0.03/0.11 WORST_CASE(?,O(n^1)) 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 : [f2/5] 0.03/0.11 1. non_recursive : [exit_location/1] 0.03/0.11 2. non_recursive : [f1/3] 0.03/0.11 3. non_recursive : [f2_loop_cont/4] 0.03/0.11 4. non_recursive : [f300/3] 0.03/0.11 0.03/0.11 #### Obtained direct recursion through partial evaluation 0.03/0.11 0. SCC is partially evaluated into f2/5 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 f2_loop_cont/4 0.03/0.11 4. SCC is partially evaluated into f300/3 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 f2/5 0.03/0.11 * CE 4 is refined into CE [7] 0.03/0.11 * CE 2 is refined into CE [8] 0.03/0.11 * CE 3 is refined into CE [9] 0.03/0.11 0.03/0.11 0.03/0.11 ### Cost equations --> "Loop" of f2/5 0.03/0.11 * CEs [9] --> Loop 7 0.03/0.11 * CEs [7] --> Loop 8 0.03/0.11 * CEs [8] --> Loop 9 0.03/0.11 0.03/0.11 ### Ranking functions of CR f2(A,B,D,E,F) 0.03/0.11 * RF of phase [7]: [A] 0.03/0.11 0.03/0.11 #### Partial ranking functions of CR f2(A,B,D,E,F) 0.03/0.11 * Partial RF of phase [7]: 0.03/0.11 - RF of loop [7:1]: 0.03/0.11 A 0.03/0.11 0.03/0.11 0.03/0.11 ### Specialization of cost equations f2_loop_cont/4 0.03/0.11 * CE 6 is refined into CE [10] 0.03/0.11 * CE 5 is refined into CE [11] 0.03/0.11 0.03/0.11 0.03/0.11 ### Cost equations --> "Loop" of f2_loop_cont/4 0.03/0.11 * CEs [10] --> Loop 10 0.03/0.11 * CEs [11] --> Loop 11 0.03/0.11 0.03/0.11 ### Ranking functions of CR f2_loop_cont(A,B,C,D) 0.03/0.11 0.03/0.11 #### Partial ranking functions of CR f2_loop_cont(A,B,C,D) 0.03/0.11 0.03/0.11 0.03/0.11 ### Specialization of cost equations f300/3 0.03/0.11 * CE 1 is refined into CE [12,13,14,15] 0.03/0.11 0.03/0.11 0.03/0.11 ### Cost equations --> "Loop" of f300/3 0.03/0.11 * CEs [12,15] --> Loop 12 0.03/0.11 * CEs [13] --> Loop 13 0.03/0.11 * CEs [14] --> Loop 14 0.03/0.11 0.03/0.11 ### Ranking functions of CR f300(A,B,D) 0.03/0.11 0.03/0.11 #### Partial ranking functions of CR f300(A,B,D) 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,D,E,F): 0.03/0.11 * Chain [[7],9]: 1*it(7)+0 0.03/0.11 Such that:it(7) =< A 0.03/0.11 0.03/0.11 with precondition: [D=2,E+1=0,A>=1] 0.03/0.11 0.03/0.11 * Chain [[7],8]: 1*it(7)+0 0.03/0.11 Such that:it(7) =< A 0.03/0.11 0.03/0.11 with precondition: [D=3,A>=1] 0.03/0.11 0.03/0.11 * Chain [9]: 0 0.03/0.11 with precondition: [D=2,A=E+1,0>=A] 0.03/0.11 0.03/0.11 * Chain [8]: 0 0.03/0.11 with precondition: [D=3] 0.03/0.11 0.03/0.11 0.03/0.11 #### Cost of chains of f2_loop_cont(A,B,C,D): 0.03/0.11 * Chain [11]: 0 0.03/0.11 with precondition: [A=2] 0.03/0.11 0.03/0.11 * Chain [10]: 0 0.03/0.11 with precondition: [A=3] 0.03/0.11 0.03/0.11 0.03/0.11 #### Cost of chains of f300(A,B,D): 0.03/0.11 * Chain [14]: 0 0.03/0.11 with precondition: [] 0.03/0.11 0.03/0.11 * Chain [13]: 0 0.03/0.11 with precondition: [0>=A] 0.03/0.11 0.03/0.11 * Chain [12]: 2*s(1)+0 0.03/0.11 Such that:aux(1) =< A 0.03/0.11 s(1) =< aux(1) 0.03/0.11 0.03/0.11 with precondition: [A>=1] 0.03/0.11 0.03/0.11 0.03/0.11 Closed-form bounds of f300(A,B,D): 0.03/0.11 ------------------------------------- 0.03/0.11 * Chain [14] with precondition: [] 0.03/0.11 - Upper bound: 0 0.03/0.11 - Complexity: constant 0.03/0.11 * Chain [13] with precondition: [0>=A] 0.03/0.11 - Upper bound: 0 0.03/0.11 - Complexity: constant 0.03/0.11 * Chain [12] with precondition: [A>=1] 0.03/0.11 - Upper bound: 2*A 0.03/0.11 - Complexity: n 0.03/0.11 0.03/0.11 ### Maximum cost of f300(A,B,D): nat(A)*2 0.03/0.11 Asymptotic class: n 0.03/0.11 * Total analysis performed in 55 ms. 0.03/0.11 0.03/0.21 EOF