0.06/0.36 WORST_CASE(?,O(n^2)) 0.06/0.36 0.06/0.36 Preprocessing Cost Relations 0.06/0.36 ===================================== 0.06/0.36 0.06/0.36 #### Computed strongly connected components 0.06/0.36 0. recursive : [eval_alain_bb4_in/6,eval_alain_bb5_in/6] 0.06/0.36 1. recursive : [eval_alain_bb2_in/5,eval_alain_bb3_in/6,eval_alain_bb4_in_loop_cont/9,eval_alain_bb6_in/8] 0.06/0.36 2. non_recursive : [eval_alain_stop/1] 0.06/0.36 3. non_recursive : [eval_alain_bb7_in/1] 0.06/0.36 4. non_recursive : [eval_alain_bb2_in_loop_cont/2] 0.06/0.36 5. non_recursive : [eval_alain_bb1_in/6] 0.06/0.36 6. non_recursive : [eval_alain_bb0_in/6] 0.06/0.36 7. non_recursive : [eval_alain_start/6] 0.06/0.36 0.06/0.36 #### Obtained direct recursion through partial evaluation 0.06/0.36 0. SCC is partially evaluated into eval_alain_bb4_in/6 0.06/0.36 1. SCC is partially evaluated into eval_alain_bb2_in/5 0.06/0.36 2. SCC is completely evaluated into other SCCs 0.06/0.36 3. SCC is completely evaluated into other SCCs 0.06/0.36 4. SCC is completely evaluated into other SCCs 0.06/0.36 5. SCC is partially evaluated into eval_alain_bb1_in/6 0.06/0.36 6. SCC is partially evaluated into eval_alain_bb0_in/6 0.06/0.36 7. SCC is partially evaluated into eval_alain_start/6 0.06/0.36 0.06/0.36 Control-Flow Refinement of Cost Relations 0.06/0.36 ===================================== 0.06/0.36 0.06/0.36 ### Specialization of cost equations eval_alain_bb4_in/6 0.06/0.36 * CE 14 is refined into CE [15] 0.06/0.36 * CE 13 is refined into CE [16] 0.06/0.36 0.06/0.36 0.06/0.36 ### Cost equations --> "Loop" of eval_alain_bb4_in/6 0.06/0.36 * CEs [16] --> Loop 15 0.06/0.36 * CEs [15] --> Loop 16 0.06/0.36 0.06/0.36 ### Ranking functions of CR eval_alain_bb4_in(V_y,V__14,V__1,B,C,D) 0.06/0.36 * RF of phase [15]: [V__14] 0.06/0.36 0.06/0.36 #### Partial ranking functions of CR eval_alain_bb4_in(V_y,V__14,V__1,B,C,D) 0.06/0.36 * Partial RF of phase [15]: 0.06/0.36 - RF of loop [15:1]: 0.06/0.36 V__14 0.06/0.36 0.06/0.36 0.06/0.36 ### Specialization of cost equations eval_alain_bb2_in/5 0.06/0.36 * CE 12 is refined into CE [17] 0.06/0.36 * CE 11 is refined into CE [18,19] 0.06/0.36 0.06/0.36 0.06/0.36 ### Cost equations --> "Loop" of eval_alain_bb2_in/5 0.06/0.36 * CEs [19] --> Loop 17 0.06/0.36 * CEs [18] --> Loop 18 0.06/0.36 * CEs [17] --> Loop 19 0.06/0.36 0.06/0.36 ### Ranking functions of CR eval_alain_bb2_in(V_y,V__03,V__02,V__01,B) 0.06/0.36 * RF of phase [17,18]: [V__02] 0.06/0.36 0.06/0.36 #### Partial ranking functions of CR eval_alain_bb2_in(V_y,V__03,V__02,V__01,B) 0.06/0.36 * Partial RF of phase [17,18]: 0.06/0.36 - RF of loop [17:1,18:1]: 0.06/0.36 V__02 0.06/0.36 0.06/0.36 0.06/0.36 ### Specialization of cost equations eval_alain_bb1_in/6 0.06/0.36 * CE 10 is refined into CE [20,21] 0.06/0.36 * CE 