0.03/0.21 WORST_CASE(?,O(1)) 0.03/0.21 0.03/0.21 Preprocessing Cost Relations 0.03/0.21 ===================================== 0.03/0.21 0.03/0.21 #### Computed strongly connected components 0.03/0.21 0. recursive : [evaleasy1bb1in/4,evaleasy1bb2in/4,evaleasy1bb3in/4,evaleasy1bbin/4] 0.03/0.21 1. non_recursive : [evaleasy1stop/3] 0.03/0.21 2. non_recursive : [evaleasy1returnin/3] 0.03/0.21 3. non_recursive : [exit_location/1] 0.03/0.21 4. non_recursive : [evaleasy1bb3in_loop_cont/4] 0.03/0.21 5. non_recursive : [evaleasy1entryin/3] 0.03/0.21 6. non_recursive : [evaleasy1start/3] 0.03/0.21 0.03/0.21 #### Obtained direct recursion through partial evaluation 0.03/0.21 0. SCC is partially evaluated into evaleasy1bb3in/4 0.03/0.21 1. SCC is completely evaluated into other SCCs 0.03/0.21 2. SCC is completely evaluated into other SCCs 0.03/0.21 3. SCC is completely evaluated into other SCCs 0.03/0.21 4. SCC is partially evaluated into evaleasy1bb3in_loop_cont/4 0.03/0.21 5. SCC is partially evaluated into evaleasy1entryin/3 0.03/0.21 6. SCC is partially evaluated into evaleasy1start/3 0.03/0.21 0.03/0.21 Control-Flow Refinement of Cost Relations 0.03/0.21 ===================================== 0.03/0.21 0.03/0.21 ### Specialization of cost equations evaleasy1bb3in/4 0.03/0.21 * CE 7 is refined into CE [10] 0.03/0.21 * CE 6 is refined into CE [11] 0.03/0.21 * CE 5 is refined into CE [12] 0.03/0.21 * CE 4 is refined into CE [13] 0.03/0.21 * CE 3 is refined into CE [14] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of evaleasy1bb3in/4 0.03/0.21 * CEs [12] --> Loop 10 0.03/0.21 * CEs [13] --> Loop 11 0.03/0.21 * CEs [14] --> Loop 12 0.03/0.21 * CEs [10] --> Loop 13 0.03/0.21 * CEs [11] --> Loop 14 0.03/0.21 0.03/0.21 ### Ranking functions of CR evaleasy1bb3in(A,B,C,D) 0.03/0.21 * RF of phase [10]: [-A/2+20] 0.03/0.21 * RF of phase [11]: [-A/2+20] 0.03/0.21 * RF of phase [12]: [-A+40] 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR evaleasy1bb3in(A,B,C,D) 0.03/0.21 * Partial RF of phase [10]: 0.03/0.21 - RF of loop [10:1]: 0.03/0.21 -A/2+20 0.03/0.21 * Partial RF of phase [11]: 0.03/0.21 - RF of loop [11:1]: 0.03/0.21 -A/2+20 0.03/0.21 * Partial RF of phase [12]: 0.03/0.21 - RF of loop [12:1]: 0.03/0.21 -A+40 0.03/0.21 0.03/0.21 0.03/0.21 ### Specialization of cost equations evaleasy1bb3in_loop_cont/4 0.03/0.21 * CE 9 is refined into CE [15] 0.03/0.21 * CE 8 is refined into CE [16] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of evaleasy1bb3in_loop_cont/4 0.03/0.21 * CEs [15] --> Loop 15 0.03/0.21 * CEs [16] --> Loop 16 0.03/0.21 0.03/0.21 ### Ranking functions of CR evaleasy1bb3in_loop_cont(A,B,C,D) 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR evaleasy1bb3in_loop_cont(A,B,C,D) 0.03/0.21 0.03/0.21 0.03/0.21 ### Specialization of cost equations evaleasy1entryin/3 0.03/0.21 * CE 2 is refined into CE [17,18,19,20,21,22,23] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of evaleasy1entryin/3 0.03/0.21 * CEs [20,22] --> Loop 17 0.03/0.21 * CEs [19,21] --> Loop 18 0.03/0.21 * CEs [17,18] --> Loop 19 0.03/0.21 * CEs [23] --> Loop 20 0.03/0.21 0.03/0.21 ### Ranking functions of CR evaleasy1entryin(A,B,C) 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR evaleasy1entryin(A,B,C) 0.03/0.21 0.03/0.21 