0.04/0.17 WORST_CASE(?,O(n^2)) 0.04/0.17 0.04/0.17 Preprocessing Cost Relations 0.04/0.17 ===================================== 0.04/0.17 0.04/0.17 #### Computed strongly connected components 0.04/0.17 0. recursive : [eval_jama_ex7_bb2_in/3,eval_jama_ex7_bb3_in/3] 0.04/0.17 1. recursive : [eval_jama_ex7_bb1_in/3,eval_jama_ex7_bb2_in_loop_cont/5,eval_jama_ex7_bb4_in/4] 0.04/0.17 2. non_recursive : [eval_jama_ex7_stop/1] 0.04/0.17 3. non_recursive : [eval_jama_ex7_bb5_in/1] 0.04/0.17 4. non_recursive : [eval_jama_ex7_bb1_in_loop_cont/2] 0.04/0.17 5. non_recursive : [eval_jama_ex7_bb0_in/3] 0.04/0.17 6. non_recursive : [eval_jama_ex7_start/3] 0.04/0.17 0.04/0.17 #### Obtained direct recursion through partial evaluation 0.04/0.17 0. SCC is partially evaluated into eval_jama_ex7_bb2_in/3 0.04/0.17 1. SCC is partially evaluated into eval_jama_ex7_bb1_in/3 0.04/0.17 2. SCC is completely evaluated into other SCCs 0.04/0.17 3. SCC is completely evaluated into other SCCs 0.04/0.17 4. SCC is completely evaluated into other SCCs 0.04/0.17 5. SCC is partially evaluated into eval_jama_ex7_bb0_in/3 0.04/0.17 6. SCC is partially evaluated into eval_jama_ex7_start/3 0.04/0.17 0.04/0.17 Control-Flow Refinement of Cost Relations 0.04/0.17 ===================================== 0.04/0.17 0.04/0.17 ### Specialization of cost equations eval_jama_ex7_bb2_in/3 0.04/0.17 * CE 6 is refined into CE [7] 0.04/0.17 * CE 5 is refined into CE [8] 0.04/0.17 0.04/0.17 0.04/0.17 ### Cost equations --> "Loop" of eval_jama_ex7_bb2_in/3 0.04/0.17 * CEs [8] --> Loop 7 0.04/0.17 * CEs [7] --> Loop 8 0.04/0.17 0.04/0.17 ### Ranking functions of CR eval_jama_ex7_bb2_in(V_j_0,B,C) 0.04/0.17 * RF of phase [7]: [V_j_0] 0.04/0.17 0.04/0.17 #### Partial ranking functions of CR eval_jama_ex7_bb2_in(V_j_0,B,C) 0.04/0.17 * Partial RF of phase [7]: 0.04/0.17 - RF of loop [7:1]: 0.04/0.17 V_j_0 0.04/0.17 0.04/0.17 0.04/0.17 ### Specialization of cost equations eval_jama_ex7_bb1_in/3 0.04/0.17 * CE 4 is refined into CE [9] 0.04/0.17 * CE 3 is refined into CE [10,11] 0.04/0.17 0.04/0.17 0.04/0.17 ### Cost equations --> "Loop" of eval_jama_ex7_bb1_in/3 0.04/0.17 * CEs [10] --> Loop 9 0.04/0.17 * CEs [11] --> Loop 10 0.04/0.17 * CEs [9] --> Loop 11 0.04/0.17 0.04/0.17 ### Ranking functions of CR eval_jama_ex7_bb1_in(V_m,V_i_0,B) 0.04/0.17 * RF of phase [9]: [V_i_0] 0.04/0.17 * RF of phase [10]: [V_i_0] 0.04/0.17 0.04/0.17 #### Partial ranking functions of CR eval_jama_ex7_bb1_in(V_m,V_i_0,B) 0.04/0.17 * Partial RF of phase [9]: 0.04/0.17 - RF of loop [9:1]: 0.04/0.17 V_i_0 0.04/0.17 * Partial RF of phase [10]: 0.04/0.17 - RF of loop [10:1]: 0.04/0.17 V_i_0 0.04/0.17 0.04/0.17 0.04/0.17 ### Specialization of cost equations eval_jama_ex7_bb0_in/3 0.04/0.17 * CE 2 is refined into CE [12,13,14] 0.04/0.17 0.04/0.17 0.04/0.17 ### Cost equations --> "Loop" of eval_jama_ex7_bb0_in/3 0.04/0.17 * CEs [14] --> Loop 12 0.04/0.17 * CEs [12] --> Loop 13 0.04/0.17 * CEs [13] --> Loop 14 0.04/0.17 0.04/0.17 ### Ranking functions of CR eval_jama_ex7_bb0_in(V_n,V_m,B) 0.04/0.17 0.04/0.17 #### Partial ranking functions of CR eval_jama_ex7_bb0_in(V_n,V_m,B) 0.04/0.17 0.04/0.17 0.04/0.17 ### Specialization of cost equations eval_jama_ex7_start/3 0.04/0.17 * CE 1 is refined into CE [15,16,17] 0.04/0.17 0.04/0.17 0.04/0.17 ### Cost equations --> "Loop" of eval_jama_ex7_start/3 0.04/0.17 * CEs [17] --> Loop 15 0.04/0.17 * CEs [16] --> Loop 16 0.04/0.17 * CEs [15] --> Loop 17 0.04/0.17 0.04/0.17 ### Ranking functions of CR eval_jama_ex7_start(V_n,V_m,B) 0.04/0.17 0.04/0.17 #### Partial ranking functions of CR eval_jama_ex7_start(V_n,V_m,B) 0.04/0.17 0.04/0.17 0.04/0.17 Computing Bounds 0.04/0.17 ===================================== 0.04/0.17 0.04/0.17 #### Cost of chains of eval_jama_ex7_bb2_in(V_j_0,B,C): 0.04/0.17 * Chain [[7],8]: 1*it(7)+0 0.04/0.17 Such that:it(7) =< V_j_0 0.04/0.17 0.04/0.17 with precondition: [B=2,C=0,V_j_0>=1] 0.04/0.17 0.04/0.17 * Chain [8]: 0 0.04/0.17 with precondition: [B=2,V_j_0=C,0>=V_j_0] 0.04/0.17 0.04/0.17 0.04/0.17 #### Cost of chains of eval_jama_ex7_bb1_in(V_m,V_i_0,B): 0.04/0.17 * Chain [[10],11]: 1*it(10)+0 0.04/0.17 Such that:it(10) =< V_i_0 0.04/0.17 0.04/0.17 with precondition: [B=3,0>=V_m,V_i_0>=1] 0.04/0.17 0.04/0.17 * Chain [[9],11]: 1*it(9)+1*s(3)+0 0.04/0.17 Such that:aux(1) =< V_m 0.04/0.17 it(9) =< V_i_0 0.04/0.17 s(3) =< it(9)*aux(1) 0.04/0.17 0.04/0.17 with precondition: [B=3,V_m>=1,V_i_0>=1] 0.04/0.17 0.04/0.17 * Chain [11]: 0 0.04/0.17 with precondition: [B=3,0>=V_i_0] 0.04/0.17 0.04/0.17 0.04/0.17 #### Cost of chains of eval_jama_ex7_bb0_in(V_n,V_m,B): 0.04/0.17 * Chain [14]: 0 0.04/0.17 with precondition: [0>=V_n] 0.04/0.17 0.04/0.17 * Chain [13]: 1*s(4)+0 0.04/0.17 Such that:s(4) =< V_n 0.04/0.17 0.04/0.17 with precondition: [0>=V_m,V_n>=1] 0.04/0.17 0.04/0.17 * Chain [12]: 1*s(6)+1*s(7)+0 0.04/0.17 Such that:s(6) =< V_n 0.04/0.17 s(5) =< V_m 0.04/0.17 s(7) =< s(6)*s(5) 0.04/0.17 0.04/0.17 with precondition: [V_n>=1,V_m>=1] 0.04/0.17 0.04/0.17 0.04/0.17 #### Cost of chains of eval_jama_ex7_start(V_n,V_m,B): 0.04/0.17 * Chain [17]: 0 0.04/0.17 with precondition: [0>=V_n] 0.04/0.17 0.04/0.17 * Chain [16]: 1*s(8)+0 0.04/0.17 Such that:s(8) =< V_n 0.04/0.17 0.04/0.17 with precondition: [0>=V_m,V_n>=1] 0.04/0.17 0.04/0.17 * Chain [15]: 1*s(9)+1*s(11)+0 0.04/0.17 Such that:s(9) =< V_n 0.04/0.17 s(10) =< V_m 0.04/0.17 s(11) =< s(9)*s(10) 0.04/0.17 0.04/0.17 with precondition: [V_n>=1,V_m>=1] 0.04/0.17 0.04/0.17 0.04/0.17 Closed-form bounds of eval_jama_ex7_start(V_n,V_m,B): 0.04/0.17 ------------------------------------- 0.04/0.17 * Chain [17] with precondition: [0>=V_n] 0.04/0.17 - Upper bound: 0 0.04/0.17 - Complexity: constant 0.04/0.17 * Chain [16] with precondition: [0>=V_m,V_n>=1] 0.04/0.17 - Upper bound: V_n 0.04/0.17 - Complexity: n 0.04/0.17 * Chain [15] with precondition: [V_n>=1,V_m>=1] 0.04/0.17 - Upper bound: V_m*V_n+V_n 0.04/0.17 - Complexity: n^2 0.04/0.17 0.04/0.17 ### Maximum cost of eval_jama_ex7_start(V_n,V_m,B): nat(V_m)*nat(V_n)+nat(V_n) 0.04/0.17 Asymptotic class: n^2 0.04/0.17 * Total analysis performed in 96 ms. 0.04/0.17 0.04/0.27 EOF