0.04/0.42 WORST_CASE(?,O(n^1)) 0.04/0.42 0.04/0.42 Preprocessing Cost Relations 0.04/0.42 ===================================== 0.04/0.42 0.04/0.42 #### Computed strongly connected components 0.04/0.42 0. recursive : [eval_start_bb3_in/4,eval_start_bb4_in/4] 0.04/0.42 1. recursive : [eval_start_bb1_in/8,eval_start_bb2_in/8,eval_start_bb3_in_loop_cont/9] 0.04/0.42 2. non_recursive : [eval_start_stop/6] 0.04/0.42 3. non_recursive : [eval_start_bb5_in/6] 0.04/0.42 4. non_recursive : [exit_location/1] 0.04/0.42 5. non_recursive : [eval_start_bb1_in_loop_cont/7] 0.04/0.42 6. non_recursive : [eval_start_9/6] 0.04/0.42 7. non_recursive : [eval_start_8/6] 0.04/0.42 8. non_recursive : [eval_start_bb6_in/6] 0.04/0.42 9. non_recursive : [eval_start_2/6] 0.04/0.42 10. non_recursive : [eval_start_1/6] 0.04/0.42 11. non_recursive : [eval_start_0/6] 0.04/0.42 12. non_recursive : [eval_start_bb0_in/6] 0.04/0.42 13. non_recursive : [eval_start_start/6] 0.04/0.42 0.04/0.42 #### Obtained direct recursion through partial evaluation 0.04/0.42 0. SCC is partially evaluated into eval_start_bb3_in/4 0.04/0.42 1. SCC is partially evaluated into eval_start_bb1_in/8 0.04/0.42 2. SCC is completely evaluated into other SCCs 0.04/0.42 3. SCC is completely evaluated into other SCCs 0.04/0.42 4. SCC is completely evaluated into other SCCs 0.04/0.42 5. SCC is partially evaluated into eval_start_bb1_in_loop_cont/7 0.04/0.42 6. SCC is completely evaluated into other SCCs 0.04/0.42 7. SCC is completely evaluated into other SCCs 0.04/0.42 8. SCC is completely evaluated into other SCCs 0.04/0.42 9. SCC is partially evaluated into eval_start_2/6 0.04/0.42 10. SCC is completely evaluated into other SCCs 0.04/0.42 11. SCC is completely evaluated into other SCCs 0.04/0.42 12. SCC is completely evaluated into other SCCs 0.04/0.42 13. SCC is partially evaluated into eval_start_start/6 0.04/0.42 0.04/0.42 Control-Flow Refinement of Cost Relations 0.04/0.42 ===================================== 0.04/0.42 0.04/0.42 ### Specialization of cost equations eval_start_bb3_in/4 0.04/0.42 * CE 12 is refined into CE [13] 0.04/0.42 * CE 11 is refined into CE [14] 0.04/0.42 * CE 10 is refined into CE [15] 0.04/0.42 0.04/0.42 0.04/0.42 ### Cost equations --> "Loop" of eval_start_bb3_in/4 0.04/0.42 * CEs [15] --> Loop 13 0.04/0.42 * CEs [13] --> Loop 14 0.04/0.42 * CEs [14] --> Loop 15 0.04/0.42 0.04/0.42 ### Ranking functions