0.05/0.17 WORST_CASE(?,O(n^1)) 0.05/0.17 0.05/0.17 Preprocessing Cost Relations 0.05/0.17 ===================================== 0.05/0.17 0.05/0.17 #### Computed strongly connected components 0.05/0.17 0. recursive : [eval_foo_bb2_in/4,eval_foo_bb3_in/4] 0.05/0.17 1. recursive : [eval_foo_bb1_in/2,eval_foo_bb2_in_loop_cont/4,eval_foo_bb4_in/3] 0.05/0.17 2. non_recursive : [eval_foo_stop/1] 0.05/0.17 3. non_recursive : [eval_foo_bb5_in/1] 0.05/0.17 4. non_recursive : [eval_foo_bb1_in_loop_cont/2] 0.05/0.17 5. non_recursive : [eval_foo_bb0_in/2] 0.05/0.17 6. non_recursive : [eval_foo_start/3] 0.05/0.17 0.05/0.17 #### Obtained direct recursion through partial evaluation 0.05/0.17 0. SCC is partially evaluated into eval_foo_bb2_in/4 0.05/0.17 1. SCC is partially evaluated into eval_foo_bb1_in/2 0.05/0.17 2. SCC is completely evaluated into other SCCs 0.05/0.17 3. SCC is completely evaluated into other SCCs 0.05/0.17 4. SCC is completely evaluated into other SCCs 0.05/0.17 5. SCC is partially evaluated into eval_foo_bb0_in/2 0.05/0.17 6. SCC is partially evaluated into eval_foo_start/3 0.05/0.17 0.05/0.17 Control-Flow Refinement of Cost Relations 0.05/0.17 ===================================== 0.05/0.17 0.05/0.17 ### Specialization of cost equations eval_foo_bb2_in/4 0.05/0.17 * CE 7 is refined into CE [8] 0.05/0.17 * CE 6 is refined into CE [9] 0.05/0.17 * CE 5 is refined into CE [10] 0.05/0.17 0.05/0.17 0.05/0.17 ### Cost equations --> "Loop" of eval_foo_bb2_in/4 0.05/0.17 * CEs [10] --> Loop 8 0.05/0.17 * CEs [8] --> Loop 9 0.05/0.17 * CEs [9] --> Loop 10 0.05/0.17 0.05/0.17 ### Ranking functions of CR eval_foo_bb2_in(V__0,V__01,B,C) 0.05/0.17 * RF of phase [8]: [-V__01+10] 0.05/0.17 0.05/0.17 #### Partial ranking functions of CR eval_foo_bb2_in(V__0,V__01,B,C) 0.05/0.17 * Partial RF of phase [8]: 0.05/0.17 - RF of loop [8:1]: 0.05/0.17 -V__01+10 0.05/0.17 0.05/0.17 0.05/0.17 ### Specialization of cost equations eval_foo_bb1_in/2 0.05/0.17 * CE 4 is refined into CE [11] 0.05/0.17 * CE 3 is refined into CE [12,13] 0.05/0.17 0.05/0.17 0.05/0.17 ### Cost equations --> "Loop" of eval_foo_bb1_in/2 0.05/0.17 * CEs [12] --> Loop 11 0.05/0.17 * CEs [13] --> Loop 12 0.05/0.17 * CEs [11] --> Loop 13 0.05/0.17 0.05/0.17 ### Ranking functions of CR eval_foo_bb1_in(V__0,B) 0.05/0.17 * RF of phase [11]: [-V__0+3] 0.05/0.17 * RF of phase [12]: [-V__0+5] 0.05/0.17 0.05/0.17 #### Partial ranking functions of CR eval_foo_bb1_in(V__0,B) 0.05/0.17 * Partial RF of phase [11]: 0.05/0.17 - RF of loop [11:1]: 0.05/0.17 -V__0+3 0.05/0.17 * Partial RF of phase [12]: 0.05/0.17 - RF of loop [12:1]: 0.05/0.17 -V__0+5 0.05/0.17 0.05/0.17 0.05/0.17 ### Specialization of cost equations eval_foo_bb0_in/2 0.05/0.17 * CE 2 is refined into CE [14,15,16] 0.05/0.17 0.05/0.17 0.05/0.17 ### Cost equations --> "Loop" of eval_foo_bb0_in/2 0.05/0.17 * CEs [16] --> Loop 14 0.05/0.17 * CEs [15] --> Loop 15 0.05/0.17 * CEs [14] --> Loop 16 0.05/0.17 0.05/0.17 ### Ranking functions of CR eval_foo_bb0_in(V_i,B) 0.05/0.17 0.05/0.17 #### Partial ranking functions of CR eval_foo_bb0_in(V_i,B) 0.05/0.17 0.05/0.17 0.05/0.17 ### Specialization of cost equations eval_foo_start/3 