0.52/0.54 WORST_CASE(?,O(n^1)) 0.52/0.54 0.52/0.54 Preprocessing Cost Relations 0.52/0.54 ===================================== 0.52/0.54 0.52/0.54 #### Computed strongly connected components 0.52/0.54 0. recursive : [eval_speedSingleSingle2_3/9,eval_speedSingleSingle2_4/9,eval_speedSingleSingle2_bb1_in/9,eval_speedSingleSingle2_bb2_in/9,eval_speedSingleSingle2_bb3_in/9,eval_speedSingleSingle2_bb4_in/9,eval_speedSingleSingle2_bb5_in/9] 0.52/0.54 1. non_recursive : [eval_speedSingleSingle2_stop/6] 0.52/0.54 2. non_recursive : [eval_speedSingleSingle2_bb6_in/6] 0.52/0.54 3. non_recursive : [exit_location/1] 0.52/0.54 4. non_recursive : [eval_speedSingleSingle2_bb1_in_loop_cont/7] 0.52/0.54 5. non_recursive : [eval_speedSingleSingle2_2/6] 0.52/0.54 6. non_recursive : [eval_speedSingleSingle2_1/6] 0.52/0.54 7. non_recursive : [eval_speedSingleSingle2_0/6] 0.52/0.54 8. non_recursive : [eval_speedSingleSingle2_bb0_in/6] 0.52/0.54 9. non_recursive : [eval_speedSingleSingle2_start/6] 0.52/0.54 0.52/0.54 #### Obtained direct recursion through partial evaluation 0.52/0.54 0. SCC is partially evaluated into eval_speedSingleSingle2_bb1_in/9 0.52/0.54 1. SCC is completely evaluated into other SCCs 0.52/0.54 2. SCC is completely evaluated into other SCCs 0.52/0.54 3. SCC is completely evaluated into other SCCs 0.52/0.54 4. SCC is partially evaluated into eval_speedSingleSingle2_bb1_in_loop_cont/7 0.52/0.54 5. SCC is partially evaluated into eval_speedSingleSingle2_2/6 0.52/0.54 6. SCC is completely evaluated into other SCCs 0.52/0.54 7. SCC is completely evaluated into other SCCs 0.52/0.54 8. SCC is completely evaluated into other SCCs 0.52/0.54 9. SCC is partially evaluated into eval_speedSingleSingle2_start/6 0.52/0.54 0.52/0.54 Control-Flow Refinement of Cost Relations 0.52/0.54 ===================================== 0.52/0.54 0.52/0.54 ### Specialization of cost equations eval_speedSingleSingle2_bb1_in/9 0.52/0.54 * CE 9 is refined into CE [12] 0.52/0.54 * CE 7 is refined into CE [13] 0.52/0.54 * CE 8 is refined into CE [14] 0.52/0.54 * CE 5 is refined into CE [15] 0.52/0.54 * CE 6 is refined into CE [16] 0.52/0.54 0.52/0.54 0.52/0.54 ### Cost equations --> "Loop" of eval_speedSingleSingle2_bb1_in/9 0.52/0.54 * CEs [16] --> Loop 12 0.52/0.54 * CEs [15] --> Loop 13 0.52/0.54 * CEs [12] --> Loop 14 0.52/0.54 * CEs [13] --> Loop 15 0.52/0.54 * CEs [14] --> Loop 16 0.52/0.54 0.52/0.54 ### Ranking functions of CR eval_speedSingleSingle2_bb1_in(V_2,V_m,V_n,V_x_0,V_y_0,B,C,D,E) 0.52/0.54 * RF of phase [12]: [V_m-V_x_0,V_m-V_y_0] 0.52/0.54 * RF of phase [13]: [V_n-V_x_0,V_n-V_y_0] 0.52/0.54 0.52/0.54 #### Partial ranking functions of CR eval_speedSingleSingle2_bb1_in(V_2,V_m,V_n,V_x_0,V_y_0,B,C,D,E) 0.52/0.54 * Partial RF of phase [12]: 0.52/0.54 - RF of loop [12:1]: 0.52/0.54 V_m-V_x_0 0.52/0.54 