of CR eval_start_bb3_in(V__0,V_z_0,B,C) 0.04/0.42 * RF of phase [13]: [V_z_0] 0.04/0.42 0.04/0.42 #### Partial ranking functions of CR eval_start_bb3_in(V__0,V_z_0,B,C) 0.04/0.42 * Partial RF of phase [13]: 0.04/0.42 - RF of loop [13:1]: 0.04/0.42 V_z_0 0.04/0.42 0.04/0.42 0.04/0.42 ### Specialization of cost equations eval_start_bb1_in/8 0.04/0.42 * CE 6 is refined into CE [16] 0.04/0.42 * CE 4 is refined into CE [17,18] 0.04/0.42 * CE 7 is refined into CE [19] 0.04/0.42 * CE 5 is refined into CE [20,21] 0.04/0.42 0.04/0.42 0.04/0.42 ### Cost equations --> "Loop" of eval_start_bb1_in/8 0.04/0.42 * CEs [21] --> Loop 16 0.04/0.42 * CEs [20] --> Loop 17 0.04/0.42 * CEs [16] --> Loop 18 0.04/0.42 * CEs [18] --> Loop 19 0.04/0.42 * CEs [17] --> Loop 20 0.04/0.42 * CEs [19] --> Loop 21 0.04/0.42 0.04/0.42 ### Ranking functions of CR eval_start_bb1_in(V__0,V_3,V_y,V_z_0,B,C,D,E) 0.04/0.42 * RF of phase [16]: [V__0/2-1/2,V__0/2-V_y/2] 0.04/0.42 * RF of phase [17]: [V__0] 0.04/0.42 0.04/0.42 #### Partial ranking functions of CR eval_start_bb1_in(V__0,V_3,V_y,V_z_0,B,C,D,E) 0.04/0.42 * Partial RF of phase [16]: 0.04/0.42 - RF of loop [16:1]: 0.04/0.42 V__0/2-1/2 0.04/0.42 V__0/2-V_y/2 0.04/0.42 * Partial RF of phase [17]: 0.04/0.42 - RF of loop [17:1]: 0.04/0.42 V__0 0.04/0.42 0.04/0.42 0.04/0.42 ### Specialization of cost equations eval_start_bb1_in_loop_cont/7 0.04/0.42 * CE 8 is refined into CE [22] 0.04/0.42 * CE 9 is refined into CE [23] 0.04/0.42 0.04/0.42 0.04/0.42 ### Cost equations --> "Loop" of eval_start_bb1_in_loop_cont/7 0.04/0.42 * CEs [22] --> Loop 22 0.04/0.42 * CEs [23] --> Loop 23 0.04/0.42 0.04/0.42 ### Ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G) 0.04/0.42 0.04/0.42 #### Partial ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G) 0.04/0.42 0.04/0.42 0.04/0.42 ### Specialization of cost equations eval_start_2/6 0.04/0.42 * CE 3 is refined into CE [24,25,26,27,28,29,30,31,32] 0.04/0.42 * CE 2 is refined into CE [33] 0.04/0.42 0.04/0.42 0.04/0.42 ### Cost equations --> "Loop" of eval_start_2/6 0.04/0.42 * CEs [30,31] --> Loop 24 0.04/0.42 * CEs [29] --> Loop 25 0.04/0.42 * CEs [28] --> Loop 26 0.04/0.42 * CEs [32] --> Loop 27 0.04/0.42 * CEs [27] --> Loop 28 0.04/0.42 * CEs [33] --> Loop 29 0.04/0.42 * CEs [25] --> Loop 30 0.04/0.42 * CEs [24,26] --> Loop 31 0.04/0.42 0.04/0.42 ### Ranking functions of CR eval_start_2(V__0,V_3,V_x,V_y,V_z_0,B) 