9 is refined into CE [22] 0.06/0.36 * CE 8 is refined into CE [23] 0.06/0.36 * CE 5 is refined into CE [24] 0.06/0.36 * CE 7 is refined into CE [25] 0.06/0.36 * CE 6 is refined into CE [26] 0.06/0.36 0.06/0.36 0.06/0.36 ### Cost equations --> "Loop" of eval_alain_bb1_in/6 0.06/0.36 * CEs [21] --> Loop 20 0.06/0.36 * CEs [22] --> Loop 21 0.06/0.36 * CEs [23] --> Loop 22 0.06/0.36 * CEs [24] --> Loop 23 0.06/0.36 * CEs [25] --> Loop 24 0.06/0.36 * CEs [26] --> Loop 25 0.06/0.36 * CEs [20] --> Loop 26 0.06/0.36 0.06/0.36 ### Ranking functions of CR eval_alain_bb1_in(V_x,V_y,V_z,V_n1,V_n2,B) 0.06/0.36 0.06/0.36 #### Partial ranking functions of CR eval_alain_bb1_in(V_x,V_y,V_z,V_n1,V_n2,B) 0.06/0.36 0.06/0.36 0.06/0.36 ### Specialization of cost equations eval_alain_bb0_in/6 0.06/0.36 * CE 3 is refined into CE [27] 0.06/0.36 * CE 2 is refined into CE [28] 0.06/0.36 * CE 4 is refined into CE [29,30,31,32,33,34,35] 0.06/0.36 0.06/0.36 0.06/0.36 ### Cost equations --> "Loop" of eval_alain_bb0_in/6 0.06/0.36 * CEs [27] --> Loop 27 0.06/0.36 * CEs [28] --> Loop 28 0.06/0.36 * CEs [35] --> Loop 29 0.06/0.36 * CEs [34] --> Loop 30 0.06/0.36 * CEs [33] --> Loop 31 0.06/0.36 * CEs [32] --> Loop 32 0.06/0.36 * CEs [31] --> Loop 33 0.06/0.36 * CEs [30] --> Loop 34 0.06/0.36 * CEs [29] --> Loop 35 0.06/0.36 0.06/0.36 ### Ranking functions of CR eval_alain_bb0_in(V_x,V_y,V_z,V_n1,V_n2,B) 0.06/0.36 0.06/0.36 #### Partial ranking functions of CR eval_alain_bb0_in(V_x,V_y,V_z,V_n1,V_n2,B) 0.06/0.36 0.06/0.36 0.06/0.36 ### Specialization of cost equations eval_alain_start/6 0.06/0.36 * CE 1 is refined into CE [36,37,38,39,40,41,42,43,44] 0.06/0.36 0.06/0.36 0.06/0.36 ### Cost equations --> "Loop" of eval_alain_start/6 0.06/0.36 * CEs [44] --> Loop 36 0.06/0.36 * CEs [43] --> Loop 37 0.06/0.36 * CEs [42] --> Loop 38 0.06/0.36 * CEs [41] --> Loop 39 0.06/0.36 * CEs [40] --> Loop 40 0.06/0.36 * CEs [39] --> Loop 41 0.06/0.36 * CEs [38] --> Loop 42 0.06/0.36 * CEs [37] --> Loop 43 0.06/0.36 * CEs [36] --> Loop 44 0.06/0.36 0.06/0.36 ### Ranking functions of CR eval_alain_start(V_x,V_y,V_z,V_n1,V_n2,B) 0.06/0.36 0.06/0.36 #### Partial ranking functions of CR eval_alain_start(V_x,V_y,V_z,V_n1,V_n2,B) 0.06/0.36 0.06/0.36 0.06/0.36 Computing Bounds 0.06/0.36 ===================================== 0.06/0.36 0.06/0.36 #### Cost of chains of eval_alain_bb4_in(V_y,V__14,V__1,B,C,D): 0.06/0.36 * Chain [[15],16]: 1*it(15)+0 0.06/0.36 Such that:it(15) =< V__14 0.06/0.36 0.06/0.36 with precondition: [B=2,C=0,V_y=D,V_y>=0,V__14>=1,V__14+V_y>=V__1] 0.06/0.36 0.06/0.36 * Chain [16]: 0 0.06/0.36 with precondition: [B=2,V__14=C,V__1=D,0>=V__14,V_y>=0,V__14+V_y>=V__1] 0.06/0.36 0.06/0.36 0.06/0.36 #### Cost of chains of eval_alain_bb2_in(V_y,V__03,V__02,V__01,B): 0.06/0.36 * Chain [[17,18],19]: 2*it(17)+1*s(3)+0 