0.04/0.16 WORST_CASE(?,O(n^2)) 0.04/0.16 0.04/0.16 Preprocessing Cost Relations 0.04/0.16 ===================================== 0.04/0.16 0.04/0.16 #### Computed strongly connected components 0.04/0.16 0. recursive : [eval_sipmabubble_2/4,eval_sipmabubble_3/4,eval_sipmabubble_4/4,eval_sipmabubble_bb2_in/4,eval_sipmabubble_bb3_in/4] 0.04/0.16 1. recursive : [eval_sipmabubble_bb1_in/2,eval_sipmabubble_bb2_in_loop_cont/4,eval_sipmabubble_bb4_in/3] 0.04/0.16 2. non_recursive : [eval_sipmabubble_stop/1] 0.04/0.16 3. non_recursive : [eval_sipmabubble_bb5_in/1] 0.04/0.16 4. non_recursive : [eval_sipmabubble_bb1_in_loop_cont/2] 0.04/0.16 5. non_recursive : [eval_sipmabubble_bb0_in/2] 0.04/0.16 6. non_recursive : [eval_sipmabubble_start/2] 0.04/0.16 0.04/0.16 #### Obtained direct recursion through partial evaluation 0.04/0.16 0. SCC is partially evaluated into eval_sipmabubble_bb2_in/4 0.04/0.16 1. SCC is partially evaluated into eval_sipmabubble_bb1_in/2 0.04/0.16 2. SCC is completely evaluated into other SCCs 0.04/0.16 3. SCC is completely evaluated into other SCCs 0.04/0.16 4. SCC is completely evaluated into other SCCs 0.04/0.16 5. SCC is partially evaluated into eval_sipmabubble_bb0_in/2 0.04/0.16 6. SCC is partially evaluated into eval_sipmabubble_start/2 0.04/0.16 0.04/0.16 Control-Flow Refinement of Cost Relations 0.04/0.16 ===================================== 0.04/0.16 0.04/0.16 ### Specialization of cost equations eval_sipmabubble_bb2_in/4 0.04/0.16 * CE 6 is refined into CE [7] 0.04/0.16 * CE 5 is refined into CE [8] 0.04/0.16 0.04/0.16 0.04/0.16 ### Cost equations --> "Loop" of eval_sipmabubble_bb2_in/4 0.04/0.16 * CEs [8] --> Loop 7 0.04/0.16 * CEs [7] --> Loop 8 0.04/0.16 0.04/0.16 ### Ranking functions of CR eval_sipmabubble_bb2_in(V_i_0,V_j_0,B,C) 0.04/0.16 * RF of phase [7]: [V_i_0-V_j_0] 0.04/0.16 0.04/0.16 #### Partial ranking functions of CR eval_sipmabubble_bb2_in(V_i_0,V_j_0,B,C) 0.04/0.16 * Partial RF of phase [7]: 0.04/0.16 - RF of loop [7:1]: 0.04/0.16 V_i_0-V_j_0 0.04/0.16 0.04/0.16 0.04/0.16 ### Specialization of cost equations eval_sipmabubble_bb1_in/2 0.04/0.16 * CE 4 is refined into CE [9] 0.04/0.16 * CE 3 is refined into CE [10,11] 0.04/0.16 0.04/0.16 0.04/0.16 ### Cost equations --> "Loop" of eval_sipmabubble_bb1_in/2 0.04/0.16 * CEs [11] --> Loop 9 0.04/0.16 * CEs [10] --> Loop 10 0.04/0.16 * CEs [9] --> Loop 11 0.04/0.16 0.04/0.16 ### Ranking functions of CR eval_sipmabubble_bb1_in(V_i_0,B) 0.04/0.16 * RF of phase [9]: [V_i_0] 0.04/0.16 0.04/0.16 #### Partial ranking functions of CR eval_sipmabubble_bb1_in(V_i_0,B) 0.04/0.16 * Partial RF of phase [9]: 0.04/0.16 - RF of loop [9:1]: 0.04/0.16 V_i_0 0.04/0.16 0.04/0.16 0.04/0.16 ### Specialization of cost equations eval_sipmabubble_bb0_in/2 0.04/0.16 * CE 2 is refined into CE [12,13,14] 0.04/0.16 0.04/0.16 0.04/0.16 ### Cost equations --> "Loop" of eval_sipmabubble_bb0_in/2 0.04/0.16 * CEs [14] --> Loop 12 0.04/0.16 * CEs [13] --> Loop 13 0.04/0.16 * CEs [12] --> Loop 14 0.04/0.16 