0.06/0.34 WORST_CASE(?,O(n^2)) 0.06/0.34 0.06/0.34 Preprocessing Cost Relations 0.06/0.34 ===================================== 0.06/0.34 0.06/0.34 #### Computed strongly connected components 0.06/0.34 0. recursive : [eval_exp_paper3_2/6,eval_exp_paper3_3/7,eval_exp_paper3_bb3_in/6,eval_exp_paper3_bb4_in/7] 0.06/0.34 1. recursive : [eval_exp_paper3_0/4,eval_exp_paper3_1/5,eval_exp_paper3_6/5,eval_exp_paper3_7/6,eval_exp_paper3_bb1_in/4,eval_exp_paper3_bb2_in/4,eval_exp_paper3_bb3_in_loop_cont/10,eval_exp_paper3_bb5_in/5,eval_exp_paper3_bb6_in/9] 0.06/0.34 2. non_recursive : [eval_exp_paper3_stop/1] 0.06/0.34 3. non_recursive : [eval_exp_paper3_bb7_in/1] 0.06/0.34 4. non_recursive : [eval_exp_paper3_bb1_in_loop_cont/2] 0.06/0.34 5. non_recursive : [eval_exp_paper3_bb0_in/4] 0.06/0.34 6. non_recursive : [eval_exp_paper3_start/4] 0.06/0.34 0.06/0.34 #### Obtained direct recursion through partial evaluation 0.06/0.34 0. SCC is partially evaluated into eval_exp_paper3_bb3_in/6 0.06/0.34 1. SCC is partially evaluated into eval_exp_paper3_bb1_in/4 0.06/0.34 2. SCC is completely evaluated into other SCCs 0.06/0.34 3. SCC is completely evaluated into other SCCs 0.06/0.34 4. SCC is completely evaluated into other SCCs 0.06/0.34 5. SCC is partially evaluated into eval_exp_paper3_bb0_in/4 0.06/0.34 6. SCC is partially evaluated into eval_exp_paper3_start/4 0.06/0.34 0.06/0.34 Control-Flow Refinement of Cost Relations 0.06/0.34 ===================================== 0.06/0.34 0.06/0.34 ### Specialization of cost equations eval_exp_paper3_bb3_in/6 0.06/0.34 * CE 9 is refined into CE [10] 0.06/0.34 * CE 8 is refined into CE [11] 0.06/0.34 * CE 7 is refined into CE [12] 0.06/0.34 0.06/0.34 0.06/0.34 ### Cost equations --> "Loop" of eval_exp_paper3_bb3_in/6 0.06/0.34 * CEs [11] --> Loop 10 0.06/0.34 * CEs [12] --> Loop 11 0.06/0.34 * CEs [10] --> Loop 12 0.06/0.34 0.06/0.34 ### Ranking functions of CR eval_exp_paper3_bb3_in(V__1,B,C,D,E,F) 0.06/0.34 * RF of phase [12]: [V__1] 0.06/0.34 0.06/0.34 #### Partial ranking functions of CR eval_exp_paper3_bb3_in(V__1,B,C,D,E,F) 0.06/0.34 * Partial RF of phase [12]: 0.06/0.34 - RF of loop [12:1]: 0.06/0.34 V__1 0.06/0.34 0.06/0.34 0.06/0.34 ### Specialization of cost equations eval_exp_paper3_bb1_in/4 0.06/0.34 * CE 6 is refined into CE [13] 0.06/0.34 * CE 3 is refined into CE [14,15,16,17] 0.06/0.34 * CE 5 is refined into CE [18] 0.06/0.34 * CE 4 is refined into CE [19] 0.06/0.34 0.06/0.34 0.06/0.34 ### Cost equations --> "Loop" of eval_exp_paper3_bb1_in/4 