0.02/0.14 MAYBE 0.02/0.14 0.02/0.14 Preprocessing Cost Relations 0.02/0.14 ===================================== 0.02/0.14 0.02/0.14 #### Computed strongly connected components 0.02/0.14 0. recursive : [l1/5] 0.02/0.14 1. non_recursive : [exit_location/1] 0.02/0.14 2. recursive : [l2/2] 0.02/0.14 3. non_recursive : [l2_loop_cont/2] 0.02/0.14 4. non_recursive : [l1_loop_cont/4] 0.02/0.14 5. non_recursive : [l0/3] 0.02/0.14 0.02/0.14 #### Obtained direct recursion through partial evaluation 0.02/0.14 0. SCC is partially evaluated into l1/5 0.02/0.14 1. SCC is completely evaluated into other SCCs 0.02/0.14 2. SCC is partially evaluated into l2/2 0.02/0.14 3. SCC is completely evaluated into other SCCs 0.02/0.14 4. SCC is partially evaluated into l1_loop_cont/4 0.02/0.14 5. SCC is partially evaluated into l0/3 0.02/0.14 0.02/0.14 Control-Flow Refinement of Cost Relations 0.02/0.14 ===================================== 0.02/0.14 0.02/0.14 ### Specialization of cost equations l1/5 0.02/0.14 * CE 3 is refined into CE [9] 0.02/0.14 * CE 4 is refined into CE [10] 0.02/0.14 * CE 2 is refined into CE [11] 0.02/0.14 0.02/0.14 0.02/0.14 ### Cost equations --> "Loop" of l1/5 0.02/0.14 * CEs [11] --> Loop 9 0.02/0.14 * CEs [9] --> Loop 10 0.02/0.14 * CEs [10] --> Loop 11 0.02/0.14 0.02/0.14 ### Ranking functions of CR l1(A,B,C,D,E) 0.02/0.14 * RF of phase [9]: [A] 0.02/0.14 0.02/0.14 #### Partial ranking functions of CR l1(A,B,C,D,E) 0.02/0.14 * Partial RF of phase [9]: 0.02/0.14 - RF of loop [9:1]: 0.02/0.14 A 0.02/0.14 0.02/0.14 0.02/0.14 ### Specialization of cost equations l2/2 0.02/0.14 * CE 8 is refined into CE [12] 0.02/0.14 * CE 7 is refined into CE [13] 0.02/0.14 0.02/0.14 0.02/0.14 ### Cost equations --> "Loop" of l2/2 0.02/0.14 * CEs [13] --> Loop 12 0.02/0.14 * CEs [12] --> Loop 13 0.02/0.14 0.02/0.14 ### Ranking functions of CR l2(B,C) 0.02/0.14 * RF of phase [12]: [B] 0.02/0.14 0.02/0.14 #### Partial ranking functions of CR l2(B,C) 0.02/0.14 * Partial RF of phase [12]: 0.02/0.14 - RF of loop [12:1]: 0.02/0.14 B 0.02/0.14 0.02/0.14 0.02/0.14 ### Specialization of cost equations l1_loop_cont/4 0.02/0.14 * CE 6 is refined into CE [14,15] 0.02/0.14 * CE 5 is refined into CE [16] 0.02/0.14 0.02/0.14 0.02/0.14 ### Cost equations --> "Loop" of l1_loop_cont/4 0.02/0.14 * CEs [15] --> Loop 14 0.02/0.14 * CEs [14] --> Loop 15 0.02/0.15 * CEs [16] --> Loop 16 0.02/0.15 0.02/0.15 ### Ranking functions of CR l1_loop_cont(A,B,C,D) 0.02/0.15 0.02/0.15 #### Partial ranking functions of CR l1_loop_cont(A,B,C,D) 0.02/0.15 0.02/0.15 0.02/0.15 ### Specialization of cost equations l0/3 0.02/0.15 * CE 1 is refined into CE [17,18,19,20,21,22] 