0.05/0.14 WORST_CASE(?,O(n^1)) 0.05/0.14 0.05/0.14 Preprocessing Cost Relations 0.05/0.14 ===================================== 0.05/0.14 0.05/0.14 #### Computed strongly connected components 0.05/0.14 0. recursive : [eval_foo_3/4,eval_foo_4/5,eval_foo_bb1_in/3,eval_foo_bb2_in/3] 0.05/0.14 1. non_recursive : [eval_foo_stop/1] 0.05/0.14 2. non_recursive : [eval_foo__critedge_in/1] 0.05/0.14 3. non_recursive : [eval_foo_bb1_in_loop_cont/2] 0.05/0.14 4. non_recursive : [eval_foo_bb0_in/3] 0.05/0.14 5. non_recursive : [eval_foo_start/3] 0.05/0.14 0.05/0.14 #### Obtained direct recursion through partial evaluation 0.05/0.14 0. SCC is partially evaluated into eval_foo_bb1_in/3 0.05/0.14 1. SCC is completely evaluated into other SCCs 0.05/0.14 2. SCC is completely evaluated into other SCCs 0.05/0.14 3. SCC is completely evaluated into other SCCs 0.05/0.14 4. SCC is partially evaluated into eval_foo_bb0_in/3 0.05/0.14 5. SCC is partially evaluated into eval_foo_start/3 0.05/0.14 0.05/0.14 Control-Flow Refinement of Cost Relations 0.05/0.14 ===================================== 0.05/0.14 0.05/0.14 ### Specialization of cost equations eval_foo_bb1_in/3 0.05/0.14 * CE 5 is refined into CE [7] 0.05/0.14 * CE 6 is refined into CE [8] 0.05/0.14 * CE 4 is refined into CE [9] 0.05/0.14 * CE 3 is refined into CE [10] 0.05/0.14 0.05/0.14 0.05/0.14 ### Cost equations --> "Loop" of eval_foo_bb1_in/3 0.05/0.14 * CEs [10] --> Loop 7 0.05/0.14 * CEs [7] --> Loop 8 0.05/0.14 * CEs [8] --> Loop 9 0.05/0.14 * CEs [9] --> Loop 10 0.05/0.14 0.05/0.14 ### Ranking functions of CR eval_foo_bb1_in(V__01,V__0,B) 0.05/0.14 * RF of phase [7]: [V__0] 0.05/0.14 0.05/0.14 #### Partial ranking functions of CR eval_foo_bb1_in(V__01,V__0,B) 0.05/0.14 * Partial RF of phase [7]: 0.05/0.14 - RF of loop [7:1]: 0.05/0.14 V__0 0.05/0.14 0.05/0.14 0.05/0.14 ### Specialization of cost equations eval_foo_bb0_in/3 0.05/0.14 * CE 2 is refined into CE [11,12,13,14] 0.05/0.14 0.05/0.14 0.05/0.14 ### Cost equations --> "Loop" of eval_foo_bb0_in/3 0.05/0.14 * CEs [14] --> Loop 11 0.05/0.14 * CEs [13] --> Loop 12 0.05/0.14 * CEs [12] --> Loop 13 0.05/0.14 * CEs [11] --> Loop 14 0.05/0.14 0.05/0.14 ### Ranking functions of CR eval_foo_bb0_in(V_x,V_tmp,B) 0.05/0.14 0.05/0.14 #### Partial ranking functions of CR eval_foo_bb0_in(V_x,V_tmp,B) 0.05/0.14 0.05/0.14 0.05/0.14 ### Specialization of cost equations eval_foo_start/3 0.05/0.14 * CE 1 is refined into CE [15,16,17,18] 0.05/0.14 0.05/0.14 0.05/0.14 ### Cost equations --> "Loop" of eval_foo_start/3 0.05/0.14 * CEs [18] --> Loop 15 0.05/0.14 * CEs [17] --> Loop 16 0.05/0.14 * CEs [16] --> Loop 17 0.05/0.14 * CEs [15] --> Loop 18 0.05/0.14 0.05/0.14 ### Ranking functions of