0.04/0.51 MAYBE 0.04/0.51 0.04/0.51 Preprocessing Cost Relations 0.04/0.51 ===================================== 0.04/0.51 0.04/0.51 #### Computed strongly connected components 0.04/0.51 0. recursive : [eval_real2_bb2_in/10,eval_real2_bb3_in/10,eval_real2_bb4_in/10,eval_real2_bb5_in/10] 0.04/0.51 1. recursive : [eval_real2_bb1_in/10,eval_real2_bb2_in_loop_cont/11] 0.04/0.51 2. non_recursive : [eval_real2_stop/6] 0.04/0.51 3. non_recursive : [eval_real2_bb6_in/6] 0.04/0.51 4. non_recursive : [exit_location/1] 0.04/0.51 5. non_recursive : [eval_real2_bb1_in_loop_cont/7] 0.04/0.51 6. non_recursive : [eval_real2_8/6] 0.04/0.51 7. non_recursive : [eval_real2_7/6] 0.04/0.51 8. non_recursive : [eval_real2_6/6] 0.04/0.51 9. non_recursive : [eval_real2_5/6] 0.04/0.51 10. non_recursive : [eval_real2_4/6] 0.04/0.51 11. non_recursive : [eval_real2_3/6] 0.04/0.51 12. non_recursive : [eval_real2_2/6] 0.04/0.51 13. non_recursive : [eval_real2_1/6] 0.04/0.51 14. non_recursive : [eval_real2_0/6] 0.04/0.51 15. non_recursive : [eval_real2_bb0_in/6] 0.04/0.51 16. non_recursive : [eval_real2_start/6] 0.04/0.51 0.04/0.51 #### Obtained direct recursion through partial evaluation 0.04/0.51 0. SCC is partially evaluated into eval_real2_bb2_in/10 0.04/0.51 1. SCC is partially evaluated into eval_real2_bb1_in/10 0.04/0.51 2. SCC is completely evaluated into other SCCs 0.04/0.51 3. SCC is completely evaluated into other SCCs 0.04/0.51 4. SCC is completely evaluated into other SCCs 0.04/0.51 5. SCC is partially evaluated into eval_real2_bb1_in_loop_cont/7 0.04/0.51 6. SCC is partially evaluated into eval_real2_8/6 0.04/0.51 7. SCC is completely evaluated into other SCCs 0.04/0.51 8. SCC is completely evaluated into other SCCs 0.04/0.51 9. SCC is completely evaluated into other SCCs 0.04/0.51 10. SCC is completely evaluated into other SCCs 0.04/0.51 11. SCC is completely evaluated into other SCCs 0.04/0.51 12. SCC is completely evaluated into other SCCs 0.04/0.51 13. SCC is completely evaluated into other SCCs 0.04/0.51 14. SCC is completely evaluated into other SCCs 0.04/0.51 15. SCC is completely evaluated into other SCCs 0.04/0.51 16. SCC is partially evaluated into eval_real2_start/6 0.04/0.51 0.04/0.51 Control-Flow Refinement of Cost Relations 0.04/0.51 ===================================== 0.04/0.51 0.04/0.51 ### Specialization of cost equations eval_real2_bb2_in/10 0.04/0.51 * CE 14 is refined into CE [15] 0.04/0.51 * CE 13 is refined into CE [16] 0.04/0.51 * CE 11 is refined into CE [17] 0.04/0.51 * CE 12 is refined into CE [18] 