/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: minus(x,0()) -> x minus(0(),y) -> 0() minus(s(x),s(y)) -> minus(p(s(x)),p(s(y))) minus(x,plus(y,z)) -> minus(minus(x,y),z) p(s(s(x))) -> s(p(s(x))) p(0()) -> s(s(0())) div(s(x),s(y)) -> s(div(minus(x,y),s(y))) div(plus(x,y),z) -> plus(div(x,z),div(y,z)) plus(0(),y) -> y plus(s(x),y) -> s(plus(y,minus(s(x),s(0())))) Proof: DP Processor: DPs: minus#(s(x),s(y)) -> p#(s(y)) minus#(s(x),s(y)) -> p#(s(x)) minus#(s(x),s(y)) -> minus#(p(s(x)),p(s(y))) minus#(x,plus(y,z)) -> minus#(x,y) minus#(x,plus(y,z)) -> minus#(minus(x,y),z) p#(s(s(x))) -> p#(s(x)) div#(s(x),s(y)) -> minus#(x,y) div#(s(x),s(y)) -> div#(minus(x,y),s(y)) div#(plus(x,y),z) -> div#(y,z) div#(plus(x,y),z) -> div#(x,z) div#(plus(x,y),z) -> plus#(div(x,z),div(y,z)) plus#(s(x),y) -> minus#(s(x),s(0())) plus#(s(x),y) -> plus#(y,minus(s(x),s(0()))) TRS: minus(x,0()) -> x minus(0(),y) -> 0() minus(s(x),s(y)) -> minus(p(s(x)),p(s(y))) minus(x,plus(y,z)) -> minus(minus(x,y),z) p(s(s(x))) -> s(p(s(x))) p(0()) -> s(s(0())) div(s(x),s(y)) -> s(div(minus(x,y),s(y))) div(plus(x,y),z) -> plus(div(x,z),div(y,z)) plus(0(),y) -> y plus(s(x),y) -> s(plus(y,minus(s(x),s(0())))) TDG Processor: DPs: minus#(s(x),s(y)) -> p#(s(y)) minus#(s(x),s(y)) -> p#(s(x)) minus#(s(x),s(y)) -> minus#(p(s(x)),p(s(y))) minus#(x,plus(y,z)) -> minus#(x,y) minus#(x,plus(y,z)) -> minus#(minus(x,y),z) p#(s(s(x))) -> p#(s(x)) div#(s(x),s(y)) -> minus#(x,y) div#(s(x),s(y)) -> div#(minus(x,y),s(y)) div#(plus(x,y),z) -> div#(y,z) div#(plus(x,y),z) -> div#(x,z) div#(plus(x,y),z) -> plus#(div(x,z),div(y,z)) plus#(s(x),y) -> minus#(s(x),s(0())) plus#(s(x),y) -> plus#(y,minus(s(x),s(0()))) TRS: minus(x,0()) -> x minus(0(),y) -> 0() minus(s(x),s(y)) -> minus(p(s(x)),p(s(y))) minus(x,plus(y,z)) -> minus(minus(x,y),z) p(s(s(x))) -> s(p(s(x))) p(0()) -> s(s(0())) div(s(x),s(y)) -> s(div(minus(x,y),s(y))) div(plus(x,y),z) -> plus(div(x,z),div(y,z)) plus(0(),y) -> y plus(s(x),y) -> s(plus(y,minus(s(x),s(0())))) graph: plus#(s(x),y) -> plus#(y,minus(s(x),s(0()))) -> plus#(s(x),y) -> plus#(y,minus(s(x),s(0()))) plus#(s(x),y) -> plus#(y,minus(s(x),s(0()))) -> plus#(s(x),y) -> minus#(s(x),s(0())) plus#(s(x),y) -> minus#(s(x),s(0())) -> minus#(x,plus(y,z)) -> minus#(minus(x,y),z) plus#(s(x),y) -> minus#(s(x),s(0())) -> minus#(x,plus(y,z)) -> minus#(x,y) plus#(s(x),y) -> minus#(s(x),s(0())) -> minus#(s(x),s(y)) -> minus#(p(s(x)),p(s(y))) plus#(s(x),y) -> minus#(s(x),s(0())) -> minus#(s(x),s(y)) -> p#(s(x)) plus#(s(x),y) -> minus#(s(x),s(0())) -> minus#(s(x),s(y)) -> p#(s(y)) div#(plus(x,y),z) -> plus#(div(x,z),div(y,z)) -> plus#(s(x),y) -> plus#(y,minus(s(x),s(0()))) div#(plus(x,y),z) -> plus#(div(x,z),div(y,z)) -> plus#(s(x),y) -> minus#(s(x),s(0())) div#(plus(x,y),z) -> div#(y,z) -> div#(plus(x,y),z) -> plus#(div(x,z),div(y,z)) div#(plus(x,y),z) -> div#(y,z) -> div#(plus(x,y),z) -> div#(x,z) div#(plus(x,y),z) -> div#(y,z) -> div#(plus(x,y),z) -> div#(y,z) div#(plus(x,y),z) -> div#(y,z) -> div#(s(x),s(y)) -> div#(minus(x,y),s(y)) div#(plus(x,y),z) -> div#(y,z) -> div#(s(x),s(y)) -> minus#(x,y) div#(plus(x,y),z) -> div#(x,z) -> div#(plus(x,y),z) -> plus#(div(x,z),div(y,z)) div#(plus(x,y),z) -> div#(x,z) -> div#(plus(x,y),z) -> div#(x,z) div#(plus(x,y),z) -> div#(x,z) -> div#(plus(x,y),z) -> div#(y,z) div#(plus(x,y),z) -> div#(x,z) -> div#(s(x),s(y)) -> div#(minus(x,y),s(y)) div#(plus(x,y),z) -> div#(x,z) -> div#(s(x),s(y)) -> minus#(x,y) div#(s(x),s(y)) -> div#(minus(x,y),s(y)) -> div#(plus(x,y),z) -> plus#(div(x,z),div(y,z)) div#(s(x),s(y)) -> div#(minus(x,y),s(y)) -> div#(plus(x,y),z) -> div#(x,z) div#(s(x),s(y)) -> div#(minus(x,y),s(y)) -> div#(plus(x,y),z) -> div#(y,z) div#(s(x),s(y)) -> div#(minus(x,y),s(y)) -> div#(s(x),s(y)) -> div#(minus(x,y),s(y)) div#(s(x),s(y)) -> div#(minus(x,y),s(y)) -> div#(s(x),s(y)) -> minus#(x,y) div#(s(x),s(y)) -> minus#(x,y) -> minus#(x,plus(y,z)) -> minus#(minus(x,y),z) div#(s(x),s(y)) -> minus#(x,y) -> minus#(x,plus(y,z)) -> minus#(x,y) div#(s(x),s(y)) -> minus#(x,y) -> minus#(s(x),s(y)) -> minus#(p(s(x)),p(s(y))) div#(s(x),s(y)) -> minus#(x,y) -> minus#(s(x),s(y)) -> p#(s(x)) div#(s(x),s(y)) -> minus#(x,y) -> minus#(s(x),s(y)) -> p#(s(y)) p#(s(s(x))) -> p#(s(x)) -> p#(s(s(x))) -> p#(s(x)) minus#(s(x),s(y)) -> p#(s(y)) -> p#(s(s(x))) -> p#(s(x)) minus#(s(x),s(y)) -> p#(s(x)) -> p#(s(s(x))) -> p#(s(x)) minus#(s(x),s(y)) -> minus#(p(s(x)),p(s(y))) -> minus#(x,plus(y,z)) -> minus#(minus(x,y),z) minus#(s(x),s(y)) -> minus#(p(s(x)),p(s(y))) -> minus#(x,plus(y,z)) -> minus#(x,y) minus#(s(x),s(y)) -> minus#(p(s(x)),p(s(y))) -> minus#(s(x),s(y)) -> minus#(p(s(x)),p(s(y))) minus#(s(x),s(y)) -> minus#(p(s(x)),p(s(y))) -> minus#(s(x),s(y)) -> p#(s(x)) minus#(s(x),s(y)) -> minus#(p(s(x)),p(s(y))) -> minus#(s(x),s(y)) -> p#(s(y)) minus#(x,plus(y,z)) -> minus#(minus(x,y),z) -> minus#(x,plus(y,z)) -> minus#(minus(x,y),z) minus#(x,plus(y,z)) -> minus#(minus(x,y),z) -> minus#(x,plus(y,z)) -> minus#(x,y) minus#(x,plus(y,z)) -> minus#(minus(x,y),z) -> minus#(s(x),s(y)) -> minus#(p(s(x)),p(s(y))) minus#(x,plus(y,z)) -> minus#