YES(?,O(n^1)) 0.16/0.28 YES(?,O(n^1)) 0.16/0.29 0.16/0.29 Problem: 0.16/0.29 active(f(f(a()))) -> mark(f(g(f(a())))) 0.16/0.29 active(g(X)) -> g(active(X)) 0.16/0.29 g(mark(X)) -> mark(g(X)) 0.16/0.29 proper(f(X)) -> f(proper(X)) 0.16/0.29 proper(a()) -> ok(a()) 0.16/0.29 proper(g(X)) -> g(proper(X)) 0.16/0.29 f(ok(X)) -> ok(f(X)) 0.16/0.29 g(ok(X)) -> ok(g(X)) 0.16/0.29 top(mark(X)) -> top(proper(X)) 0.16/0.29 top(ok(X)) -> top(active(X)) 0.16/0.29 0.16/0.29 Proof: 0.16/0.29 Bounds Processor: 0.16/0.29 bound: 2 0.16/0.29 enrichment: match 0.16/0.29 automaton: 0.16/0.29 final states: {8,7,6,5,4} 0.16/0.29 transitions: 0.16/0.29 top1(46) -> 47* 0.16/0.29 active1(69) -> 70* 0.16/0.29 active1(61) -> 62* 0.16/0.29 active1(63) -> 64* 0.16/0.29 proper1(55) -> 56* 0.16/0.29 proper1(45) -> 46* 0.16/0.29 proper1(53) -> 54* 0.16/0.29 ok1(25) -> 26* 0.16/0.29 ok1(43) -> 44* 0.16/0.29 ok1(28) -> 29* 0.16/0.29 g1(17) -> 18* 0.16/0.29 g1(19) -> 20* 0.16/0.29 g1(9) -> 10* 0.16/0.29 f1(35) -> 36* 0.16/0.29 f1(37) -> 38* 0.16/0.29 f1(27) -> 28* 0.16/0.29 a1() -> 25* 0.16/0.29 mark1(10) -> 11* 0.16/0.29 top2(75) -> 76* 0.16/0.29 active0(2) -> 4* 0.16/0.29 active0(1) -> 4* 0.16/0.29 active0(3) -> 4* 0.16/0.29 active2(74) -> 75* 0.16/0.29 f0(2) -> 7* 0.16/0.29 f0(1) -> 7* 0.16/0.29 f0(3) -> 7* 0.16/0.29 a0() -> 1* 0.16/0.29 mark0(2) -> 2* 0.16/0.29 mark0(1) -> 2* 0.16/0.29 mark0(3) -> 2* 0.16/0.29 g0(2) -> 5* 0.16/0.29 g0(1) -> 5* 0.16/0.30 g0(3) -> 5* 0.16/0.30 proper0(2) -> 6* 0.16/0.30 proper0(1) -> 6* 0.16/0.30 proper0(3) -> 6* 0.16/0.30 ok0(2) -> 3* 0.16/0.30 ok0(1) -> 3* 0.16/0.30 ok0(3) -> 3* 0.16/0.30 top0(2) -> 8* 0.16/0.30 top0(1) -> 8* 0.16/0.30 top0(3) -> 8* 0.16/0.30 1 -> 63,53,35,17 0.16/0.30 2 -> 61,45,27,9 0.16/0.30 3 -> 69,55,37,19 0.16/0.30 10 -> 43* 0.16/0.30 11 -> 10,43,5 0.16/0.30 18 -> 10* 0.16/0.30 20 -> 10* 0.16/0.30 25 -> 74* 0.16/0.30 26 -> 54,46,6 0.16/0.30 29 -> 38,28,7 0.16/0.30 36 -> 28* 0.16/0.30 38 -> 28* 0.16/0.30 44 -> 20,10,43,5 0.16/0.30 47 -> 8* 0.16/0.30 54 -> 46* 0.16/0.30 56 -> 46* 0.16/0.30 62 -> 46* 0.16/0.30 64 -> 46* 0.16/0.30 70 -> 46* 0.16/0.30 76 -> 47,8 0.16/0.30 problem: 0.16/0.30 0.16/0.30 Qed 0.16/0.30 EOF