0.03/0.15 MAYBE 0.03/0.15 0.03/0.15 Preprocessing Cost Relations 0.03/0.15 ===================================== 0.03/0.15 0.03/0.15 #### Computed strongly connected components 0.03/0.15 0. recursive : [g/5] 0.03/0.15 1. non_recursive : [exit_location/1] 0.03/0.15 2. recursive : [h/2] 0.03/0.15 3. non_recursive : [h_loop_cont/2] 0.03/0.15 4. non_recursive : [g_loop_cont/4] 0.03/0.15 5. non_recursive : [f/3] 0.03/0.15 0.03/0.15 #### Obtained direct recursion through partial evaluation 0.03/0.15 0. SCC is partially evaluated into g/5 0.03/0.15 1. SCC is completely evaluated into other SCCs 0.03/0.15 2. SCC is partially evaluated into h/2 0.03/0.15 3. SCC is completely evaluated into other SCCs 0.03/0.15 4. SCC is partially evaluated into g_loop_cont/4 0.03/0.15 5. SCC is partially evaluated into f/3 0.03/0.15 0.03/0.15 Control-Flow Refinement of Cost Relations 0.03/0.15 ===================================== 0.03/0.15 0.03/0.15 ### Specialization of cost equations g/5 0.03/0.15 * CE 3 is refined into CE [9] 0.03/0.15 * CE 4 is refined into CE [10] 0.03/0.15 * CE 2 is refined into CE [11] 0.03/0.15 0.03/0.15 0.03/0.15 ### Cost equations --> "Loop" of g/5 0.03/0.15 * CEs [11] --> Loop 9 0.03/0.15 * CEs [9] --> Loop 10 0.03/0.15 * CEs [10] --> Loop 11 0.03/0.15 0.03/0.15 ### Ranking functions of CR g(A,B,C,D,E) 0.03/0.15 * RF of phase [9]: [A] 0.03/0.15 0.03/0.15 #### Partial ranking functions of CR g(A,B,C,D,E) 0.03/0.15 * Partial RF of phase [9]: 0.03/0.15 - RF of loop [9:1]: 0.03/0.15 A 0.03/0.15 0.03/0.15 0.03/0.15 ### Specialization of cost equations h/2 0.03/0.15 * CE 8 is refined into CE [12] 0.03/0.15 * CE 7 is refined into CE [13] 0.03/0.15 0.03/0.15 0.03/0.15 ### Cost equations --> "Loop" of h/2 0.03/0.15 * CEs [13] --> Loop 12 0.03/0.15 * CEs [12] --> Loop 13 0.03/0.15 0.03/0.15 ### Ranking functions of CR h(B,C) 0.03/0.15 * RF of phase [12]: [B] 0.03/0.15 0.03/0.15 #### Partial ranking functions of CR h(B,C) 0.03/0.15 * Partial RF of phase [12]: 0.03/0.15 - RF of loop [12:1]: 0.03/0.15 B 0.03/0.15 0.03/0.15 0.03/0.15 ### Specialization of cost equations g_loop_cont/4 0.03/0.15 * CE 6 is refined into CE [14,15] 0.03/0.15 * CE 5 is refined into CE [16] 0.03/0.15 0.03/0.15 0.03/0.15 ### Cost equations --> "Loop" of g_loop_cont/4 0.03/0.15 * CEs [15] --> Loop 14 0.03/0.15 * CEs [14] --> Loop 15 0.03/0.15 * CEs [16] --> Loop 16 0.03/0.15 0.03/0.15 ### Ranking functions of CR g_loop_cont(A,B,C,D) 0.03/0.15 0.03/0.15 #### Partial ranking functions of CR g_loop_cont(A,B,C,D) 0.03/0.15 