0.06/0.19 WORST_CASE(?,O(n^1)) 0.06/0.19 0.06/0.19 Preprocessing Cost Relations 0.06/0.19 ===================================== 0.06/0.19 0.06/0.19 #### Computed strongly connected components 0.06/0.19 0. recursive : [eval_noiseTickSize_0/4,eval_noiseTickSize_1/5,eval_noiseTickSize_bb1_in/4] 0.06/0.19 1. non_recursive : [eval_noiseTickSize_stop/1] 0.06/0.19 2. non_recursive : [eval_noiseTickSize_bb2_in/1] 0.06/0.19 3. non_recursive : [eval_noiseTickSize_bb1_in_loop_cont/2] 0.06/0.19 4. non_recursive : [eval_noiseTickSize_bb0_in/2] 0.06/0.19 5. non_recursive : [eval_noiseTickSize_start/2] 0.06/0.19 0.06/0.19 #### Obtained direct recursion through partial evaluation 0.06/0.19 0. SCC is partially evaluated into eval_noiseTickSize_bb1_in/4 0.06/0.19 1. SCC is completely evaluated into other SCCs 0.06/0.19 2. SCC is completely evaluated into other SCCs 0.06/0.19 3. SCC is partially evaluated into eval_noiseTickSize_bb1_in_loop_cont/2 0.06/0.19 4. SCC is partially evaluated into eval_noiseTickSize_bb0_in/2 0.06/0.19 5. SCC is partially evaluated into eval_noiseTickSize_start/2 0.06/0.19 0.06/0.19 Control-Flow Refinement of Cost Relations 0.06/0.19 ===================================== 0.06/0.19 0.06/0.19 ### Specialization of cost equations eval_noiseTickSize_bb1_in/4 0.06/0.19 * CE 5 is refined into CE [8] 0.06/0.19 * CE 6 is refined into CE [9] 0.06/0.19 * CE 3 is refined into CE [10] 0.06/0.19 * CE 4 is refined into CE [11] 0.06/0.19 0.06/0.19 0.06/0.19 ### Cost equations --> "Loop" of eval_noiseTickSize_bb1_in/4 0.06/0.19 * CEs [10] --> Loop 8 0.06/0.19 * CEs [11] --> Loop 9 0.06/0.19 * CEs [8] --> Loop 10 0.06/0.19 * CEs [9] --> Loop 11 0.06/0.19 0.06/0.19 ### Ranking functions of CR eval_noiseTickSize_bb1_in(V_DELTAS,V_j_0,V_i_0,B) 0.06/0.19 0.06/0.19 #### Partial ranking functions of CR eval_noiseTickSize_bb1_in(V_DELTAS,V_j_0,V_i_0,B) 0.06/0.19 * Partial RF of phase [10,11]: 0.06/0.19 - RF of loop [10:1]: 0.06/0.19 -V_j_0+10001 depends on loops [11:1] 0.06/0.19 - RF of loop [11:1]: 0.06/0.19 V_DELTAS-V_i_0-1 0.06/0.19 0.06/0.19 0.06/0.19 ### Specialization of cost equations eval_noiseTickSize_bb1_in_loop_cont/2 0.06/0.19 * CE 7 is refined into CE [12] 0.06/0.19 0.06/0.19 0.06/0.19 ### Cost equations --> "Loop" of eval_noiseTickSize_bb1_in_loop_cont/2 0.06/0.19 * CEs [12] --> Loop 12 0.06/0.19 0.06/0.19 ### Ranking functions of CR eval_noiseTickSize_bb1_in_loop_cont(A,B) 0.06/0.19 0.06/0.19 #### Partial ranking functions of CR eval_noiseTickSize_bb1_in_loop_cont(A,B) 0.06/0.19 0.06/0.19 0.06/0.19 ### Specialization of cost equations eval_noiseTickSize_bb0_in/2 0.06/0.19 * CE 2 is refined into CE [13,14] 0.06/0.19 0.06/0.19 0.06/0.19 ### Cost equations --> "Loop" of eval_noiseTickSize_bb0_in/2 0.06/0.19 * CEs [14] --> Loop 13 0.06/0.19 * CEs [13] --> Loop 14 0.06/0.19 0.06/0.19 ### Ranking functions of CR eval_noiseTickSize_bb0_in(V_DELTAS,B) 0.06/0.19 0.06/0.19 #### Partial ranking functions of CR