0.04/0.21 WORST_CASE(?,O(n^2)) 0.04/0.21 0.04/0.21 Preprocessing Cost Relations 0.04/0.21 ===================================== 0.04/0.21 0.04/0.21 #### Computed strongly connected components 0.04/0.21 0. recursive : [eval_jama_ex4_bb2_in/4,eval_jama_ex4_bb3_in/4] 0.04/0.21 1. recursive : [eval_jama_ex4_bb1_in/5,eval_jama_ex4_bb2_in_loop_cont/7,eval_jama_ex4_bb4_in/6] 0.04/0.21 2. non_recursive : [eval_jama_ex4_stop/1] 0.04/0.21 3. non_recursive : [eval_jama_ex4_bb5_in/1] 0.04/0.21 4. non_recursive : [eval_jama_ex4_bb1_in_loop_cont/2] 0.04/0.21 5. non_recursive : [eval_jama_ex4_bb0_in/5] 0.04/0.21 6. non_recursive : [eval_jama_ex4_start/5] 0.04/0.21 0.04/0.21 #### Obtained direct recursion through partial evaluation 0.04/0.21 0. SCC is partially evaluated into eval_jama_ex4_bb2_in/4 0.04/0.21 1. SCC is partially evaluated into eval_jama_ex4_bb1_in/5 0.04/0.21 2. SCC is completely evaluated into other SCCs 0.04/0.21 3. SCC is completely evaluated into other SCCs 0.04/0.21 4. SCC is completely evaluated into other SCCs 0.04/0.21 5. SCC is partially evaluated into eval_jama_ex4_bb0_in/5 0.04/0.21 6. SCC is partially evaluated into eval_jama_ex4_start/5 0.04/0.21 0.04/0.21 Control-Flow Refinement of Cost Relations 0.04/0.21 ===================================== 0.04/0.21 0.04/0.21 ### Specialization of cost equations eval_jama_ex4_bb2_in/4 0.04/0.21 * CE 6 is refined into CE [7] 0.04/0.21 * CE 5 is refined into CE [8] 0.04/0.21 0.04/0.21 0.04/0.21 ### Cost equations --> "Loop" of eval_jama_ex4_bb2_in/4 0.04/0.21 * CEs [8] --> Loop 7 0.04/0.21 * CEs [7] --> Loop 8 0.04/0.21 0.04/0.21 ### Ranking functions of CR eval_jama_ex4_bb2_in(V_d,V_j_0,B,C) 0.04/0.21 * RF of phase [7]: [V_d-V_j_0+1] 0.04/0.21 0.04/0.21 #### Partial ranking functions of CR eval_jama_ex4_bb2_in(V_d,V_j_0,B,C) 0.04/0.21 * Partial RF of phase [7]: 0.04/0.21 - RF of loop [7:1]: 0.04/0.21 V_d-V_j_0+1 0.04/0.21 0.04/0.21 0.04/0.21 ### Specialization of cost equations eval_jama_ex4_bb1_in/5 0.04/0.21 * CE 4 is refined into CE [9] 0.04/0.21 * CE 3 is refined into CE [10,11] 0.04/0.21 0.04/0.21 0.04/0.21 ### Cost equations --> "Loop" of eval_jama_ex4_bb1_in/5 0.04/0.21 * CEs [11] --> Loop 9 0.04/0.21 * CEs [10] --> Loop 10 0.04/0.21 * CEs [9] --> Loop 11 0.04/0.21 0.04/0.21 ### Ranking functions of CR eval_jama_ex4_bb1_in(V_b,V_c,V_d,V_i_0,B) 0.04/0.21 * RF of phase [9]: [V_b-V_i_0+1] 0.04/0.21 * RF of phase [10]: [V_b-V_i_0+1] 0.04/0.21 0.04/0.21 #### Partial ranking functions of CR eval_jama_ex4_bb1_in(V_b,V_c,V_d,V_i_0,B) 0.04/0.21 * Partial RF of phase [9]: 0.04/0.21 - RF of loop [9:1]: 0.04/0.21 V_b-V_i_0+1 0.04/0.21 * Partial RF of phase [10]: 0.04/0.21 - RF of loop [10:1]: 0.04/0.21 V_b-V_i_0+1 0.04/0.21 0.04/0.21 0.04/0.21 ### Specialization of cost equations eval_jama_ex4_bb0_in/5 0.04/0.21 * CE 2 is refined into CE [12,13,14] 0.04/0.21 0.04/0.21 0.04/0.21 ### Cost equations --> "Loop" of eval_jama_ex4_bb0_in/5 0.04/0.21 * CEs [12] --> Loop 12 0.04/0.21 * CEs [14] --> Loop 13 0.04/0.21 * CEs [13] --> Loop 14 0.04/0.21 0.04/0.21 ### Ranking functions of CR eval_jama_ex4_bb0_in(V_a,V_b,V_c,V_d,B) 0.04/0.21 0.04/0.21 #### Partial ranking functions of CR eval_jama_ex4_bb0_in(V_a,V_b,V_c,V_d,B) 0.04/0.21 0.04/0.21 