0.05/0.23 WORST_CASE(?,O(n^1)) 0.05/0.23 0.05/0.23 Preprocessing Cost Relations 0.05/0.23 ===================================== 0.05/0.23 0.05/0.23 #### Computed strongly connected components 0.05/0.23 0. recursive : [eval_t28_bb1_in/5,eval_t28_bb2_in/5] 0.05/0.23 1. recursive : [eval_t28_bb3_in/2,eval_t28_bb4_in/2] 0.05/0.23 2. recursive : [eval_t28_bb5_in/2,eval_t28_bb6_in/2] 0.05/0.23 3. non_recursive : [eval_t28_stop/1] 0.05/0.23 4. non_recursive : [eval_t28_bb7_in/1] 0.05/0.23 5. non_recursive : [eval_t28_bb5_in_loop_cont/2] 0.05/0.23 6. non_recursive : [eval_t28_bb3_in_loop_cont/3] 0.05/0.23 7. non_recursive : [eval_t28_bb1_in_loop_cont/4] 0.05/0.23 8. non_recursive : [eval_t28_bb0_in/3] 0.05/0.23 9. non_recursive : [eval_t28_start/3] 0.05/0.23 0.05/0.23 #### Obtained direct recursion through partial evaluation 0.05/0.23 0. SCC is partially evaluated into eval_t28_bb1_in/5 0.05/0.23 1. SCC is partially evaluated into eval_t28_bb3_in/2 0.05/0.23 2. SCC is partially evaluated into eval_t28_bb5_in/2 0.05/0.23 3. SCC is completely evaluated into other SCCs 0.05/0.23 4. SCC is completely evaluated into other SCCs 0.05/0.23 5. SCC is completely evaluated into other SCCs 0.05/0.23 6. SCC is partially evaluated into eval_t28_bb3_in_loop_cont/3 0.05/0.23 7. SCC is partially evaluated into eval_t28_bb1_in_loop_cont/4 0.05/0.23 8. SCC is partially evaluated into eval_t28_bb0_in/3 0.05/0.23 9. SCC is partially evaluated into eval_t28_start/3 0.05/0.23 0.05/0.23 Control-Flow Refinement of Cost Relations 0.05/0.23 ===================================== 0.05/0.23 0.05/0.23 ### Specialization of cost equations eval_t28_bb1_in/5 0.05/0.23 * CE 4 is refined into CE [11] 0.05/0.23 * CE 3 is refined into CE [12] 0.05/0.23 0.05/0.23 0.05/0.23 ### Cost equations --> "Loop" of eval_t28_bb1_in/5 0.05/0.23 * CEs [12] --> Loop 11 0.05/0.23 * CEs [11] --> Loop 12 0.05/0.23 0.05/0.23 ### Ranking functions of CR eval_t28_bb1_in(V__01,V__0,B,C,D) 0.05/0.23 * RF of phase [11]: [-V__01+V__0] 0.05/0.23 0.05/0.23 #### Partial ranking functions of CR eval_t28_bb1_in(V__01,V__0,B,C,D) 0.05/0.23 * Partial RF of phase [11]: 0.05/0.23 - RF of loop [11:1]: 0.05/0.23 -V__01+V__0 0.05/0.23 0.05/0.23 0.05/0.23 ### Specialization of cost equations eval_t28_bb3_in/2 0.05/0.23 * CE 7 is refined into CE [13] 0.05/0.23 * CE 6 is refined into CE [14] 0.05/0.23 0.05/0.23 0.05/0.23 ### Cost equations --> "Loop" of eval_t28_bb3_in/2 0.05/0.23 * CEs [14] --> Loop 13 0.05/0.23 * CEs [13] --> Loop 14 0.05/0.23 0.05/0.23 ### Ranking functions of CR eval_t28_bb3_in(V__12,B) 0.05/0.23 * RF of phase [13]: [V__12] 0.05/0.23 0.05/0.23 #### Partial ranking functions of CR eval_t28_bb3_in(V__12,B) 0.05/0.23 * Partial RF of phase [13]: 0.05/0.23 - RF of loop [13:1]: 0.05/0.23 V__12 