0.03/0.14 WORST_CASE(?,O(n^1)) 0.03/0.14 0.03/0.14 Preprocessing Cost Relations 0.03/0.14 ===================================== 0.03/0.14 0.03/0.14 #### Computed strongly connected components 0.03/0.14 0. recursive : [f300/7] 0.03/0.14 1. non_recursive : [exit_location/1] 0.03/0.14 2. non_recursive : [f1/4] 0.03/0.14 3. non_recursive : [f300_loop_cont/5] 0.03/0.14 4. non_recursive : [f2/4] 0.03/0.14 0.03/0.14 #### Obtained direct recursion through partial evaluation 0.03/0.14 0. SCC is partially evaluated into f300/7 0.03/0.14 1. SCC is completely evaluated into other SCCs 0.03/0.14 2. SCC is completely evaluated into other SCCs 0.03/0.14 3. SCC is partially evaluated into f300_loop_cont/5 0.03/0.14 4. SCC is partially evaluated into f2/4 0.03/0.14 0.03/0.14 Control-Flow Refinement of Cost Relations 0.03/0.14 ===================================== 0.03/0.14 0.03/0.14 ### Specialization of cost equations f300/7 0.03/0.14 * CE 5 is refined into CE [8] 0.03/0.14 * CE 4 is refined into CE [9] 0.03/0.14 * CE 3 is refined into CE [10] 0.03/0.14 * CE 2 is refined into CE [11] 0.03/0.14 0.03/0.14 0.03/0.14 ### Cost equations --> "Loop" of f300/7 0.03/0.14 * CEs [11] --> Loop 8 0.03/0.14 * CEs [8] --> Loop 9 0.03/0.14 * CEs [9] --> Loop 10 0.03/0.14 * CEs [10] --> Loop 11 0.03/0.14 0.03/0.14 ### Ranking functions of CR f300(A,B,C,E,F,G,H) 0.03/0.14 * RF of phase [8]: [A] 0.03/0.14 0.03/0.14 #### Partial ranking functions of CR f300(A,B,C,E,F,G,H) 0.03/0.14 * Partial RF of phase [8]: 0.03/0.14 - RF of loop [8:1]: 0.03/0.14 A 0.03/0.14 0.03/0.14 0.03/0.14 ### Specialization of cost equations f300_loop_cont/5 0.03/0.14 * CE 7 is refined into CE [12] 0.03/0.14 * CE 6 is refined into CE [13] 0.03/0.14 0.03/0.14 0.03/0.14 ### Cost equations --> "Loop" of f300_loop_cont/5 0.03/0.14 * CEs [12] --> Loop 12 0.03/0.14 * CEs [13] --> Loop 13 0.03/0.14 0.03/0.14 ### Ranking functions of CR f300_loop_cont(A,B,C,D,E) 0.03/0.14 0.03/0.14 #### Partial ranking functions of CR f300_loop_cont(A,B,C,D,E) 0.03/0.14 0.03/0.14 0.03/0.14 ### Specialization of cost equations f2/4 0.03/0.14 * CE 1 is refined into CE [14,15,16,17,18] 0.03/0.14 0.03/0.14 0.03/0.14 ### Cost equations --> "Loop" of f2/4 0.03/0.14 * CEs [16,18] --> Loop 14 0.03/0.14 * CEs [14] --> Loop 15 0.03/0.14 * CEs [15] --> Loop 16 0.03/0.14 * CEs [17] --> Loop 17 0.03/0.14 0.03/0.14 ### Ranking functions of CR f2(A,B,C,E) 0.03/0.14 0.03/0.14 #### Partial ranking functions of CR f2(A,B,C,E) 0.03/0.14 0.03/0.14 0.03/0.14 Computing Bounds 0.03/0.14 ===================================== 0.03/0.14 0.03/0.14 #### Cost of chains of f300(A,B,C,E,F,G,H): 0.03/0.14 * Chain [[8],10]: 1*it(8)+0 0.03/0.14 Such that:it(8) =< A 0.03/0.14 it(8) =< A-F 0.03/0.14 0.03/0.14 with precondition: [E=2,F=G+1,1>=F,A>=1,B>=1,A>=F+1] 0.03/0.14 0.03/0.14 * Chain [[8],9]: 1*it(8)+0 0.03/0.14 Such that:it(8) =< A 0.03/0.14 0.03/0.14 with precondition: [E=3,A>=1,B>=1] 0.03/0.14 0.03/0.14 * Chain [11]: 0 0.03/0.14 with precondition: [E=2,A=F,B=G,0>=A,B>=1] 0.03/0.14 0.03/0.14 * Chain [10]: 0 0.03/0.14 with precondition: [E=2,F=A,B=G,0>=B] 0.03/0.14 0.03/0.14 * Chain [9]: 0 0.03/0.14 with precondition: [E=3] 0.03/0.14 0.03/0.14 0.03/0.14 #### Cost of chains of f300_loop_cont(A,B,C,D,E): 0.03/0.14 * Chain [13]: 0 0.03/0.14 with precondition: [A=2] 0.03/0.14 0.03/0.14 * Chain [12]: 0 0.03/0.14 with precondition: [A=3] 0.03/0.14 0.03/0.14 0.03/0.14 #### Cost of chains of f2(A,B,C,E): 0.03/0.14 * Chain [17]: 0 0.03/0.14 with precondition: [] 0.03/0.14 0.03/0.14 * Chain [16]: 0 0.03/0.14 with precondition: [0>=A,B>=1] 0.03/0.14 0.03/0.14 * Chain [15]: 0 0.03/0.14 with precondition: [0>=B] 0.03/0.14 0.03/0.14 * Chain [14]: 2*s(1)+0 0.03/0.14 Such that:aux(1) =< A 0.03/0.14 s(1) =< aux(1) 0.03/0.14 0.03/0.14 with precondition: [A>=1,B>=1] 0.03/0.14 0.03/0.14 0.03/0.14 Closed-form bounds of f2(A,B,C,E): 0.03/0.14 ------------------------------------- 0.03/0.14 * Chain [17] with precondition: [] 0.03/0.14 - Upper bound: 0 0.03/0.14 - Complexity: constant 0.03/0.14 * Chain [16] with precondition: [0>=A,B>=1] 0.03/0.14 - Upper bound: 0 0.03/0.14 - Complexity: constant 0.03/0.14 * Chain [15] with precondition: [0>=B] 0.03/0.14 - Upper bound: 0 0.03/0.14 - Complexity: constant 0.03/0.14 * Chain [14] with precondition: [A>=1,B>=1] 0.03/0.14 - Upper bound: 2*A 0.03/0.14 - Complexity: n 0.03/0.14 0.03/0.14 ### Maximum cost of f2(A,B,C,E): nat(A)*2 0.03/0.14 Asymptotic class: n 0.03/0.14 * Total analysis performed in 86 ms. 0.03/0.14 0.03/0.25 EOF