YES(?,O(n^1)) 0.15/0.32 YES(?,O(n^1)) 0.15/0.32 0.15/0.32 Problem: 0.15/0.32 f(a()) -> g(h(a())) 0.15/0.32 h(g(x)) -> g(h(f(x))) 0.15/0.32 k(x,h(x),a()) -> h(x) 0.15/0.32 k(f(x),y,x) -> f(x) 0.15/0.32 0.15/0.32 Proof: 0.15/0.32 Bounds Processor: 0.15/0.32 bound: 2 0.15/0.32 enrichment: match 0.15/0.32 automaton: 0.15/0.32 final states: {5,4,3} 0.15/0.32 transitions: 0.15/0.32 f0(2) -> 3* 0.15/0.32 f0(1) -> 3* 0.15/0.32 a0() -> 1* 0.15/0.32 g0(2) -> 2* 0.15/0.32 g0(1) -> 2* 0.15/0.32 h0(2) -> 4* 0.15/0.32 h0(1) -> 4* 0.15/0.32 k0(1,1,1) -> 5* 0.15/0.32 k0(2,2,1) -> 5* 0.15/0.32 k0(1,1,2) -> 5* 0.15/0.32 k0(2,2,2) -> 5* 0.15/0.32 k0(1,2,1) -> 5* 0.15/0.32 k0(2,1,1) -> 5* 0.15/0.32 k0(1,2,2) -> 5* 0.15/0.32 k0(2,1,2) -> 5* 0.15/0.32 g1(10) -> 4* 0.15/0.32 g1(4) -> 3* 0.15/0.32 h1(1) -> 4* 0.15/0.32 h1(3) -> 10* 0.15/0.32 f1(2) -> 3* 0.15/0.32 f1(1) -> 3* 0.15/0.32 a1() -> 1* 0.15/0.32 g2(15) -> 10* 0.15/0.32 g2(4) -> 3* 0.15/0.32 h2(14) -> 15* 0.15/0.32 h2(1) -> 4* 0.15/0.32 a2() -> 1* 0.15/0.32 f2(4) -> 14* 0.15/0.32 problem: 0.15/0.32 0.15/0.32 Qed 0.15/0.32 EOF