0.04/0.15 WORST_CASE(?,O(n^1)) 0.04/0.15 0.04/0.15 Preprocessing Cost Relations 0.04/0.15 ===================================== 0.04/0.15 0.04/0.15 #### Computed strongly connected components 0.04/0.15 0. recursive : [eval_foo_3/3,eval_foo_4/4,eval_foo_bb1_in/3,eval_foo_bb2_in/3,eval_foo_bb3_in/3] 0.04/0.15 1. non_recursive : [eval_foo_stop/1] 0.04/0.15 2. non_recursive : [eval_foo__critedge_in/1] 0.04/0.15 3. non_recursive : [eval_foo_bb1_in_loop_cont/2] 0.04/0.15 4. non_recursive : [eval_foo_bb0_in/3] 0.04/0.15 5. non_recursive : [eval_foo_start/3] 0.04/0.15 0.04/0.15 #### Obtained direct recursion through partial evaluation 0.04/0.15 0. SCC is partially evaluated into eval_foo_bb1_in/3 0.04/0.15 1. SCC is completely evaluated into other SCCs 0.04/0.15 2. SCC is completely evaluated into other SCCs 0.04/0.15 3. SCC is completely evaluated into other SCCs 0.04/0.15 4. SCC is partially evaluated into eval_foo_bb0_in/3 0.04/0.15 5. SCC is partially evaluated into eval_foo_start/3 0.04/0.15 0.04/0.15 Control-Flow Refinement of Cost Relations 0.04/0.15 ===================================== 0.04/0.15 0.04/0.15 ### Specialization of cost equations eval_foo_bb1_in/3 0.04/0.15 * CE 6 is refined into CE [7] 0.04/0.15 * CE 5 is refined into CE [8] 0.04/0.15 * CE 3 is refined into CE [9] 0.04/0.15 * CE 4 is refined into CE [10] 0.04/0.15 0.04/0.15 0.04/0.15 ### Cost equations --> "Loop" of eval_foo_bb1_in/3 0.04/0.15 * CEs [10] --> Loop 7 0.04/0.15 * CEs [7] --> Loop 8 0.04/0.15 * CEs [8] --> Loop 9 0.04/0.15 * CEs [9] --> Loop 10 0.04/0.15 0.04/0.15 ### Ranking functions of CR eval_foo_bb1_in(V__01,V__0,B) 0.04/0.15 * RF of phase [7]: [-2/11*V__01+90/11] 0.04/0.15 0.04/0.15 #### Partial ranking functions of CR eval_foo_bb1_in(V__01,V__0,B) 0.04/0.15 * Partial RF of phase [7]: 0.04/0.15 - RF of loop [7:1]: 0.04/0.15 -2/11*V__01+90/11 0.04/0.15 0.04/0.15 0.04/0.15 ### Specialization of cost equations eval_foo_bb0_in/3 0.04/0.15 * CE 2 is refined into CE [11,12,13,14] 0.04/0.15 0.04/0.15 0.04/0.15 ### Cost equations --> "Loop" of eval_foo_bb0_in/3 0.04/0.15 * CEs [14] --> Loop 11 0.04/0.15 * CEs [13] --> Loop 12 0.04/0.15 * CEs [12] --> Loop 13 0.04/0.15 * CEs [11] --> Loop 14 0.04/0.15 0.04/0.15 ### Ranking functions of CR eval_foo_bb0_in(V_x,V_oldx,B) 0.04/0.15 0.04/0.15 #### Partial ranking functions of CR eval_foo_bb0_in(V_x,V_oldx,B) 0.04/0.15 0.04/0.15 0.04/0.15 ### Specialization of cost equations eval_foo_start/3 0.04/0.15 * CE 1 is refined into CE [15,16,17,18] 0.04/0.15 0.04/0.15 0.04/0.15 ### Cost equations --> "Loop" of eval_foo_start/3 0.04/0.15 * CEs [18] --> Loop 15 0.04/0.15 * CEs [17] --> Loop 16 0.04/0.15 * CEs [16] --> Loop 17 0.04/0.15 * CEs [15] --> Loop 18 0.04/0.15 0.04/0.15 ### Ranking functions of CR eval_foo_start(V_x,V_oldx,B) 0.04/0.15 0.04/0.15 #### Partial ranking