YES(?,O(n^1)) 0.17/0.35 YES(?,O(n^1)) 0.17/0.36 0.17/0.36 Problem: 0.17/0.36 active(f(f(X))) -> mark(c(f(g(f(X))))) 0.17/0.36 active(c(X)) -> mark(d(X)) 0.17/0.36 active(h(X)) -> mark(c(d(X))) 0.17/0.36 active(f(X)) -> f(active(X)) 0.17/0.36 active(h(X)) -> h(active(X)) 0.17/0.36 f(mark(X)) -> mark(f(X)) 0.17/0.36 h(mark(X)) -> mark(h(X)) 0.17/0.36 proper(f(X)) -> f(proper(X)) 0.17/0.36 proper(c(X)) -> c(proper(X)) 0.17/0.36 proper(g(X)) -> g(proper(X)) 0.17/0.36 proper(d(X)) -> d(proper(X)) 0.17/0.36 proper(h(X)) -> h(proper(X)) 0.17/0.36 f(ok(X)) -> ok(f(X)) 0.17/0.36 c(ok(X)) -> ok(c(X)) 0.17/0.36 g(ok(X)) -> ok(g(X)) 0.17/0.36 d(ok(X)) -> ok(d(X)) 0.17/0.36 h(ok(X)) -> ok(h(X)) 0.17/0.36 top(mark(X)) -> top(proper(X)) 0.17/0.36 top(ok(X)) -> top(active(X)) 0.17/0.36 0.17/0.36 Proof: 0.17/0.36 Bounds Processor: 0.17/0.36 bound: 1 0.17/0.36 enrichment: match 0.17/0.36 automaton: 0.17/0.36 final states: {10,9,8,7,6,5,4,3} 0.17/0.36 transitions: 0.17/0.36 top1(70) -> 71* 0.17/0.36 active1(85) -> 86* 0.17/0.36 active1(79) -> 80* 0.17/0.36 proper1(77) -> 78* 0.17/0.36 proper1(69) -> 70* 0.17/0.36 ok1(67) -> 68* 0.17/0.36 ok1(59) -> 60* 0.17/0.36 ok1(49) -> 50* 0.17/0.36 ok1(39) -> 40* 0.17/0.36 ok1(31) -> 32* 0.17/0.36 h1(29) -> 30* 0.17/0.36 h1(21) -> 22* 0.17/0.36 d1(61) -> 62* 0.17/0.36 d1(58) -> 59* 0.17/0.36 g1(51) -> 52* 0.17/0.36 g1(48) -> 49* 0.17/0.36 c1(41) -> 42* 0.17/0.36 c1(38) -> 39* 0.17/0.36 f1(19) -> 20* 0.17/0.36 f1(11) -> 12* 0.17/0.36 mark1(22) -> 23* 0.17/0.36 mark1(12) -> 13* 0.17/0.36 active0(2) -> 3* 0.17/0.36 active0(1) -> 3* 0.17/0.36 f0(2) -> 4* 0.17/0.36 f0(1) -> 4* 0.17/0.36 mark0(2) -> 1* 0.17/0.36 mark0(1) -> 1* 0.17/0.36 c0(2) -> 7* 0.17/0.36 c0(1) -> 7* 0.17/0.36 g0(2) -> 8* 0.17/0.36 g0(1) -> 8* 0.17/0.36 d0(2) -> 9* 0.17/0.36 d0(1) -> 9* 0.17/0.36 h0(2) -> 5* 0.17/0.36 h0(1) -> 5* 0.17/0.36 proper0(2) -> 6* 0.17/0.36 proper0(1) -> 6* 0.17/0.36 ok0(2) -> 2* 0.17/0.36 ok0(1) -> 2* 0.17/0.36 top0(2) -> 10* 0.17/0.36 top0(1) -> 10* 0.17/0.36 1 -> 85,77,61,51,41,29,19 0.17/0.36 2 -> 79,69,58,48,38,21,11 0.17/0.36 12 -> 31* 0.17/0.36 13 -> 20,12,31,4 0.17/0.36 20 -> 12* 0.17/0.36 22 -> 67* 0.17/0.36 23 -> 30,22,67,5 0.17/0.36 30 -> 22* 0.17/0.36 32 -> 12,31,4 0.17/0.36 40 -> 39,7 0.17/0.36 42 -> 39* 0.17/0.36 50 -> 49,8 0.17/0.36 52 -> 49* 0.17/0.36 60 -> 59,9 0.17/0.36 62 -> 59* 0.17/0.36 68 -> 22,67,5 0.17/0.36 71 -> 10* 0.17/0.36 78 -> 70* 0.17/0.36 80 -> 70* 0.17/0.36 86 -> 70* 0.17/0.36 problem: 0.17/0.36 0.17/0.36 Qed 0.17/0.36 EOF