0.04/0.42 0.04/0.42 #### Partial ranking functions of CR eval_start_2(V__0,V_3,V_x,V_y,V_z_0,B) 0.04/0.42 0.04/0.42 0.04/0.42 ### Specialization of cost equations eval_start_start/6 0.04/0.42 * CE 1 is refined into CE [34,35,36,37,38,39,40,41] 0.04/0.42 0.04/0.42 0.04/0.42 ### Cost equations --> "Loop" of eval_start_start/6 0.04/0.42 * CEs [41] --> Loop 32 0.04/0.42 * CEs [40] --> Loop 33 0.04/0.42 * CEs [39] --> Loop 34 0.04/0.42 * CEs [38] --> Loop 35 0.04/0.42 * CEs [37] --> Loop 36 0.04/0.42 * CEs [36] --> Loop 37 0.04/0.42 * CEs [35] --> Loop 38 0.04/0.42 * CEs [34] --> Loop 39 0.04/0.42 0.04/0.42 ### Ranking functions of CR eval_start_start(V__0,V_3,V_x,V_y,V_z_0,B) 0.04/0.42 0.04/0.42 #### Partial ranking functions of CR eval_start_start(V__0,V_3,V_x,V_y,V_z_0,B) 0.04/0.42 0.04/0.42 0.04/0.42 Computing Bounds 0.04/0.42 ===================================== 0.04/0.42 0.04/0.42 #### Cost of chains of eval_start_bb3_in(V__0,V_z_0,B,C): 0.04/0.42 * Chain [[13],15]: 1*it(13)+0 0.04/0.42 Such that:it(13) =< V_z_0 0.04/0.42 0.04/0.42 with precondition: [B=2,C=0,V_z_0>=1,V__0>=V_z_0+1] 0.04/0.42 0.04/0.42 * Chain [[13],14]: 1*it(13)+0 0.04/0.42 Such that:it(13) =< V_z_0 0.04/0.42 0.04/0.42 with precondition: [B=3,V_z_0>=1,V__0>=V_z_0+1] 0.04/0.42 0.04/0.42 * Chain [15]: 0 0.04/0.42 with precondition: [V_z_0=0,B=2,C=0,V__0>=1] 0.04/0.42 0.04/0.42 * Chain [14]: 0 0.04/0.42 with precondition: [B=3,V_z_0>=0,V__0>=V_z_0+1] 0.04/0.42 0.04/0.42 0.04/0.42 #### Cost of chains of eval_start_bb1_in(V__0,V_3,V_y,V_z_0,B,C,D,E): 0.04/0.42 * Chain [[17],21]: 1*it(17)+0 0.04/0.42 Such that:it(17) =< V__0 0.04/0.42 0.04/0.42 with precondition: [V_y=0,B=3,V__0>=1] 0.04/0.42 0.04/0.42 * Chain [[17],20]: 1*it(17)+0 0.04/0.42 Such that:it(17) =< V__0 0.04/0.42 0.04/0.42 with precondition: [V_y=0,B=3,V__0>=2] 0.04/0.42 0.04/0.42 * Chain [[17],18]: 1*it(17)+0 0.04/0.42 Such that:it(17) =< V__0 0.04/0.42 0.04/0.42 with precondition: [V_y=0,B=4,C=0,D=0,E=0,V__0>=1] 0.04/0.42 0.04/0.42 * Chain [[16],21]: 1*it(16)+1*s(3)+0 0.04/0.42 Such that:s(3) =< V__0 0.04/0.42 it(16) =< V__0/2-V_y/2 0.04/0.42 0.04/0.42 with precondition: [B=3,V_y>=1,V__0>=V_y+1] 0.04/0.42 0.04/0.42 * Chain [[16],20]: 1*it(16)+1*s(3)+0 0.04/0.42 Such that:s(3) =< V__0-V_y 0.04/0.42 it(16) =< V__0/2-V_y/2 0.04/0.42 0.04/0.42 with precondition: [B=3,V_y>=1,V__0>=2*V_y+2] 0.04/0.42 0.04/0.42 * Chain [[16],19]: 1*it(16)+1*s(3)+1*s(4)+0 