0.06/0.34 * CEs [17] --> Loop 13 0.06/0.34 * CEs [16] --> Loop 14 0.06/0.34 * CEs [15] --> Loop 15 0.06/0.34 * CEs [18] --> Loop 16 0.06/0.34 * CEs [19] --> Loop 17 0.06/0.34 * CEs [14] --> Loop 18 0.06/0.34 * CEs [13] --> Loop 19 0.06/0.34 0.06/0.34 ### Ranking functions of CR eval_exp_paper3_bb1_in(V_z,V__01,V__0,B) 0.06/0.34 * RF of phase [13,14,15,16,17,18]: [V__0] 0.06/0.34 0.06/0.34 #### Partial ranking functions of CR eval_exp_paper3_bb1_in(V_z,V__01,V__0,B) 0.06/0.34 * Partial RF of phase [13,14,15,16,17,18]: 0.06/0.34 - RF of loop [13:1,14:1,15:1,16:1,17:1,18:1]: 0.06/0.34 V__0 0.06/0.34 - RF of loop [13:1,18:1]: 0.06/0.34 V__01 depends on loops [16:1,17:1] 0.06/0.34 0.06/0.34 0.06/0.34 ### Specialization of cost equations eval_exp_paper3_bb0_in/4 0.06/0.34 * CE 2 is refined into CE [20,21] 0.06/0.34 0.06/0.34 0.06/0.34 ### Cost equations --> "Loop" of eval_exp_paper3_bb0_in/4 0.06/0.34 * CEs [21] --> Loop 20 0.06/0.34 * CEs [20] --> Loop 21 0.06/0.34 0.06/0.34 ### Ranking functions of CR eval_exp_paper3_bb0_in(V_x,V_y,V_z,B) 0.06/0.34 0.06/0.34 #### Partial ranking functions of CR eval_exp_paper3_bb0_in(V_x,V_y,V_z,B) 0.06/0.34 0.06/0.34 0.06/0.34 ### Specialization of cost equations eval_exp_paper3_start/4 0.06/0.34 * CE 1 is refined into CE [22,23] 0.06/0.34 0.06/0.34 0.06/0.34 ### Cost equations --> "Loop" of eval_exp_paper3_start/4 0.06/0.34 * CEs [23] --> Loop 22 0.06/0.34 * CEs [22] --> Loop 23 0.06/0.34 0.06/0.34 ### Ranking functions of CR eval_exp_paper3_start(V_x,V_y,V_z,B) 0.06/0.34 0.06/0.34 #### Partial ranking functions of CR eval_exp_paper3_start(V_x,V_y,V_z,B) 0.06/0.34 0.06/0.34 0.06/0.34 Computing Bounds 0.06/0.34 ===================================== 0.06/0.34 0.06/0.34 #### Cost of chains of eval_exp_paper3_bb3_in(V__1,B,C,D,E,F): 0.06/0.34 * Chain [[12],11]: 1*it(12)+0 0.06/0.34 Such that:it(12) =< V__1 0.06/0.34 0.06/0.34 with precondition: [B=2,C=0,F=0,V__1>=1] 0.06/0.34 0.06/0.34 * Chain [[12],10]: 1*it(12)+0 0.06/0.34 Such that:it(12) =< V__1-F 0.06/0.34 0.06/0.34 with precondition: [B=2,C=F,0>=D,C>=0,V__1>=C+1] 0.06/0.34 0.06/0.34 * Chain [11]: 0 0.06/0.34 with precondition: [B=2,V__1=C,V__1=F,0>=V__1] 0.06/0.34 0.06/0.34 * Chain [10]: 0 0.06/0.34 with precondition: [B=2,V__1=C,V__1=F,0>=D] 0.06/0.34 0.06/0.34 0.06/0.34 #### Cost of chains of eval_exp_paper3_bb1_in(V_z,V__01,V__0,B): 0.06/0.34 * Chain [[13,14,15,16,17,18],19]: 2*it(13)+4*it(14)+1*s(5)+1*s(6)+0 0.06/0.34 Such that:aux(6) =< V_z 0.06/0.34 aux(11) =< V__01 0.06/0.34 