V_m-V_y_0 0.52/0.54 * Partial RF of phase [13]: 0.52/0.54 - RF of loop [13:1]: 0.52/0.54 V_n-V_x_0 0.52/0.54 V_n-V_y_0 0.52/0.54 0.52/0.54 0.52/0.54 ### Specialization of cost equations eval_speedSingleSingle2_bb1_in_loop_cont/7 0.52/0.54 * CE 11 is refined into CE [17] 0.52/0.54 * CE 10 is refined into CE [18] 0.52/0.54 0.52/0.54 0.52/0.54 ### Cost equations --> "Loop" of eval_speedSingleSingle2_bb1_in_loop_cont/7 0.52/0.54 * CEs [17] --> Loop 17 0.52/0.54 * CEs [18] --> Loop 18 0.52/0.54 0.52/0.54 ### Ranking functions of CR eval_speedSingleSingle2_bb1_in_loop_cont(A,B,C,D,E,F,G) 0.52/0.54 0.52/0.54 #### Partial ranking functions of CR eval_speedSingleSingle2_bb1_in_loop_cont(A,B,C,D,E,F,G) 0.52/0.54 0.52/0.54 0.52/0.54 ### Specialization of cost equations eval_speedSingleSingle2_2/6 0.52/0.54 * CE 4 is refined into CE [19,20,21,22,23,24,25,26,27,28,29,30] 0.52/0.54 * CE 2 is refined into CE [31] 0.52/0.54 * CE 3 is refined into CE [32] 0.52/0.54 0.52/0.54 0.52/0.54 ### Cost equations --> "Loop" of eval_speedSingleSingle2_2/6 0.52/0.54 * CEs [22,26,30] --> Loop 19 0.52/0.54 * CEs [23] --> Loop 20 0.52/0.54 * CEs [24,28] --> Loop 21 0.52/0.54 * CEs [19,27] --> Loop 22 0.52/0.54 * CEs [31] --> Loop 23 0.52/0.54 * CEs [32] --> Loop 24 0.52/0.54 * CEs [21,25,29] --> Loop 25 0.52/0.54 * CEs [20] --> Loop 26 0.52/0.54 0.52/0.54 ### Ranking functions of CR eval_speedSingleSingle2_2(V_2,V_m,V_n,V_x_0,V_y_0,B) 0.52/0.54 0.52/0.54 #### Partial ranking functions of CR eval_speedSingleSingle2_2(V_2,V_m,V_n,V_x_0,V_y_0,B) 0.52/0.54 0.52/0.54 0.52/0.54 ### Specialization of cost equations eval_speedSingleSingle2_start/6 0.52/0.54 * CE 1 is refined into CE [33,34,35,36,37,38,39,40] 0.52/0.54 0.52/0.54 0.52/0.54 ### Cost equations --> "Loop" of eval_speedSingleSingle2_start/6 0.52/0.54 * CEs [40] --> Loop 27 0.52/0.54 * CEs [39] --> Loop 28 0.52/0.54 * CEs [38] --> Loop 29 0.52/0.54 * CEs [37] --> Loop 30 0.52/0.54 * CEs [36] --> Loop 31 0.52/0.54 * CEs [35] --> Loop 32 0.52/0.54 * CEs [34] --> Loop 33 0.52/0.54 * CEs [33] --> Loop 34 0.52/0.54 0.52/0.54 ### Ranking functions of CR eval_speedSingleSingle2_start(V_2,V_m,V_n,V_x_0,V_y_0,B) 0.52/0.54 0.52/0.54 #### Partial ranking functions of CR eval_speedSingleSingle2_start(V_2,V_m,V_n,V_x_0,V_y_0,B) 0.52/0.54 0.52/0.54 0.52/0.54 Computing Bounds 0.52/0.54 ===================================== 0.52/0.54 0.52/0.54 #### Cost of chains of eval_speedSingleSingle2_bb1_in(V_2,V_m,V_n,V_x_0,V_y_0,B,C,D,E): 0.52/0.54 * Chain [[13],[12],16]: 1*it(12)+1*it(13)+0 0.52/0.54 Such that:it(12) =< -V_n+D 0.52/0.54 it(13) =< V_n-V_x_0 0.52/0.54 0.52/0.54 with precondition: [B=2,V_x_0=V_y_0,D=E,0>=C,V_x_0>=0,D>=V_n+1,V_n>=V_x_0+1,V_m>=D] 0.52/0.54 0.52/0.54 * Chain [[13],[12],15]: 1*it(12)+1*it(13)+0 0.52/0.54 Such that:it(12) =< -V_n+D 0.52/0.54 