0.04/0.42 Such that:s(3) =< V__0-V_y 0.04/0.42 it(16) =< V__0/2-V_y/2 0.04/0.42 s(4) =< V_y 0.04/0.42 0.04/0.42 with precondition: [B=3,V_y>=1,V__0>=2*V_y+2] 0.04/0.42 0.04/0.42 * Chain [[16],18]: 1*it(16)+1*s(3)+0 0.04/0.42 Such that:s(3) =< V__0-D 0.04/0.42 it(16) =< V__0/2-V_y/2 0.04/0.42 0.04/0.42 with precondition: [B=4,E=0,C=D,V_y>=1,C>=0,V_y>=C,V__0>=V_y+C+1] 0.04/0.42 0.04/0.42 * Chain [21]: 0 0.04/0.42 with precondition: [B=3,V_y>=0] 0.04/0.42 0.04/0.42 * Chain [20]: 0 0.04/0.42 with precondition: [B=3,V_y>=0,V__0>=V_y+1] 0.04/0.42 0.04/0.42 * Chain [19]: 1*s(4)+0 0.04/0.42 Such that:s(4) =< V_y 0.04/0.42 0.04/0.42 with precondition: [B=3,V_y>=1,V__0>=V_y+1] 0.04/0.42 0.04/0.42 * Chain [18]: 0 0.04/0.42 with precondition: [B=4,D=V_3,E=V_z_0,V__0=C,V_y>=0,V_y>=V__0] 0.04/0.42 0.04/0.42 0.04/0.42 #### Cost of chains of eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G): 0.04/0.42 * Chain [23]: 0 0.04/0.42 with precondition: [A=3,E>=0] 0.04/0.42 0.04/0.42 * Chain [22]: 0 0.04/0.42 with precondition: [A=4,E>=0] 0.04/0.42 0.04/0.42 0.04/0.42 #### Cost of chains of eval_start_2(V__0,V_3,V_x,V_y,V_z_0,B): 0.04/0.42 * Chain [31]: 2*s(13)+0 0.04/0.42 Such that:aux(3) =< V_x 0.04/0.42 s(13) =< aux(3) 0.04/0.42 0.04/0.42 with precondition: [V_y=0,V_x>=1] 0.04/0.42 0.04/0.42 * Chain [30]: 1*s(15)+0 0.04/0.42 Such that:s(15) =< V_x 0.04/0.42 0.04/0.42 with precondition: [V_y=0,V_x>=2] 0.04/0.42 0.04/0.42 * Chain [29]: 0 0.04/0.42 with precondition: [0>=V_y+1] 0.04/0.42 0.04/0.42 * Chain [28]: 0 0.04/0.42 with precondition: [V_y>=0] 0.04/0.42 0.04/0.42 * Chain [27]: 0 0.04/0.42 with precondition: [V_y>=0,V_y>=V_x] 0.04/0.42 0.04/0.42 * Chain [26]: 0 0.04/0.42 with precondition: [V_y>=0,V_x>=V_y+1] 0.04/0.42 0.04/0.42 * Chain [25]: 1*s(16)+2*s(19)+2*s(20)+0 0.04/0.42 Such that:s(17) =< V_x-V_y 0.04/0.42 s(18) =< V_x/2-V_y/2 0.04/0.42 s(16) =< V_y 0.04/0.42 s(19) =< s(17) 0.04/0.42 s(20) =< s(18) 0.04/0.42 0.04/0.42 with precondition: [V_y>=1,V_x>=2*V_y+2] 0.04/0.42 0.04/0.42 * Chain [24]: 2*s(21)+2*s(22)+1*s(23)+0 0.04/0.42 Such that:s(23) =< V_y 0.04/0.42 aux(4) =< V_x 0.04/0.42 aux(5) =< V_x/2-V_y/2 0.04/0.42 s(21) =< aux(4) 0.04/0.42 s(22) =< aux(5) 0.04/0.42 0.04/0.42 with precondition: [V_y>=1,V_x>=V_y+1] 0.04/0.42 0.04/0.42 0.04/0.42 #### Cost of chains of eval_start_start(V__0,V_3,V_x,V_y,V_z_0,B): 0.04/0.42 * Chain [39]: 2*s(27)+0 0.04/0.42 Such that:s(26) =< V_x 