0.03/0.11 MAYBE 0.03/0.11 0.03/0.11 Preprocessing Cost Relations 0.03/0.11 ===================================== 0.03/0.11 0.03/0.11 #### Computed strongly connected components 0.03/0.11 0. recursive : [f2/2] 0.03/0.11 1. non_recursive : [exit_location/1] 0.03/0.11 2. non_recursive : [f2_loop_cont/2] 0.03/0.11 3. non_recursive : [f3/2] 0.03/0.11 0.03/0.11 #### Obtained direct recursion through partial evaluation 0.03/0.11 0. SCC is partially evaluated into f2/2 0.03/0.11 1. SCC is completely evaluated into other SCCs 0.03/0.11 2. SCC is completely evaluated into other SCCs 0.03/0.11 3. SCC is partially evaluated into f3/2 0.03/0.11 0.03/0.11 Control-Flow Refinement of Cost Relations 0.03/0.11 ===================================== 0.03/0.11 0.03/0.11 ### Specialization of cost equations f2/2 0.03/0.11 * CE 4 is refined into CE [5] 0.03/0.11 * CE 2 is refined into CE [6] 0.03/0.11 * CE 3 is refined into CE [7] 0.03/0.11 0.03/0.11 0.03/0.11 ### Cost equations --> "Loop" of f2/2 0.03/0.11 * CEs [6] --> Loop 5 0.03/0.11 * CEs [7] --> Loop 6 0.03/0.11 * CEs [5] --> Loop 7 0.03/0.11 0.03/0.11 ### Ranking functions of CR f2(A,B) 0.03/0.11 * RF of phase [5]: [A-1] 0.03/0.11 0.03/0.11 #### Partial ranking functions of CR f2(A,B) 0.03/0.11 * Partial RF of phase [5]: 0.03/0.11 - RF of loop [5:1]: 0.03/0.11 A-1 0.03/0.11 0.03/0.11 0.03/0.11 ### Specialization of cost equations f3/2 0.03/0.11 * CE 1 is refined into CE [8,9,10,11,12] 0.03/0.11 0.03/0.11 0.03/0.11 ### Cost equations --> "Loop" of f3/2 0.03/0.11 * CEs [11] --> Loop 8 0.03/0.11 * CEs [12] --> Loop 9 0.03/0.11 * CEs [10] --> Loop 10 0.03/0.11 * CEs [9] --> Loop 11 0.03/0.11 * CEs [8] --> Loop 12 0.03/0.11 0.03/0.11 ### Ranking functions of CR f3(A,B) 0.03/0.11 0.03/0.11 #### Partial ranking functions of CR f3(A,B) 0.03/0.11 0.03/0.11 0.03/0.11 Computing Bounds 0.03/0.11 ===================================== 0.03/0.11 0.03/0.11 #### Cost of chains of f2(A,B): 0.03/0.11 * Chain [[6]]...: 1*it(6)+0 0.03/0.11 with precondition: [1>=A,B=2] 0.03/0.11 0.03/0.11 * Chain [[6],7]: 1*it(6)+0 0.03/0.11 with precondition: [B=2,1>=A] 0.03/0.11 0.03/0.11 * Chain [[5],[6]]...: 1*it(5)+1*it(6)+0 0.03/0.11 Such that:it(5) =< A 0.03/0.11 0.03/0.11 with precondition: [B=2,A>=2] 0.03/0.11 0.03/0.11 * Chain [[5],[6],7]: 1*it(5)+1*it(6)+0 0.03/0.11 Such that:it(5) =< A 0.03/0.11 0.03/0.11 with precondition: [B=2,A>=2] 0.03/0.11 0.03/0.11 * Chain [[5],7]: 1*it(5)+0 0.03/0.11 Such that:it(5) =< A 0.03/0.11 0.03/0.11 with precondition: [B=2,A>=2] 0.03/0.11 0.03/0.11 * Chain [7]: 0 0.03/0.11 with precondition: [B=2] 0.03/0.11 0.03/0.11 0.03/0.11 #### Cost of chains of f3(A,B): 0.03/0.11 * Chain [12]: 0 0.03/0.11 with precondition: [] 0.03/0.11 0.03/0.11 * Chain [11]: 1*s(4)+0 0.03/0.11 with precondition: [1>=A] 0.03/0.11 0.03/0.11 * Chain [10]: 2*s(6)+1*s(7)+0 0.03/0.11 Such that:s(5) =< A 0.03/0.11 s(6) =< s(5) 0.03/0.11 0.03/0.11 with precondition: [A>=2] 0.03/0.11 0.03/0.11 * Chain [9]...: 1*s(8)+0 0.03/0.11 with precondition: [1>=A] 0.03/0.11 0.03/0.11 * Chain [8]...: 1*s(9)+1*s(10)+0 0.03/0.11 Such that:s(9) =< A 0.03/0.11 0.03/0.11 with precondition: [A>=2] 0.03/0.11 0.03/0.11 0.03/0.11 Closed-form bounds of f3(A,B): 0.03/0.11 ------------------------------------- 0.03/0.11 * Chain [12] with precondition: [] 0.03/0.11 - Upper bound: 0 0.03/0.11 - Complexity: constant 0.03/0.11 * Chain [11] with precondition: [1>=A] 0.03/0.11 - Upper bound: inf 0.03/0.11 - Complexity: infinity 0.03/0.11 * Chain [10] with precondition: [A>=2] 0.03/0.11 - Upper bound: inf 0.03/0.11 - Complexity: infinity 0.03/0.11 * Chain [9]... with precondition: [1>=A] 0.03/0.11 - Upper bound: inf 0.03/0.11 - Complexity: infinity 0.03/0.11 * Chain [8]... with precondition: [A>=2] 0.03/0.11 - Upper bound: inf 0.03/0.11 - Complexity: infinity 0.03/0.11 0.03/0.11 ### Maximum cost of f3(A,B): inf 0.03/0.11 Asymptotic class: infinity 0.03/0.11 * Total analysis performed in 52 ms. 0.03/0.11 0.03/0.21 EOF