0.05/0.19 WORST_CASE(?,O(n^2)) 0.05/0.19 0.05/0.19 Preprocessing Cost Relations 0.05/0.19 ===================================== 0.05/0.19 0.05/0.19 #### Computed strongly connected components 0.05/0.19 0. recursive : [eval_foo_bb2_in/5,eval_foo_bb3_in/5] 0.05/0.19 1. recursive : [eval_foo_bb1_in/4,eval_foo_bb2_in_loop_cont/6,eval_foo_bb4_in/5] 0.05/0.19 2. non_recursive : [eval_foo_stop/1] 0.05/0.19 3. non_recursive : [eval_foo_bb5_in/1] 0.05/0.19 4. non_recursive : [eval_foo_bb1_in_loop_cont/2] 0.05/0.19 5. non_recursive : [eval_foo_bb0_in/3] 0.05/0.19 6. non_recursive : [eval_foo_start/5] 0.05/0.19 0.05/0.19 #### Obtained direct recursion through partial evaluation 0.05/0.19 0. SCC is partially evaluated into eval_foo_bb2_in/5 0.05/0.19 1. SCC is partially evaluated into eval_foo_bb1_in/4 0.05/0.19 2. SCC is completely evaluated into other SCCs 0.05/0.19 3. SCC is completely evaluated into other SCCs 0.05/0.19 4. SCC is completely evaluated into other SCCs 0.05/0.19 5. SCC is partially evaluated into eval_foo_bb0_in/3 0.05/0.19 6. SCC is partially evaluated into eval_foo_start/5 0.05/0.19 0.05/0.19 Control-Flow Refinement of Cost Relations 0.05/0.19 ===================================== 0.05/0.19 0.05/0.19 ### Specialization of cost equations eval_foo_bb2_in/5 0.05/0.19 * CE 7 is refined into CE [8] 0.05/0.19 * CE 6 is refined into CE [9] 0.05/0.19 0.05/0.19 0.05/0.19 ### Cost equations --> "Loop" of eval_foo_bb2_in/5 0.05/0.19 * CEs [9] --> Loop 8 0.05/0.19 * CEs [8] --> Loop 9 0.05/0.19 0.05/0.19 ### Ranking functions of CR eval_foo_bb2_in(V_k,V__0,V__01,B,C) 0.05/0.19 * RF of phase [8]: [V__0-V__01+1] 0.05/0.19 0.05/0.19 #### Partial ranking functions of CR eval_foo_bb2_in(V_k,V__0,V__01,B,C) 0.05/0.19 * Partial RF of phase [8]: 0.05/0.19 - RF of loop [8:1]: 0.05/0.19 V__0-V__01+1 0.05/0.19 0.05/0.19 0.05/0.19 ### Specialization of cost equations eval_foo_bb1_in/4 0.05/0.19 * CE 5 is refined into CE [10] 0.05/0.19 * CE 4 is refined into CE [11] 0.05/0.19 0.05/0.19 0.05/0.19 ### Cost equations --> "Loop" of eval_foo_bb1_in/4 0.05/0.19 * CEs [11] --> Loop 10 0.05/0.19 * CEs [10] --> Loop 11 0.05/0.19 0.05/0.19 ### Ranking functions of CR eval_foo_bb1_in(V_k,V_n,V__0,B) 0.05/0.19 * RF of phase [10]: [V_n-V__0] 0.05/0.19 0.05/0.19 #### Partial ranking functions of CR eval_foo_bb1_in(V_k,V_n,V__0,B) 0.05/0.19 * Partial RF of phase [10]: 0.05/0.19 - RF of loop [10:1]: 0.05/0.19 V_n-V__0 0.05/0.19 0.05/0.19 0.05/0.19 ### Specialization of cost equations eval_foo_bb0_in/3 0.05/0.19 * CE 3 is refined into CE [12,13] 0.05/0.19 * CE 2 is refined into CE [14] 0.05/0.19 0.05/0.19 0.05/0.19 ### Cost equations --> "Loop" of eval_foo_bb0_in/3 0.05/0.19 * CEs [13] --> Loop 12 0.05/0.19 * CEs [12] --> Loop 13 0.05/0.19 * CEs [14] --> Loop 14 0.05/0.19 0.05/0.19 ### Ranking functions of CR eval_foo_bb0_in(V_k,V_n,B) 