YES(?,O(n^1)) 0.16/0.22 YES(?,O(n^1)) 0.16/0.22 0.16/0.22 Problem: 0.16/0.22 f(f(a())) -> f(g(n__f(a()))) 0.16/0.22 f(X) -> n__f(X) 0.16/0.22 activate(n__f(X)) -> f(X) 0.16/0.22 activate(X) -> X 0.16/0.22 0.16/0.22 Proof: 0.16/0.22 Bounds Processor: 0.16/0.22 bound: 2 0.16/0.22 enrichment: match 0.16/0.22 automaton: 0.16/0.22 final states: {5,4} 0.16/0.22 transitions: 0.16/0.22 f1(24) -> 25* 0.16/0.22 f1(26) -> 27* 0.16/0.22 f1(18) -> 19* 0.16/0.22 n__f1(10) -> 11* 0.16/0.22 n__f1(16) -> 17* 0.16/0.22 n__f1(8) -> 9* 0.16/0.22 n__f2(30) -> 31* 0.16/0.22 n__f2(36) -> 37* 0.16/0.22 n__f2(38) -> 39* 0.16/0.22 f0(2) -> 4* 0.16/0.22 f0(1) -> 4* 0.16/0.22 f0(3) -> 4* 0.16/0.22 a0() -> 1* 0.16/0.22 g0(2) -> 2* 0.16/0.22 g0(1) -> 2* 0.16/0.22 g0(3) -> 2* 0.16/0.22 n__f0(2) -> 3* 0.16/0.22 n__f0(1) -> 3* 0.16/0.22 n__f0(3) -> 3* 0.16/0.22 activate0(2) -> 5* 0.16/0.22 activate0(1) -> 5* 0.16/0.22 activate0(3) -> 5* 0.16/0.22 1 -> 5,24,10 0.16/0.22 2 -> 5,18,16 0.16/0.22 3 -> 5,26,8 0.16/0.22 9 -> 4* 0.16/0.22 11 -> 4* 0.16/0.22 17 -> 4* 0.16/0.22 18 -> 36* 0.16/0.22 19 -> 5* 0.16/0.22 24 -> 38* 0.16/0.22 25 -> 5* 0.16/0.22 26 -> 30* 0.16/0.22 27 -> 5* 0.16/0.22 31 -> 27* 0.16/0.22 37 -> 19,5 0.16/0.22 39 -> 25,5 0.16/0.22 problem: 0.16/0.22 0.16/0.22 Qed 0.16/0.22 EOF