0.04/0.42 s(27) =< s(26) 0.04/0.42 0.04/0.42 with precondition: [V_y=0,V_x>=1] 0.04/0.42 0.04/0.42 * Chain [38]: 1*s(28)+0 0.04/0.42 Such that:s(28) =< V_x 0.04/0.42 0.04/0.42 with precondition: [V_y=0,V_x>=2] 0.04/0.42 0.04/0.42 * Chain [37]: 0 0.04/0.42 with precondition: [0>=V_y+1] 0.04/0.42 0.04/0.42 * Chain [36]: 0 0.04/0.42 with precondition: [V_y>=0] 0.04/0.42 0.04/0.42 * Chain [35]: 0 0.04/0.42 with precondition: [V_y>=0,V_y>=V_x] 0.04/0.42 0.04/0.42 * Chain [34]: 0 0.04/0.42 with precondition: [V_y>=0,V_x>=V_y+1] 0.04/0.42 0.04/0.42 * Chain [33]: 1*s(31)+2*s(32)+2*s(33)+0 0.04/0.42 Such that:s(29) =< V_x-V_y 0.04/0.42 s(30) =< V_x/2-V_y/2 0.04/0.42 s(31) =< V_y 0.04/0.42 s(32) =< s(29) 0.04/0.42 s(33) =< s(30) 0.04/0.42 0.04/0.42 with precondition: [V_y>=1,V_x>=2*V_y+2] 0.04/0.42 0.04/0.42 * Chain [32]: 1*s(34)+2*s(37)+2*s(38)+0 0.04/0.42 Such that:s(35) =< V_x 0.04/0.42 s(36) =< V_x/2-V_y/2 0.04/0.42 s(34) =< V_y 0.04/0.42 s(37) =< s(35) 0.04/0.42 s(38) =< s(36) 0.04/0.42 0.04/0.42 with precondition: [V_y>=1,V_x>=V_y+1] 0.04/0.42 0.04/0.42 0.04/0.42 Closed-form bounds of eval_start_start(V__0,V_3,V_x,V_y,V_z_0,B): 0.04/0.42 ------------------------------------- 0.04/0.42 * Chain [39] with precondition: [V_y=0,V_x>=1] 0.04/0.42 - Upper bound: 2*V_x 0.04/0.42 - Complexity: n 0.04/0.42 * Chain [38] with precondition: [V_y=0,V_x>=2] 0.04/0.42 - Upper bound: V_x 0.04/0.42 - Complexity: n 0.04/0.42 * Chain [37] with precondition: [0>=V_y+1] 0.04/0.42 - Upper bound: 0 0.04/0.42 - Complexity: constant 0.04/0.42 * Chain [36] with precondition: [V_y>=0] 0.04/0.42 - Upper bound: 0 0.04/0.42 - Complexity: constant 0.04/0.42 * Chain [35] with precondition: [V_y>=0,V_y>=V_x] 0.04/0.42 - Upper bound: 0 0.04/0.42 - Complexity: constant 0.04/0.42 * Chain [34] with precondition: [V_y>=0,V_x>=V_y+1] 0.04/0.42 - Upper bound: 0 0.04/0.42 - Complexity: constant 0.04/0.42 * Chain [33] with precondition: [V_y>=1,V_x>=2*V_y+2] 0.04/0.42 - Upper bound: 3*V_x-2*V_y 0.04/0.42 - Complexity: n 0.04/0.42 * Chain [32] with precondition: [V_y>=1,V_x>=V_y+1] 0.04/0.42 - Upper bound: 3*V_x 0.04/0.42 - Complexity: n 0.04/0.42 0.04/0.42 ### Maximum cost of eval_start_start(V__0,V_3,V_x,V_y,V_z_0,B): max([nat(V_x-V_y)*2+nat(V_y)+nat(V_x/2-V_y/2)*2,nat(V_x/2-V_y/2)*2+nat(V_y)+nat(V_x)+nat(V_x)]) 0.04/0.42 Asymptotic class: n 0.04/0.42 * Total analysis performed in 338 ms. 0.04/0.42 0.04/0.52 EOF