YES(?,O(n^1)) 0.16/0.80 YES(?,O(n^1)) 0.16/0.81 0.16/0.81 Problem: 0.16/0.81 active(c()) -> mark(f(g(c()))) 0.16/0.81 active(f(g(X))) -> mark(g(X)) 0.16/0.81 proper(c()) -> ok(c()) 0.16/0.81 proper(f(X)) -> f(proper(X)) 0.16/0.81 proper(g(X)) -> g(proper(X)) 0.16/0.81 f(ok(X)) -> ok(f(X)) 0.16/0.81 g(ok(X)) -> ok(g(X)) 0.16/0.81 top(mark(X)) -> top(proper(X)) 0.16/0.81 top(ok(X)) -> top(active(X)) 0.16/0.81 0.16/0.81 Proof: 0.16/0.81 Bounds Processor: 0.16/0.81 bound: 6 0.16/0.81 enrichment: match 0.16/0.81 automaton: 0.16/0.81 final states: {8,7,6,5,4} 0.16/0.81 transitions: 0.16/0.81 f3(137) -> 138* 0.16/0.81 f3(119) -> 120* 0.16/0.81 ok2(111) -> 112* 0.16/0.81 ok3(131) -> 132* 0.16/0.81 ok3(138) -> 139* 0.16/0.81 ok3(135) -> 136* 0.16/0.81 g3(122) -> 123* 0.16/0.81 g3(130) -> 131* 0.16/0.81 c3() -> 135* 0.16/0.81 active3(149) -> 150* 0.16/0.81 ok4(144) -> 145* 0.16/0.81 ok4(201) -> 202* 0.16/0.81 ok4(163) -> 164* 0.16/0.81 g4(156) -> 157* 0.16/0.81 g4(143) -> 144* 0.16/0.81 f4(162) -> 163* 0.16/0.81 active0(2) -> 4* 0.16/0.81 active0(1) -> 4* 0.16/0.81 active0(3) -> 4* 0.16/0.81 mark4(157) -> 158* 0.16/0.81 c0() -> 1* 0.16/0.81 top4(169) -> 170* 0.16/0.81 mark0(2) -> 2* 0.16/0.81 mark0(1) -> 2* 0.16/0.81 mark0(3) -> 2* 0.16/0.81 active4(173) -> 174* 0.16/0.81 f0(2) -> 6* 0.16/0.81 f0(1) -> 6* 0.16/0.81 f0(3) -> 6* 0.16/0.81 proper4(168) -> 169* 0.16/0.81 g0(2) -> 7* 0.16/0.81 g0(1) -> 7* 0.16/0.81 g0(3) -> 7* 0.16/0.81 g5(182) -> 183* 0.16/0.81 g5(210) -> 211* 0.16/0.81 g5(175) -> 176* 0.16/0.81 proper0(2) -> 5* 0.16/0.81 proper0(1) -> 5* 0.16/0.81 proper0(3) -> 5* 0.16/0.81 proper5(187) -> 188* 0.16/0.81 proper5(181) -> 182* 0.16/0.81 ok0(2) -> 3* 0.16/0.81 ok0(1) -> 3* 0.16/0.81 ok0(3) -> 3* 0.16/0.81 mark5(176) -> 177* 0.16/0.81 top0(2) -> 8* 0.16/0.81 top0(1) -> 8* 0.16/0.81 top0(3) -> 8* 0.16/0.81 top5(188) -> 189* 0.16/0.81 top1(53) -> 54* 0.16/0.81 g6(194) -> 195* 0.16/0.81 active1(69) -> 70* 0.16/0.81 active1(71) -> 72* 0.16/0.81 active1(63) -> 64* 0.16/0.81 proper6(193) -> 194* 0.16/0.81 proper1(55) -> 56* 0.16/0.81 proper1(52) -> 53* 0.16/0.81 proper1(61) -> 62* 0.16/0.81 active5(203) -> 204* 0.16/0.81 ok1(25) -> 26* 0.16/0.81 ok1(17) -> 18* 0.16/0.81 ok1(36) -> 37* 0.16/0.81 c4() -> 