0.05/0.19 0.05/0.19 #### Partial ranking functions of CR eval_foo_bb0_in(V_k,V_n,B) 0.05/0.19 0.05/0.19 0.05/0.19 ### Specialization of cost equations eval_foo_start/5 0.05/0.19 * CE 1 is refined into CE [15,16,17] 0.05/0.19 0.05/0.19 0.05/0.19 ### Cost equations --> "Loop" of eval_foo_start/5 0.05/0.19 * CEs [17] --> Loop 15 0.05/0.19 * CEs [16] --> Loop 16 0.05/0.19 * CEs [15] --> Loop 17 0.05/0.19 0.05/0.19 ### Ranking functions of CR eval_foo_start(V_k,V_i,V_j,V_n,B) 0.05/0.19 0.05/0.19 #### Partial ranking functions of CR eval_foo_start(V_k,V_i,V_j,V_n,B) 0.05/0.19 0.05/0.19 0.05/0.19 Computing Bounds 0.05/0.19 ===================================== 0.05/0.19 0.05/0.19 #### Cost of chains of eval_foo_bb2_in(V_k,V__0,V__01,B,C): 0.05/0.19 * Chain [[8],9]: 1*it(8)+0 0.05/0.19 Such that:it(8) =< V__0-V__01+1 0.05/0.19 0.05/0.19 with precondition: [B=2,V__01>=0,C>=V__0+1,C>=V__01+V_k,V__0+V_k>=C] 0.05/0.19 0.05/0.19 0.05/0.19 #### Cost of chains of eval_foo_bb1_in(V_k,V_n,V__0,B): 0.05/0.19 * Chain [[10],11]: 1*it(10)+1*s(3)+0 0.05/0.19 Such that:aux(1) =< V_n 0.05/0.19 it(10) =< V_n-V__0 0.05/0.19 s(3) =< it(10)*aux(1) 0.05/0.19 0.05/0.19 with precondition: [B=3,V_k>=1,V__0>=0,V_n>=V__0+1] 0.05/0.19 0.05/0.19 * Chain [11]: 0 0.05/0.19 with precondition: [B=3,V_k>=1,V__0>=0,V__0>=V_n] 0.05/0.19 0.05/0.19 0.05/0.19 #### Cost of chains of eval_foo_bb0_in(V_k,V_n,B): 0.05/0.19 * Chain [14]: 0 0.05/0.19 with precondition: [0>=V_k] 0.05/0.19 0.05/0.19 * Chain [13]: 0 0.05/0.19 with precondition: [0>=V_n,V_k>=1] 0.05/0.19 0.05/0.19 * Chain [12]: 1*s(5)+1*s(6)+0 0.05/0.19 Such that:aux(2) =< V_n 0.05/0.19 s(5) =< aux(2) 0.05/0.19 s(6) =< s(5)*aux(2) 0.05/0.19 0.05/0.19 with precondition: [V_k>=1,V_n>=1] 0.05/0.19 0.05/0.19 0.05/0.19 #### Cost of chains of eval_foo_start(V_k,V_i,V_j,V_n,B): 0.05/0.19 * Chain [17]: 0 0.05/0.19 with precondition: [0>=V_k] 0.05/0.19 0.05/0.19 * Chain [16]: 0 0.05/0.19 with precondition: [0>=V_n,V_k>=1] 0.05/0.19 0.05/0.19 * Chain [15]: 1*s(8)+1*s(9)+0 0.05/0.19 Such that:s(7) =< V_n 0.05/0.19 s(8) =< s(7) 0.05/0.19 s(9) =< s(8)*s(7) 0.05/0.19 0.05/0.19 with precondition: [V_k>=1,V_n>=1] 0.05/0.19 0.05/0.19 0.05/0.19 Closed-form bounds of eval_foo_start(V_k,V_i,V_j,V_n,B): 0.05/0.19 ------------------------------------- 0.05/0.19 * Chain [17] with precondition: [0>=V_k] 0.05/0.19 - Upper bound: 0 0.05/0.19 - Complexity: constant 0.05/0.19 * Chain [16] with precondition: [0>=V_n,V_k>=1] 0.05/0.19 - Upper bound: 0 0.05/0.19 - Complexity: constant 0.05/0.19 * Chain [15] with precondition: [V_k>=1,V_n>=1] 0.05/0.19 - Upper bound: V_n*V_n+V_n 0.05/0.19 - Complexity: n^2 0.05/0.19 0.05/0.19 ### Maximum cost of eval_foo_start(V_k,V_i,V_j,V_n,B): nat(V_n)*nat(V_n)+nat(V_n) 0.05/0.19 Asymptotic class: n^2 0.05/0.19 * Total analysis performed in 119 ms. 0.05/0.19 0.05/0.29 EOF