YES(?,O(n^1)) 0.16/0.32 YES(?,O(n^1)) 0.16/0.33 0.16/0.33 Problem: 0.16/0.33 f(f(a())) -> c(n__f(n__g(n__f(n__a())))) 0.16/0.33 f(X) -> n__f(X) 0.16/0.33 g(X) -> n__g(X) 0.16/0.33 a() -> n__a() 0.16/0.33 activate(n__f(X)) -> f(activate(X)) 0.16/0.33 activate(n__g(X)) -> g(activate(X)) 0.16/0.33 activate(n__a()) -> a() 0.16/0.33 activate(X) -> X 0.16/0.33 0.16/0.33 Proof: 0.16/0.33 Bounds Processor: 0.16/0.33 bound: 2 0.16/0.33 enrichment: match 0.16/0.33 automaton: 0.16/0.33 final states: {8,7,6,5} 0.16/0.33 transitions: 0.16/0.33 a1() -> 65* 0.16/0.33 g1(63) -> 64* 0.16/0.33 activate1(55) -> 56* 0.16/0.33 activate1(57) -> 58* 0.16/0.33 activate1(49) -> 50* 0.16/0.33 activate1(46) -> 47* 0.16/0.33 f1(47) -> 48* 0.16/0.33 n__a1() -> 41* 0.16/0.33 n__g1(25) -> 26* 0.16/0.33 n__g1(39) -> 40* 0.16/0.33 n__g1(31) -> 32* 0.16/0.33 n__g1(33) -> 34* 0.16/0.33 n__f1(15) -> 16* 0.16/0.33 n__f1(17) -> 18* 0.16/0.33 n__f1(9) -> 10* 0.16/0.33 n__f1(23) -> 24* 0.16/0.33 n__a2() -> 76* 0.16/0.33 n__g2(73) -> 74* 0.16/0.33 f0(2) -> 5* 0.16/0.33 f0(4) -> 5* 0.16/0.33 f0(1) -> 5* 0.16/0.33 f0(3) -> 5* 0.16/0.33 n__f2(69) -> 70* 0.16/0.33 a0() -> 7* 0.16/0.33 c2(79) -> 80* 0.16/0.33 c0(2) -> 1* 0.16/0.33 c0(4) -> 1* 0.16/0.33 c0(1) -> 1* 0.16/0.33 c0(3) -> 1* 0.16/0.33 n__f0(2) -> 2* 0.16/0.33 n__f0(4) -> 2* 0.16/0.33 n__f0(1) -> 2* 0.16/0.33 n__f0(3) -> 2* 0.16/0.33 n__g0(2) -> 3* 0.16/0.33 n__g0(4) -> 3* 0.16/0.33 n__g0(1) -> 3* 0.16/0.33 n__g0(3) -> 3* 0.16/0.33 n__a0() -> 4* 0.16/0.33 g0(2) -> 6* 0.16/0.33 g0(4) -> 6* 0.16/0.33 g0(1) -> 6* 0.16/0.33 g0(3) -> 6* 0.16/0.33 activate0(2) -> 8* 0.16/0.33 activate0(4) -> 8* 0.16/0.33 activate0(1) -> 8* 0.16/0.33 activate0(3) -> 8* 0.16/0.33 1 -> 8,55,31,15 0.16/0.33 2 -> 8,46,39,23 0.16/0.33 3 -> 8,57,25,9 0.16/0.33 4 -> 8,49,33,17 0.16/0.33 10 -> 5* 0.16/0.33 16 -> 5* 0.16/0.33 18 -> 5* 0.16/0.33 24 -> 5* 0.16/0.33 26 -> 6* 0.16/0.33 32 -> 6* 0.16/0.33 34 -> 6* 0.16/0.33 40 -> 6* 0.16/0.33 41 -> 7* 0.16/0.33 46 -> 47* 0.16/0.33 47 -> 69,63 0.16/0.33 48 -> 47,63,8 0.16/0.33 49 -> 50,47 0.16/0.33 50 -> 47* 0.16/0.33 55 -> 56,47 0.16/0.33 56 -> 47* 0.16/0.33 57 -> 58* 0.16/0.33 58 -> 47* 0.16/0.33 63 -> 73* 0.16/0.33 64 -> 58,47,63,8 0.16/0.33 65 -> 50,47,63,8 0.16/0.33 70 -> 79,48,8 0.16/0.33 74 -> 64,8 0.16/0.33 76 -> 65,8 0.16/0.33 80 -> 48,8,47,73 0.16/0.33 problem: 0.16/0.33 0.16/0.33 Qed 0.16/0.33 EOF