0.03/0.15 0.03/0.15 ### Specialization of cost equations f/3 0.03/0.15 * CE 1 is refined into CE [17,18,19,20,21,22] 0.03/0.15 0.03/0.15 0.03/0.15 ### Cost equations --> "Loop" of f/3 0.03/0.15 * CEs [17,19,20] --> Loop 17 0.03/0.15 * CEs [21,22] --> Loop 18 0.03/0.15 * CEs [18] --> Loop 19 0.03/0.15 0.03/0.15 ### Ranking functions of CR f(A,B,C) 0.03/0.15 0.03/0.15 #### Partial ranking functions of CR f(A,B,C) 0.03/0.15 0.03/0.15 0.03/0.15 Computing Bounds 0.03/0.15 ===================================== 0.03/0.15 0.03/0.15 #### Cost of chains of g(A,B,C,D,E): 0.03/0.15 * Chain [[9],11]: 1*it(9)+0 0.03/0.15 Such that:it(9) =< A 0.03/0.15 0.03/0.15 with precondition: [C=2,A>=1,B>=1] 0.03/0.15 0.03/0.15 * Chain [[9],10]: 1*it(9)+0 0.03/0.15 Such that:it(9) =< A 0.03/0.15 0.03/0.15 with precondition: [C=3,D=0,A>=1,B>=1,E+2>=2*A+2*B] 0.03/0.15 0.03/0.15 * Chain [11]: 0 0.03/0.15 with precondition: [C=2,B>=1] 0.03/0.15 0.03/0.15 * Chain [10]: 0 0.03/0.15 with precondition: [C=3,A=D,B=E,0>=A,B>=1] 0.03/0.15 0.03/0.15 0.03/0.15 #### Cost of chains of h(B,C): 0.03/0.15 * Chain [[12],13]: 1*it(12)+0 0.03/0.15 Such that:it(12) =< B 0.03/0.15 0.03/0.15 with precondition: [C=2,B>=1] 0.03/0.15 0.03/0.15 * Chain [13]: 0 0.03/0.15 with precondition: [C=2] 0.03/0.15 0.03/0.15 0.03/0.15 #### Cost of chains of g_loop_cont(A,B,C,D): 0.03/0.15 * Chain [16]: 0 0.03/0.15 with precondition: [A=2] 0.03/0.15 0.03/0.15 * Chain [15]: 0 0.03/0.15 with precondition: [A=3] 0.03/0.15 0.03/0.15 * Chain [14]: 1*s(1)+0 0.03/0.15 Such that:s(1) =< C 0.03/0.15 0.03/0.15 with precondition: [A=3,C>=1] 0.03/0.15 0.03/0.15 0.03/0.15 #### Cost of chains of f(A,B,C): 0.03/0.15 * Chain [19]: 0 0.03/0.15 with precondition: [] 0.03/0.15 0.03/0.15 * Chain [18]: 1 0.03/0.15 with precondition: [0>=A] 0.03/0.15 0.03/0.15 * Chain [17]: 3*s(3)+1*s(6)+0 0.03/0.15 Such that:aux(1) =< A 0.03/0.15 s(3) =< aux(1) 0.03/0.15 0.03/0.15 with precondition: [A>=1] 0.03/0.15 0.03/0.15 0.03/0.15 Closed-form bounds of f(A,B,C): 0.03/0.15 ------------------------------------- 0.03/0.15 * Chain [19] with precondition: [] 0.03/0.15 - Upper bound: 0 0.03/0.15 - Complexity: constant 0.03/0.15 * Chain [18] with precondition: [0>=A] 0.03/0.15 - Upper bound: 1 0.03/0.15 - Complexity: constant 0.03/0.15 * Chain [17] with precondition: [A>=1] 0.03/0.15 - Upper bound: inf 0.03/0.15 - Complexity: infinity 0.03/0.15 0.03/0.15 ### Maximum cost of f(A,B,C): inf 0.03/0.15 Asymptotic class: infinity 0.03/0.15 * Total analysis performed in 93 ms. 0.03/0.15 0.03/0.25 EOF