0.05/0.23 0.05/0.23 0.05/0.23 ### Specialization of cost equations eval_t28_bb5_in/2 0.05/0.23 * CE 10 is refined into CE [15] 0.05/0.23 * CE 9 is refined into CE [16] 0.05/0.23 0.05/0.23 0.05/0.23 ### Cost equations --> "Loop" of eval_t28_bb5_in/2 0.05/0.23 * CEs [16] --> Loop 15 0.05/0.23 * CEs [15] --> Loop 16 0.05/0.23 0.05/0.23 ### Ranking functions of CR eval_t28_bb5_in(V__1,B) 0.05/0.23 * RF of phase [15]: [-V__1] 0.05/0.23 0.05/0.23 #### Partial ranking functions of CR eval_t28_bb5_in(V__1,B) 0.05/0.23 * Partial RF of phase [15]: 0.05/0.23 - RF of loop [15:1]: 0.05/0.23 -V__1 0.05/0.23 0.05/0.23 0.05/0.23 ### Specialization of cost equations eval_t28_bb3_in_loop_cont/3 0.05/0.23 * CE 8 is refined into CE [17,18] 0.05/0.23 0.05/0.23 0.05/0.23 ### Cost equations --> "Loop" of eval_t28_bb3_in_loop_cont/3 0.05/0.23 * CEs [18] --> Loop 17 0.05/0.23 * CEs [17] --> Loop 18 0.05/0.23 0.05/0.23 ### Ranking functions of CR eval_t28_bb3_in_loop_cont(A,B,C) 0.05/0.23 0.05/0.23 #### Partial ranking functions of CR eval_t28_bb3_in_loop_cont(A,B,C) 0.05/0.23 0.05/0.23 0.05/0.23 ### Specialization of cost equations eval_t28_bb1_in_loop_cont/4 0.05/0.23 * CE 5 is refined into CE [19,20,21,22] 0.05/0.23 0.05/0.23 0.05/0.23 ### Cost equations --> "Loop" of eval_t28_bb1_in_loop_cont/4 0.05/0.23 * CEs [22] --> Loop 19 0.05/0.23 * CEs [20] --> Loop 20 0.05/0.23 * CEs [21] --> Loop 21 0.05/0.23 * CEs [19] --> Loop 22 0.05/0.23 0.05/0.23 ### Ranking functions of CR eval_t28_bb1_in_loop_cont(A,B,C,D) 0.05/0.23 0.05/0.23 #### Partial ranking functions of CR eval_t28_bb1_in_loop_cont(A,B,C,D) 0.05/0.23 0.05/0.23 0.05/0.23 ### Specialization of cost equations eval_t28_bb0_in/3 0.05/0.23 * CE 2 is refined into CE [23,24,25,26,27,28,29] 0.05/0.23 0.05/0.23 0.05/0.23 ### Cost equations --> "Loop" of eval_t28_bb0_in/3 0.05/0.23 * CEs [29] --> Loop 23 0.05/0.23 * CEs [27] --> Loop 24 0.05/0.23 * CEs [26] --> Loop 25 0.05/0.23 * CEs [24] --> Loop 26 0.05/0.23 * CEs [23] --> Loop 27 0.05/0.23 * CEs [28] --> Loop 28 0.05/0.23 * CEs [25] --> Loop 29 0.05/0.23 0.05/0.23 ### Ranking functions of CR eval_t28_bb0_in(V_x,V_y,B) 0.05/0.23 0.05/0.23 #### Partial ranking functions of CR eval_t28_bb0_in(V_x,V_y,B) 0.05/0.23 0.05/0.23 0.05/0.23 ### Specialization of cost equations eval_t28_start/3 0.05/0.23 * CE 1 is refined into CE [30,31,32,33,34,35,36] 0.05/0.23 0.05/0.23 0.05/0.23 ### Cost equations --> "Loop" of eval_t28_start/3 0.05/0.23 * CEs [36] --> Loop 30 0.05/0.23 * CEs [35] --> Loop 31 0.05/0.23 * CEs [34] --> Loop 32 0.05/0.23 * CEs [33] --> Loop 33 0.05/0.23 * CEs [32] --> Loop 34 0.05/0.23 * CEs [31] --> Loop 35 0.05/0.23 * CEs [30] --> Loop 36 0.05/0.23 0.05/0.23 ### Ranking functions of CR eval_t28_start(V_x,V_y,B) 0.05/0.23 0.05/0.23 #### Partial ranking