0.04/0.19 WORST_CASE(?,O(n^1)) 0.04/0.19 0.04/0.19 Preprocessing Cost Relations 0.04/0.19 ===================================== 0.04/0.19 0.04/0.19 #### Computed strongly connected components 0.04/0.19 0. recursive : [eval_foo_0/3,eval_foo_1/3,eval_foo_bb1_in/3,eval_foo_bb2_in/3] 0.04/0.19 1. non_recursive : [eval_foo_stop/1] 0.04/0.19 2. non_recursive : [eval_foo_bb3_in/1] 0.04/0.19 3. non_recursive : [eval_foo_bb1_in_loop_cont/2] 0.04/0.19 4. non_recursive : [eval_foo_bb0_in/3] 0.04/0.19 5. non_recursive : [eval_foo_start/3] 0.04/0.19 0.04/0.19 #### Obtained direct recursion through partial evaluation 0.04/0.19 0. SCC is partially evaluated into eval_foo_bb1_in/3 0.04/0.19 1. SCC is completely evaluated into other SCCs 0.04/0.19 2. SCC is completely evaluated into other SCCs 0.04/0.19 3. SCC is completely evaluated into other SCCs 0.04/0.19 4. SCC is partially evaluated into eval_foo_bb0_in/3 0.04/0.19 5. SCC is partially evaluated into eval_foo_start/3 0.04/0.19 0.04/0.19 Control-Flow Refinement of Cost Relations 0.04/0.19 ===================================== 0.04/0.19 0.04/0.19 ### Specialization of cost equations eval_foo_bb1_in/3 0.04/0.19 * CE 7 is refined into CE [8] 0.04/0.19 * CE 5 is refined into CE [9] 0.04/0.19 * CE 6 is refined into CE [10] 0.04/0.19 * CE 3 is refined into CE [11] 0.04/0.19 * CE 4 is refined into CE [12] 0.04/0.19 0.04/0.19 0.04/0.19 ### Cost equations --> "Loop" of eval_foo_bb1_in/3 0.04/0.19 * CEs [9] --> Loop 8 0.04/0.19 * CEs [10] --> Loop 9 0.04/0.19 * CEs [11] --> Loop 10 0.04/0.19 * CEs [12] --> Loop 11 0.04/0.19 * CEs [8] --> Loop 12 0.04/0.19 0.04/0.19 ### Ranking functions of CR eval_foo_bb1_in(V__01,V__0,B) 0.04/0.19 * RF of phase [8]: [V__0] 0.04/0.19 0.04/0.19 #### Partial ranking functions of CR eval_foo_bb1_in(V__01,V__0,B) 0.04/0.19 * Partial RF of phase [8]: 0.04/0.19 - RF of loop [8:1]: 0.04/0.19 V__0 0.04/0.19 0.04/0.19 0.04/0.19 ### Specialization of cost equations eval_foo_bb0_in/3 0.04/0.19 * CE 2 is refined into CE [13,14,15,16,17,18] 0.04/0.19 0.04/0.19 0.04/0.19 ### Cost equations --> "Loop" of eval_foo_bb0_in/3 0.04/0.19 * CEs [18] --> Loop 13 0.04/0.19 * CEs [16] --> Loop 14 0.04/0.19 * CEs [17] --> Loop 15 0.04/0.19 * CEs [15] --> Loop 16 0.04/0.19 * CEs [13] --> Loop 17 0.04/0.19 * CEs [14] --> Loop 18 0.04/0.19 0.04/0.19 ### Ranking functions of CR eval_foo_bb0_in(V_x,V_b,B) 0.04/0.19 0.04/0.19 #### Partial ranking functions of CR eval_foo_bb0_in(V_x,V_b,B) 0.04/0.19 0.04/0.19 0.04/0.19 ### Specialization of cost equations eval_foo_start/3 0.04/0.19 * CE 1 is refined into CE [19,20,21,22,23,24] 0.04/0.19 0.04/0.19 0.04/0.19 ### Cost equations --> "Loop" of eval_foo_start/3 0.04/0.19 * CEs [24] --> Loop 19 0.04/0.19 * CEs [23] --> Loop 20 0.04/0.19 * CEs [22] --> Loop 21 0.04/0.19 * CEs [21] --> Loop 22 0.04/0.19 * CEs [20] --> Loop 23 0.04/0.19 * CEs [19] --> Loop 24 0.04/0.19 0.04/0.19 ### Ranking functions of CR eval_foo_start(V_x,V_b,B) 0.04/0.19 0.04/0.19 #### Partial ranking functions of CR eval_foo_start(V_x,V_b,B) 0.04/0.19 0.04/0.19 0.04/0.19 Computing Bounds 