0.04/0.51 0.04/0.51 0.04/0.51 ### Cost equations --> "Loop" of eval_real2_bb2_in/10 0.04/0.51 * CEs [17] --> Loop 15 0.04/0.51 * CEs [18] --> Loop 16 0.04/0.51 * CEs [15] --> Loop 17 0.04/0.51 * CEs [16] --> Loop 18 0.04/0.51 0.04/0.51 ### Ranking functions of CR eval_real2_bb2_in(V_again_0,V_again_1,V_again_2,V_i_0,V_len,B,C,D,E,F) 0.04/0.51 * RF of phase [15,16]: [-V_i_0+V_len-1] 0.04/0.51 0.04/0.51 #### Partial ranking functions of CR eval_real2_bb2_in(V_again_0,V_again_1,V_again_2,V_i_0,V_len,B,C,D,E,F) 0.04/0.51 * Partial RF of phase [15,16]: 0.04/0.51 - RF of loop [15:1,16:1]: 0.04/0.51 -V_i_0+V_len-1 0.04/0.51 0.04/0.51 0.04/0.51 ### Specialization of cost equations eval_real2_bb1_in/10 0.04/0.51 * CE 3 is refined into CE [19,20] 0.04/0.51 * CE 4 is refined into CE [21,22] 0.04/0.51 * CE 8 is refined into CE [23] 0.04/0.51 * CE 7 is refined into CE [24] 0.04/0.51 * CE 5 is refined into CE [25,26] 0.04/0.51 * CE 6 is refined into CE [27,28] 0.04/0.51 0.04/0.51 0.04/0.51 ### Cost equations --> "Loop" of eval_real2_bb1_in/10 0.04/0.51 * CEs [26] --> Loop 19 0.04/0.51 * CEs [28] --> Loop 20 0.04/0.51 * CEs [25] --> Loop 21 0.04/0.51 * CEs [27] --> Loop 22 0.04/0.51 * CEs [20] --> Loop 23 0.04/0.51 * CEs [19] --> Loop 24 0.04/0.51 * CEs [22] --> Loop 25 0.04/0.51 * CEs [21] --> Loop 26 0.04/0.51 * CEs [23] --> Loop 27 0.04/0.51 * CEs [24] --> Loop 28 0.04/0.51 0.04/0.51 ### Ranking functions of CR eval_real2_bb1_in(V_again_0,V_again_1,V_again_2,V_i_0,V_len,B,C,D,E,F) 0.04/0.51 0.04/0.51 #### Partial ranking functions of CR eval_real2_bb1_in(V_again_0,V_again_1,V_again_2,V_i_0,V_len,B,C,D,E,F) 0.04/0.51 0.04/0.51 0.04/0.51 ### Specialization of cost equations eval_real2_bb1_in_loop_cont/7 0.04/0.51 * CE 9 is refined into CE [29] 0.04/0.51 * CE 10 is refined into CE [30] 0.04/0.51 0.04/0.51 0.04/0.51 ### Cost equations --> "Loop" of eval_real2_bb1_in_loop_cont/7 0.04/0.51 * CEs [29] --> Loop 29 0.04/0.51 * CEs [30] --> Loop 30 0.04/0.51 0.04/0.51 ### Ranking functions of CR eval_real2_bb1_in_loop_cont(A,B,C,D,E,F,G) 0.04/0.51 0.04/0.51 #### Partial ranking functions of CR eval_real2_bb1_in_loop_cont(A,B,C,D,E,F,G) 0.04/0.51 0.04/0.51 0.04/0.51 ### Specialization of cost equations eval_real2_8/6 0.04/0.51 * CE 2 is refined into CE [31,32,33,34,35,36,37,38] 0.04/0.51 0.04/0.51 0.04/0.51 ### Cost equations --> "Loop" of eval_real2_8/6 0.04/0.51 * CEs [37,38] --> Loop 31 0.04/0.51 * CEs [35,36] --> Loop 32 0.04/0.51 * CEs [31,32] --> Loop 33 0.04/0.51 * CEs [33,34] --> Loop 34 0.04/0.51 0.04/0.51 ### Ranking