0.04/0.15 MAYBE 0.04/0.15 0.04/0.15 Preprocessing Cost Relations 0.04/0.15 ===================================== 0.04/0.15 0.04/0.15 #### Computed strongly connected components 0.04/0.15 0. recursive : [eval_foo_bb1_in/2,eval_foo_bb2_in/2] 0.04/0.15 1. non_recursive : [eval_foo_stop/1] 0.04/0.15 2. non_recursive : [eval_foo_bb3_in/1] 0.04/0.15 3. non_recursive : [eval_foo_bb1_in_loop_cont/2] 0.04/0.15 4. non_recursive : [eval_foo_bb0_in/2] 0.04/0.15 5. non_recursive : [eval_foo_start/2] 0.04/0.15 0.04/0.15 #### Obtained direct recursion through partial evaluation 0.04/0.15 0. SCC is partially evaluated into eval_foo_bb1_in/2 0.04/0.15 1. SCC is completely evaluated into other SCCs 0.04/0.15 2. SCC is completely evaluated into other SCCs 0.04/0.15 3. SCC is completely evaluated into other SCCs 0.04/0.15 4. SCC is partially evaluated into eval_foo_bb0_in/2 0.04/0.15 5. SCC is partially evaluated into eval_foo_start/2 0.04/0.15 0.04/0.15 Control-Flow Refinement of Cost Relations 0.04/0.15 ===================================== 0.04/0.15 0.04/0.15 ### Specialization of cost equations eval_foo_bb1_in/2 0.04/0.15 * CE 7 is refined into CE [8] 0.04/0.15 * CE 6 is refined into CE [9] 0.04/0.15 * CE 5 is refined into CE [10] 0.04/0.15 * CE 4 is refined into CE [11] 0.04/0.15 * CE 3 is refined into CE [12] 0.04/0.15 0.04/0.15 0.04/0.15 ### Cost equations --> "Loop" of eval_foo_bb1_in/2 0.04/0.15 * CEs [10] --> Loop 8 0.04/0.15 * CEs [11] --> Loop 9 0.04/0.15 * CEs [12] --> Loop 10 0.04/0.15 * CEs [8] --> Loop 11 0.04/0.15 * CEs [9] --> Loop 12 0.04/0.15 0.04/0.15 ### Ranking functions of CR eval_foo_bb1_in(V__0,B) 0.04/0.15 * RF of phase [8]: [V__0] 0.04/0.15 * RF of phase [9]: [-V__0] 0.04/0.15 0.04/0.15 #### Partial ranking functions of CR eval_foo_bb1_in(V__0,B) 0.04/0.15 * Partial RF of phase [8]: 0.04/0.15 - RF of loop [8:1]: 0.04/0.15 V__0 0.04/0.15 * Partial RF of phase [9]: 0.04/0.15 - RF of loop [9:1]: 0.04/0.15 -V__0 0.04/0.15 0.04/0.15 0.04/0.15 ### Specialization of cost equations eval_foo_bb0_in/2 0.04/0.15 * CE 2 is refined into CE [13,14,15,16,17] 0.04/0.15 0.04/0.15 0.04/0.15 ### Cost equations --> "Loop" of eval_foo_bb0_in/2 0.04/0.15 * CEs [17] --> Loop 13 0.04/0.15 * CEs [16] --> Loop 14 0.04/0.15 * CEs [15] --> Loop 15 0.04/0.15 * CEs [14] --> Loop 16 0.04/0.15 * CEs [13] --> Loop 17 0.04/0.15 0.04/0.15 ### Ranking functions of CR eval_foo_bb0_in(V_i,B) 0.04/0.15 0.04/0.15 #### Partial ranking functions of CR eval_foo_bb0_in(V_i,B) 0.04/0.15 0.04/0.15 0.04/0.15 ### Specialization of cost equations eval_foo_start/2 0.04/0.15 * CE 1 is refined into CE [18,19,20,21,22] 0.04/0.15 0.04/0.15 0.04/0.15 ### Cost equations --> "Loop" of eval_foo_start/2 0.04/0.15 * CEs [22] --> Loop 18 0.04/0.15 * CEs [21] --> Loop 19 0.04/0.15 * CEs [20] --> Loop 20 0.04/0.15 * CEs [19] --> Loop 21 0.04/0.15 * CEs [18] --> Loop 22 0.04/0.15 0.04/0.15 ### Ranking