0.02/0.09 WORST_CASE(?,O(n^1)) 0.02/0.09 0.02/0.09 Preprocessing Cost Relations 0.02/0.09 ===================================== 0.02/0.09 0.02/0.09 #### Computed strongly connected components 0.02/0.09 0. recursive : [eval/4] 0.02/0.09 1. non_recursive : [exit_location/1] 0.02/0.09 2. non_recursive : [eval_loop_cont/2] 0.02/0.09 3. non_recursive : [start/4] 0.02/0.09 0.02/0.09 #### Obtained direct recursion through partial evaluation 0.02/0.09 0. SCC is partially evaluated into eval/4 0.02/0.09 1. SCC is completely evaluated into other SCCs 0.02/0.09 2. SCC is completely evaluated into other SCCs 0.02/0.09 3. SCC is partially evaluated into start/4 0.02/0.09 0.02/0.09 Control-Flow Refinement of Cost Relations 0.02/0.09 ===================================== 0.02/0.09 0.02/0.09 ### Specialization of cost equations eval/4 0.02/0.09 * CE 3 is refined into CE [4] 0.02/0.09 * CE 2 is refined into CE [5] 0.02/0.09 0.02/0.09 0.02/0.09 ### Cost equations --> "Loop" of eval/4 0.02/0.09 * CEs [5] --> Loop 4 0.02/0.09 * CEs [4] --> Loop 5 0.02/0.09 0.02/0.09 ### Ranking functions of CR eval(A,B,C,D) 0.02/0.09 * RF of phase [4]: [-A/2+B/2-C/2+101/2] 0.02/0.09 0.02/0.09 #### Partial ranking functions of CR eval(A,B,C,D) 0.02/0.09 * Partial RF of phase [4]: 0.02/0.09 - RF of loop [4:1]: 0.02/0.09 -A/2+B/2-C/2+101/2 0.02/0.09 0.02/0.09 0.02/0.09 ### Specialization of cost equations start/4 0.02/0.09 * CE 1 is refined into CE [6,7] 0.02/0.09 0.02/0.09 0.02/0.09 ### Cost equations --> "Loop" of start/4 0.02/0.09 * CEs [7] --> Loop 6 0.02/0.09 * CEs [6] --> Loop 7 0.02/0.09 0.02/0.09 ### Ranking functions of CR start(A,B,C,D) 0.02/0.09 0.02/0.09 #### Partial ranking functions of CR start(A,B,C,D) 0.02/0.09 0.02/0.09 0.02/0.09 Computing Bounds 0.02/0.09 ===================================== 0.02/0.09 0.02/0.09 #### Cost of chains of eval(A,B,C,D): 0.02/0.09 * Chain [[4],5]: 1*it(4)+0 0.02/0.09 Such that:it(4) =< -A/2+B/2-C/2+101/2 0.02/0.09 0.02/0.09 with precondition: [D=2,100>=A,B>=C] 0.02/0.09 0.02/0.09 * Chain [5]: 0 0.02/0.09 with precondition: [D=2] 0.02/0.09 0.02/0.09 0.02/0.09 #### Cost of chains of start(A,B,C,D): 0.02/0.09 * Chain [7]: 0 0.02/0.09 with precondition: [] 0.02/0.09 0.02/0.09 * Chain [6]: 1*s(1)+0 0.02/0.09 Such that:s(1) =< -A/2+B/2-C/2+101/2 0.02/0.09 0.02/0.09 with precondition: [100>=A,B>=C] 0.02/0.09 0.02/0.09 0.02/0.09 Closed-form bounds of start(A,B,C,D): 0.02/0.09 ------------------------------------- 0.02/0.09 * Chain [7] with precondition: [] 0.02/0.09 - Upper bound: 0 0.02/0.09 - Complexity: constant 0.02/0.09 * Chain [6] with precondition: [100>=A,B>=C] 0.02/0.09 - Upper bound: -A/2+B/2-C/2+101/2 0.02/0.09 - Complexity: n 0.02/0.09 0.02/0.09 ### Maximum cost of start(A,B,C,D): nat(-A/2+B/2-C/2+101/2) 0.02/0.09 Asymptotic class: n 0.02/0.09 * Total analysis performed in 39 ms. 0.02/0.09 0.02/0.10 EOF