(minus(x,y),z) -> minus#(s(x),s(y)) -> p#(s(x)) minus#(x,plus(y,z)) -> minus#(minus(x,y),z) -> minus#(s(x),s(y)) -> p#(s(y)) minus#(x,plus(y,z)) -> minus#(x,y) -> minus#(x,plus(y,z)) -> minus#(minus(x,y),z) minus#(x,plus(y,z)) -> minus#(x,y) -> minus#(x,plus(y,z)) -> minus#(x,y) minus#(x,plus(y,z)) -> minus#(x,y) -> minus#(s(x),s(y)) -> minus#(p(s(x)),p(s(y))) minus#(x,plus(y,z)) -> minus#(x,y) -> minus#(s(x),s(y)) -> p#(s(x)) minus#(x,plus(y,z)) -> minus#(x,y) -> minus#(s(x),s(y)) -> p#(s(y)) SCC Processor: #sccs: 4 #rules: 8 #arcs: 47/169 DPs: div#(plus(x,y),z) -> div#(y,z) div#(s(x),s(y)) -> div#(minus(x,y),s(y)) div#(plus(x,y),z) -> div#(x,z) TRS: minus(x,0()) -> x minus(0(),y) -> 0() minus(s(x),s(y)) -> minus(p(s(x)),p(s(y))) minus(x,plus(y,z)) -> minus(minus(x,y),z) p(s(s(x))) -> s(p(s(x))) p(0()) -> s(s(0())) div(s(x),s(y)) -> s(div(minus(x,y),s(y))) div(plus(x,y),z) -> plus(div(x,z),div(y,z)) plus(0(),y) -> y plus(s(x),y) -> s(plus(y,minus(s(x),s(0())))) Subterm Criterion Processor: simple projection: pi(minus) = 0 pi(s) = 0 pi(p) = 0 pi(div#) = 0 problem: DPs: div#(s(x),s(y)) -> div#(minus(x,y),s(y)) TRS: minus(x,0()) -> x minus(0(),y) -> 0() minus(s(x),s(y)) -> minus(p(s(x)),p(s(y))) minus(x,plus(y,z)) -> minus(minus(x,y),z) p(s(s(x))) -> s(p(s(x))) p(0()) -> s(s(0())) div(s(x),s(y)) -> s(div(minus(x,y),s(y))) div(plus(x,y),z) -> plus(div(x,z),div(y,z)) plus(0(),y) -> y plus(s(x),y) -> s(plus(y,minus(s(x),s(0())))) Usable Rule Processor: DPs: div#(s(x),s(y)) -> div#(minus(x,y),s(y)) TRS: minus(x,0()) -> x minus(0(),y) -> 0() minus(s(x),s(y)) -> minus(p(s(x)),p(s(y))) minus(x,plus(y,z)) -> minus(minus(x,y),z) p(s(s(x))) -> s(p(s(x))) Arctic Interpretation Processor: dimension: 1 usable rules: minus(x,0()) -> x minus(0(),y) -> 0() minus(s(x),s(y)) -> minus(p(s(x)),p(s(y))) minus(x,plus(y,z)) -> minus(minus(x,y),z) p(s(s(x))) -> s(p(s(x))) interpretation: [div#](x0, x1) = x0, [plus](x0, x1) = 8x0 + -4x1 + 0, [p](x0) = x0, [s](x0) = 1x0, [minus](x0, x1) = x0, [0] = 4 orientation: div#(s(x),s(y)) = 1x >= x = div#(minus(x,y),s(y)) minus(x,0()) = x >= x = x minus(0(),y) = 4 >= 4 = 0() minus(s(x),s(y)) = 1x >= 1x = minus(p(s(x)),p(s(y))) minus(x,plus(y,z)) = x >= x = minus(minus(x,y),z) p(s(s(x))) = 2x >= 2x = s(p(s(x))) problem: DPs: TRS: minus(x,0()) -> x minus(0(),y) -> 0() minus(s(x),s(y)) -> minus(p(s(x)),p(s(y))) minus(x,plus(y,z)) -> minus(minus(x,y),z) p(s(s(x))) -> s(p(s(x))) Qed DPs: plus#(s(x),y) -> plus#(y,minus(s(x),s(0()))) TRS: minus(x,0()) -> x minus(0(),y) -> 