0.05/0.22 WORST_CASE(?,O(n^1)) 0.05/0.22 0.05/0.22 Preprocessing Cost Relations 0.05/0.22 ===================================== 0.05/0.22 0.05/0.22 #### Computed strongly connected components 0.05/0.22 0. recursive : [eval_t13_bb4_in/6,eval_t13_bb5_in/6] 0.05/0.22 1. recursive : [eval_t13_1/4,eval_t13_2/5,eval_t13_bb1_in/3,eval_t13_bb2_in/3,eval_t13_bb3_in/5,eval_t13_bb4_in_loop_cont/4] 0.05/0.22 2. non_recursive : [eval_t13_stop/1] 0.05/0.22 3. non_recursive : [eval_t13_bb6_in/1] 0.05/0.22 4. non_recursive : [eval_t13_bb1_in_loop_cont/2] 0.05/0.22 5. non_recursive : [eval_t13_bb0_in/3] 0.05/0.22 6. non_recursive : [eval_t13_start/3] 0.05/0.22 0.05/0.22 #### Obtained direct recursion through partial evaluation 0.05/0.22 0. SCC is partially evaluated into eval_t13_bb4_in/6 0.05/0.22 1. SCC is partially evaluated into eval_t13_bb1_in/3 0.05/0.22 2. SCC is completely evaluated into other SCCs 0.05/0.22 3. SCC is completely evaluated into other SCCs 0.05/0.22 4. SCC is completely evaluated into other SCCs 0.05/0.22 5. SCC is partially evaluated into eval_t13_bb0_in/3 0.05/0.22 6. SCC is partially evaluated into eval_t13_start/3 0.05/0.22 0.05/0.22 Control-Flow Refinement of Cost Relations 0.05/0.22 ===================================== 0.05/0.22 0.05/0.22 ### Specialization of cost equations eval_t13_bb4_in/6 0.05/0.22 * CE 7 is refined into CE [8] 0.05/0.22 * CE 6 is refined into CE [9] 0.05/0.22 0.05/0.22 0.05/0.22 ### Cost equations --> "Loop" of eval_t13_bb4_in/6 0.05/0.22 * CEs [9] --> Loop 8 0.05/0.22 * CEs [8] --> Loop 9 0.05/0.22 0.05/0.22 ### Ranking functions of CR eval_t13_bb4_in(V__01,V__0,V_2,V__1,B,C) 0.05/0.22 * RF of phase [8]: [V__1] 0.05/0.22 0.05/0.22 #### Partial ranking functions of CR eval_t13_bb4_in(V__01,V__0,V_2,V__1,B,C) 0.05/0.22 * Partial RF of phase [8]: 0.05/0.22 - RF of loop [8:1]: 0.05/0.22 V__1 0.05/0.22 0.05/0.22 0.05/0.22 ### Specialization of cost equations eval_t13_bb1_in/3 0.05/0.22 * CE 5 is refined into CE [10] 0.05/0.22 * CE 4 is refined into CE [11,12] 0.05/0.22 * CE 3 is refined into CE [13] 0.05/0.22 0.05/0.22 0.05/0.22 ### Cost equations --> "Loop" of eval_t13_bb1_in/3 0.05/0.22 * CEs [12] --> Loop 10 0.05/0.22 * CEs [13] --> Loop 11 0.05/0.22 * CEs [11] --> Loop 12 0.05/0.22 * CEs [10] --> Loop 13 0.05/0.22 0.05/0.22 ### Ranking functions of CR eval_t13_bb1_in(V__01,V__0,B) 0.05/0.22 * RF of phase [10,11,12]: [V__0] 0.05/0.22 0.05/0.22 #### Partial ranking functions of CR eval_t13_bb1_in(V__01,V__0,B) 0.05/0.22 * Partial RF of phase [10,11,12]: 0.05/0.22 - RF of loop [10:1,11:1,12:1]: 0.05/0.22 V__0 0.05/0.22 - RF of loop [12:1]: 0.05/0.22 V__01 depends on loops [11:1] 0.05/0.22 0.05/0.22 0.05/0.22 ### Specialization of cost equations eval_t13_bb0_in/3 0.05/0.22 * CE 2 is refined into CE [14,15] 0.05/0.22 0.05/0.22 0.05/0.22 ### Cost equations --> "Loop" of eval_t13_bb0_in/3 0.05/0.22 * CEs [15] --> Loop 14 0.05/0.22 * CEs [14] --> Loop 15 0.05/0.22 0.05/0.22 ### Ranking functions of CR