0.05/0.20 WORST_CASE(?,O(n^1)) 0.05/0.20 0.05/0.20 Preprocessing Cost Relations 0.05/0.20 ===================================== 0.05/0.20 0.05/0.20 #### Computed strongly connected components 0.05/0.20 0. recursive : [eval_t19_bb1_in/3,eval_t19_bb2_in/3] 0.05/0.20 1. recursive : [eval_t19_bb4_in/2,eval_t19_bb5_in/2] 0.05/0.20 2. non_recursive : [eval_t19_stop/1] 0.05/0.20 3. non_recursive : [eval_t19_bb6_in/1] 0.05/0.20 4. non_recursive : [eval_t19_bb4_in_loop_cont/2] 0.05/0.20 5. non_recursive : [eval_t19_bb3_in/3] 0.05/0.20 6. non_recursive : [eval_t19_bb1_in_loop_cont/4] 0.05/0.20 7. non_recursive : [eval_t19_bb0_in/3] 0.05/0.20 8. non_recursive : [eval_t19_start/3] 0.05/0.20 0.05/0.20 #### Obtained direct recursion through partial evaluation 0.05/0.20 0. SCC is partially evaluated into eval_t19_bb1_in/3 0.05/0.20 1. SCC is partially evaluated into eval_t19_bb4_in/2 0.05/0.20 2. SCC is completely evaluated into other SCCs 0.05/0.20 3. SCC is completely evaluated into other SCCs 0.05/0.20 4. SCC is completely evaluated into other SCCs 0.05/0.20 5. SCC is partially evaluated into eval_t19_bb3_in/3 0.05/0.20 6. SCC is completely evaluated into other SCCs 0.05/0.20 7. SCC is partially evaluated into eval_t19_bb0_in/3 0.05/0.20 8. SCC is partially evaluated into eval_t19_start/3 0.05/0.20 0.05/0.20 Control-Flow Refinement of Cost Relations 0.05/0.20 ===================================== 0.05/0.20 0.05/0.20 ### Specialization of cost equations eval_t19_bb1_in/3 0.05/0.20 * CE 4 is refined into CE [8] 0.05/0.20 * CE 3 is refined into CE [9] 0.05/0.20 0.05/0.20 0.05/0.20 ### Cost equations --> "Loop" of eval_t19_bb1_in/3 0.05/0.20 * CEs [9] --> Loop 8 0.05/0.20 * CEs [8] --> Loop 9 0.05/0.20 0.05/0.20 ### Ranking functions of CR eval_t19_bb1_in(V__0,B,C) 0.05/0.20 * RF of phase [8]: [V__0-100] 0.05/0.20 0.05/0.20 #### Partial ranking functions of CR eval_t19_bb1_in(V__0,B,C) 0.05/0.20 * Partial RF of phase [8]: 0.05/0.20 - RF of loop [8:1]: 0.05/0.20 V__0-100 0.05/0.20 0.05/0.20 0.05/0.20 ### Specialization of cost equations eval_t19_bb4_in/2 0.05/0.20 * CE 7 is refined into CE [10] 0.05/0.20 * CE 6 is refined into CE [11] 0.05/0.20 0.05/0.20 0.05/0.20 ### Cost equations --> "Loop" of eval_t19_bb4_in/2 0.05/0.20 * CEs [11] --> Loop 10 0.05/0.20 * CEs [10] --> Loop 11 0.05/0.20 0.05/0.20 ### Ranking functions of CR eval_t19_bb4_in(V__1,B) 0.05/0.20 * RF of phase [10]: [V__1+1] 0.05/0.20 0.05/0.20 #### Partial ranking functions of CR eval_t19_bb4_in(V__1,B) 0.05/0.20 * Partial RF of phase [10]: 0.05/0.20 - RF of loop [10:1]: 0.05/0.20 V__1+1 0.05/0.20 0.05/0.20 0.05/0.20 ### Specialization of cost equations eval_t19_bb3_in/3 0.05/0.20 * CE 5 is refined into CE [12,13] 0.05/0.20 0.05/0.20 0.05/0.20 ### Cost equations --> "Loop" of eval_t19_bb3_in/3 0.05/0.20 * CEs [13] --> Loop 12 0.05/0.20 * CEs [12] --> Loop 13 0.05/0.20 0.05/0.20 ### Ranking functions of CR eval_t19_bb3_in(V_k,V__0,B) 0.05/0.20 0.05/0.20 #### Partial ranking functions of CR eval_t19_bb3_in(V_k,V__0,B) 0.05/0.20 0.05/0.20 0.05/0.20 ### Specialization of cost equations eval_t19_bb0_in/3 0.05/0.20 * CE 2 is refined into CE [14,15,16,17] 0.05/0.20 0.05/0.20 0.05/0.20 ### Cost equations --> "Loop" of eval_t19_bb0_in/3 0.05/0.20 * CEs [15] --> Loop 14 0.05/0.20 * CEs [14] --> Loop 15 0.05/0.20 * CEs [17] --> Loop 16 0.05/0.20 * CEs [16] --> Loop 17 0.05/0.20 0.05/0.20 ### Ranking functions of CR eval_t19_bb0_in(V_i,V_k,B) 0.05/0.20 0.05/0.20 #### Partial ranking functions of CR eval_t19_bb0_in(V_i,V_k,B) 