/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(f(),0()) -> a(s(),0()) a(d(),0()) -> 0() a(d(),a(s(),x)) -> a(s(),a(s(),a(d(),a(p(),a(s(),x))))) a(f(),a(s(),x)) -> a(d(),a(f(),a(p(),a(s(),x)))) a(p(),a(s(),x)) -> x Proof: Extended Uncurrying Processor: application symbol: a symbol table: p ==> p0/0 p1/1 d ==> d0/0 d1/1 s ==> s0/0 s1/1 0 ==> 00/0 f ==> f0/0 f1/1 uncurry-rules: a(f0(),x1) -> f1(x1) a(s0(),x4) -> s1(x4) a(d0(),x6) -> d1(x6) a(p0(),x8) -> p1(x8) eta-rules: problem: f1(00()) -> s1(00()) d1(00()) -> 00() d1(s1(x)) -> s1(s1(d1(p1(s1(x))))) f1(s1(x)) -> d1(f1(p1(s1(x)))) p1(s1(x)) -> x a(f0(),x1) -> f1(x1) a(s0(),x4) -> s1(x4) a(d0(),x6) -> d1(x6) a(p0(),x8) -> p1(x8) Matrix Interpretation Processor: dim=3 interpretation: [p1](x0) = x0 , [0] [p0] = [0] [0], [1 0 0] [0] [d1](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [0] [d0] = [0] [0], [s1](x0) = x0 , [0] [s0] = [0] [0], [0] [00] = [0] [0], [1 0 1] [1] [f1](x0) = [0 0 0]x0 + [0] [0 0 0] [1], [0] [f0] = [0] [1], [1 0 1] [1 1 1] [0] [a](x0, x1) = [0 0 0]x0 + [0 1 0]x1 + [0] [0 0 0] [0 1 1] [1] orientation: [1] [0] f1(00()) = [0] >= [0] = s1(00()) [1] [0] [0] [0] d1(00()) = [0] >= [0] = 00() [1] [0] [1 0 0] [0] [1 0 0] [0] d1(s1(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = s1(s1(d1(p1(s1(x))))) [0 0 0] [1] [0 0 0] [1] [1 0 1] [1] [1 0 1] [1] f1(s1(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = d1(f1(p1(s1(x)))) [0 0 0] [1] [0 0 0] [1] p1(s1(x)) = x >= x = x [1 1 1] [1] [1 0 1] [1] a(f0(),x1) = [0 1 0]x1 + [0] >= [0 0 0]x1 + [0] = f1(x1) [0 1 1] [1] [0 0 0] [1] [1 1 1] [0] a(s0(),x4) = [0 1 0]x4 + [0] >= x4 = s1(x4) [0 1 1] [1] [1 1 1] [0] [1 0 0] [0] a(d0(),x6) = [0 1 0]x6 + [0] >= [0 0 0]x6 + [0] = d1(x6) [0 1 1] [1] [0 0 0] [1] [1 1 1] [0] a(p0(),x8) = [0 1 0]x8 + [0] >= x8 = p1(x8) [0 1 1] [1] problem: d1(00()) -> 00() d1(s1(x)) -> s1(s1(d1(p1(s1(x))))) f1(s1(x)) -> d1(f1(p1(s1(x)))) p1(s1(x)) -> x a(f0(),x1) -> f1(x1) a(s0(),x4) -> s1(x4) a(d0(),x6) -> d1(x6) a(p0(),x8) -> p1(x8) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [p1](x0) = [0 1 0]x0 [0 1 0] , [0] [p0] = [0] [1], [1 1 0] [d1](x0) = [0 1 0]x0 [0 0 0] , [0] [d0] = [1] [0], [1 0 0] [s1](x0) = [0 1 1]x0 [0 0 0] , [0] [s0] = [0] [0], [0] [00] = [1] [0], [1 0 0] [1] [f1](x0) = [0 0 0]x0 + [0] [0 1 0] [0], [0] [f0] = [0] [0], [1 1 1] [1] [a](x0, x1) = x0 + [0 1 1]x1 + [0] [1 1 1] [0] orientation: [1] [0] d1(00()) = [1] >= [1] = 00() [0] [0] [1 1 1] [1 1 1] d1(s1(x)) = [0 1 1]x >= [0 1 1]x = s1(s1(d1(p1(s1(x))))) [0 0 0] [0 0 0] [1 0 0] [1] [1 0 0] [1] f1(s1(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = d1(f1(p1(s1(x)))) [0 1 1] [0] [0 0 0] [0] [1 0 0] p1(s1(x)) = [0 1 1]x >= x = x [0 1 1] [1 1 1] [1] [1 0 0] [1] a(f0(),x1) = [0 1 1]x1 + [0] >= [0 0 0]x1 + [0] = f1(x1) [1 1 1] [0] [0 1 0] [0] [1 1 1] [1] [1 0 0] a(s0(),x4) = [0 1 1]x4 + [0] >= [0 1 1]x4 = s1(x4) [1 1 1] [0] [0 