it(13) =< V_n-V_y_0 0.52/0.54 0.52/0.54 with precondition: [B=2,V_x_0=V_y_0,V_m=D,V_m=E,V_x_0>=0,C>=1,V_m>=V_n+1,V_n>=V_x_0+1] 0.52/0.54 0.52/0.54 * Chain [[13],[12],14]: 1*it(12)+1*it(13)+0 0.52/0.54 Such that:it(12) =< V_m-V_n 0.52/0.54 it(13) =< V_n-V_y_0 0.52/0.54 0.52/0.54 with precondition: [B=3,V_x_0=V_y_0,V_x_0>=0,V_m>=V_n+1,V_n>=V_x_0+1] 0.52/0.54 0.52/0.54 * Chain [[13],16]: 1*it(13)+0 0.52/0.54 Such that:it(13) =< -V_y_0+D 0.52/0.54 0.52/0.54 with precondition: [B=2,V_x_0=V_y_0,D=E,0>=C,V_m>=0,V_x_0>=0,D>=V_x_0+1,V_n>=D] 0.52/0.54 0.52/0.54 * Chain [[13],15]: 1*it(13)+0 0.52/0.54 Such that:it(13) =< -V_y_0+D 0.52/0.54 0.52/0.54 with precondition: [B=2,V_x_0=V_y_0,V_n=D,V_n=E,V_m>=0,V_x_0>=0,C>=1,V_n>=V_m,V_n>=V_x_0+1] 0.52/0.54 0.52/0.54 * Chain [[13],14]: 1*it(13)+0 0.52/0.54 Such that:it(13) =< V_n-V_y_0 0.52/0.54 0.52/0.54 with precondition: [B=3,V_x_0=V_y_0,V_m>=0,V_x_0>=0,V_n>=V_x_0+1] 0.52/0.54 0.52/0.54 * Chain [[12],16]: 1*it(12)+0 0.52/0.54 Such that:it(12) =< -V_y_0+D 0.52/0.54 0.52/0.54 with precondition: [B=2,V_x_0=V_y_0,D=E,0>=C,V_n>=0,V_x_0>=V_n,D>=V_x_0+1,V_m>=D] 0.52/0.54 0.52/0.54 * Chain [[12],15]: 1*it(12)+0 0.52/0.54 Such that:it(12) =< -V_y_0+D 0.52/0.54 0.52/0.54 with precondition: [B=2,V_x_0=V_y_0,V_m=D,V_m=E,V_n>=0,C>=1,V_x_0>=V_n,V_m>=V_x_0+1] 0.52/0.54 0.52/0.54 * Chain [[12],14]: 1*it(12)+0 0.52/0.54 Such that:it(12) =< V_m-V_y_0 0.52/0.54 0.52/0.54 with precondition: [B=3,V_x_0=V_y_0,V_n>=0,V_x_0>=V_n,V_m>=V_x_0+1] 0.52/0.54 0.52/0.54 * Chain [16]: 0 0.52/0.54 with precondition: [B=2,V_y_0=V_x_0,V_y_0=D,V_y_0=E,0>=C,V_m>=0,V_n>=0,V_y_0>=0,V_m+V_n>=V_y_0] 0.52/0.54 0.52/0.54 * Chain [15]: 0 0.52/0.54 with precondition: [B=2,V_y_0=V_x_0,V_y_0=D,V_y_0=E,C>=1,V_y_0>=V_m,V_y_0>=V_n,V_m+V_n>=V_y_0] 0.52/0.54 0.52/0.54 * Chain [14]: 0 0.52/0.54 with precondition: [B=3,V_y_0=V_x_0,V_m>=0,V_n>=0,V_y_0>=0,V_m+V_n>=V_y_0] 0.52/0.54 0.52/0.54 0.52/0.54 #### Cost of chains of eval_speedSingleSingle2_bb1_in_loop_cont(A,B,C,D,E,F,G): 0.52/0.54 * Chain [18]: 0 0.52/0.54 with precondition: [A=2,C>=0,D>=0] 0.52/0.54 0.52/0.54 * Chain [17]: 0 0.52/0.54 with precondition: [A=3,C>=0,D>=0] 0.52/0.54 0.52/0.54 0.52/0.54 #### Cost of chains of eval_speedSingleSingle2_2(V_2,V_m,V_n,V_x_0,V_y_0,B): 0.52/0.54 * Chain [26]: 0 0.52/0.54 with precondition: [V_m=0,V_n=0] 0.52/0.54 0.52/0.54 * Chain [25]: 3*s(1)+0 0.52/0.54 Such that:aux(1) =< V_m 0.52/0.54 s(1) =< aux(1) 0.52/0.54 0.52/0.54 with precondition: [V_n=0,V_m>=1] 0.52/0.54 0.52/0.54 * Chain [24]: 0 0.52/0.54 with precondition: [0>=V_m+1] 0.52/0.54 0.52/0.54 * Chain [23]: 0 0.52/0.54 with precondition: [0>=V_n+1] 0.52/0.54 0.52/0.54 * Chain [22]: 0 0.52/0.54 with precondition: [V_m>=0,V_n>=0] 0.52/0.54 0.52/0.54 * Chain [21]: 2*s(4)+0 0.52/0.54 Such that:aux(2) =< V_n 0.52/0.54 s(4) =< aux(2) 0.52/0.54 0.52/0.54 with