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(0()) -> s(0()) 0.16/0.26 f(s(0())) -> s(s(0())) 0.16/0.26 f(s(0())) -> *(s(s(0())),f(0())) 0.16/0.26 f(+(x,s(0()))) -> +(s(s(0())),f(x)) 0.16/0.26 f(+(x,y)) -> *(f(x),f(y)) 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: {5} 0.16/0.26 transitions: 0.16/0.26 *1(5,9) -> 10,5 0.16/0.26 *1(10,10) -> 10,5 0.16/0.26 f1(7) -> 9* 0.16/0.26 f1(2) -> 10* 0.16/0.26 f1(4) -> 10* 0.16/0.26 f1(1) -> 10* 0.16/0.26 f1(3) -> 10* 0.16/0.26 +1(5,10) -> 10,5 0.16/0.26 s1(5) -> 10,5 0.16/0.26 s1(7) -> 10,5 0.16/0.26 01() -> 7* 0.16/0.26 s2(12) -> 9* 0.16/0.26 f0(2) -> 5* 0.16/0.26 f0(4) -> 5* 0.16/0.26 f0(1) -> 5* 0.16/0.26 f0(3) -> 5* 0.16/0.26 02() -> 12* 0.16/0.26 00() -> 1* 0.16/0.26 s0(2) -> 2* 0.16/0.26 s0(4) -> 2* 0.16/0.26 s0(1) -> 2* 0.16/0.26 s0(3) -> 2* 0.16/0.26 *0(3,1) -> 3* 0.16/0.26 *0(3,3) -> 3* 0.16/0.26 *0(4,2) -> 3* 0.16/0.26 *0(4,4) -> 3* 0.16/0.26 *0(1,2) -> 3* 0.16/0.26 *0(1,4) -> 3* 0.16/0.26 *0(2,1) -> 3* 0.16/0.26 *0(2,3) -> 3* 0.16/0.26 *0(3,2) -> 3* 0.16/0.26 *0(3,4) -> 3* 0.16/0.26 *0(4,1) -> 3* 0.16/0.26 *0(4,3) -> 3* 0.16/0.26 *0(1,1) -> 3* 0.16/0.26 *0(1,3) -> 3* 0.16/0.26 *0(2,2) -> 3* 0.16/0.26 *0(2,4) -> 3* 0.16/0.26 +0(3,1) -> 4* 0.16/0.26 +0(3,3) -> 4* 0.16/0.26 +0(4,2) -> 4* 0.16/0.26 +0(4,4) -> 4* 0.16/0.26 +0(1,2) -> 4* 0.16/0.26 +0(1,4) -> 4* 0.16/0.26 +0(2,1) -> 4* 0.16/0.26 +0(2,3) -> 4* 0.16/0.26 +0(3,2) -> 4* 0.16/0.26 +0(3,4) -> 4* 0.16/0.26 +0(4,1) -> 4* 0.16/0.26 +0(4,3) -> 4* 0.16/0.26 +0(1,1) -> 4* 0.16/0.26 +0(1,3) -> 4* 0.16/0.26 +0(2,2) -> 4* 0.16/0.26 +0(2,4) -> 4* 0.16/0.26 problem: 0.16/0.26 0.16/0.26 Qed 0.16/0.26 EOF