0 0] [1 1 1] [1] [1 1 0] a(d0(),x6) = [0 1 1]x6 + [1] >= [0 1 0]x6 = d1(x6) [1 1 1] [0] [0 0 0] [1 1 1] [1] [1 0 0] a(p0(),x8) = [0 1 1]x8 + [0] >= [0 1 0]x8 = p1(x8) [1 1 1] [1] [0 1 0] problem: d1(s1(x)) -> s1(s1(d1(p1(s1(x))))) f1(s1(x)) -> d1(f1(p1(s1(x)))) p1(s1(x)) -> x a(f0(),x1) -> f1(x1) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [p1](x0) = [1 1 0]x0 + [1] [1 1 1] [1], [1 0 0] [d1](x0) = [0 0 0]x0 [0 0 0] , [s1](x0) = x0 , [1 0 0] [f1](x0) = [0 1 0]x0 [0 0 0] , [0] [f0] = [0] [1], [1 0 0] [1 1 1] [1] [a](x0, x1) = [0 0 1]x0 + [0 1 0]x1 + [0] [0 0 0] [0 1 0] [1] orientation: [1 0 0] [1 0 0] d1(s1(x)) = [0 0 0]x >= [0 0 0]x = s1(s1(d1(p1(s1(x))))) [0 0 0] [0 0 0] [1 0 0] [1 0 0] f1(s1(x)) = [0 1 0]x >= [0 0 0]x = d1(f1(p1(s1(x)))) [0 0 0] [0 0 0] [1 0 0] [0] p1(s1(x)) = [1 1 0]x + [1] >= x = x [1 1 1] [1] [1 1 1] [1] [1 0 0] a(f0(),x1) = [0 1 0]x1 + [1] >= [0 1 0]x1 = f1(x1) [0 1 0] [1] [0 0 0] problem: d1(s1(x)) -> s1(s1(d1(p1(s1(x))))) f1(s1(x)) -> d1(f1(p1(s1(x)))) p1(s1(x)) -> x DP Processor: DPs: d{1,#}(s1(x)) -> p{1,#}(s1(x)) d{1,#}(s1(x)) -> d{1,#}(p1(s1(x))) f{1,#}(s1(x)) -> p{1,#}(s1(x)) f{1,#}(s1(x)) -> f{1,#}(p1(s1(x))) f{1,#}(s1(x)) -> d{1,#}(f1(p1(s1(x)))) TRS: d1(s1(x)) -> s1(s1(d1(p1(s1(x))))) f1(s1(x)) -> d1(f1(p1(s1(x)))) p1(s1(x)) -> x TDG Processor: DPs: d{1,#}(s1(x)) -> p{1,#}(s1(x)) d{1,#}(s1(x)) -> d{1,#}(p1(s1(x))) f{1,#}(s1(x)) -> p{1,#}(s1(x)) f{1,#}(s1(x)) -> f{1,#}(p1(s1(x))) f{1,#}(s1(x)) -> d{1,#}(f1(p1(s1(x)))) TRS: d1(s1(x)) -> s1(s1(d1(p1(s1(x))))) f1(s1(x)) -> d1(f1(p1(s1(x)))) p1(s1(x)) -> x graph: f{1,#}(s1(x)) -> f{1,#}(p1(s1(x))) -> f{1,#}(s1(x)) -> d{1,#}(f1(p1(s1(x)))) f{1,#}(s1(x)) -> f{1,#}(p1(s1(x))) -> f{1,#}(s1(x)) -> f{1,#}(p1(s1(x))) f{1,#}(s1(x)) -> f{1,#}(p1(s1(x))) -> f{1,#}(s1(x)) -> p{1,#}(s1(x)) f{1,#}(s1(x)) -> d{1,#}(f1(p1(s1(x)))) -> d{1,#}(s1(x)) -> d{1,#}(p1(s1(x))) f{1,#}(s1(x)) -> d{1,#}(f1(p1(s1(x)))) -> d{1,#}(s1(x)) -> p{1,#}(s1(x)) d{1,#}(s1(x)) -> d{1,#}(p1(s1(x))) -> d{1,#}(s1(x)) -> d{1,#}(p1(s1(x))) d{1,#}(s1(x)) -> d{1,#}(p1(s1(x))) -> d{1,#}(s1(x)) -> p{1,#}(s1(x)) SCC Processor: #sccs: 2 #rules: 2 #arcs: 7/25 DPs: f{1,#}(s1(x)) -> f{1,#}(p1(s1(x))) TRS: d1(s1(x)) -> s1(s1(d1(p1(s1(x))))) f1(s1(x)) -> d1(f1(p1(s1(x)))) p1(s1(x)) -> x Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {1} transitions: f180() -> 2* f{1,#,0}(4) -> 1* p{1,0}(3) -> 4* s{1,0}(2) -> 3* 2 -> 4* problem: DPs: TRS: d1(s1(x)) -> s1(s1(d1(p1(s1(x))))) f1(s1(x)) -> d1(f1(p1(s1(x)))) p1(s1(x)) -> x Qed DPs: d{1,#}(s1(x)) -> d{1,#}(p1(s1(x))) TRS: d1(s1(x)) -> s1(s1(d1(p1(s1(x))))) f1(s1(x)) -> d1(f1(p1(s1(x)))) p1(s1(x)) -> x Bounds Processor: bound: 0 enrichment: match-dp automaton: final states: {1} transitions: f230() -> 2* d{1,#,0}(4) -> 1* p{1,0}(3) -> 4* s{1,0}(2) -> 3* 2 -> 4* problem: DPs: TRS: d1(s1(x)) -> s1(s1(d1(p1(s1(x))))) f1(s1(x)) -> d1(f1(p1(s1(x)))) p1(s1(x)) -> x Qed