0.04/0.16 ### Ranking functions of CR eval_sipmabubble_bb0_in(V_n,B) 0.04/0.16 0.04/0.16 #### Partial ranking functions of CR eval_sipmabubble_bb0_in(V_n,B) 0.04/0.16 0.04/0.16 0.04/0.16 ### Specialization of cost equations eval_sipmabubble_start/2 0.04/0.16 * CE 1 is refined into CE [15,16,17] 0.04/0.16 0.04/0.16 0.04/0.16 ### Cost equations --> "Loop" of eval_sipmabubble_start/2 0.04/0.16 * CEs [17] --> Loop 15 0.04/0.16 * CEs [16] --> Loop 16 0.04/0.16 * CEs [15] --> Loop 17 0.04/0.16 0.04/0.16 ### Ranking functions of CR eval_sipmabubble_start(V_n,B) 0.04/0.16 0.04/0.16 #### Partial ranking functions of CR eval_sipmabubble_start(V_n,B) 0.04/0.16 0.04/0.16 0.04/0.16 Computing Bounds 0.04/0.16 ===================================== 0.04/0.16 0.04/0.16 #### Cost of chains of eval_sipmabubble_bb2_in(V_i_0,V_j_0,B,C): 0.04/0.16 * Chain [[7],8]: 1*it(7)+0 0.04/0.16 Such that:it(7) =< -V_j_0+C 0.04/0.16 0.04/0.16 with precondition: [B=2,V_i_0=C,V_j_0>=0,V_i_0>=V_j_0+1] 0.04/0.16 0.04/0.16 * Chain [8]: 0 0.04/0.16 with precondition: [B=2,V_j_0=V_i_0,V_j_0=C,V_j_0>=0] 0.04/0.16 0.04/0.16 0.04/0.16 #### Cost of chains of eval_sipmabubble_bb1_in(V_i_0,B): 0.04/0.16 * Chain [[9],10,11]: 1*it(9)+1*s(3)+1 0.04/0.16 Such that:aux(3) =< V_i_0 0.04/0.16 it(9) =< aux(3) 0.04/0.16 s(3) =< it(9)*aux(3) 0.04/0.16 0.04/0.16 with precondition: [B=3,V_i_0>=1] 0.04/0.16 0.04/0.16 * Chain [11]: 0 0.04/0.16 with precondition: [B=3,0>=V_i_0+1] 0.04/0.16 0.04/0.16 * Chain [10,11]: 1 0.04/0.16 with precondition: [V_i_0=0,B=3] 0.04/0.16 0.04/0.16 0.04/0.16 #### Cost of chains of eval_sipmabubble_bb0_in(V_n,B): 0.04/0.16 * Chain [14]: 1 0.04/0.16 with precondition: [V_n=0] 0.04/0.16 0.04/0.16 * Chain [13]: 0 0.04/0.16 with precondition: [0>=V_n+1] 0.04/0.16 0.04/0.16 * Chain [12]: 1*s(5)+1*s(6)+1 0.04/0.16 Such that:s(4) =< V_n 0.04/0.16 s(5) =< s(4) 0.04/0.16 s(6) =< s(5)*s(4) 0.04/0.16 0.04/0.16 with precondition: [V_n>=1] 0.04/0.16 0.04/0.16 0.04/0.16 #### Cost of chains of eval_sipmabubble_start(V_n,B): 0.04/0.16 * Chain [17]: 1 0.04/0.16 with precondition: [V_n=0] 0.04/0.16 0.04/0.16 * Chain [16]: 0 0.04/0.16 with precondition: [0>=V_n+1] 0.04/0.16 0.04/0.16 * Chain [15]: 1*s(8)+1*s(9)+1 0.04/0.16 Such that:s(7) =< V_n 0.04/0.16 s(8) =< s(7) 0.04/0.16 s(9) =< s(8)*s(7) 0.04/0.16 0.04/0.16 with precondition: [V_n>=1] 0.04/0.16 0.04/0.16 0.04/0.16 Closed-form bounds of eval_sipmabubble_start(V_n,B): 0.04/0.16 ------------------------------------- 0.04/0.16 * Chain [17] with precondition: [V_n=0] 0.04/0.16 - Upper bound: 1 0.04/0.16 - Complexity: constant 0.04/0.16 * Chain [16] with precondition: [0>=V_n+1] 0.04/0.16 - Upper bound: 0 0.04/0.16 - Complexity: constant 0.04/0.16 * Chain [15] with precondition: [V_n>=1] 0.04/0.16 - Upper bound: V_n+1+V_n*V_n 0.04/0.16 - Complexity: n^2 0.04/0.16 0.04/0.16 ### Maximum cost of eval_sipmabubble_start(V_n,B): max([1,nat(V_n)+1+nat(V_n)*nat(V_n)]) 0.04/0.16 Asymptotic class: n^2 0.04/0.16 * Total analysis performed in 90 ms. 0.04/0.16 0.04/0.26 EOF