functions of CR eval_real2_8(V_again_0,V_again_1,V_again_2,V_i_0,V_len,B) 0.04/0.51 0.04/0.51 #### Partial ranking functions of CR eval_real2_8(V_again_0,V_again_1,V_again_2,V_i_0,V_len,B) 0.04/0.51 0.04/0.51 0.04/0.51 ### Specialization of cost equations eval_real2_start/6 0.04/0.51 * CE 1 is refined into CE [39,40,41,42] 0.04/0.51 0.04/0.51 0.04/0.51 ### Cost equations --> "Loop" of eval_real2_start/6 0.04/0.51 * CEs [42] --> Loop 35 0.04/0.51 * CEs [41] --> Loop 36 0.04/0.51 * CEs [40] --> Loop 37 0.04/0.51 * CEs [39] --> Loop 38 0.04/0.51 0.04/0.51 ### Ranking functions of CR eval_real2_start(V_again_0,V_again_1,V_again_2,V_i_0,V_len,B) 0.04/0.51 0.04/0.51 #### Partial ranking functions of CR eval_real2_start(V_again_0,V_again_1,V_again_2,V_i_0,V_len,B) 0.04/0.51 0.04/0.51 0.04/0.51 Computing Bounds 0.04/0.51 ===================================== 0.04/0.51 0.04/0.51 #### Cost of chains of eval_real2_bb2_in(V_again_0,V_again_1,V_again_2,V_i_0,V_len,B,C,D,E,F): 0.04/0.51 * Chain [[15,16],18]: 2*it(15)+0 0.04/0.51 Such that:aux(2) =< -V_i_0+F 0.04/0.51 aux(1) =< -V_i_0+F+1 0.04/0.51 it(15) =< aux(1) 0.04/0.51 it(15) =< aux(2) 0.04/0.51 0.04/0.51 with precondition: [B=2,C=D,C=E,V_len=F+1,V_again_1>=0,C>=0,V_i_0>=V_again_1,V_len>=V_i_0+2,V_again_1+V_len>=V_i_0+C+1] 0.04/0.51 0.04/0.51 * Chain [[15,16],17]: 2*it(15)+0 0.04/0.51 Such that:aux(3) =< -V_i_0+V_len 0.04/0.51 it(15) =< aux(3) 0.04/0.51 0.04/0.51 with precondition: [B=3,V_again_1>=0,V_i_0>=V_again_1,V_len>=V_i_0+2] 0.04/0.51 0.04/0.51 * Chain [18]: 0 0.04/0.51 with precondition: [B=2,E=V_again_2,V_again_1=C,V_again_1=D,V_i_0=F,V_again_1>=0,V_i_0>=V_again_1,V_i_0+1>=V_len] 0.04/0.51 0.04/0.51 * Chain [17]: 0 0.04/0.51 with precondition: [B=3,V_again_1>=0,V_i_0>=V_again_1] 0.04/0.51 0.04/0.51 0.04/0.51 #### Cost of chains of eval_real2_bb1_in(V_again_0,V_again_1,V_again_2,V_i_0,V_len,B,C,D,E,F): 0.04/0.51 * Chain [[19]]...: 3*it(19)+0 0.04/0.51 with precondition: [V_again_0>=1,V_len>=2] 0.04/0.51 0.04/0.51 * Chain [[19],28]: 3*it(19)+0 0.04/0.51 with precondition: [B=4,C=0,D=0,E=0,V_len=F+1,V_again_0>=1,V_len>=2] 0.04/0.51 0.04/0.51 * Chain [[19],27]: 3*it(19)+0 0.04/0.51 with precondition: [B=3,V_again_0>=1,V_len>=2] 0.04/0.51 0.04/0.51 * Chain [[19],24]: 3*it(19)+0 0.04/0.51 with precondition: [B=3,V_again_0>=1,V_len>=2] 0.04/0.51 0.04/0.51 * Chain [[19],23]: 3*it(19)+2*s(9)+0 0.04/0.51 Such that:s(8) =< V_len 0.04/0.51 s(9) =< s(8) 0.04/0.51 0.04/0.51 with precondition: [B=3,V_again_0>=1,V_len>=2] 0.04/0.51 0.04/0.51 * Chain [27]: 0 0.04/0.51 with