eval_noiseTickSize_bb0_in(V_DELTAS,B) 0.06/0.19 0.06/0.19 0.06/0.19 ### Specialization of cost equations eval_noiseTickSize_start/2 0.06/0.19 * CE 1 is refined into CE [15,16] 0.06/0.19 0.06/0.19 0.06/0.19 ### Cost equations --> "Loop" of eval_noiseTickSize_start/2 0.06/0.19 * CEs [16] --> Loop 15 0.06/0.19 * CEs [15] --> Loop 16 0.06/0.19 0.06/0.19 ### Ranking functions of CR eval_noiseTickSize_start(V_DELTAS,B) 0.06/0.19 0.06/0.19 #### Partial ranking functions of CR eval_noiseTickSize_start(V_DELTAS,B) 0.06/0.19 0.06/0.19 0.06/0.19 Computing Bounds 0.06/0.19 ===================================== 0.06/0.19 0.06/0.19 #### Cost of chains of eval_noiseTickSize_bb1_in(V_DELTAS,V_j_0,V_i_0,B): 0.06/0.19 * Chain [[10,11],9]: 1*it(10)+1*it(11)+0 0.06/0.19 Such that:aux(2) =< -V_j_0+10001 0.06/0.19 aux(6) =< V_DELTAS-V_i_0 0.06/0.19 it(11) =< aux(6) 0.06/0.19 aux(1) =< aux(6)*10000 0.06/0.19 it(10) =< aux(1)+aux(2) 0.06/0.19 0.06/0.19 with precondition: [B=2,V_i_0>=0,V_DELTAS>=V_i_0+1] 0.06/0.19 0.06/0.19 * Chain [[10,11],8]: 1*it(10)+1*it(11)+0 0.06/0.19 Such that:aux(2) =< -V_j_0+10001 0.06/0.19 aux(7) =< V_DELTAS-V_i_0 0.06/0.19 it(11) =< aux(7) 0.06/0.19 aux(1) =< aux(7)*10000 0.06/0.19 it(10) =< aux(1)+aux(2) 0.06/0.19 0.06/0.19 with precondition: [B=2,V_i_0>=0,V_DELTAS>=V_i_0+1] 0.06/0.19 0.06/0.19 * Chain [8]: 0 0.06/0.19 with precondition: [B=2,V_i_0>=0,V_i_0+1>=V_DELTAS] 0.06/0.19 0.06/0.19 0.06/0.19 #### Cost of chains of eval_noiseTickSize_bb1_in_loop_cont(A,B): 0.06/0.19 * Chain [12]: 0 0.06/0.19 with precondition: [A=2] 0.06/0.19 0.06/0.19 0.06/0.19 #### Cost of chains of eval_noiseTickSize_bb0_in(V_DELTAS,B): 0.06/0.19 * Chain [14]: 0 0.06/0.19 with precondition: [1>=V_DELTAS] 0.06/0.19 0.06/0.19 * Chain [13]: 2*s(13)+2*s(15)+0 0.06/0.19 Such that:s(12) =< 10001 0.06/0.19 s(11) =< V_DELTAS 0.06/0.19 s(13) =< s(11) 0.06/0.19 s(14) =< s(11)*10000 0.06/0.19 s(15) =< s(14)+s(12) 0.06/0.19 0.06/0.19 with precondition: [V_DELTAS>=1] 0.06/0.19 0.06/0.19 0.06/0.19 #### Cost of chains of eval_noiseTickSize_start(V_DELTAS,B): 0.06/0.19 * Chain [16]: 0 0.06/0.19 with precondition: [1>=V_DELTAS] 0.06/0.19 0.06/0.19 * Chain [15]: 2*s(18)+2*s(20)+0 0.06/0.19 Such that:s(16) =< 10001 0.06/0.19 s(17) =< V_DELTAS 0.06/0.19 s(18) =< s(17) 0.06/0.19 s(19) =< s(17)*10000 0.06/0.19 s(20) =< s(19)+s(16) 0.06/0.19 0.06/0.19 with precondition: [V_DELTAS>=1] 0.06/0.19 0.06/0.19 0.06/0.19 Closed-form bounds of eval_noiseTickSize_start(V_DELTAS,B): 0.06/0.19 ------------------------------------- 0.06/0.19 * Chain [16] with precondition: [1>=V_DELTAS] 0.06/0.19 - Upper bound: 0 0.06/0.19 - Complexity: constant 0.06/0.19 * Chain [15] with precondition: [V_DELTAS>=1] 0.06/0.19 - Upper bound: 20002*V_DELTAS+20002 0.06/0.19 - Complexity: n 0.06/0.19 0.06/0.19 ### Maximum cost of eval_noiseTickSize_start(V_DELTAS,B): nat(V_DELTAS)*20002+20002 0.06/0.19 Asymptotic class: n 0.06/0.19 * Total analysis performed in 102 ms. 0.06/0.19 0.06/0.29 EOF