orientation: c(a(a(x1))) = 12x1 >= 12x1 = a(a(a(x1))) c(a(c(x1))) = 12x1 >= 12x1 = a(a(a(x1))) a(b(b(x1))) = 22x1 >= 12x1 = c(c(c(x1))) a(b(c(x1))) = 17x1 >= 17x1 = b(c(a(x1))) b(b(b(x1))) = 27x1 >= 22x1 = b(c(b(x1))) a(a(c(x1))) = 12x1 >= 12x1 = a(c(c(x1))) problem: strict: c(a(a(x1))) -> a(a(a(x1))) c(a(c(x1))) -> a(a(a(x1))) weak: a(b(c(x1))) -> b(c(a(x1))) a(a(c(x1))) -> a(c(c(x1))) String Reversal Processor: strict: a(a(c(x1))) -> a(a(a(x1))) c(a(c(x1))) -> a(a(a(x1))) weak: c(b(a(x1))) -> a(c(b(x1))) c(a(a(x1))) -> c(c(a(x1))) Matrix Interpretation Processor: dim=2 interpretation: [0] [a](x0) = x0 + [1], [0] [c](x0) = x0 + [1], [1 2] [b](x0) = [0 1]x0 orientation: [0] [0] a(a(c(x1))) = x1 + [3] >= x1 + [3] = a(a(a(x1))) [0] [0] c(a(c(x1))) = x1 + [3] >= x1 + [3] = a(a(a(x1))) [1 2] [2] [1 2] [0] c(b(a(x1))) = [0 1]x1 + [2] >= [0 1]x1 + [2] = a(c(b(x1))) [0] [0] c(a(a(x1))) = x1 + [3] >= x1 + [3] = c(c(a(x1))) problem: strict: a(a(c(x1))) -> a(a(a(x1))) c(a(c(x1))) -> a(a(a(x1))) weak: c(a(a(x1))) -> c(c(a(x1))) RT Transformation Processor: a(a(c(x1))) -> a(a(a(x1))) c(a(c(x1))) -> a(a(a(x1))) c(a(a(x1))) -> c(c(a(x1))) DP Processor: DPs: a#(a(c(x1))) -> a#(x1) a#(a(c(x1))) -> a#(a(x1)) a#(a(c(x1))) -> a#(a(a(x1))) c#(a(c(x1))) -> a#(x1) c#(a(c(x1))) -> a#(a(x1)) c#(a(c(x1))) -> a#(a(a(x1))) c#(a(a(x1))) -> c#(a(x1)) c#(a(a(x1))) -> c#(c(a(x1))) TRS: a(a(c(x1))) -> a(a(a(x1))) c(a(c(x1))) -> a(a(a(x1))) c(a(a(x1))) -> c(c(a(x1))) TDG Processor: DPs: a#(a(c(x1))) -> a#(x1) a#(a(c(x1))) -> a#(a(x1)) a#(a(c(x1))) -> a#(a(a(x1))) c#(a(c(x1))) -> a#(x1) c#(a(c(x1))) -> a#(a(x1)) c#(a(c(x1))) -> a#(a(a(x1))) c#(a(a(x1))) -> c#(a(x1)) c#(a(a(x1))) -> c#(c(a(x1))) TRS: a(a(c(x1))) -> a(a(a(x1))) c(a(c(x1))) -> a(a(a(x1))) c(a(a(x1))) -> c(c(a(x1))) graph: c#(a(a(x1))) -> c#(a(x1)) -> c#(a(a(x1))) -> c#(c(a(x1))) c#(a(a(x1))) -> c#(a(x1)) -> c#(a(a(x1))) -> c#(a(x1)) c#(a(a(x1))) -> c#(a(x1)) -> c#(a(c(x1))) -> a#(a(a(x1))) c#(a(a(x1))) -> c#(a(x1)) -> c#(a(c(x1))) -> a#(a(x1)) c#(a(a(x1))) -> c#(a(x1)) -> c#(a(c(x1))) -> a#(x1) c#(a(a(x1))) -> c#(c(a(x1))) -> c#(a(a(x1))) -> c#(c(a(x1))) c#(a(a(x1))) -> c#(c(a(x1))) -> c#(a(a(x1))) -> c#(a(x1)) c#(a(a(x1))) -> c#(c(a(x1))) -> c#(a(c(x1))) -> a#(a(a(x1))) c#(a(a(x1))) -> c#(c(a(x1))) -> c#(a(c(x1))) -> a#(a(x1)) c#(a(a(x1))) -> c#(c(a(x1))) -> c#(a(c(x1))) -> a#(x1) c#(a(c(x1))) -> a#(a(a(x1))) -> a#(a(c