aux(14) =< V__0 0.06/0.34 it(13) =< aux(14) 0.06/0.34 it(14) =< aux(14) 0.06/0.34 aux(7) =< aux(6) 0.06/0.34 aux(4) =< max([aux(11),aux(6)])+it(14) 0.06/0.34 aux(10) =< aux(4) 0.06/0.34 aux(1) =< it(14)*aux(7) 0.06/0.34 it(13) =< aux(1)+it(14)+aux(11) 0.06/0.34 s(6) =< aux(1)+it(14)+aux(11) 0.06/0.34 s(5) =< aux(1)+it(14)+aux(11) 0.06/0.34 s(6) =< it(13)*aux(10) 0.06/0.34 s(5) =< it(13)*aux(4) 0.06/0.34 0.06/0.34 with precondition: [B=3,V__0>=1] 0.06/0.34 0.06/0.34 * Chain [19]: 0 0.06/0.34 with precondition: [B=3,0>=V__0] 0.06/0.34 0.06/0.34 0.06/0.34 #### Cost of chains of eval_exp_paper3_bb0_in(V_x,V_y,V_z,B): 0.06/0.34 * Chain [21]: 0 0.06/0.34 with precondition: [0>=V_x] 0.06/0.34 0.06/0.34 * Chain [20]: 2*s(10)+4*s(11)+1*s(16)+1*s(17)+0 0.06/0.34 Such that:s(9) =< V_x 0.06/0.34 s(8) =< V_y 0.06/0.34 s(7) =< V_z 0.06/0.34 s(10) =< s(9) 0.06/0.34 s(11) =< s(9) 0.06/0.34 s(12) =< s(7) 0.06/0.34 s(13) =< max([s(8),s(7)])+s(11) 0.06/0.34 s(14) =< s(13) 0.06/0.34 s(15) =< s(11)*s(12) 0.06/0.34 s(10) =< s(15)+s(11)+s(8) 0.06/0.34 s(16) =< s(15)+s(11)+s(8) 0.06/0.34 s(17) =< s(15)+s(11)+s(8) 0.06/0.34 s(16) =< s(10)*s(14) 0.06/0.34 s(17) =< s(10)*s(13) 0.06/0.34 0.06/0.34 with precondition: [V_x>=1] 0.06/0.34 0.06/0.34 0.06/0.34 #### Cost of chains of eval_exp_paper3_start(V_x,V_y,V_z,B): 0.06/0.34 * Chain [23]: 0 0.06/0.34 with precondition: [0>=V_x] 0.06/0.34 0.06/0.34 * Chain [22]: 2*s(21)+4*s(22)+1*s(27)+1*s(28)+0 0.06/0.34 Such that:s(18) =< V_x 0.06/0.34 s(19) =< V_y 0.06/0.34 s(20) =< V_z 0.06/0.34 s(21) =< s(18) 0.06/0.34 s(22) =< s(18) 0.06/0.34 s(23) =< s(20) 0.06/0.34 s(24) =< max([s(19),s(20)])+s(22) 0.06/0.34 s(25) =< s(24) 0.06/0.34 s(26) =< s(22)*s(23) 0.06/0.34 s(21) =< s(26)+s(22)+s(19) 0.06/0.34 s(27) =< s(26)+s(22)+s(19) 0.06/0.34 s(28) =< s(26)+s(22)+s(19) 0.06/0.34 s(27) =< s(21)*s(25) 0.06/0.34 s(28) =< s(21)*s(24) 0.06/0.34 0.06/0.34 with precondition: [V_x>=1] 0.06/0.34 0.06/0.34 0.06/0.34 Closed-form bounds of eval_exp_paper3_start(V_x,V_y,V_z,B): 0.06/0.34 ------------------------------------- 0.06/0.34 * Chain [23] with precondition: [0>=V_x] 0.06/0.34 - Upper bound: 0 0.06/0.34 - Complexity: constant 0.06/0.34 * Chain [22] with precondition: [V_x>=1] 0.06/0.34 - Upper bound: 2*V_x*nat(V_z)+8*V_x+nat(V_y)*2 0.06/0.34 - Complexity: n^2 0.06/0.34 0.06/0.34 ### Maximum cost of eval_exp_paper3_start(V_x,V_y,V_z,B): nat(V_x)*2*nat(V_z)+nat(V_x)*8+nat(V_y)*2 0.06/0.34 Asymptotic class: n^2 0.06/0.34 * Total analysis performed in 235 ms. 0.06/0.34 0.06/0.44 EOF