0.02/0.08 WORST_CASE(?,O(n^1)) 0.02/0.08 0.02/0.08 Preprocessing Cost Relations 0.02/0.08 ===================================== 0.02/0.08 0.02/0.08 #### Computed strongly connected components 0.02/0.08 0. recursive : [eval/2] 0.02/0.08 1. non_recursive : [exit_location/1] 0.02/0.08 2. non_recursive : [eval_loop_cont/2] 0.02/0.08 3. non_recursive : [start/2] 0.02/0.08 0.02/0.08 #### Obtained direct recursion through partial evaluation 0.02/0.08 0. SCC is partially evaluated into eval/2 0.02/0.08 1. SCC is completely evaluated into other SCCs 0.02/0.08 2. SCC is completely evaluated into other SCCs 0.02/0.08 3. SCC is partially evaluated into start/2 0.02/0.08 0.02/0.08 Control-Flow Refinement of Cost Relations 0.02/0.08 ===================================== 0.02/0.08 0.02/0.08 ### Specialization of cost equations eval/2 0.02/0.08 * CE 3 is refined into CE [4] 0.02/0.08 * CE 2 is refined into CE [5] 0.02/0.08 0.02/0.08 0.02/0.08 ### Cost equations --> "Loop" of eval/2 0.02/0.08 * CEs [5] --> Loop 4 0.02/0.08 * CEs [4] --> Loop 5 0.02/0.08 0.02/0.08 ### Ranking functions of CR eval(A,C) 0.02/0.08 * RF of phase [4]: [A] 0.02/0.08 0.02/0.08 #### Partial ranking functions of CR eval(A,C) 0.02/0.08 * Partial RF of phase [4]: 0.02/0.08 - RF of loop [4:1]: 0.02/0.08 A 0.02/0.08 0.02/0.08 0.02/0.08 ### Specialization of cost equations start/2 0.02/0.08 * CE 1 is refined into CE [6,7] 0.02/0.08 0.02/0.08 0.02/0.08 ### Cost equations --> "Loop" of start/2 0.02/0.08 * CEs [7] --> Loop 6 0.02/0.08 * CEs [6] --> Loop 7 0.02/0.08 0.02/0.08 ### Ranking functions of CR start(A,C) 0.02/0.08 0.02/0.08 #### Partial ranking functions of CR start(A,C) 0.02/0.08 0.02/0.08 0.02/0.08 Computing Bounds 0.02/0.08 ===================================== 0.02/0.08 0.02/0.08 #### Cost of chains of eval(A,C): 0.02/0.08 * Chain [[4],5]: 1*it(4)+0 0.02/0.08 Such that:it(4) =< A 0.02/0.08 0.02/0.08 with precondition: [C=2,A>=1] 0.02/0.08 0.02/0.08 * Chain [5]: 0 0.02/0.08 with precondition: [C=2] 0.02/0.08 0.02/0.08 0.02/0.08 #### Cost of chains of start(A,C): 0.02/0.08 * Chain [7]: 0 0.02/0.08 with precondition: [] 0.02/0.08 0.02/0.08 * Chain [6]: 1*s(1)+0 0.02/0.08 Such that:s(1) =< A 0.02/0.08 0.02/0.08 with precondition: [A>=1] 0.02/0.08 0.02/0.08 0.02/0.08 Closed-form bounds of start(A,C): 0.02/0.08 ------------------------------------- 0.02/0.08 * Chain [7] with precondition: [] 0.02/0.08 - Upper bound: 0 0.02/0.08 - Complexity: constant 0.02/0.08 * Chain [6] with precondition: [A>=1] 0.02/0.08 - Upper bound: A 0.02/0.08 - Complexity: n 0.02/0.08 0.02/0.08 ### Maximum cost of start(A,C): nat(A) 0.02/0.08 Asymptotic class: n 0.02/0.08 * Total analysis performed in 23 ms. 0.02/0.08 0.02/0.08 EOF