0.06/0.29 MAYBE 0.06/0.29 0.06/0.29 Preprocessing Cost Relations 0.06/0.29 ===================================== 0.06/0.29 0.06/0.29 #### Computed strongly connected components 0.06/0.29 0. recursive : [eval_foo_bb3_in/6,eval_foo_bb4_in/6] 0.06/0.29 1. recursive : [eval_foo_bb1_in/4,eval_foo_bb2_in/4,eval_foo_bb3_in_loop_cont/7,eval_foo_bb5_in/6] 0.06/0.29 2. non_recursive : [eval_foo_stop/1] 0.06/0.29 3. non_recursive : [eval_foo_bb6_in/1] 0.06/0.29 4. non_recursive : [eval_foo_bb1_in_loop_cont/2] 0.06/0.29 5. non_recursive : [eval_foo_bb0_in/4] 0.06/0.29 6. non_recursive : [eval_foo_start/4] 0.06/0.29 0.06/0.29 #### Obtained direct recursion through partial evaluation 0.06/0.29 0. SCC is partially evaluated into eval_foo_bb3_in/6 0.06/0.29 1. SCC is partially evaluated into eval_foo_bb1_in/4 0.06/0.29 2. SCC is completely evaluated into other SCCs 0.06/0.29 3. SCC is completely evaluated into other SCCs 0.06/0.29 4. SCC is completely evaluated into other SCCs 0.06/0.29 5. SCC is partially evaluated into eval_foo_bb0_in/4 0.06/0.29 6. SCC is partially evaluated into eval_foo_start/4 0.06/0.29 0.06/0.29 Control-Flow Refinement of Cost Relations 0.06/0.29 ===================================== 0.06/0.29 0.06/0.29 ### Specialization of cost equations eval_foo_bb3_in/6 0.06/0.29 * CE 10 is refined into CE [11] 0.06/0.29 * CE 9 is refined into CE [12] 0.06/0.29 0.06/0.29 0.06/0.29 ### Cost equations --> "Loop" of eval_foo_bb3_in/6 0.06/0.29 * CEs [12] --> Loop 11 0.06/0.29 * CEs [11] --> Loop 12 0.06/0.29 0.06/0.29 ### Ranking functions of CR eval_foo_bb3_in(V__01,V__13,V__1,B,C,D) 0.06/0.29 * RF of phase [11]: [-V__01+V__13,V__13-1] 0.06/0.29 0.06/0.29 #### Partial ranking functions of CR eval_foo_bb3_in(V__01,V__13,V__1,B,C,D) 0.06/0.29 * Partial RF of phase [11]: 0.06/0.29 - RF of loop [11:1]: 0.06/0.29 -V__01+V__13 0.06/0.29 V__13-1 0.06/0.29 0.06/0.29 0.06/0.29 ### Specialization of cost equations eval_foo_bb1_in/4 0.06/0.29 * CE 8 is refined into CE [13] 0.06/0.29 * CE 7 is refined into CE [14,15] 0.06/0.29 0.06/0.29 0.06/0.29 ### Cost equations --> "Loop" of eval_foo_bb1_in/4 0.06/0.29 * CEs [15] --> Loop 13 0.06/0.29 * CEs [14] --> Loop 14 0.06/0.29 * CEs [13] --> Loop 15 0.06/0.29 0.06/0.29 ### Ranking functions of CR eval_foo_bb1_in(V__02,V__01,V__0,B) 0.06/0.29 0.06/0.29 #### Partial ranking functions of CR eval_foo_bb1_in(V__02,V__01,V__0,B) 0.06/0.29 * Partial RF of phase [13,14]: 0.06/0.29 - RF of loop [13:1]: 0.06/0.29 V__02-1 0.06/0.29 0.06/0.29 0.06/0.29 ### Specialization of cost equations eval_foo_bb0_in/4 0.06/0.29 * CE 5 is refined into CE [16] 0.06/0.29 * CE 4 is refined into CE [17] 0.06/0.29 * CE 2 is refined into CE [18] 0.06/0.29 * CE 3 is refined into CE [19] 0.06/0.29 * CE 6 is refined into CE [20,21,22] 0.06/0.29 0.06/0.29 0.06/0.29 ### Cost equations --> "Loop" of eval_foo_bb0_in/4 0.06/0.29 * CEs [22] --> Loop 16 0.06/0.29 * CEs [16] --> Loop 