0.06/0.36 Such that:aux(2) =< V__03 0.06/0.36 aux(5) =< V__02 0.06/0.36 it(17) =< aux(5) 0.06/0.36 s(3) =< it(17)*aux(2) 0.06/0.36 0.06/0.36 with precondition: [B=3,V_y>=0,V__02>=1,V__01>=0,V__03>=2*V_y,V__03>=V__01] 0.06/0.36 0.06/0.36 * Chain [19]: 0 0.06/0.36 with precondition: [V__02=0,B=3,V_y>=0,V__01>=0,V__03>=2*V_y,V__03>=V__01] 0.06/0.36 0.06/0.36 0.06/0.36 #### Cost of chains of eval_alain_bb1_in(V_x,V_y,V_z,V_n1,V_n2,B): 0.06/0.36 * Chain [26]: 0 0.06/0.36 with precondition: [V_n1=0,V_x>=0,V_y>=0,V_z>=0,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 0.06/0.36 * Chain [25]: 0 0.06/0.36 with precondition: [0>=V_x+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 0.06/0.36 * Chain [24]: 0 0.06/0.36 with precondition: [0>=V_y+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 0.06/0.36 * Chain [23]: 0 0.06/0.36 with precondition: [0>=V_z+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 0.06/0.36 * Chain [22]: 0 0.06/0.36 with precondition: [0>=V_n1+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 0.06/0.36 * Chain [21]: 0 0.06/0.36 with precondition: [0>=V_n2+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 0.06/0.36 * Chain [20]: 2*s(6)+1*s(7)+0 0.06/0.36 Such that:s(5) =< V_n1 0.06/0.36 s(4) =< V_n2 0.06/0.36 s(6) =< s(5) 0.06/0.36 s(7) =< s(6)*s(4) 0.06/0.36 0.06/0.36 with precondition: [V_x>=0,V_y>=0,V_z>=0,V_n1>=1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 0.06/0.36 0.06/0.36 #### Cost of chains of eval_alain_bb0_in(V_x,V_y,V_z,V_n1,V_n2,B): 0.06/0.36 * Chain [35]: 0 0.06/0.36 with precondition: [V_n1=0,V_x>=0,V_y>=0,V_z>=0,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 0.06/0.36 * Chain [34]: 0 0.06/0.36 with precondition: [0>=V_x+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 0.06/0.36 * Chain [33]: 0 0.06/0.36 with precondition: [0>=V_y+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 0.06/0.36 * Chain [32]: 0 0.06/0.36 with precondition: [0>=V_z+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 0.06/0.36 * Chain [31]: 0 0.06/0.36 with precondition: [0>=V_n1+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 0.06/0.36 * Chain [30]: 0 0.06/0.36 with precondition: [0>=V_n2+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 0.06/0.36 * Chain [29]: 2*s(10)+1*s(11)+0 0.06/0.36 Such that:s(8) =< V_n1 0.06/0.36 s(9) =< V_n2 0.06/0.36 s(10) =< s(8) 0.06/0.36 s(11) =< s(10)*s(9) 0.06/0.36 0.06/0.36 with precondition: [V_x>=0,V_y>=0,V_z>=0,V_n1>=1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 0.06/0.36 * Chain [28]: 0 0.06/0.36 with precondition: [2*V_y>=V_n2] 0.06/0.36 0.06/0.36 * Chain [27]: 0 0.06/0.36 with precondition: [V_y+V_z>=V_n2] 0.06/0.36 0.06/0.36 0.06/0.36 #### Cost of chains of eval_alain_start(V_x,V_y,V_z,V_n1,V_n2,B): 0.06/0.36 * Chain [44]: 0 0.06/0.36 with precondition: [V_n1=0,V_x>=0,V_y>=0,V_z>=0,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 0.06/0.36 * Chain [43]: 0 0.06/0.36 with precondition: [0>=V_x+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 0.06/0.36 * Chain [42]: 0 0.06/0.36 with precondition: [0>=V_y+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 0.06/0.36 * Chain [41]: 0 0.06/0.36 with precondition: [0>=V_z+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 0.06/0.36 * Chain [40]: 0 0.06/0.36 with precondition: [0>=V_n1+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 0.06/0.36 * Chain [39]: 0 0.06/0.36 with precondition: [0>=V_n2+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 0.06/0.36 * Chain [38]: 2*s(14)+1*s(15)+0 0.06/0.36 Such that:s(12) =< V_n1 0.06/0.36 s(13) =< V_n2 0.06/0.36 s(14) =< s(12) 0.06/0.36 s(15) =< s(14)*s(13) 0.06/0.36 0.06/0.36 with precondition: [V_x>=0,V_y>=0,V_z>=0,V_n1>=1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 0.06/0.36 * Chain [37]: 0 0.06/0.36 with precondition: [2*V_y>=V_n2] 0.06/0.36 0.06/0.36 * Chain [36]: 0 0.06/0.36 with precondition: [V_y+V_z>=V_n2] 0.06/0.36 0.06/0.36 0.06/0.36 Closed-form bounds of eval_alain_start(V_x,V_y,V_z,V_n1,V_n2,B): 0.06/0.36 ------------------------------------- 0.06/0.36 * Chain [44] with precondition: [V_n1=0,V_x>=0,V_y>=0,V_z>=0,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 - Upper bound: 0 0.06/0.36 - Complexity: constant 0.06/0.36 * Chain [43] with precondition: [0>=V_x+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 - Upper bound: 0 0.06/0.36 - Complexity: constant 0.06/0.36 * Chain [42] with precondition: [0>=V_y+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 - Upper bound: 0 0.06/0.36 - Complexity: constant 0.06/0.36 * Chain [41] with precondition: [0>=V_z+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 - Upper bound: 0 0.06/0.36 - Complexity: constant 0.06/0.36 * Chain [40] with precondition: [0>=V_n1+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 - Upper bound: 0 0.06/0.36 - Complexity: constant 0.06/0.36 * Chain [39] with precondition: [0>=V_n2+1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 - Upper bound: 0 0.06/0.36 - Complexity: constant 0.06/0.36 * Chain [38] with precondition: [V_x>=0,V_y>=0,V_z>=0,V_n1>=1,V_n2>=2*V_y+1,V_n2>=V_y+V_z+1] 0.06/0.36 - Upper bound: 2*V_n1+V_n2*V_n1 0.06/0.36 - Complexity: n^2 0.06/0.36 * Chain [37] with precondition: [2*V_y>=V_n2] 0.06/0.36 - Upper bound: 0 0.06/0.36 - Complexity: constant 0.06/0.36 * Chain [36] with precondition: [V_y+V_z>=V_n2] 0.06/0.36 - Upper bound: 0 0.06/0.36 - Complexity: constant 0.06/0.36 0.06/0.36 ### Maximum cost of eval_alain_start(V_x,V_y,V_z,V_n1,V_n2,B): nat(V_n2)*nat(V_n1)+nat(V_n1)*2 0.06/0.36 Asymptotic class: n^2 0.06/0.36 * Total analysis performed in 274 ms. 0.06/0.36 0.06/0.46 EOF