functions of CR eval_foo_start(V_i,B) 0.04/0.15 0.04/0.15 #### Partial ranking functions of CR eval_foo_start(V_i,B) 0.04/0.15 0.04/0.15 0.04/0.15 Computing Bounds 0.04/0.15 ===================================== 0.04/0.15 0.04/0.15 #### Cost of chains of eval_foo_bb1_in(V__0,B): 0.04/0.15 * Chain [[10]]...: 1*it(10)+0 0.04/0.15 with precondition: [V__0=0,B=2] 0.04/0.15 0.04/0.15 * Chain [[9],[10]]...: 1*it(9)+1*it(10)+0 0.04/0.15 Such that:it(9) =< -V__0 0.04/0.15 0.04/0.15 with precondition: [B=2,0>=V__0+1,V__0+5>=0] 0.04/0.15 0.04/0.15 * Chain [[8],[10]]...: 1*it(8)+1*it(10)+0 0.04/0.15 Such that:it(8) =< V__0 0.04/0.15 0.04/0.15 with precondition: [B=2,5>=V__0,V__0>=1] 0.04/0.15 0.04/0.15 * Chain [12]: 0 0.04/0.15 with precondition: [B=2,0>=V__0+6] 0.04/0.15 0.04/0.15 * Chain [11]: 0 0.04/0.15 with precondition: [B=2,V__0>=6] 0.04/0.15 0.04/0.15 0.04/0.15 #### Cost of chains of eval_foo_bb0_in(V_i,B): 0.04/0.15 * Chain [17]: 0 0.04/0.15 with precondition: [0>=V_i+6] 0.04/0.15 0.04/0.15 * Chain [16]: 0 0.04/0.15 with precondition: [V_i>=6] 0.04/0.15 0.04/0.15 * Chain [15]...: 1*s(1)+0 0.04/0.15 with precondition: [V_i=0] 0.04/0.15 0.04/0.15 * Chain [14]...: 1*s(2)+1*s(3)+0 0.04/0.15 Such that:s(2) =< V_i 0.04/0.15 0.04/0.15 with precondition: [5>=V_i,V_i>=1] 0.04/0.15 0.04/0.15 * Chain [13]...: 1*s(4)+1*s(5)+0 0.04/0.15 Such that:s(4) =< -V_i 0.04/0.15 0.04/0.15 with precondition: [0>=V_i+1,V_i+5>=0] 0.04/0.15 0.04/0.15 0.04/0.15 #### Cost of chains of eval_foo_start(V_i,B): 0.04/0.15 * Chain [22]: 0 0.04/0.15 with precondition: [0>=V_i+6] 0.04/0.15 0.04/0.15 * Chain [21]: 0 0.04/0.15 with precondition: [V_i>=6] 0.04/0.15 0.04/0.15 * Chain [20]...: 1*s(6)+0 0.04/0.15 with precondition: [V_i=0] 0.04/0.15 0.04/0.15 * Chain [19]...: 1*s(7)+1*s(8)+0 0.04/0.15 Such that:s(7) =< V_i 0.04/0.15 0.04/0.15 with precondition: [5>=V_i,V_i>=1] 0.04/0.15 0.04/0.15 * Chain [18]...: 1*s(9)+1*s(10)+0 0.04/0.15 Such that:s(9) =< -V_i 0.04/0.15 0.04/0.15 with precondition: [0>=V_i+1,V_i+5>=0] 0.04/0.15 0.04/0.15 0.04/0.15 Closed-form bounds of eval_foo_start(V_i,B): 0.04/0.15 ------------------------------------- 0.04/0.15 * Chain [22] with precondition: [0>=V_i+6] 0.04/0.15 - Upper bound: 0 0.04/0.15 - Complexity: constant 0.04/0.15 * Chain [21] with precondition: [V_i>=6] 0.04/0.15 - Upper bound: 0 0.04/0.15 - Complexity: constant 0.04/0.15 * Chain [20]... with precondition: [V_i=0] 0.04/0.15 - Upper bound: inf 0.04/0.15 - Complexity: infinity 0.04/0.15 * Chain [19]... with precondition: [5>=V_i,V_i>=1] 0.04/0.15 - Upper bound: inf 0.04/0.15 - Complexity: infinity 0.04/0.15 * Chain [18]... with precondition: [0>=V_i+1,V_i+5>=0] 0.04/0.15 - Upper bound: inf 0.04/0.15 - Complexity: infinity 0.04/0.15 0.04/0.15 ### Maximum cost of eval_foo_start(V_i,B): inf 0.04/0.15 Asymptotic class: infinity 0.04/0.15 * Total analysis performed in 82 ms. 0.04/0.15 0.04/0.25 EOF