0.05/0.17 * CE 1 is refined into CE [17,18,19] 0.05/0.17 0.05/0.17 0.05/0.17 ### Cost equations --> "Loop" of eval_foo_start/3 0.05/0.17 * CEs [19] --> Loop 17 0.05/0.17 * CEs [18] --> Loop 18 0.05/0.17 * CEs [17] --> Loop 19 0.05/0.17 0.05/0.17 ### Ranking functions of CR eval_foo_start(V_i,V_j,B) 0.05/0.17 0.05/0.17 #### Partial ranking functions of CR eval_foo_start(V_i,V_j,B) 0.05/0.17 0.05/0.17 0.05/0.17 Computing Bounds 0.05/0.17 ===================================== 0.05/0.17 0.05/0.17 #### Cost of chains of eval_foo_bb2_in(V__0,V__01,B,C): 0.05/0.17 * Chain [[8],9]: 1*it(8)+0 0.05/0.17 Such that:it(8) =< -V__01+10 0.05/0.17 0.05/0.17 with precondition: [B=2,C=10,4>=V__0,9>=V__01,V__0>=3,V__01>=0] 0.05/0.17 0.05/0.17 * Chain [10]: 0 0.05/0.17 with precondition: [V__01=0,B=2,C=0,2>=V__0] 0.05/0.17 0.05/0.17 0.05/0.17 #### Cost of chains of eval_foo_bb1_in(V__0,B): 0.05/0.17 * Chain [[12],13]: 1*it(12)+1*s(3)+0 0.05/0.17 Such that:aux(4) =< -V__0+5 0.05/0.17 it(12) =< aux(4) 0.05/0.17 s(3) =< aux(4)*10 0.05/0.17 0.05/0.17 with precondition: [B=3,4>=V__0,V__0>=3] 0.05/0.17 0.05/0.17 * Chain [[11],[12],13]: 1*it(11)+1*it(12)+1*s(3)+0 0.05/0.17 Such that:aux(4) =< 2 0.05/0.17 it(11) =< -V__0+3 0.05/0.17 it(12) =< aux(4) 0.05/0.17 s(3) =< aux(4)*10 0.05/0.17 0.05/0.17 with precondition: [B=3,2>=V__0] 0.05/0.17 0.05/0.17 * Chain [13]: 0 0.05/0.17 with precondition: [B=3,V__0>=5] 0.05/0.17 0.05/0.17 0.05/0.17 #### Cost of chains of eval_foo_bb0_in(V_i,B): 0.05/0.17 * Chain [16]: 1*s(5)+1*s(6)+0 0.05/0.17 Such that:s(4) =< -V_i+5 0.05/0.17 s(5) =< s(4) 0.05/0.17 s(6) =< s(4)*10 0.05/0.17 0.05/0.17 with precondition: [4>=V_i,V_i>=3] 0.05/0.17 0.05/0.17 * Chain [15]: 1*s(8)+1*s(9)+1*s(10)+0 0.05/0.17 Such that:s(7) =< 2 0.05/0.17 s(8) =< -V_i+3 0.05/0.17 s(9) =< s(7) 0.05/0.17 s(10) =< s(7)*10 0.05/0.17 0.05/0.17 with precondition: [2>=V_i] 0.05/0.17 0.05/0.17 * Chain [14]: 0 0.05/0.17 with precondition: [V_i>=5] 0.05/0.17 0.05/0.17 0.05/0.17 #### Cost of chains of eval_foo_start(V_i,V_j,B): 0.05/0.17 * Chain [19]: 1*s(12)+1*s(13)+0 0.05/0.17 Such that:s(11) =< -V_i+5 0.05/0.17 s(12) =< s(11) 0.05/0.17 s(13) =< s(11)*10 0.05/0.17 0.05/0.17 with precondition: [4>=V_i,V_i>=3] 0.05/0.17 0.05/0.17 * Chain [18]: 1*s(15)+1*s(16)+1*s(17)+0 0.05/0.17 Such that:s(14) =< 2 0.05/0.17 s(15) =< -V_i+3 0.05/0.17 s(16) =< s(14) 0.05/0.17 s(17) =< s(14)*10 0.05/0.17 0.05/0.17 with precondition: [2>=V_i] 0.05/0.17 0.05/0.17 * Chain [17]: 0 0.05/0.17 with precondition: [V_i>=5] 0.05/0.17 0.05/0.17 0.05/0.17 Closed-form bounds of eval_foo_start(V_i,V_j,B): 0.05/0.17 ------------------------------------- 0.05/0.17 * Chain [19] with precondition: [4>=V_i,V_i>=3] 0.05/0.17 - Upper bound: -11*V_i+55 0.05/0.17 - Complexity: n 0.05/0.17 * Chain [18] with precondition: [2>=V_i] 0.05/0.17 - Upper bound: -V_i+25 0.05/0.17 - Complexity: n 0.05/0.17 * Chain [17] with precondition: [V_i>=5] 0.05/0.17 - Upper bound: 0 0.05/0.17 - Complexity: constant 0.05/0.17 0.05/0.17 ### Maximum cost of eval_foo_start(V_i,V_j,B): max([nat(-V_i+5)*11,nat(-V_i+3)+22]) 0.05/0.17 Asymptotic class: n 0.05/0.17 * Total analysis performed in 101 ms. 0.05/0.17 0.05/0.28 EOF