functions of CR eval_t28_start(V_x,V_y,B) 0.05/0.23 0.05/0.23 0.05/0.23 Computing Bounds 0.05/0.23 ===================================== 0.05/0.23 0.05/0.23 #### Cost of chains of eval_t28_bb1_in(V__01,V__0,B,C,D): 0.05/0.23 * Chain [[11],12]: 1*it(11)+0 0.05/0.23 Such that:it(11) =< -V__01/1000+C/1000 0.05/0.23 0.05/0.23 with precondition: [B=4,C+999*V__01=1000*V__0,D+999*V__01=1000*V__0,V__0>=V__01+1] 0.05/0.23 0.05/0.23 * Chain [12]: 0 0.05/0.23 with precondition: [B=4,V__0=C,V__01=D,V__01>=V__0] 0.05/0.23 0.05/0.23 0.05/0.23 #### Cost of chains of eval_t28_bb3_in(V__12,B): 0.05/0.23 * Chain [[13],14]: 1*it(13)+0 0.05/0.23 Such that:it(13) =< V__12 0.05/0.23 0.05/0.23 with precondition: [B=3,V__12>=1] 0.05/0.23 0.05/0.23 * Chain [14]: 0 0.05/0.23 with precondition: [B=3,0>=V__12] 0.05/0.23 0.05/0.23 0.05/0.23 #### Cost of chains of eval_t28_bb5_in(V__1,B): 0.05/0.23 * Chain [[15],16]: 1*it(15)+0 0.05/0.23 Such that:it(15) =< -V__1 0.05/0.23 0.05/0.23 with precondition: [B=2,0>=V__1+1] 0.05/0.23 0.05/0.23 * Chain [16]: 0 0.05/0.23 with precondition: [B=2,V__1>=0] 0.05/0.23 0.05/0.23 0.05/0.23 #### Cost of chains of eval_t28_bb3_in_loop_cont(A,B,C): 0.05/0.23 * Chain [18]: 1*s(1)+0 0.05/0.23 Such that:s(1) =< -B 0.05/0.23 0.05/0.23 with precondition: [A=3,0>=B+1] 0.05/0.23 0.05/0.23 * Chain [17]: 0 0.05/0.23 with precondition: [A=3,B>=0] 0.05/0.23 0.05/0.23 0.05/0.23 #### Cost of chains of eval_t28_bb1_in_loop_cont(A,B,C,D): 0.05/0.23 * Chain [22]: 1*s(2)+0 0.05/0.23 Such that:s(2) =< -B 0.05/0.23 0.05/0.23 with precondition: [A=4,0>=B+1,0>=C] 0.05/0.23 0.05/0.23 * Chain [21]: 1*s(3)+1*s(4)+0 0.05/0.23 Such that:s(4) =< -B 0.05/0.23 s(3) =< C 0.05/0.23 0.05/0.23 with precondition: [A=4,0>=B+1,C>=1] 0.05/0.23 0.05/0.23 * Chain [20]: 0 0.05/0.23 with precondition: [A=4,0>=C,B>=0] 0.05/0.23 0.05/0.23 * Chain [19]: 1*s(5)+0 0.05/0.23 Such that:s(5) =< C 0.05/0.23 0.05/0.23 with precondition: [A=4,B>=0,C>=1] 0.05/0.23 0.05/0.23 0.05/0.23 #### Cost of chains of eval_t28_bb0_in(V_x,V_y,B): 0.05/0.23 * Chain [29]: 0 0.05/0.23 with precondition: [V_x=0,V_y=0] 0.05/0.23 0.05/0.23 * Chain [28]: 1*s(6)+0 0.05/0.23 Such that:s(6) =< -V_y/1000 0.05/0.23 0.05/0.23 with precondition: [1000*V_x=999*V_y,0>=V_x+999] 0.05/0.23 0.05/0.23 * Chain [27]: 1*s(7)+0 0.05/0.23 Such that:s(7) =< -V_x 0.05/0.23 0.05/0.23 with precondition: [0>=V_x+1,0>=V_y,V_y>=V_x] 0.05/0.23 0.05/0.23 * Chain [26]: 1*s(8)+1*s(9)+0 0.05/0.23 Such that:s(8) =< -V_x 0.05/0.23 s(9) =< V_y 0.05/0.23 0.05/0.23 with precondition: [0>=V_x+1,V_y>=1] 0.05/0.23 0.05/0.23 * Chain [25]: 1*s(10)+0 0.05/0.23 Such that:s(10) =< V_y 0.05/0.23 0.05/0.23 with precondition: [V_x>=0,V_y>=1,V_y>=V_x] 0.05/0.23 0.05/0.23 * Chain [24]: 1*s(11)+1*s(12)+0 0.05/0.23 Such that:s(12) =< -1000*V_x+999*V_y 