201* 0.16/0.81 g1(45) -> 46* 0.16/0.81 g1(35) -> 36* 0.16/0.81 g1(43) -> 44* 0.16/0.81 g1(13) -> 14* 0.16/0.81 ok5(211) -> 212* 0.16/0.81 f1(27) -> 28* 0.16/0.81 f1(24) -> 25* 0.16/0.81 f1(14) -> 15* 0.16/0.81 f1(33) -> 34* 0.16/0.81 top6(217) -> 218* 0.16/0.81 c1() -> 13* 0.16/0.81 active6(216) -> 217* 0.16/0.81 mark1(15) -> 16* 0.16/0.81 top2(79) -> 80* 0.16/0.81 active2(83) -> 84* 0.16/0.81 proper2(102) -> 103* 0.16/0.81 proper2(93) -> 94* 0.16/0.81 proper2(78) -> 79* 0.16/0.81 f2(94) -> 95* 0.16/0.81 f2(86) -> 87* 0.16/0.81 mark2(87) -> 88* 0.16/0.81 g2(85) -> 86* 0.16/0.81 g2(103) -> 104* 0.16/0.81 c2() -> 85* 0.16/0.81 top3(106) -> 107* 0.16/0.81 proper3(121) -> 122* 0.16/0.81 proper3(118) -> 119* 0.16/0.81 proper3(105) -> 106* 0.16/0.81 1 -> 69,55,43,27 0.16/0.81 2 -> 63,52,35,24 0.16/0.81 3 -> 71,61,45,33 0.16/0.81 13 -> 102,17 0.16/0.81 14 -> 93* 0.16/0.81 15 -> 78* 0.16/0.81 16 -> 70,53,4 0.16/0.81 17 -> 83* 0.16/0.81 18 -> 56,53,5 0.16/0.81 26 -> 34,25,6 0.16/0.81 28 -> 25* 0.16/0.81 34 -> 25* 0.16/0.81 37 -> 46,36,7 0.16/0.81 44 -> 36* 0.16/0.81 46 -> 36* 0.16/0.81 54 -> 8* 0.16/0.81 56 -> 53* 0.16/0.81 62 -> 53* 0.16/0.81 64 -> 53* 0.16/0.81 70 -> 53* 0.16/0.81 72 -> 53* 0.16/0.81 80 -> 54,8 0.16/0.81 84 -> 79* 0.16/0.81 85 -> 121,111 0.16/0.81 86 -> 118* 0.16/0.81 87 -> 105* 0.16/0.81 88 -> 84,79 0.16/0.81 95 -> 79* 0.16/0.81 104 -> 94* 0.16/0.81 107 -> 80,54 0.16/0.81 111 -> 130* 0.16/0.81 112 -> 103* 0.16/0.81 120 -> 106* 0.16/0.81 123 -> 119* 0.16/0.81 130 -> 156* 0.16/0.81 131 -> 137* 0.16/0.81 132 -> 104,94 0.16/0.81 135 -> 143* 0.16/0.81 136 -> 182,122 0.16/0.81 138 -> 149* 0.16/0.81 139 -> 95,79 0.16/0.81 143 -> 175* 0.16/0.81 144 -> 203,162 0.16/0.81 145 -> 183,169,123,119 0.16/0.81 150 -> 106* 0.16/0.81 156 -> 181* 0.16/0.81 157 -> 168* 0.16/0.81 158 -> 150,106 0.16/0.81 163 -> 173* 0.16/0.81 164 -> 120,106 0.16/0.81 170 -> 107,80 0.16/0.81 174 -> 169* 0.16/0.81 175 -> 193* 0.16/0.81 176 -> 187* 0.16/0.81 177 -> 174,169 0.16/0.81 183 -> 169* 0.16/0.81 189 -> 170,107 0.16/0.81 195 -> 188* 0.16/0.81 201 -> 210* 0.16/0.81 202 -> 194* 0.16/0.81 204 -> 188* 0.16/0.81 211 -> 216* 0.16/0.81 212 -> 195,188 0.16/0.81 218 -> 189,170 0.16/0.81 problem: 0.16/0.81 0.16/0.81 Qed 0.16/0.81 EOF