0.02/0.15 0.02/0.15 0.02/0.15 ### Cost equations --> "Loop" of l0/3 0.02/0.15 * CEs [18,19,20] --> Loop 17 0.02/0.15 * CEs [22] --> Loop 18 0.02/0.15 * CEs [21] --> Loop 19 0.02/0.15 * CEs [17] --> Loop 20 0.02/0.15 0.02/0.15 ### Ranking functions of CR l0(A,B,C) 0.02/0.15 0.02/0.15 #### Partial ranking functions of CR l0(A,B,C) 0.02/0.15 0.02/0.15 0.02/0.15 Computing Bounds 0.02/0.15 ===================================== 0.02/0.15 0.02/0.15 #### Cost of chains of l1(A,B,C,D,E): 0.02/0.15 * Chain [[9],11]: 1*it(9)+0 0.02/0.15 Such that:it(9) =< A 0.02/0.15 0.02/0.15 with precondition: [C=2,A>=1] 0.02/0.15 0.02/0.15 * Chain [[9],10]: 1*it(9)+0 0.02/0.15 Such that:it(9) =< A 0.02/0.15 0.02/0.15 with precondition: [C=3,D=0,A>=1] 0.02/0.15 0.02/0.15 * Chain [11]: 0 0.02/0.15 with precondition: [C=2] 0.02/0.15 0.02/0.15 * Chain [10]: 0 0.02/0.15 with precondition: [C=3,E=B,A=D,0>=A] 0.02/0.15 0.02/0.15 0.02/0.15 #### Cost of chains of l2(B,C): 0.02/0.15 * Chain [[12],13]: 1*it(12)+0 0.02/0.15 Such that:it(12) =< B 0.02/0.15 0.02/0.15 with precondition: [C=2,B>=1] 0.02/0.15 0.02/0.15 * Chain [13]: 0 0.02/0.15 with precondition: [C=2] 0.02/0.15 0.02/0.15 0.02/0.15 #### Cost of chains of l1_loop_cont(A,B,C,D): 0.02/0.15 * Chain [16]: 0 0.02/0.15 with precondition: [A=2] 0.02/0.15 0.02/0.15 * Chain [15]: 0 0.02/0.15 with precondition: [A=3] 0.02/0.15 0.02/0.15 * Chain [14]: 1*s(1)+0 0.02/0.15 Such that:s(1) =< C 0.02/0.15 0.02/0.15 with precondition: [A=3,C>=1] 0.02/0.15 0.02/0.15 0.02/0.15 #### Cost of chains of l0(A,B,C): 0.02/0.15 * Chain [20]: 0 0.02/0.15 with precondition: [] 0.02/0.15 0.02/0.15 * Chain [19]: 0 0.02/0.15 with precondition: [0>=A] 0.02/0.15 0.02/0.15 * Chain [18]: 1*s(2)+0 0.02/0.15 Such that:s(2) =< B 0.02/0.15 0.02/0.15 with precondition: [0>=A,B>=1] 0.02/0.15 0.02/0.15 * Chain [17]: 3*s(3)+1*s(6)+0 0.02/0.15 Such that:aux(1) =< A 0.02/0.15 s(3) =< aux(1) 0.02/0.15 0.02/0.15 with precondition: [A>=1] 0.02/0.15 0.02/0.15 0.02/0.15 Closed-form bounds of l0(A,B,C): 0.02/0.15 ------------------------------------- 0.02/0.15 * Chain [20] with precondition: [] 0.02/0.15 - Upper bound: 0 0.02/0.15 - Complexity: constant 0.02/0.15 * Chain [19] with precondition: [0>=A] 0.02/0.15 - Upper bound: 0 0.02/0.15 - Complexity: constant 0.02/0.15 * Chain [18] with precondition: [0>=A,B>=1] 0.02/0.15 - Upper bound: B 0.02/0.15 - Complexity: n 0.02/0.15 * Chain [17] with precondition: [A>=1] 0.02/0.15 - Upper bound: inf 0.02/0.15 - Complexity: infinity 0.02/0.15 0.02/0.15 ### Maximum cost of l0(A,B,C): inf 0.02/0.15 Asymptotic class: infinity 0.02/0.15 * Total analysis performed in 88 ms. 0.02/0.15 0.02/0.25 EOF