functions of CR eval_foo_start(V_x,V_oldx,B) 0.04/0.15 0.04/0.15 0.04/0.15 Computing Bounds 0.04/0.15 ===================================== 0.04/0.15 0.04/0.15 #### Cost of chains of eval_foo_bb1_in(V__01,V__0,B): 0.04/0.15 * Chain [[7],10]: 1*it(7)+0 0.04/0.15 Such that:it(7) =< -2/11*V__01+90/11 0.04/0.15 0.04/0.15 with precondition: [B=2,99>=V__0,V__0>=1,V__0>=2*V__01+10] 0.04/0.15 0.04/0.15 * Chain [[7],9]: 1*it(7)+0 0.04/0.15 Such that:it(7) =< -2/11*V__01+90/11 0.04/0.15 0.04/0.15 with precondition: [B=2,99>=V__0,V__0>=1,V__0>=2*V__01+10] 0.04/0.15 0.04/0.15 * Chain [[7],8]: 1*it(7)+0 0.04/0.15 Such that:it(7) =< -2/11*V__01+90/11 0.04/0.15 0.04/0.15 with precondition: [B=2,99>=V__0,V__0>=1,V__0>=2*V__01+10] 0.04/0.15 0.04/0.15 * Chain [10]: 0 0.04/0.15 with precondition: [B=2,99>=V__0,V__0>=1,2*V__01+9>=V__0] 0.04/0.15 0.04/0.15 * Chain [9]: 0 0.04/0.15 with precondition: [B=2,0>=V__0] 0.04/0.15 0.04/0.15 * Chain [8]: 0 0.04/0.15 with precondition: [B=2,V__0>=100] 0.04/0.15 0.04/0.15 0.04/0.15 #### Cost of chains of eval_foo_bb0_in(V_x,V_oldx,B): 0.04/0.15 * Chain [14]: 3*s(5)+0 0.04/0.15 Such that:s(4) =< -2/11*V_oldx+90/11 0.04/0.15 s(5) =< s(4) 0.04/0.15 0.04/0.15 with precondition: [99>=V_x,V_x>=1,V_x>=2*V_oldx+10] 0.04/0.15 0.04/0.15 * Chain [13]: 0 0.04/0.15 with precondition: [99>=V_x,V_x>=1,2*V_oldx+9>=V_x] 0.04/0.15 0.04/0.15 * Chain [12]: 0 0.04/0.15 with precondition: [0>=V_x] 0.04/0.15 0.04/0.15 * Chain [11]: 0 0.04/0.15 with precondition: [V_x>=100] 0.04/0.15 0.04/0.15 0.04/0.15 #### Cost of chains of eval_foo_start(V_x,V_oldx,B): 0.04/0.15 * Chain [18]: 3*s(7)+0 0.04/0.15 Such that:s(6) =< -2/11*V_oldx+90/11 0.04/0.15 s(7) =< s(6) 0.04/0.15 0.04/0.15 with precondition: [99>=V_x,V_x>=1,V_x>=2*V_oldx+10] 0.04/0.15 0.04/0.15 * Chain [17]: 0 0.04/0.15 with precondition: [99>=V_x,V_x>=1,2*V_oldx+9>=V_x] 0.04/0.15 0.04/0.15 * Chain [16]: 0 0.04/0.15 with precondition: [0>=V_x] 0.04/0.15 0.04/0.15 * Chain [15]: 0 0.04/0.15 with precondition: [V_x>=100] 0.04/0.15 0.04/0.15 0.04/0.15 Closed-form bounds of eval_foo_start(V_x,V_oldx,B): 0.04/0.15 ------------------------------------- 0.04/0.15 * Chain [18] with precondition: [99>=V_x,V_x>=1,V_x>=2*V_oldx+10] 0.04/0.15 - Upper bound: -6/11*V_oldx+270/11 0.04/0.15 - Complexity: n 0.04/0.15 * Chain [17] with precondition: [99>=V_x,V_x>=1,2*V_oldx+9>=V_x] 0.04/0.15 - Upper bound: 0 0.04/0.15 - Complexity: constant 0.04/0.15 * Chain [16] with precondition: [0>=V_x] 0.04/0.15 - Upper bound: 0 0.04/0.15 - Complexity: constant 0.04/0.15 * Chain [15] with precondition: [V_x>=100] 0.04/0.15 - Upper bound: 0 0.04/0.15 - Complexity: constant 0.04/0.15 0.04/0.15 ### Maximum cost of eval_foo_start(V_x,V_oldx,B): nat(-2/11*V_oldx+90/11)*3 0.04/0.15 Asymptotic class: n 0.04/0.15 * Total analysis performed in 79 ms. 0.04/0.15 0.04/0.25 EOF