17 0.06/0.29 * CEs [17] --> Loop 18 0.06/0.29 * CEs [18] --> Loop 19 0.06/0.29 * CEs [19] --> Loop 20 0.06/0.29 * CEs [20] --> Loop 21 0.06/0.29 * CEs [21] --> Loop 22 0.06/0.29 0.06/0.29 ### Ranking functions of CR eval_foo_bb0_in(V_x,V_y,V_z,B) 0.06/0.29 0.06/0.29 #### Partial ranking functions of CR eval_foo_bb0_in(V_x,V_y,V_z,B) 0.06/0.29 0.06/0.29 0.06/0.29 ### Specialization of cost equations eval_foo_start/4 0.06/0.29 * CE 1 is refined into CE [23,24,25,26,27,28,29] 0.06/0.29 0.06/0.29 0.06/0.29 ### Cost equations --> "Loop" of eval_foo_start/4 0.06/0.29 * CEs [29] --> Loop 23 0.06/0.29 * CEs [28] --> Loop 24 0.06/0.29 * CEs [27] --> Loop 25 0.06/0.29 * CEs [26] --> Loop 26 0.06/0.29 * CEs [25] --> Loop 27 0.06/0.29 * CEs [24] --> Loop 28 0.06/0.29 * CEs [23] --> Loop 29 0.06/0.29 0.06/0.29 ### Ranking functions of CR eval_foo_start(V_x,V_y,V_z,B) 0.06/0.29 0.06/0.29 #### Partial ranking functions of CR eval_foo_start(V_x,V_y,V_z,B) 0.06/0.29 0.06/0.29 0.06/0.29 Computing Bounds 0.06/0.29 ===================================== 0.06/0.29 0.06/0.29 #### Cost of chains of eval_foo_bb3_in(V__01,V__13,V__1,B,C,D): 0.06/0.29 * Chain [[11],12]: 1*it(11)+0 0.06/0.29 Such that:it(11) =< V__13-C 0.06/0.29 0.06/0.29 with precondition: [B=2,V__01=C,V__01+D=V__1+V__13,V__01>=1,V__13>=V__01+1] 0.06/0.29 0.06/0.29 * Chain [12]: 0 0.06/0.29 with precondition: [B=2,D=V__1,V__13=C,V__01>=1,V__01>=V__13] 0.06/0.29 0.06/0.29 0.06/0.29 #### Cost of chains of eval_foo_bb1_in(V__02,V__01,V__0,B): 0.06/0.29 * Chain [[13,14]]...: 1*it(13)+1*it(14)+1*s(3)+0 0.06/0.29 Such that:aux(3) =< 9999 0.06/0.29 aux(4) =< V__02 0.06/0.29 aux(3) =< aux(4) 0.06/0.29 it(13) =< aux(4) 0.06/0.29 s(3) =< aux(4) 0.06/0.29 s(3) =< it(13)*aux(3) 0.06/0.29 0.06/0.29 with precondition: [V__01>=1,B=3] 0.06/0.29 0.06/0.29 * Chain [[13,14],15]: 1*it(13)+1*it(14)+1*s(3)+0 0.06/0.29 Such that:aux(3) =< 9999 0.06/0.29 aux(4) =< V__02 0.06/0.29 aux(3) =< aux(4) 0.06/0.29 it(13) =< aux(4) 0.06/0.29 s(3) =< aux(4) 0.06/0.29 s(3) =< it(13)*aux(3) 0.06/0.29 0.06/0.29 with precondition: [B=3,10000>=V__02,V__01>=1] 0.06/0.29 0.06/0.29 * Chain [15]: 0 0.06/0.29 with precondition: [B=3,10000>=V__02,0>=V__01,19998>=V__0,199970000>=9999*V__0+9998*V__02] 0.06/0.29 0.06/0.29 0.06/0.29 #### Cost of chains of eval_foo_bb0_in(V_x,V_y,V_z,B): 0.06/0.29 * Chain [22]: 1*s(6)+1*s(7)+1*s(8)+0 0.06/0.29 Such that:s(4) =< 9999 0.06/0.29 s(5) =< 10000 0.06/0.29 s(5) =< V_z 0.06/0.29 s(4) =< s(5) 0.06/0.29 s(6) =< s(5) 0.06/0.29 s(7) =< s(5) 0.06/0.29 s(7) =< s(6)*s(4) 0.06/0.29 0.06/0.29 with precondition: [10000>=V_x,10000>=V_y,10000>=V_z,V_x+10000>=0,V_y>=1] 0.06/0.29 0.06/0.29 * Chain [21]: 0 0.06/0.29 with precondition: [10000>=V_x,0>=V_y,10000>=V_z,V_x+10000>=0] 0.06/0.29 0.06/0.29 * Chain [20]: 0 0.06/0.29 with precondition: [0>=V_x+10001] 0.06/0.29 0.06/0.29 * Chain [19]: 0 0.06/0.29 with precondition: [V_x>=10001] 0.06/0.29 