(x1))) -> a#(a(a(x1))) c#(a(c(x1))) -> a#(a(a(x1))) -> a#(a(c(x1))) -> a#(a(x1)) c#(a(c(x1))) -> a#(a(a(x1))) -> a#(a(c(x1))) -> a#(x1) c#(a(c(x1))) -> a#(a(x1)) -> a#(a(c(x1))) -> a#(a(a(x1))) c#(a(c(x1))) -> a#(a(x1)) -> a#(a(c(x1))) -> a#(a(x1)) c#(a(c(x1))) -> a#(a(x1)) -> a#(a(c(x1))) -> a#(x1) c#(a(c(x1))) -> a#(x1) -> a#(a(c(x1))) -> a#(a(a(x1))) c#(a(c(x1))) -> a#(x1) -> a#(a(c(x1))) -> a#(a(x1)) c#(a(c(x1))) -> a#(x1) -> a#(a(c(x1))) -> a#(x1) a#(a(c(x1))) -> a#(a(a(x1))) -> a#(a(c(x1))) -> a#(a(a(x1))) a#(a(c(x1))) -> a#(a(a(x1))) -> a#(a(c(x1))) -> a#(a(x1)) a#(a(c(x1))) -> a#(a(a(x1))) -> a#(a(c(x1))) -> a#(x1) a#(a(c(x1))) -> a#(a(x1)) -> a#(a(c(x1))) -> a#(a(a(x1))) a#(a(c(x1))) -> a#(a(x1)) -> a#(a(c(x1))) -> a#(a(x1)) a#(a(c(x1))) -> a#(a(x1)) -> a#(a(c(x1))) -> a#(x1) a#(a(c(x1))) -> a#(x1) -> a#(a(c(x1))) -> a#(a(a(x1))) a#(a(c(x1))) -> a#(x1) -> a#(a(c(x1))) -> a#(a(x1)) a#(a(c(x1))) -> a#(x1) -> a#(a(c(x1))) -> a#(x1) SCC Processor: #sccs: 2 #rules: 5 #arcs: 28/64 DPs: c#(a(a(x1))) -> c#(a(x1)) c#(a(a(x1))) -> c#(c(a(x1))) TRS: a(a(c(x1))) -> a(a(a(x1))) c(a(c(x1))) -> a(a(a(x1))) c(a(a(x1))) -> c(c(a(x1))) Bounds Processor: bound: 1 enrichment: match automaton: final states: {8,6,4,1} transitions: f50() -> 2* a0(7) -> 6* a0(3) -> 7* a0(2) -> 3* c{#,0}(5) -> 4* c{#,0}(3) -> 1* c{#,1}(13) -> 14* c0(5) -> 8* c0(3) -> 5* a1(15) -> 16* a1(12) -> 13* a1(25) -> 26* c1(21) -> 22* 7 -> 12* 14 -> 4,1 16 -> 13* 4 -> 1* 2 -> 25* 22 -> 8,5,13 6 -> 22,8,26,16,5,3,7 26 -> 13* 13 -> 21* 3 -> 15* problem: DPs: TRS: a(a(c(x1))) -> a(a(a(x1))) c(a(c(x1))) -> a(a(a(x1))) c(a(a(x1))) -> c(c(a(x1))) Qed DPs: a#(a(c(x1))) -> a#(x1) a#(a(c(x1))) -> a#(a(x1)) a#(a(c(x1))) -> a#(a(a(x1))) TRS: a(a(c(x1))) -> a(a(a(x1))) c(a(c(x1))) -> a(a(a(x1))) c(a(a(x1))) -> c(c(a(x1))) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {6} transitions: f130() -> 7* a0(15) -> 16* a0(7) -> 8* a0(8) -> 9* a{#,0}(9) -> 6* 16 -> 8,9 9 -> 15* problem: DPs: a#(a(c(x1))) -> a#(x1) a#(a(c(x1))) -> a#(a(x1)) TRS: a(a(c(x1))) -> a(a(a(x1))) c(a(c(x1))) -> a(a(a(x1))) c(a(a(x1))) -> c(c(a(x1))) Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {3,1} transitions: a{#,0}(4) -> 3* a{#,0}(2) -> 1* a0(8) -> 9* a0(9) -> 10* a0(2) -> 4* f160() -> 2* 4 -> 8* 1 -> 3* 3 -> 1* 10 -> 9,4 problem: DPs: TRS: a(a(c(x1))) -> a(a(a(x1))) c(a(c(x1))) -> a(a(a(x1))) c(a(a(x1))) -> c(c(a(x1))) Qed