eval_t13_bb0_in(V_x,V_y,B) 0.05/0.22 0.05/0.22 #### Partial ranking functions of CR eval_t13_bb0_in(V_x,V_y,B) 0.05/0.22 0.05/0.22 0.05/0.22 ### Specialization of cost equations eval_t13_start/3 0.05/0.22 * CE 1 is refined into CE [16,17] 0.05/0.22 0.05/0.22 0.05/0.22 ### Cost equations --> "Loop" of eval_t13_start/3 0.05/0.22 * CEs [17] --> Loop 16 0.05/0.22 * CEs [16] --> Loop 17 0.05/0.22 0.05/0.22 ### Ranking functions of CR eval_t13_start(V_x,V_y,B) 0.05/0.22 0.05/0.22 #### Partial ranking functions of CR eval_t13_start(V_x,V_y,B) 0.05/0.22 0.05/0.22 0.05/0.22 Computing Bounds 0.05/0.22 ===================================== 0.05/0.22 0.05/0.22 #### Cost of chains of eval_t13_bb4_in(V__01,V__0,V_2,V__1,B,C): 0.05/0.22 * Chain [[8],9]: 1*it(8)+0 0.05/0.22 Such that:it(8) =< V__1 0.05/0.22 0.05/0.22 with precondition: [B=2,C=0,0>=V_2,V__0>=1,V__1>=1,V__01>=V__1] 0.05/0.22 0.05/0.22 * Chain [9]: 0 0.05/0.22 with precondition: [B=2,V__1=C,0>=V_2,0>=V__1,V__0>=1,V__01>=V__1] 0.05/0.22 0.05/0.22 0.05/0.22 #### Cost of chains of eval_t13_bb1_in(V__01,V__0,B): 0.05/0.22 * Chain [[10,11,12],13]: 2*it(10)+1*it(12)+1*s(3)+0 0.05/0.22 Such that:aux(6) =< V__01 0.05/0.22 aux(5) =< V__01+V__0 0.05/0.22 aux(10) =< V__0 0.05/0.22 it(10) =< aux(10) 0.05/0.22 it(12) =< aux(10) 0.05/0.22 s(3) =< it(10)+aux(6) 0.05/0.22 it(12) =< it(10)+aux(6) 0.05/0.22 s(3) =< it(12)*aux(5) 0.05/0.22 0.05/0.22 with precondition: [B=3,V__0>=1] 0.05/0.22 0.05/0.22 * Chain [13]: 0 0.05/0.22 with precondition: [B=3,0>=V__0] 0.05/0.22 0.05/0.22 0.05/0.22 #### Cost of chains of eval_t13_bb0_in(V_x,V_y,B): 0.05/0.22 * Chain [15]: 0 0.05/0.22 with precondition: [0>=V_x] 0.05/0.22 0.05/0.22 * Chain [14]: 2*s(7)+1*s(8)+1*s(9)+0 0.05/0.22 Such that:s(6) =< V_x 0.05/0.22 s(5) =< V_x+V_y 0.05/0.22 s(4) =< V_y 0.05/0.22 s(7) =< s(6) 0.05/0.22 s(8) =< s(6) 0.05/0.22 s(9) =< s(7)+s(4) 0.05/0.22 s(8) =< s(7)+s(4) 0.05/0.22 s(9) =< s(8)*s(5) 0.05/0.22 0.05/0.22 with precondition: [V_x>=1] 0.05/0.22 0.05/0.22 0.05/0.22 #### Cost of chains of eval_t13_start(V_x,V_y,B): 0.05/0.22 * Chain [17]: 0 0.05/0.22 with precondition: [0>=V_x] 0.05/0.22 0.05/0.22 * Chain [16]: 2*s(13)+1*s(14)+1*s(15)+0 0.05/0.22 Such that:s(10) =< V_x 0.05/0.22 s(11) =< V_x+V_y 0.05/0.22 s(12) =< V_y 0.05/0.22 s(13) =< s(10) 0.05/0.22 s(14) =< s(10) 0.05/0.22 s(15) =< s(13)+s(12) 0.05/0.22 s(14) =< s(13)+s(12) 0.05/0.22 s(15) =< s(14)*s(11) 0.05/0.22 0.05/0.22 with precondition: [V_x>=1] 0.05/0.22 0.05/0.22 0.05/0.22 Closed-form bounds of eval_t13_start(V_x,V_y,B): 0.05/0.22 ------------------------------------- 0.05/0.22 * Chain [17] with precondition: [0>=V_x] 0.05/0.22 - Upper bound: 0 0.05/0.22 - Complexity: constant 0.05/0.22 * Chain [16] with precondition: [V_x>=1] 0.05/0.22 - Upper bound: 4*V_x+nat(V_y) 0.05/0.22 - Complexity: n 0.05/0.22 0.05/0.22 ### Maximum cost of eval_t13_start(V_x,V_y,B): nat(V_x)*4+nat(V_y) 0.05/0.22 Asymptotic class: n 0.05/0.22 * Total analysis performed in 137 ms. 0.05/0.22 0.05/0.32 EOF