0.03/0.23 WORST_CASE(?,O(n^1)) 0.03/0.23 0.03/0.23 Preprocessing Cost Relations 0.03/0.23 ===================================== 0.03/0.23 0.03/0.23 #### Computed strongly connected components 0.03/0.23 0. recursive : [evalfbb1in/4,evalfbb2in/4,evalfbb3in/4,evalfbbin/4] 0.03/0.23 1. non_recursive : [evalfstop/3] 0.03/0.23 2. non_recursive : [evalfreturnin/3] 0.03/0.23 3. non_recursive : [exit_location/1] 0.03/0.23 4. non_recursive : [evalfbb3in_loop_cont/4] 0.03/0.23 5. non_recursive : [evalfentryin/3] 0.03/0.23 6. non_recursive : [evalfstart/3] 0.03/0.23 0.03/0.23 #### Obtained direct recursion through partial evaluation 0.03/0.23 0. SCC is partially evaluated into evalfbb3in/4 0.03/0.23 1. SCC is completely evaluated into other SCCs 0.03/0.23 2. SCC is completely evaluated into other SCCs 0.03/0.23 3. SCC is completely evaluated into other SCCs 0.03/0.23 4. SCC is partially evaluated into evalfbb3in_loop_cont/4 0.03/0.23 5. SCC is partially evaluated into evalfentryin/3 0.03/0.23 6. SCC is partially evaluated into evalfstart/3 0.03/0.23 0.03/0.23 Control-Flow Refinement of Cost Relations 0.03/0.23 ===================================== 0.03/0.23 0.03/0.23 ### Specialization of cost equations evalfbb3in/4 0.03/0.23 * CE 8 is refined into CE [11] 0.03/0.23 * CE 7 is refined into CE [12] 0.03/0.23 * CE 6 is refined into CE [13] 0.03/0.23 * CE 4 is refined into CE [14] 0.03/0.23 * CE 3 is refined into CE [15] 0.03/0.23 * CE 5 is refined into CE [16] 0.03/0.23 0.03/0.23 0.03/0.23 ### Cost equations --> "Loop" of evalfbb3in/4 0.03/0.23 * CEs [14] --> Loop 11 0.03/0.23 * CEs [15] --> Loop 12 0.03/0.23 * CEs [16] --> Loop 13 0.03/0.23 * CEs [11] --> Loop 14 0.03/0.23 * CEs [12] --> Loop 15 0.03/0.23 * CEs [13] --> Loop 16 0.03/0.23 0.03/0.23 ### Ranking functions of CR evalfbb3in(A,B,C,D) 0.03/0.23 * RF of phase [11]: [-B+255] 0.03/0.23 * RF of phase [12]: [-B+255] 0.03/0.23 * RF of phase [13]: [B] 0.03/0.23 0.03/0.23 #### Partial ranking functions of CR evalfbb3in(A,B,C,D) 0.03/0.23 * Partial RF of phase [11]: 0.03/0.23 - RF of loop [11:1]: 0.03/0.23 -B+255 0.03/0.23 * Partial RF of phase [12]: 0.03/0.23 - RF of loop [12:1]: 0.03/0.23 -B+255 0.03/0.23 * Partial RF of phase [13]: 0.03/0.23 - RF of loop [13:1]: 0.03/0.23 B 0.03/0.23 0.03/0.23 0.03/0.23 ### Specialization of cost equations evalfbb3in_loop_cont/4 0.03/0.23 * CE 10 is refined into CE [17] 0.03/0.23 * CE 9 is refined into CE [18] 0.03/0.23 0.03/0.23 0.03/0.23 ### Cost equations --> "Loop" of evalfbb3in_loop_cont/4 0.03/0.23 * CEs [17] --> Loop 17 0.03/0.23 * CEs [18] --> Loop 18 0.03/0.23 0.03/0.23 ### Ranking functions of CR