0() minus(s(x),s(y)) -> minus(p(s(x)),p(s(y))) minus(x,plus(y,z)) -> minus(minus(x,y),z) p(s(s(x))) -> s(p(s(x))) p(0()) -> s(s(0())) div(s(x),s(y)) -> s(div(minus(x,y),s(y))) div(plus(x,y),z) -> plus(div(x,z),div(y,z)) plus(0(),y) -> y plus(s(x),y) -> s(plus(y,minus(s(x),s(0())))) Bounds Processor: bound: 2 enrichment: top-dp automaton: final states: {9} transitions: p0(8) -> 8* plus0(8,8) -> 8* div0(8,8) -> 8* plus{#,1}(8,17) -> 9* minus1(16,15) -> 17* s1(14) -> 15* s1(16) -> 16* s1(8) -> 16* 01() -> 14* plus{#,2}(17,21) -> 9* minus2(20,19) -> 21* s2(20) -> 20* s2(18) -> 19* s2(8) -> 20* 02() -> 18* plus{#,0}(8,8) -> 9* p2(20) -> 20* p2(19) -> 19* s0(8) -> 8* p1(15) -> 15* p1(16) -> 16* minus0(8,8) -> 8* 00() -> 8* problem: DPs: TRS: minus(x,0()) -> x minus(0(),y) -> 0() minus(s(x),s(y)) -> minus(p(s(x)),p(s(y))) minus(x,plus(y,z)) -> minus(minus(x,y),z) p(s(s(x))) -> s(p(s(x))) p(0()) -> s(s(0())) div(s(x),s(y)) -> s(div(minus(x,y),s(y))) div(plus(x,y),z) -> plus(div(x,z),div(y,z)) plus(0(),y) -> y plus(s(x),y) -> s(plus(y,minus(s(x),s(0())))) Qed DPs: minus#(s(x),s(y)) -> minus#(p(s(x)),p(s(y))) minus#(x,plus(y,z)) -> minus#(x,y) minus#(x,plus(y,z)) -> minus#(minus(x,y),z) TRS: minus(x,0()) -> x minus(0(),y) -> 0() minus(s(x),s(y)) -> minus(p(s(x)),p(s(y))) minus(x,plus(y,z)) -> minus(minus(x,y),z) p(s(s(x))) -> s(p(s(x))) p(0()) -> s(s(0())) div(s(x),s(y)) -> s(div(minus(x,y),s(y))) div(plus(x,y),z) -> plus(div(x,z),div(y,z)) plus(0(),y) -> y plus(s(x),y) -> s(plus(y,minus(s(x),s(0())))) EDG Processor: DPs: minus#(s(x),s(y)) -> minus#(p(s(x)),p(s(y))) minus#(x,plus(y,z)) -> minus#(x,y) minus#(x,plus(y,z)) -> minus#(minus(x,y),z) TRS: minus(x,0()) -> x minus(0(),y) -> 0() minus(s(x),s(y)) -> minus(p(s(x)),p(s(y))) minus(x,plus(y,z)) -> minus(minus(x,y),z) p(s(s(x))) -> s(p(s(x))) p(0()) -> s(s(0())) div(s(x),s(y)) -> s(div(minus(x,y),s(y))) div(plus(x,y),z) -> plus(div(x,z),div(y,z)) plus(0(),y) -> y plus(s(x),y) -> s(plus(y,minus(s(x),s(0())))) graph: minus#(s(x),s(y)) -> minus#(p(s(x)),p(s(y))) -> minus#(s(x),s(y)) -> minus#(p(s(x)),p(s(y))) minus#(x,plus(y,z)) -> minus#(minus(x,y),z) -> minus#(s(x),s(y)) -> minus#(p(s(x)),p(s(y))) minus#(x,plus(y,z)) -> minus#(minus(x,y),z) -> minus#(x,plus(y,z)) -> minus#(x,y) minus#(x,plus(y,z)) -> minus#(minus(x,y),z) -> minus#(x,plus(y,z)) -> minus#(minus(x,y),z) minus#(x,plus(y,z)) -> minus#(x,y) -> minus#(s(x),s(y)) -> minus#(p(s(x)),p(s(y))) minus#(x,plus(y,z)) -> minus#(x,y) -> minus#(x,plus(y,z)) -> minus#(x,y) minus#(x,plus(y,z)) -> minus#(x,y) -> minus#(x,plus(y,z)) -> minus#(minus(x,y),z) SCC