0.04/0.21 ### Specialization of cost equations eval_jama_ex4_start/5 0.04/0.21 * CE 1 is refined into CE [15,16,17] 0.04/0.21 0.04/0.21 0.04/0.21 ### Cost equations --> "Loop" of eval_jama_ex4_start/5 0.04/0.21 * CEs [17] --> Loop 15 0.04/0.21 * CEs [16] --> Loop 16 0.04/0.21 * CEs [15] --> Loop 17 0.04/0.21 0.04/0.21 ### Ranking functions of CR eval_jama_ex4_start(V_a,V_b,V_c,V_d,B) 0.04/0.21 0.04/0.21 #### Partial ranking functions of CR eval_jama_ex4_start(V_a,V_b,V_c,V_d,B) 0.04/0.21 0.04/0.21 0.04/0.21 Computing Bounds 0.04/0.21 ===================================== 0.04/0.21 0.04/0.21 #### Cost of chains of eval_jama_ex4_bb2_in(V_d,V_j_0,B,C): 0.04/0.21 * Chain [[7],8]: 1*it(7)+0 0.04/0.21 Such that:it(7) =< V_d-V_j_0+1 0.04/0.21 0.04/0.21 with precondition: [B=2,V_d+1=C,V_d>=V_j_0] 0.04/0.21 0.04/0.21 * Chain [8]: 0 0.04/0.21 with precondition: [B=2,V_j_0=C,V_j_0>=V_d+1] 0.04/0.21 0.04/0.21 0.04/0.21 #### Cost of chains of eval_jama_ex4_bb1_in(V_b,V_c,V_d,V_i_0,B): 0.04/0.21 * Chain [[10],11]: 1*it(10)+1*s(3)+0 0.04/0.21 Such that:it(10) =< V_b-V_i_0+1 0.04/0.21 aux(1) =< -V_c+V_d+1 0.04/0.21 s(3) =< it(10)*aux(1) 0.04/0.21 0.04/0.21 with precondition: [B=3,V_d>=V_c,V_b>=V_i_0] 0.04/0.21 0.04/0.21 * Chain [[9],11]: 1*it(9)+0 0.04/0.21 Such that:it(9) =< V_b-V_i_0+1 0.04/0.21 0.04/0.21 with precondition: [B=3,V_c>=V_d+1,V_b>=V_i_0] 0.04/0.21 0.04/0.21 * Chain [11]: 0 0.04/0.21 with precondition: [B=3,V_i_0>=V_b+1] 0.04/0.21 0.04/0.21 0.04/0.21 #### Cost of chains of eval_jama_ex4_bb0_in(V_a,V_b,V_c,V_d,B): 0.04/0.21 * Chain [14]: 1*s(4)+1*s(6)+0 0.04/0.21 Such that:s(4) =< -V_a+V_b+1 0.04/0.21 s(5) =< -V_c+V_d+1 0.04/0.21 s(6) =< s(4)*s(5) 0.04/0.21 0.04/0.21 with precondition: [V_b>=V_a,V_d>=V_c] 0.04/0.21 0.04/0.21 * Chain [13]: 1*s(7)+0 0.04/0.21 Such that:s(7) =< -V_a+V_b+1 0.04/0.21 0.04/0.21 with precondition: [V_b>=V_a,V_c>=V_d+1] 0.04/0.21 0.04/0.21 * Chain [12]: 0 0.04/0.21 with precondition: [V_a>=V_b+1] 0.04/0.21 0.04/0.21 0.04/0.21 #### Cost of chains of eval_jama_ex4_start(V_a,V_b,V_c,V_d,B): 0.04/0.21 * Chain [17]: 1*s(8)+1*s(10)+0 0.04/0.21 Such that:s(8) =< -V_a+V_b+1 0.04/0.21 s(9) =< -V_c+V_d+1 0.04/0.21 s(10) =< s(8)*s(9) 0.04/0.21 0.04/0.21 with precondition: [V_b>=V_a,V_d>=V_c] 0.04/0.21 0.04/0.21 * Chain [16]: 1*s(11)+0 0.04/0.21 Such that:s(11) =< -V_a+V_b+1 0.04/0.21 0.04/0.21 with precondition: [V_b>=V_a,V_c>=V_d+1] 0.04/0.21 0.04/0.21 * Chain [15]: 0 0.04/0.21 with precondition: [V_a>=V_b+1] 0.04/0.21 0.04/0.21 0.04/0.21 Closed-form bounds of eval_jama_ex4_start(V_a,V_b,V_c,V_d,B): 0.04/0.21 ------------------------------------- 0.04/0.21 * Chain [17] with precondition: [V_b>=V_a,V_d>=V_c] 0.04/0.21 - Upper bound: -V_a+V_b+1+(-V_c+V_d+1)*(-V_a+V_b+1) 0.04/0.21 - Complexity: n^2 0.04/0.21 * Chain [16] with precondition: [V_b>=V_a,V_c>=V_d+1] 0.04/0.21 - Upper bound: -V_a+V_b+1 0.04/0.21 - Complexity: n 0.04/0.21 * Chain [15] with precondition: [V_a>=V_b+1] 0.04/0.21 - Upper bound: 0 0.04/0.21 - Complexity: constant 0.04/0.21 0.04/0.21 ### Maximum cost of eval_jama_ex4_start(V_a,V_b,V_c,V_d,B): nat(-V_c+V_d+1)*nat(-V_a+V_b+1)+nat(-V_a+V_b+1) 0.04/0.21 Asymptotic class: n^2 0.04/0.21 * Total analysis performed in 135 ms. 0.04/0.21 0.04/0.31 EOF