precondition: [V_m>=0,V_n>=1] 0.52/0.54 0.52/0.54 * Chain [20]: 1*s(6)+0 0.52/0.54 Such that:s(6) =< V_n 0.52/0.54 0.52/0.54 with precondition: [V_m>=0,V_n>=1,V_n>=V_m] 0.52/0.54 0.52/0.54 * Chain [19]: 3*s(7)+3*s(8)+0 0.52/0.54 Such that:aux(3) =< V_m-V_n 0.52/0.54 aux(4) =< V_n 0.52/0.54 s(7) =< aux(3) 0.52/0.54 s(8) =< aux(4) 0.52/0.54 0.52/0.54 with precondition: [V_n>=1,V_m>=V_n+1] 0.52/0.54 0.52/0.54 0.52/0.54 #### Cost of chains of eval_speedSingleSingle2_start(V_2,V_m,V_n,V_x_0,V_y_0,B): 0.52/0.54 * Chain [34]: 0 0.52/0.54 with precondition: [V_m=0,V_n=0] 0.52/0.54 0.52/0.54 * Chain [33]: 3*s(14)+0 0.52/0.54 Such that:s(13) =< V_m 0.52/0.54 s(14) =< s(13) 0.52/0.54 0.52/0.54 with precondition: [V_n=0,V_m>=1] 0.52/0.54 0.52/0.54 * Chain [32]: 0 0.52/0.54 with precondition: [0>=V_m+1] 0.52/0.54 0.52/0.54 * Chain [31]: 0 0.52/0.54 with precondition: [0>=V_n+1] 0.52/0.54 0.52/0.54 * Chain [30]: 0 0.52/0.54 with precondition: [V_m>=0,V_n>=0] 0.52/0.54 0.52/0.54 * Chain [29]: 2*s(16)+0 0.52/0.54 Such that:s(15) =< V_n 0.52/0.54 s(16) =< s(15) 0.52/0.54 0.52/0.54 with precondition: [V_m>=0,V_n>=1] 0.52/0.54 0.52/0.54 * Chain [28]: 1*s(17)+0 0.52/0.54 Such that:s(17) =< V_n 0.52/0.54 0.52/0.54 with precondition: [V_m>=0,V_n>=1,V_n>=V_m] 0.52/0.54 0.52/0.54 * Chain [27]: 3*s(20)+3*s(21)+0 0.52/0.54 Such that:s(18) =< V_m-V_n 0.52/0.54 s(19) =< V_n 0.52/0.54 s(20) =< s(18) 0.52/0.54 s(21) =< s(19) 0.52/0.54 0.52/0.54 with precondition: [V_n>=1,V_m>=V_n+1] 0.52/0.54 0.52/0.54 0.52/0.54 Closed-form bounds of eval_speedSingleSingle2_start(V_2,V_m,V_n,V_x_0,V_y_0,B): 0.52/0.54 ------------------------------------- 0.52/0.54 * Chain [34] with precondition: [V_m=0,V_n=0] 0.52/0.54 - Upper bound: 0 0.52/0.54 - Complexity: constant 0.52/0.54 * Chain [33] with precondition: [V_n=0,V_m>=1] 0.52/0.54 - Upper bound: 3*V_m 0.52/0.54 - Complexity: n 0.52/0.54 * Chain [32] with precondition: [0>=V_m+1] 0.52/0.54 - Upper bound: 0 0.52/0.54 - Complexity: constant 0.52/0.54 * Chain [31] with precondition: [0>=V_n+1] 0.52/0.54 - Upper bound: 0 0.52/0.54 - Complexity: constant 0.52/0.54 * Chain [30] with precondition: [V_m>=0,V_n>=0] 0.52/0.54 - Upper bound: 0 0.52/0.54 - Complexity: constant 0.52/0.54 * Chain [29] with precondition: [V_m>=0,V_n>=1] 0.52/0.54 - Upper bound: 2*V_n 0.52/0.54 - Complexity: n 0.52/0.54 * Chain [28] with precondition: [V_m>=0,V_n>=1,V_n>=V_m] 0.52/0.54 - Upper bound: V_n 0.52/0.54 - Complexity: n 0.52/0.54 * Chain [27] with precondition: [V_n>=1,V_m>=V_n+1] 0.52/0.54 - Upper bound: 3*V_m 0.52/0.54 - Complexity: n 0.52/0.54 0.52/0.54 ### Maximum cost of eval_speedSingleSingle2_start(V_2,V_m,V_n,V_x_0,V_y_0,B): max([nat(V_m)*3,nat(V_m-V_n)*3+nat(V_n)+nat(V_n)+nat(V_n)]) 0.52/0.54 Asymptotic class: n 0.52/0.54 * Total analysis performed in 458 ms. 0.52/0.54 0.53/0.64 EOF