precondition: [B=3,V_again_0>=0] 0.04/0.51 0.04/0.51 * Chain [24]: 0 0.04/0.51 with precondition: [B=3,V_again_0>=1] 0.04/0.51 0.04/0.51 * Chain [23]: 2*s(9)+0 0.04/0.51 Such that:s(8) =< V_len 0.04/0.51 s(9) =< s(8) 0.04/0.51 0.04/0.51 with precondition: [B=3,V_again_0>=1,V_len>=2] 0.04/0.51 0.04/0.51 * Chain [21,28]: 1 0.04/0.51 with precondition: [V_again_0=1,B=4,C=0,D=0,F=0,V_again_2=E,1>=V_len] 0.04/0.51 0.04/0.51 * Chain [21,27]: 1 0.04/0.51 with precondition: [V_again_0=1,B=3,1>=V_len] 0.04/0.51 0.04/0.51 0.04/0.51 #### Cost of chains of eval_real2_bb1_in_loop_cont(A,B,C,D,E,F,G): 0.04/0.51 * Chain [30]: 0 0.04/0.51 with precondition: [A=3] 0.04/0.51 0.04/0.51 * Chain [29]: 0 0.04/0.51 with precondition: [A=4] 0.04/0.51 0.04/0.51 0.04/0.51 #### Cost of chains of eval_real2_8(V_again_0,V_again_1,V_again_2,V_i_0,V_len,B): 0.04/0.51 * Chain [34]: 0 0.04/0.51 with precondition: [] 0.04/0.51 0.04/0.51 * Chain [33]: 1 0.04/0.51 with precondition: [1>=V_len] 0.04/0.51 0.04/0.51 * Chain [32]: 4*s(18)+12*s(19)+0 0.04/0.51 Such that:s(17) =< V_len 0.04/0.51 s(18) =< s(17) 0.04/0.51 0.04/0.51 with precondition: [V_len>=2] 0.04/0.51 0.04/0.51 * Chain [31]...: 1*aux(7)+0 0.04/0.51 with precondition: [V_len>=2] 0.04/0.51 0.04/0.51 0.04/0.51 #### Cost of chains of eval_real2_start(V_again_0,V_again_1,V_again_2,V_i_0,V_len,B): 0.04/0.51 * Chain [38]: 0 0.04/0.51 with precondition: [] 0.04/0.51 0.04/0.51 * Chain [37]: 1 0.04/0.51 with precondition: [1>=V_len] 0.04/0.51 0.04/0.51 * Chain [36]: 4*s(24)+12*s(25)+0 0.04/0.51 Such that:s(23) =< V_len 0.04/0.51 s(24) =< s(23) 0.04/0.51 0.04/0.51 with precondition: [V_len>=2] 0.04/0.51 0.04/0.51 * Chain [35]...: 1*s(26)+0 0.04/0.51 with precondition: [V_len>=2] 0.04/0.51 0.04/0.51 0.04/0.51 Closed-form bounds of eval_real2_start(V_again_0,V_again_1,V_again_2,V_i_0,V_len,B): 0.04/0.51 ------------------------------------- 0.04/0.51 * Chain [38] with precondition: [] 0.04/0.51 - Upper bound: 0 0.04/0.51 - Complexity: constant 0.04/0.51 * Chain [37] with precondition: [1>=V_len] 0.04/0.51 - Upper bound: 1 0.04/0.51 - Complexity: constant 0.04/0.51 * Chain [36] with precondition: [V_len>=2] 0.04/0.51 - Upper bound: inf 0.04/0.51 - Complexity: infinity 0.04/0.51 * Chain [35]... with precondition: [V_len>=2] 0.04/0.51 - Upper bound: inf 0.04/0.51 - Complexity: infinity 0.04/0.51 0.04/0.51 ### Maximum cost of eval_real2_start(V_again_0,V_again_1,V_again_2,V_i_0,V_len,B): inf 0.04/0.51 Asymptotic class: infinity 0.04/0.51 * Total analysis performed in 421 ms. 0.04/0.51 0.51/0.61 EOF