0.04/0.19 ===================================== 0.04/0.19 0.04/0.19 #### Cost of chains of eval_foo_bb1_in(V__01,V__0,B): 0.04/0.19 * Chain [[8],10,12]: 1*it(8)+1 0.04/0.19 Such that:it(8) =< V__0 0.04/0.19 0.04/0.19 with precondition: [B=2,V__01>=1,V__0>=1] 0.04/0.19 0.04/0.19 * Chain [12]: 0 0.04/0.19 with precondition: [V__01=0,B=2] 0.04/0.19 0.04/0.19 * Chain [11,12]: 1 0.04/0.19 with precondition: [B=2,0>=V__01+1,0>=V__0] 0.04/0.19 0.04/0.19 * Chain [10,12]: 1 0.04/0.19 with precondition: [B=2,0>=V__0,V__01>=1] 0.04/0.19 0.04/0.19 * Chain [9,[8],10,12]: 1*it(8)+2 0.04/0.19 Such that:it(8) =< V__0 0.04/0.19 0.04/0.19 with precondition: [B=2,0>=V__01+1,V__0>=2] 0.04/0.19 0.04/0.19 * Chain [9,10,12]: 2 0.04/0.19 with precondition: [V__0=1,B=2,0>=V__01+1] 0.04/0.19 0.04/0.19 0.04/0.19 #### Cost of chains of eval_foo_bb0_in(V_x,V_b,B): 0.04/0.19 * Chain [18]: 2 0.04/0.19 with precondition: [V_x=1,0>=V_b+1] 0.04/0.19 0.04/0.19 * Chain [17]: 0 0.04/0.19 with precondition: [V_b=0] 0.04/0.19 0.04/0.19 * Chain [16]: 1 0.04/0.19 with precondition: [0>=V_x,0>=V_b+1] 0.04/0.19 0.04/0.19 * Chain [15]: 1 0.04/0.19 with precondition: [0>=V_x,V_b>=1] 0.04/0.19 0.04/0.19 * Chain [14]: 1*s(1)+2 0.04/0.19 Such that:s(1) =< V_x 0.04/0.19 0.04/0.19 with precondition: [0>=V_b+1,V_x>=2] 0.04/0.19 0.04/0.19 * Chain [13]: 1*s(2)+1 0.04/0.19 Such that:s(2) =< V_x 0.04/0.19 0.04/0.19 with precondition: [V_x>=1,V_b>=1] 0.04/0.19 0.04/0.19 0.04/0.19 #### Cost of chains of eval_foo_start(V_x,V_b,B): 0.04/0.19 * Chain [24]: 2 0.04/0.19 with precondition: [V_x=1,0>=V_b+1] 0.04/0.19 0.04/0.19 * Chain [23]: 0 0.04/0.19 with precondition: [V_b=0] 0.04/0.19 0.04/0.19 * Chain [22]: 1 0.04/0.19 with precondition: [0>=V_x,0>=V_b+1] 0.04/0.19 0.04/0.19 * Chain [21]: 1 0.04/0.19 with precondition: [0>=V_x,V_b>=1] 0.04/0.19 0.04/0.19 * Chain [20]: 1*s(3)+2 0.04/0.19 Such that:s(3) =< V_x 0.04/0.19 0.04/0.19 with precondition: [0>=V_b+1,V_x>=2] 0.04/0.19 0.04/0.19 * Chain [19]: 1*s(4)+1 0.04/0.19 Such that:s(4) =< V_x 0.04/0.19 0.04/0.19 with precondition: [V_x>=1,V_b>=1] 0.04/0.19 0.04/0.19 0.04/0.19 Closed-form bounds of eval_foo_start(V_x,V_b,B): 0.04/0.19 ------------------------------------- 0.04/0.19 * Chain [24] with precondition: [V_x=1,0>=V_b+1] 0.04/0.19 - Upper bound: 2 0.04/0.19 - Complexity: constant 0.04/0.19 * Chain [23] with precondition: [V_b=0] 0.04/0.19 - Upper bound: 0 0.04/0.19 - Complexity: constant 0.04/0.19 * Chain [22] with precondition: [0>=V_x,0>=V_b+1] 0.04/0.19 - Upper bound: 1 0.04/0.19 - Complexity: constant 0.04/0.19 * Chain [21] with precondition: [0>=V_x,V_b>=1] 0.04/0.19 - Upper bound: 1 0.04/0.19 - Complexity: constant 0.04/0.19 * Chain [20] with precondition: [0>=V_b+1,V_x>=2] 0.04/0.19 - Upper bound: V_x+2 0.04/0.19 - Complexity: n 0.04/0.19 * Chain [19] with precondition: [V_x>=1,V_b>=1] 0.04/0.19 - Upper bound: V_x+1 0.04/0.19 - Complexity: n 0.04/0.19 0.04/0.19 ### Maximum cost of eval_foo_start(V_x,V_b,B): max([2,nat(V_x)+2]) 0.04/0.19 Asymptotic class: n 0.04/0.19 * Total analysis performed in 118 ms. 0.04/0.19 0.04/0.29 EOF