0.05/0.23 s(11) =< V_x-V_y 0.05/0.23 0.05/0.23 with precondition: [999*V_y>=1000*V_x+1,V_x>=V_y+1] 0.05/0.23 0.05/0.23 * Chain [23]: 1*s(13)+1*s(14)+0 0.05/0.23 Such that:s(13) =< V_x-V_y 0.05/0.23 s(14) =< 1000*V_x-999*V_y 0.05/0.23 0.05/0.23 with precondition: [1000*V_x>=999*V_y+1,V_x>=V_y+1] 0.05/0.23 0.05/0.23 0.05/0.23 #### Cost of chains of eval_t28_start(V_x,V_y,B): 0.05/0.23 * Chain [36]: 0 0.05/0.23 with precondition: [V_x=0,V_y=0] 0.05/0.23 0.05/0.23 * Chain [35]: 1*s(15)+0 0.05/0.23 Such that:s(15) =< -V_y/1000 0.05/0.23 0.05/0.23 with precondition: [1000*V_x=999*V_y,0>=V_x+999] 0.05/0.23 0.05/0.23 * Chain [34]: 1*s(16)+0 0.05/0.23 Such that:s(16) =< -V_x 0.05/0.23 0.05/0.23 with precondition: [0>=V_x+1,0>=V_y,V_y>=V_x] 0.05/0.23 0.05/0.23 * Chain [33]: 1*s(17)+1*s(18)+0 0.05/0.23 Such that:s(17) =< -V_x 0.05/0.23 s(18) =< V_y 0.05/0.23 0.05/0.23 with precondition: [0>=V_x+1,V_y>=1] 0.05/0.23 0.05/0.23 * Chain [32]: 1*s(19)+0 0.05/0.23 Such that:s(19) =< V_y 0.05/0.23 0.05/0.23 with precondition: [V_x>=0,V_y>=1,V_y>=V_x] 0.05/0.23 0.05/0.23 * Chain [31]: 1*s(20)+1*s(21)+0 0.05/0.23 Such that:s(20) =< -1000*V_x+999*V_y 0.05/0.23 s(21) =< V_x-V_y 0.05/0.23 0.05/0.23 with precondition: [999*V_y>=1000*V_x+1,V_x>=V_y+1] 0.05/0.23 0.05/0.23 * Chain [30]: 1*s(22)+1*s(23)+0 0.05/0.23 Such that:s(22) =< V_x-V_y 0.05/0.23 s(23) =< 1000*V_x-999*V_y 0.05/0.23 0.05/0.23 with precondition: [1000*V_x>=999*V_y+1,V_x>=V_y+1] 0.05/0.23 0.05/0.23 0.05/0.23 Closed-form bounds of eval_t28_start(V_x,V_y,B): 0.05/0.23 ------------------------------------- 0.05/0.23 * Chain [36] with precondition: [V_x=0,V_y=0] 0.05/0.23 - Upper bound: 0 0.05/0.23 - Complexity: constant 0.05/0.23 * Chain [35] with precondition: [1000*V_x=999*V_y,0>=V_x+999] 0.05/0.23 - Upper bound: -V_y/1000 0.05/0.23 - Complexity: n 0.05/0.23 * Chain [34] with precondition: [0>=V_x+1,0>=V_y,V_y>=V_x] 0.05/0.23 - Upper bound: -V_x 0.05/0.23 - Complexity: n 0.05/0.23 * Chain [33] with precondition: [0>=V_x+1,V_y>=1] 0.05/0.23 - Upper bound: -V_x+V_y 0.05/0.23 - Complexity: n 0.05/0.23 * Chain [32] with precondition: [V_x>=0,V_y>=1,V_y>=V_x] 0.05/0.23 - Upper bound: V_y 0.05/0.23 - Complexity: n 0.05/0.23 * Chain [31] with precondition: [999*V_y>=1000*V_x+1,V_x>=V_y+1] 0.05/0.23 - Upper bound: -999*V_x+998*V_y 0.05/0.23 - Complexity: n 0.05/0.23 * Chain [30] with precondition: [1000*V_x>=999*V_y+1,V_x>=V_y+1] 0.05/0.23 - Upper bound: 1001*V_x-1000*V_y 0.05/0.23 - Complexity: n 0.05/0.23 0.05/0.23 ### Maximum cost of eval_t28_start(V_x,V_y,B): max([max([max([nat(-V_x),nat(-V_y/1000)]),nat(V_x-V_y)+max([nat(-1000*V_x+999*V_y),nat(1000*V_x-999*V_y)])]),nat(-V_x)+nat(V_y)]) 0.05/0.23 Asymptotic class: n 0.05/0.24 * Total analysis performed in 161 ms. 0.05/0.24 0.05/0.34 EOF