0.03/0.21 ### Specialization of cost equations evaleasy1start/3 0.03/0.21 * CE 1 is refined into CE [24,25,26,27] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of evaleasy1start/3 0.03/0.21 * CEs [27] --> Loop 21 0.03/0.21 * CEs [26] --> Loop 22 0.03/0.21 * CEs [25] --> Loop 23 0.03/0.21 * CEs [24] --> Loop 24 0.03/0.21 0.03/0.21 ### Ranking functions of CR evaleasy1start(A,B,C) 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR evaleasy1start(A,B,C) 0.03/0.21 0.03/0.21 0.03/0.21 Computing Bounds 0.03/0.21 ===================================== 0.03/0.21 0.03/0.21 #### Cost of chains of evaleasy1bb3in(A,B,C,D): 0.03/0.21 * Chain [[12],14]: 1*it(12)+0 0.03/0.21 Such that:it(12) =< -A+40 0.03/0.21 0.03/0.21 with precondition: [B=0,C=2,D=40,39>=A,A>=0] 0.03/0.21 0.03/0.21 * Chain [[12],13]: 1*it(12)+0 0.03/0.21 Such that:it(12) =< -A+40 0.03/0.21 0.03/0.21 with precondition: [B=0,C=3,39>=A,A>=0] 0.03/0.21 0.03/0.21 * Chain [[11],14]: 1*it(11)+0 0.03/0.21 Such that:it(11) =< -A/2+20 0.03/0.21 0.03/0.21 with precondition: [C=2,0>=B+1,41>=D,A>=0,D>=40,D>=A+2] 0.03/0.21 0.03/0.21 * Chain [[11],13]: 1*it(11)+0 0.03/0.21 Such that:it(11) =< -A/2+20 0.03/0.21 0.03/0.21 with precondition: [C=3,39>=A,0>=B+1,A>=0] 0.03/0.21 0.03/0.21 * Chain [[10],14]: 1*it(10)+0 0.03/0.21 Such that:it(10) =< -A/2+20 0.03/0.21 0.03/0.21 with precondition: [C=2,41>=D,A>=0,B>=1,D>=40,D>=A+2] 0.03/0.21 0.03/0.21 * Chain [[10],13]: 1*it(10)+0 0.03/0.21 Such that:it(10) =< -A/2+20 0.03/0.21 0.03/0.21 with precondition: [C=3,39>=A,A>=0,B>=1] 0.03/0.21 0.03/0.21 * Chain [13]: 0 0.03/0.21 with precondition: [C=3,A>=0] 0.03/0.21 0.03/0.21 0.03/0.21 #### Cost of chains of evaleasy1bb3in_loop_cont(A,B,C,D): 0.03/0.21 * Chain [16]: 0 0.03/0.21 with precondition: [A=2] 0.03/0.21 0.03/0.21 * Chain [15]: 0 0.03/0.21 with precondition: [A=3] 0.03/0.21 0.03/0.21 0.03/0.21 #### Cost of chains of evaleasy1entryin(A,B,C): 0.03/0.21 * Chain [20]: 0 0.03/0.21 with precondition: [] 0.03/0.21 0.03/0.21 * Chain [19]: 80 0.03/0.21 with precondition: [B=0] 0.03/0.21 0.03/0.21 * Chain [18]: 40 0.03/0.21 with precondition: [0>=B+1] 0.03/0.21 0.03/0.21 * Chain [17]: 40 0.03/0.21 with precondition: [B>=1] 0.03/0.21 0.03/0.21 0.03/0.21 #### Cost of chains of evaleasy1start(A,B,C): 0.03/0.21 * Chain [24]: 0 0.03/0.21 with precondition: [] 0.03/0.21 0.03/0.21 * Chain [23]: 80 0.03/0.21 with precondition: [B=0] 0.03/0.21 0.03/0.21 * Chain [22]: 40 0.03/0.21 with precondition: [0>=B+1] 0.03/0.21 0.03/0.21 * Chain [21]: 40 0.03/0.21 with precondition: [B>=1] 0.03/0.21 0.03/0.21 0.03/0.21 Closed-form bounds of evaleasy1start(A,B,C): 0.03/0.21 ------------------------------------- 0.03/0.21 * Chain [24] with precondition: [] 0.03/0.21 - Upper bound: 0 0.03/0.21 - Complexity: constant 0.03/0.21 * Chain [23] with precondition: [B=0] 0.03/0.21 - Upper bound: 80 0.03/0.21 - Complexity: constant 0.03/0.21 * Chain [22] with precondition: [0>=B+1] 0.03/0.21 - Upper bound: 40 0.03/0.21 - Complexity: constant 0.03/0.21 * Chain [21] with precondition: [B>=1] 0.03/0.21 - Upper bound: 40 0.03/0.21 - Complexity: constant 0.03/0.21 0.03/0.21 ### Maximum cost of evaleasy1start(A,B,C): 80 0.03/0.21 Asymptotic class: constant 0.03/0.21 * Total analysis performed in 153 ms. 0.03/0.21 0.03/0.31 EOF