YES(?,O(n^1)) 0.16/0.26 YES(?,O(n^1)) 0.16/0.26 0.16/0.26 Problem: 0.16/0.26 f(n__f(n__a())) -> f(n__g(f(n__a()))) 0.16/0.26 f(X) -> n__f(X) 0.16/0.26 a() -> n__a() 0.16/0.26 g(X) -> n__g(X) 0.16/0.26 activate(n__f(X)) -> f(X) 0.16/0.26 activate(n__a()) -> a() 0.16/0.26 activate(n__g(X)) -> g(X) 0.16/0.26 activate(X) -> X 0.16/0.26 0.16/0.26 Proof: 0.16/0.26 Bounds Processor: 0.16/0.26 bound: 2 0.16/0.26 enrichment: match 0.16/0.26 automaton: 0.16/0.26 final states: {7,6,5,4} 0.16/0.26 transitions: 0.16/0.26 g1(64) -> 65* 0.16/0.26 g1(56) -> 57* 0.16/0.26 g1(58) -> 59* 0.16/0.26 a1() -> 52* 0.16/0.26 f1(50) -> 51* 0.16/0.26 f1(42) -> 43* 0.16/0.26 f1(12) -> 13* 0.16/0.26 f1(44) -> 45* 0.16/0.26 f1(14) -> 15* 0.16/0.26 n__g1(34) -> 35* 0.16/0.26 n__g1(36) -> 37* 0.16/0.26 n__g1(28) -> 29* 0.16/0.26 n__g1(13) -> 14* 0.16/0.26 n__a1() -> 12* 0.16/0.26 n__f1(22) -> 23* 0.16/0.26 n__f1(24) -> 25* 0.16/0.26 n__f1(16) -> 17* 0.16/0.26 n__g2(96) -> 97* 0.16/0.26 n__g2(88) -> 89* 0.16/0.26 n__g2(90) -> 91* 0.16/0.26 n__a2() -> 86* 0.16/0.26 f0(2) -> 4* 0.16/0.26 f0(1) -> 4* 0.16/0.26 f0(3) -> 4* 0.16/0.26 n__f2(70) -> 71* 0.16/0.26 n__f2(84) -> 85* 0.16/0.26 n__f2(76) -> 77* 0.16/0.26 n__f2(78) -> 79* 0.16/0.26 n__f2(68) -> 69* 0.16/0.26 n__f0(2) -> 1* 0.16/0.26 n__f0(1) -> 1* 0.16/0.26 n__f0(3) -> 1* 0.16/0.26 n__a0() -> 2* 0.16/0.26 n__g0(2) -> 3* 0.16/0.26 n__g0(1) -> 3* 0.16/0.26 n__g0(3) -> 3* 0.16/0.26 a0() -> 5* 0.16/0.26 g0(2) -> 6* 0.16/0.26 g0(1) -> 6* 0.16/0.26 g0(3) -> 6* 0.16/0.26 activate0(2) -> 7* 0.16/0.26 activate0(1) -> 7* 0.16/0.26 activate0(3) -> 7* 0.16/0.26 1 -> 7,58,44,34,22 0.16/0.26 2 -> 7,56,42,36,24 0.16/0.26 3 -> 7,64,50,28,16 0.16/0.26 12 -> 84,5 0.16/0.26 14 -> 76* 0.16/0.26 15 -> 45,7,4 0.16/0.26 17 -> 4* 0.16/0.26 23 -> 4* 0.16/0.26 25 -> 4* 0.16/0.26 29 -> 6* 0.16/0.26 35 -> 6* 0.16/0.26 37 -> 6* 0.16/0.26 42 -> 68* 0.16/0.26 43 -> 7* 0.16/0.26 44 -> 70* 0.16/0.26 45 -> 7* 0.16/0.26 50 -> 78* 0.16/0.26 51 -> 7* 0.16/0.26 52 -> 7* 0.16/0.26 56 -> 88* 0.16/0.26 57 -> 7* 0.16/0.26 58 -> 90* 0.16/0.26 59 -> 7* 0.16/0.26 64 -> 96* 0.16/0.26 65 -> 7* 0.16/0.26 69 -> 43* 0.16/0.26 71 -> 45* 0.16/0.26 77 -> 15* 0.16/0.26 79 -> 51,7 0.16/0.26 85 -> 13* 0.16/0.26 86 -> 52,7 0.16/0.26 89 -> 57* 0.16/0.26 91 -> 59,7 0.16/0.26 97 -> 65,7 0.16/0.26 problem: 0.16/0.26 0.16/0.26 Qed 0.16/0.27 EOF