0.05/0.20 0.05/0.20 0.05/0.20 ### Specialization of cost equations eval_t19_start/3 0.05/0.20 * CE 1 is refined into CE [18,19,20,21] 0.05/0.20 0.05/0.20 0.05/0.20 ### Cost equations --> "Loop" of eval_t19_start/3 0.05/0.20 * CEs [21] --> Loop 18 0.05/0.20 * CEs [20] --> Loop 19 0.05/0.20 * CEs [19] --> Loop 20 0.05/0.20 * CEs [18] --> Loop 21 0.05/0.20 0.05/0.20 ### Ranking functions of CR eval_t19_start(V_i,V_k,B) 0.05/0.20 0.05/0.20 #### Partial ranking functions of CR eval_t19_start(V_i,V_k,B) 0.05/0.20 0.05/0.20 0.05/0.20 Computing Bounds 0.05/0.20 ===================================== 0.05/0.20 0.05/0.20 #### Cost of chains of eval_t19_bb1_in(V__0,B,C): 0.05/0.20 * Chain [[8],9]: 1*it(8)+0 0.05/0.20 Such that:it(8) =< V__0 0.05/0.20 0.05/0.20 with precondition: [B=2,C=100,V__0>=101] 0.05/0.20 0.05/0.20 * Chain [9]: 0 0.05/0.20 with precondition: [B=2,V__0=C,100>=V__0] 0.05/0.20 0.05/0.20 0.05/0.20 #### Cost of chains of eval_t19_bb4_in(V__1,B): 0.05/0.20 * Chain [[10],11]: 1*it(10)+0 0.05/0.20 Such that:it(10) =< V__1+1 0.05/0.20 0.05/0.20 with precondition: [B=3,V__1>=0] 0.05/0.20 0.05/0.20 * Chain [11]: 0 0.05/0.20 with precondition: [B=3,0>=V__1+1] 0.05/0.20 0.05/0.20 0.05/0.20 #### Cost of chains of eval_t19_bb3_in(V_k,V__0,B): 0.05/0.20 * Chain [13]: 0 0.05/0.20 with precondition: [0>=V__0+V_k+51] 0.05/0.20 0.05/0.20 * Chain [12]: 1*s(1)+0 0.05/0.20 Such that:s(1) =< V_k+V__0+51 0.05/0.20 0.05/0.20 with precondition: [V__0+V_k+50>=0] 0.05/0.20 0.05/0.20 0.05/0.20 #### Cost of chains of eval_t19_bb0_in(V_i,V_k,B): 0.05/0.20 * Chain [17]: 0 0.05/0.20 with precondition: [100>=V_i,0>=V_i+V_k+51] 0.05/0.20 0.05/0.20 * Chain [16]: 1*s(2)+0 0.05/0.20 Such that:s(2) =< V_i+V_k+51 0.05/0.20 0.05/0.20 with precondition: [100>=V_i,V_i+V_k+50>=0] 0.05/0.20 0.05/0.20 * Chain [15]: 1*s(3)+0 0.05/0.20 Such that:s(3) =< V_i 0.05/0.20 0.05/0.20 with precondition: [0>=V_k+151,V_i>=101] 0.05/0.20 0.05/0.20 * Chain [14]: 1*s(4)+1*s(5)+0 0.05/0.20 Such that:s(4) =< V_i 0.05/0.20 s(5) =< V_k+151 0.05/0.20 0.05/0.20 with precondition: [V_i>=101,V_k+150>=0] 0.05/0.20 0.05/0.20 0.05/0.20 #### Cost of chains of eval_t19_start(V_i,V_k,B): 0.05/0.20 * Chain [21]: 0 0.05/0.20 with precondition: [100>=V_i,0>=V_i+V_k+51] 0.05/0.20 0.05/0.20 * Chain [20]: 1*s(6)+0 0.05/0.20 Such that:s(6) =< V_i+V_k+51 0.05/0.20 0.05/0.20 with precondition: [100>=V_i,V_i+V_k+50>=0] 0.05/0.20 0.05/0.20 * Chain [19]: 1*s(7)+0 0.05/0.20 Such that:s(7) =< V_i 0.05/0.20 0.05/0.20 with precondition: [0>=V_k+151,V_i>=101] 0.05/0.20 0.05/0.20 * Chain [18]: 1*s(8)+1*s(9)+0 0.05/0.20 Such that:s(8) =< V_i 0.05/0.20 s(9) =< V_k+151 0.05/0.20 0.05/0.20 with precondition: [V_i>=101,V_k+150>=0] 0.05/0.20 0.05/0.20 0.05/0.20 Closed-form bounds of eval_t19_start(V_i,V_k,B): 0.05/0.20 ------------------------------------- 0.05/0.20 * Chain [21] with precondition: [100>=V_i,0>=V_i+V_k+51] 0.05/0.20 - Upper bound: 0 0.05/0.20 - Complexity: constant 0.05/0.20 * Chain [20] with precondition: [100>=V_i,V_i+V_k+50>=0] 0.05/0.20 - Upper bound: V_i+V_k+51 0.05/0.20 - Complexity: n 0.05/0.20 * Chain [19] with precondition: [0>=V_k+151,V_i>=101] 0.05/0.20 - Upper bound: V_i 0.05/0.20 - Complexity: n 0.05/0.20 * Chain [18] with precondition: [V_i>=101,V_k+150>=0] 0.05/0.20 - Upper bound: V_i+V_k+151 0.05/0.20 - Complexity: n 0.05/0.20 0.05/0.20 ### Maximum cost of eval_t19_start(V_i,V_k,B): max([nat(V_i+V_k+51),nat(V_k+151)+nat(V_i)]) 0.05/0.20 Asymptotic class: n 0.05/0.20 * Total analysis performed in 85 ms. 0.05/0.20 0.05/0.30 EOF