0.06/0.29 * Chain [18]: 0 0.06/0.29 with precondition: [V_y>=10001] 0.06/0.29 0.06/0.29 * Chain [17]: 0 0.06/0.29 with precondition: [V_z>=10001] 0.06/0.29 0.06/0.29 * Chain [16]...: 1*s(11)+1*s(12)+1*s(13)+0 0.06/0.29 Such that:s(9) =< 9999 0.06/0.29 s(10) =< 10000 0.06/0.29 s(10) =< V_z 0.06/0.29 s(9) =< s(10) 0.06/0.29 s(11) =< s(10) 0.06/0.29 s(12) =< s(10) 0.06/0.29 s(12) =< s(11)*s(9) 0.06/0.29 0.06/0.29 with precondition: [10000>=V_x,10000>=V_y,10000>=V_z,V_x+10000>=0,V_y>=1] 0.06/0.29 0.06/0.29 0.06/0.29 #### Cost of chains of eval_foo_start(V_x,V_y,V_z,B): 0.06/0.29 * Chain [29]: 1*s(16)+1*s(17)+1*s(18)+0 0.06/0.29 Such that:s(14) =< 9999 0.06/0.29 s(15) =< 10000 0.06/0.29 s(15) =< V_z 0.06/0.29 s(14) =< s(15) 0.06/0.29 s(16) =< s(15) 0.06/0.29 s(17) =< s(15) 0.06/0.29 s(17) =< s(16)*s(14) 0.06/0.29 0.06/0.29 with precondition: [10000>=V_x,10000>=V_y,10000>=V_z,V_x+10000>=0,V_y>=1] 0.06/0.29 0.06/0.29 * Chain [28]: 0 0.06/0.29 with precondition: [10000>=V_x,0>=V_y,10000>=V_z,V_x+10000>=0] 0.06/0.29 0.06/0.29 * Chain [27]: 0 0.06/0.29 with precondition: [0>=V_x+10001] 0.06/0.29 0.06/0.29 * Chain [26]: 0 0.06/0.29 with precondition: [V_x>=10001] 0.06/0.29 0.06/0.29 * Chain [25]: 0 0.06/0.29 with precondition: [V_y>=10001] 0.06/0.29 0.06/0.29 * Chain [24]: 0 0.06/0.29 with precondition: [V_z>=10001] 0.06/0.29 0.06/0.29 * Chain [23]...: 1*s(21)+1*s(22)+1*s(23)+0 0.06/0.29 Such that:s(19) =< 9999 0.06/0.29 s(20) =< 10000 0.06/0.29 s(20) =< V_z 0.06/0.29 s(19) =< s(20) 0.06/0.29 s(21) =< s(20) 0.06/0.29 s(22) =< s(20) 0.06/0.29 s(22) =< s(21)*s(19) 0.06/0.29 0.06/0.29 with precondition: [10000>=V_x,10000>=V_y,10000>=V_z,V_x+10000>=0,V_y>=1] 0.06/0.29 0.06/0.29 0.06/0.29 Closed-form bounds of eval_foo_start(V_x,V_y,V_z,B): 0.06/0.29 ------------------------------------- 0.06/0.29 * Chain [29] with precondition: [10000>=V_x,10000>=V_y,10000>=V_z,V_x+10000>=0,V_y>=1] 0.06/0.29 - Upper bound: inf 0.06/0.29 - Complexity: infinity 0.06/0.29 * Chain [28] with precondition: [10000>=V_x,0>=V_y,10000>=V_z,V_x+10000>=0] 0.06/0.29 - Upper bound: 0 0.06/0.29 - Complexity: constant 0.06/0.29 * Chain [27] with precondition: [0>=V_x+10001] 0.06/0.29 - Upper bound: 0 0.06/0.29 - Complexity: constant 0.06/0.29 * Chain [26] with precondition: [V_x>=10001] 0.06/0.29 - Upper bound: 0 0.06/0.29 - Complexity: constant 0.06/0.29 * Chain [25] with precondition: [V_y>=10001] 0.06/0.29 - Upper bound: 0 0.06/0.29 - Complexity: constant 0.06/0.29 * Chain [24] with precondition: [V_z>=10001] 0.06/0.29 - Upper bound: 0 0.06/0.29 - Complexity: constant 0.06/0.29 * Chain [23]... with precondition: [10000>=V_x,10000>=V_y,10000>=V_z,V_x+10000>=0,V_y>=1] 0.06/0.29 - Upper bound: inf 0.06/0.29 - Complexity: infinity 0.06/0.29 0.06/0.29 ### Maximum cost of eval_foo_start(V_x,V_y,V_z,B): inf 0.06/0.29 Asymptotic class: infinity 0.06/0.29 * Total analysis performed in 206 ms. 0.06/0.29 0.06/0.39 EOF