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_t27_bb3_in/5,eval_t27_bb4_in/5] 0.05/0.22 1. recursive : [eval_t27_bb1_in/3,eval_t27_bb2_in/3,eval_t27_bb3_in_loop_cont/4] 0.05/0.22 2. non_recursive : [eval_t27_stop/1] 0.05/0.22 3. non_recursive : [eval_t27_bb5_in/1] 0.05/0.22 4. non_recursive : [eval_t27_bb1_in_loop_cont/2] 0.05/0.22 5. non_recursive : [eval_t27_bb0_in/3] 0.05/0.22 6. non_recursive : [eval_t27_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_t27_bb3_in/5 0.05/0.22 1. SCC is partially evaluated into eval_t27_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_t27_bb0_in/3 0.05/0.22 6. SCC is partially evaluated into eval_t27_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_t27_bb3_in/5 0.05/0.22 * CE 6 is refined into CE [7] 0.05/0.22 * CE 5 is refined into CE [8] 0.05/0.22 0.05/0.22 0.05/0.22 ### Cost equations --> "Loop" of eval_t27_bb3_in/5 0.05/0.22 * CEs [8] --> Loop 7 0.05/0.22 * CEs [7] --> Loop 8 0.05/0.22 0.05/0.22 ### Ranking functions of CR eval_t27_bb3_in(V__01,V__0,V__1,B,C) 0.05/0.22 * RF of phase [7]: [V__1/100-99/100] 0.05/0.22 0.05/0.22 #### Partial ranking functions of CR eval_t27_bb3_in(V__01,V__0,V__1,B,C) 0.05/0.22 * Partial RF of phase [7]: 0.05/0.22 - RF of loop [7:1]: 0.05/0.22 V__1/100-99/100 0.05/0.22 0.05/0.22 0.05/0.22 ### Specialization of cost equations eval_t27_bb1_in/3 0.05/0.22 * CE 4 is refined into CE [9] 0.05/0.22 * CE 3 is refined into CE [10,11] 0.05/0.22 0.05/0.22 0.05/0.22 ### Cost equations --> "Loop" of eval_t27_bb1_in/3 0.05/0.22 * CEs [11] --> Loop 9 0.05/0.22 * CEs [10] --> Loop 10 0.05/0.22 * CEs [9] --> Loop 11 0.05/0.22 0.05/0.22 ### Ranking functions of CR eval_t27_bb1_in(V__01,V__0,B) 0.05/0.22 * RF of phase [9]: [-V__0] 0.05/0.22 * RF of phase [10]: [-V__0,-V__01/1000-9/10] 0.05/0.22 0.05/0.22 #### Partial ranking functions of CR eval_t27_bb1_in(V__01,V__0,B) 0.05/0.22 * Partial RF of phase [9]: 0.05/0.22 - RF of loop [9:1]: 0.05/0.22 -V__0 0.05/0.22 * Partial RF of phase [10]: 0.05/0.22 - RF of loop [10:1]: 0.05/0.22 -V__0 0.05/0.22 -V__01/1000-9/10 0.05/0.22 0.05/0.22 0.05/0.22 ### Specialization of cost equations eval_t27_bb0_in/3 0.05/0.22 * CE 2 is refined into CE [12,13,14,15] 0.05/0.22 0.05/0.22 0.05/0.22 ### Cost equations --> "Loop" of eval_t27_bb0_in/3 0.05/0.22 * CEs [15] --> Loop 12 0.05/0.22 * CEs [12] --> Loop 13 0.05/0.22 * CEs [14] --> Loop 14 0.05/0.22 * CEs [13] --> Loop 15 0.05/0.22 0.05/0.22 ### Ranking functions of CR eval_t27_bb0_in(V_n,V_y,B) 0.05/0.22 0.05/0.22 #### Partial ranking functions of CR eval_t27_bb0_in(V_n,V_y,B) 0.05/0.22 0.05/0.22 0.05/0.22 ### Specialization of cost equations eval_t27_start/3 0.05/0.22 * CE 1 is refined into CE [16,17,18,19] 0.05/0.22 0.05/0.22 0.05/0.22 ### Cost equations --> "Loop" of eval_t27_start/3 0.05/0.22 * CEs [19] --> Loop 16 0.05/0.22 * CEs [18] --> Loop 17 0.05/0.22 * CEs [17] --> Loop 18 0.05/0.22 * CEs [16] --> Loop 19 0.05/0.22 0.05/0.22 ### Ranking functions of CR eval_t27_start(V_n,V_y,B) 0.05/0.22 0.05/0.22 #### Partial ranking functions of CR eval_t27_start(V_n,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_t27_bb3_in(V__01,V__0,V__1,B,C): 0.05/0.22 * Chain [[7],8]: 1*it(7)+0 0.05/0.22 Such that:it(7) =< V__1/100-C/100 0.05/0.22 0.05/0.22 with precondition: [B=2,0>=V__0+1,99>=C,C>=0,V__01+1000>=V__1,V__1>=C+100] 0.05/0.22 0.05/0.22 * Chain [8]: 0 0.05/0.22 with precondition: [B=2,V__1=C,0>=V__0+1,99>=V__1,V__01+1000>=V__1] 0.05/0.22 0.05/0.22 0.05/0.22 #### Cost of chains of eval_t27_bb1_in(V__01,V__0,B): 0.05/0.22 * Chain [[10],[9],11]: 1*it(9)+1*it(10)+1*s(3)+0 0.05/0.22 Such that:it(10) =< -V__01/1000 0.05/0.22 s(3) =< V__01/100-10*V__0 0.05/0.22 aux(1) =< -V__0 0.05/0.22 it(9) =< aux(1) 0.05/0.22 it(10) =< aux(1) 0.05/0.22 0.05/0.22 with precondition: [B=3,0>=V__01+901,0>=V__0+2,V__01>=1000*V__0+100] 0.05/0.22 0.05/0.22 * Chain [[10],11]: 1*it(10)+0 0.05/0.22 Such that:it(10) =< -V__01/1000 0.05/0.22 it(10) =< -V__0 0.05/0.22 0.05/0.22 with precondition: [B=3,0>=V__0+1,1000*V__0+99>=V__01] 0.05/0.22 0.05/0.22 * Chain [[9],11]: 1*it(9)+1*s(3)+0 0.05/0.22 Such that:s(3) =< V__01/100-10*V__0 0.05/0.22 it(9) =< -V__0 0.05/0.22 0.05/0.22 with precondition: [B=3,0>=V__0+1,V__01+900>=0] 0.05/0.22 0.05/0.22 * Chain [11]: 0 0.05/0.22 with precondition: [B=3,V__0>=0] 0.05/0.22 0.05/0.22 0.05/0.22 #### Cost of chains of eval_t27_bb0_in(V_n,V_y,B): 0.05/0.22 * Chain [15]: 1*s(4)+1*s(5)+0 0.05/0.22 Such that:s(4) =< -10*V_n+V_y/100 0.05/0.22 s(5) =< -V_n 0.05/0.22 0.05/0.22 with precondition: [0>=V_n+1,V_y+900>=0] 0.05/0.22 0.05/0.22 * Chain [14]: 1*s(6)+0 0.05/0.22 Such that:s(6) =< -V_n 0.05/0.22 s(6) =< -V_y/1000 0.05/0.22 0.05/0.22 with precondition: [0>=V_n+1,1000*V_n+99>=V_y] 0.05/0.22 0.05/0.22 * Chain [13]: 1*s(7)+1*s(8)+1*s(10)+0 0.05/0.22 Such that:s(8) =< -10*V_n+V_y/100 0.05/0.22 s(9) =< -V_n 0.05/0.22 s(7) =< -V_y/1000 0.05/0.22 s(10) =< s(9) 0.05/0.22 s(7) =< s(9) 0.05/0.22 0.05/0.22 with precondition: [0>=V_n+2,0>=V_y+901,V_y>=1000*V_n+100] 0.05/0.22 0.05/0.22 * Chain [12]: 0 0.05/0.22 with precondition: [V_n>=0] 0.05/0.22 0.05/0.22 0.05/0.22 #### Cost of chains of eval_t27_start(V_n,V_y,B): 0.05/0.22 * Chain [19]: 1*s(11)+1*s(12)+0 0.05/0.22 Such that:s(11) =< -10*V_n+V_y/100 0.05/0.22 s(12) =< -V_n 0.05/0.22 0.05/0.22 with precondition: [0>=V_n+1,V_y+900>=0] 0.05/0.22 0.05/0.22 * Chain [18]: 1*s(13)+0 0.05/0.22 Such that:s(13) =< -V_n 0.05/0.22 s(13) =< -V_y/1000 0.05/0.22 0.05/0.22 with precondition: [0>=V_n+1,1000*V_n+99>=V_y] 0.05/0.22 0.05/0.22 * Chain [17]: 1*s(14)+1*s(16)+1*s(17)+0 0.05/0.22 Such that:s(14) =< -10*V_n+V_y/100 0.05/0.22 s(15) =< -V_n 0.05/0.22 s(16) =< -V_y/1000 0.05/0.22 s(17) =< s(15) 0.05/0.22 s(16) =< s(15) 0.05/0.22 0.05/0.22 with precondition: [0>=V_n+2,0>=V_y+901,V_y>=1000*V_n+100] 0.05/0.22 0.05/0.22 * Chain [16]: 0 0.05/0.22 with precondition: [V_n>=0] 0.05/0.22 0.05/0.22 0.05/0.22 Closed-form bounds of eval_t27_start(V_n,V_y,B): 0.05/0.22 ------------------------------------- 0.05/0.22 * Chain [19] with precondition: [0>=V_n+1,V_y+900>=0] 0.05/0.22 - Upper bound: -11*V_n+V_y/100 0.05/0.22 - Complexity: n 0.05/0.22 * Chain [18] with precondition: [0>=V_n+1,1000*V_n+99>=V_y] 0.05/0.22 - Upper bound: -V_n 0.05/0.22 - Complexity: n 0.05/0.22 * Chain [17] with precondition: [0>=V_n+2,0>=V_y+901,V_y>=1000*V_n+100] 0.05/0.22 - Upper bound: -11*V_n+9/1000*V_y 0.05/0.22 - Complexity: n 0.05/0.22 * Chain [16] with precondition: [V_n>=0] 0.05/0.22 - Upper bound: 0 0.05/0.22 - Complexity: constant 0.05/0.22 0.05/0.22 ### Maximum cost of eval_t27_start(V_n,V_y,B): nat(-V_y/1000)+nat(-10*V_n+V_y/100)+nat(-V_n) 0.05/0.22 Asymptotic class: n 0.05/0.22 * Total analysis performed in 148 ms. 0.05/0.22 0.05/0.32 EOF