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 : [f1/3] 0.02/0.09 1. non_recursive : [exit_location/1] 0.02/0.09 2. non_recursive : [f1_loop_cont/2] 0.02/0.09 3. non_recursive : [f0/3] 0.02/0.09 0.02/0.09 #### Obtained direct recursion through partial evaluation 0.02/0.09 0. SCC is partially evaluated into f1/3 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 f0/3 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 f1/3 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 f1/3 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 f1(A,B,C) 0.02/0.09 * RF of phase [4]: [B] 0.02/0.09 0.02/0.09 #### Partial ranking functions of CR f1(A,B,C) 0.02/0.09 * Partial RF of phase [4]: 0.02/0.09 - RF of loop [4:1]: 0.02/0.09 B 0.02/0.09 0.02/0.09 0.02/0.09 ### Specialization of cost equations f0/3 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 f0/3 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 f0(A,B,C) 0.02/0.09 0.02/0.09 #### Partial ranking functions of CR f0(A,B,C) 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 f1(A,B,C): 0.02/0.09 * Chain [[4],5]: 1*it(4)+0 0.02/0.09 Such that:it(4) =< B 0.02/0.09 0.02/0.09 with precondition: [C=2,A>=1,B>=1] 0.02/0.09 0.02/0.09 * Chain [5]: 0 0.02/0.09 with precondition: [C=2,A>=1] 0.02/0.09 0.02/0.09 0.02/0.09 #### Cost of chains of f0(A,B,C): 0.02/0.09 * Chain [7]: 0 0.02/0.09 with precondition: [A>=1] 0.02/0.09 0.02/0.09 * Chain [6]: 1*s(1)+0 0.02/0.09 Such that:s(1) =< B 0.02/0.09 0.02/0.09 with precondition: [A>=1,B>=1] 0.02/0.09 0.02/0.09 0.02/0.09 Closed-form bounds of f0(A,B,C): 0.02/0.09 ------------------------------------- 0.02/0.09 * Chain [7] with precondition: [A>=1] 0.02/0.09 - Upper bound: 0 0.02/0.09 - Complexity: constant 0.02/0.09 * Chain [6] with precondition: [A>=1,B>=1] 0.02/0.09 - Upper bound: B 0.02/0.09 - Complexity: n 0.02/0.09 0.02/0.09 ### Maximum cost of f0(A,B,C): nat(B) 0.02/0.09 Asymptotic class: n 0.02/0.09 * Total analysis performed in 33 ms. 0.02/0.09 0.02/0.09 EOF