evalfbb3in_loop_cont(A,B,C,D) 0.03/0.23 0.03/0.23 #### Partial ranking functions of CR evalfbb3in_loop_cont(A,B,C,D) 0.03/0.23 0.03/0.23 0.03/0.23 ### Specialization of cost equations evalfentryin/3 0.03/0.23 * CE 2 is refined into CE [19,20,21,22,23,24,25,26,27] 0.03/0.23 0.03/0.23 0.03/0.23 ### Cost equations --> "Loop" of evalfentryin/3 0.03/0.23 * CEs [24] --> Loop 19 0.03/0.23 * CEs [23] --> Loop 20 0.03/0.23 * CEs [22,27] --> Loop 21 0.03/0.23 * CEs [21,26] --> Loop 22 0.03/0.23 * CEs [19,20] --> Loop 23 0.03/0.23 * CEs [25] --> Loop 24 0.03/0.23 0.03/0.23 ### Ranking functions of CR evalfentryin(A,B,C) 0.03/0.23 0.03/0.23 #### Partial ranking functions of CR evalfentryin(A,B,C) 0.03/0.23 0.03/0.23 0.03/0.23 ### Specialization of cost equations evalfstart/3 0.03/0.23 * CE 1 is refined into CE [28,29,30,31,32,33] 0.03/0.23 0.03/0.23 0.03/0.23 ### Cost equations --> "Loop" of evalfstart/3 0.03/0.23 * CEs [33] --> Loop 25 0.03/0.23 * CEs [32] --> Loop 26 0.03/0.23 * CEs [31] --> Loop 27 0.03/0.23 * CEs [30] --> Loop 28 0.03/0.23 * CEs [29] --> Loop 29 0.03/0.23 * CEs [28] --> Loop 30 0.03/0.23 0.03/0.23 ### Ranking functions of CR evalfstart(A,B,C) 0.03/0.23 0.03/0.23 #### Partial ranking functions of CR evalfstart(A,B,C) 0.03/0.23 0.03/0.23 0.03/0.23 Computing Bounds 0.03/0.23 ===================================== 0.03/0.23 0.03/0.23 #### Cost of chains of evalfbb3in(A,B,C,D): 0.03/0.23 * Chain [[13],16]: 1*it(13)+0 0.03/0.23 Such that:it(13) =< B 0.03/0.23 0.03/0.23 with precondition: [A=0,C=2,D=0,254>=B,B>=1] 0.03/0.23 0.03/0.23 * Chain [[13],14]: 1*it(13)+0 0.03/0.23 Such that:it(13) =< B 0.03/0.23 0.03/0.23 with precondition: [A=0,C=3,254>=B,B>=1] 0.03/0.23 0.03/0.23 * Chain [[12],15]: 1*it(12)+0 0.03/0.23 Such that:it(12) =< -B+255 0.03/0.23 0.03/0.23 with precondition: [C=2,D=255,0>=A+1,254>=B,B>=1] 0.03/0.23 0.03/0.23 * Chain [[12],14]: 1*it(12)+0 0.03/0.23 Such that:it(12) =< -B+255 0.03/0.23 0.03/0.23 with precondition: [C=3,0>=A+1,254>=B,B>=1] 0.03/0.23 0.03/0.23 * Chain [[11],15]: 1*it(11)+0 0.03/0.23 Such that:it(11) =< -B+255 0.03/0.23 0.03/0.23 with precondition: [C=2,D=255,254>=B,A>=1,B>=1] 0.03/0.23 0.03/0.23 * Chain [[11],14]: 1*it(11)+0 0.03/0.23 Such that:it(11) =< -B+255 0.03/0.23 0.03/0.23 with precondition: [C=3,254>=B,A>=1,B>=1] 0.03/0.23 0.03/0.23 * Chain [16]: 0 0.03/0.23 with precondition: [C=2,B=D,0>=B] 0.03/0.23 0.03/0.23 * Chain [15]: 0 0.03/0.23 with precondition: [C=2,B=D,B>=255] 0.03/0.23 0.03/0.23 * Chain [14]: 0 0.03/0.23 with precondition: [C=3] 0.03/0.23 0.03/0.23 0.03/0.23 #### Cost of chains of evalfbb3in_loop_cont(A,B,C,D): 0.03/0.23 * Chain [18]: 0 0.03/0.23 with precondition: [A=2] 0.03/0.23 0.03/0.23 * Chain [17]: 0 0.03/0.23 with precondition: [A=3] 0.03/0.23 0.03/0.23 0.03/0.23 #### Cost of chains of evalfentryin(A,B,C): 0.03/0.23 * Chain [24]: 0 0.03/0.23 with precondition: [] 0.03/0.23 0.03/0.23 * Chain [23]: 2*s(1)+0 0.03/0.23 Such that:aux(1) =< A 0.03/0.23 s(1) =< aux(1) 0.03/0.23 0.03/0.23 with precondition: [B=0,254>=A,A>=1] 0.03/0.23 0.03/0.23 * Chain [22]: 2*s(3)+0 0.03/0.23 Such that:aux(2) =< -A+255 0.03/0.23 s(3) =< aux(2) 0.03/0.23 0.03/0.23 with precondition: [254>=A,0>=B+1,A>=1] 0.03/0.23 0.03/0.23 * Chain [21]: 2*s(5)+0 0.03/0.23 Such that:aux(3) =< -A+255 0.03/0.23 s(5) =< aux(3) 0.03/0.23 0.03/0.23 with precondition: [254>=A,A>=1,B>=1] 0.03/0.23 0.03/0.23 * Chain [20]: 0 0.03/0.23 with precondition: [0>=A] 0.03/0.23 0.03/0.23 * Chain [19]: 0 0.03/0.23 with precondition: [A>=255] 0.03/0.23 0.03/0.23 0.03/0.23 #### Cost of chains of evalfstart(A,B,C): 0.03/0.23 * Chain [30]: 0 0.03/0.23 with precondition: [] 0.03/0.23 0.03/0.23 * Chain [29]: 2*s(8)+0 0.03/0.23 Such that:s(7) =< A 0.03/0.23 s(8) =< s(7) 0.03/0.23 0.03/0.23 with precondition: [B=0,254>=A,A>=1] 0.03/0.23 0.03/0.23 * Chain [28]: 2*s(10)+0 0.03/0.23 Such that:s(9) =< -A+255 0.03/0.23 s(10) =< s(9) 0.03/0.23 0.03/0.23 with precondition: [254>=A,0>=B+1,A>=1] 0.03/0.23 0.03/0.23 * Chain [27]: 2*s(12)+0 0.03/0.23 Such that:s(11) =< -A+255 0.03/0.23 s(12) =< s(11) 0.03/0.23 0.03/0.23 with precondition: [254>=A,A>=1,B>=1] 0.03/0.23 0.03/0.23 * Chain [26]: 0 0.03/0.23 with precondition: [0>=A] 0.03/0.23 0.03/0.23 * Chain [25]: 0 0.03/0.23 with precondition: [A>=255] 0.03/0.23 0.03/0.23 0.03/0.23 Closed-form bounds of evalfstart(A,B,C): 0.03/0.23 ------------------------------------- 0.03/0.23 * Chain [30] with precondition: [] 0.03/0.23 - Upper bound: 0 0.03/0.23 - Complexity: constant 0.03/0.23 * Chain [29] with precondition: [B=0,254>=A,A>=1] 0.03/0.23 - Upper bound: 2*A 0.03/0.23 - Complexity: n 0.03/0.23 * Chain [28] with precondition: [254>=A,0>=B+1,A>=1] 0.03/0.23 - Upper bound: -2*A+510 0.03/0.23 - Complexity: n 0.03/0.23 * Chain [27] with precondition: [254>=A,A>=1,B>=1] 0.03/0.23 - Upper bound: -2*A+510 0.03/0.23 - Complexity: n 0.03/0.23 * Chain [26] with precondition: [0>=A] 0.03/0.23 - Upper bound: 0 0.03/0.23 - Complexity: constant 0.03/0.23 * Chain [25] with precondition: [A>=255] 0.03/0.23 - Upper bound: 0 0.03/0.23 - Complexity: constant 0.03/0.23 0.03/0.23 ### Maximum cost of evalfstart(A,B,C): max([nat(A)*2,nat(-A+255)*2]) 0.03/0.23 Asymptotic class: n 0.03/0.23 * Total analysis performed in 170 ms. 0.03/0.23 0.03/0.33 EOF