Processor: #sccs: 2 #rules: 3 #arcs: 7/9 DPs: minus#(x,plus(y,z)) -> minus#(minus(x,y),z) minus#(x,plus(y,z)) -> minus#(x,y) TRS: minus(x,0()) -> x minus(0(),y) -> 0() minus(s(x),s(y)) -> minus(p(s(x)),p(s(y))) minus(x,plus(y,z)) -> minus(minus(x,y),z) p(s(s(x))) -> s(p(s(x))) p(0()) -> s(s(0())) div(s(x),s(y)) -> s(div(minus(x,y),s(y))) div(plus(x,y),z) -> plus(div(x,z),div(y,z)) plus(0(),y) -> y plus(s(x),y) -> s(plus(y,minus(s(x),s(0())))) Size-Change Termination Processor: DPs: TRS: minus(x,0()) -> x minus(0(),y) -> 0() minus(s(x),s(y)) -> minus(p(s(x)),p(s(y))) minus(x,plus(y,z)) -> minus(minus(x,y),z) p(s(s(x))) -> s(p(s(x))) p(0()) -> s(s(0())) div(s(x),s(y)) -> s(div(minus(x,y),s(y))) div(plus(x,y),z) -> plus(div(x,z),div(y,z)) plus(0(),y) -> y plus(s(x),y) -> s(plus(y,minus(s(x),s(0())))) The DP: minus#(x,plus(y,z)) -> minus#(minus(x,y),z) has the edges: 1 > 1 The DP: minus#(x,plus(y,z)) -> minus#(x,y) has the edges: 0 >= 0 1 > 1 Qed DPs: minus#(s(x),s(y)) -> minus#(p(s(x)),p(s(y))) TRS: minus(x,0()) -> x minus(0(),y) -> 0() minus(s(x),s(y)) -> minus(p(s(x)),p(s(y))) minus(x,plus(y,z)) -> minus(minus(x,y),z) p(s(s(x))) -> s(p(s(x))) p(0()) -> s(s(0())) div(s(x),s(y)) -> s(div(minus(x,y),s(y))) div(plus(x,y),z) -> plus(div(x,z),div(y,z)) plus(0(),y) -> y plus(s(x),y) -> s(plus(y,minus(s(x),s(0())))) Usable Rule Processor: DPs: minus#(s(x),s(y)) -> minus#(p(s(x)),p(s(y))) TRS: p(s(s(x))) -> s(p(s(x))) Semantic Labeling Processor: dimension: 2 usable rules: p(s(s(x))) -> s(p(s(x))) interpretation: [0 1] [p](x0) = [0 1]x0, [1 0] [1] [s](x0) = [1 0]x0 + [0] labeled: minus# s p usable (for model): minus# s p argument filtering: pi(s) = [] pi(p) = [] pi(minus#) = 1 precedence: p > minus# ~ s problem: DPs: TRS: p(s(s(x))) -> s(p(s(x))) Qed DPs: p#(s(s(x))) -> p#(s(x)) TRS: minus(x,0()) -> x minus(0(),y) -> 0() minus(s(x),s(y)) -> minus(p(s(x)),p(s(y))) minus(x,plus(y,z)) -> minus(minus(x,y),z) p(s(s(x))) -> s(p(s(x))) p(0()) -> s(s(0())) div(s(x),s(y)) -> s(div(minus(x,y),s(y))) div(plus(x,y),z) -> plus(div(x,z),div(y,z)) plus(0(),y) -> y plus(s(x),y) -> s(plus(y,minus(s(x),s(0())))) Subterm Criterion Processor: simple projection: pi(p#) = 0 problem: DPs: TRS: minus(x,0()) -> x minus(0(),y) -> 0() minus(s(x),s(y)) -> minus(p(s(x)),p(s(y))) minus(x,plus(y,z)) -> minus(minus(x,y),z) p(s(s(x))) -> s(p(s(x))) p(0()) -> s(s(0())) div(s(x),s(y)) -> s(div(minus(x,y),s(y))) div(plus(x,y),z) -> plus(div(x,z),div(y,z)) plus(0(),y) -> y plus(s(x),y) -> s(plus(y,minus(s(x),s(0())))) Qed