CR eval_foo_start(V_x,V_tmp,B) 0.05/0.14 0.05/0.14 #### Partial ranking functions of CR eval_foo_start(V_x,V_tmp,B) 0.05/0.14 0.05/0.14 0.05/0.14 Computing Bounds 0.05/0.14 ===================================== 0.05/0.14 0.05/0.14 #### Cost of chains of eval_foo_bb1_in(V__01,V__0,B): 0.05/0.14 * Chain [[7],10]: 1*it(7)+0 0.05/0.14 Such that:it(7) =< 2*V__01 0.05/0.14 0.05/0.14 with precondition: [B=2,2*V__01=V__0,2*V__01>=1] 0.05/0.14 0.05/0.14 * Chain [[7],9]: 1*it(7)+0 0.05/0.14 Such that:it(7) =< 2*V__01 0.05/0.14 0.05/0.14 with precondition: [B=2,2*V__01=V__0,2*V__01>=1] 0.05/0.14 0.05/0.14 * Chain [[7],8]: 1*it(7)+0 0.05/0.14 Such that:it(7) =< 2*V__01 0.05/0.14 0.05/0.14 with precondition: [B=2,2*V__01=V__0,2*V__01>=1] 0.05/0.14 0.05/0.14 * Chain [10]: 0 0.05/0.14 with precondition: [B=2,0>=V__0] 0.05/0.14 0.05/0.14 * Chain [9]: 0 0.05/0.14 with precondition: [B=2,V__0>=2*V__01+1] 0.05/0.14 0.05/0.14 * Chain [8]: 0 0.05/0.14 with precondition: [B=2,2*V__01>=V__0+1] 0.05/0.14 0.05/0.14 0.05/0.14 #### Cost of chains of eval_foo_bb0_in(V_x,V_tmp,B): 0.05/0.14 * Chain [14]: 3*s(5)+0 0.05/0.14 Such that:s(4) =< 2*V_tmp 0.05/0.14 s(5) =< s(4) 0.05/0.14 0.05/0.14 with precondition: [V_x=2*V_tmp,V_x>=1] 0.05/0.14 0.05/0.14 * Chain [13]: 0 0.05/0.14 with precondition: [0>=V_x] 0.05/0.14 0.05/0.14 * Chain [12]: 0 0.05/0.14 with precondition: [V_x>=2*V_tmp+1] 0.05/0.14 0.05/0.14 * Chain [11]: 0 0.05/0.14 with precondition: [2*V_tmp>=V_x+1] 0.05/0.14 0.05/0.14 0.05/0.14 #### Cost of chains of eval_foo_start(V_x,V_tmp,B): 0.05/0.14 * Chain [18]: 3*s(7)+0 0.05/0.14 Such that:s(6) =< 2*V_tmp 0.05/0.14 s(7) =< s(6) 0.05/0.14 0.05/0.14 with precondition: [V_x=2*V_tmp,V_x>=1] 0.05/0.14 0.05/0.14 * Chain [17]: 0 0.05/0.14 with precondition: [0>=V_x] 0.05/0.14 0.05/0.14 * Chain [16]: 0 0.05/0.14 with precondition: [V_x>=2*V_tmp+1] 0.05/0.14 0.05/0.14 * Chain [15]: 0 0.05/0.14 with precondition: [2*V_tmp>=V_x+1] 0.05/0.14 0.05/0.14 0.05/0.14 Closed-form bounds of eval_foo_start(V_x,V_tmp,B): 0.05/0.14 ------------------------------------- 0.05/0.14 * Chain [18] with precondition: [V_x=2*V_tmp,V_x>=1] 0.05/0.14 - Upper bound: 6*V_tmp 0.05/0.14 - Complexity: n 0.05/0.14 * Chain [17] with precondition: [0>=V_x] 0.05/0.14 - Upper bound: 0 0.05/0.14 - Complexity: constant 0.05/0.14 * Chain [16] with precondition: [V_x>=2*V_tmp+1] 0.05/0.14 - Upper bound: 0 0.05/0.14 - Complexity: constant 0.05/0.14 * Chain [15] with precondition: [2*V_tmp>=V_x+1] 0.05/0.14 - Upper bound: 0 0.05/0.14 - Complexity: constant 0.05/0.14 0.05/0.14 ### Maximum cost of eval_foo_start(V_x,V_tmp,B): nat(2*V_tmp)*3 0.05/0.14 Asymptotic class: n 0.05/0.14 * Total analysis performed in 71 ms. 0.05/0.14 0.05/0.24 EOF