0.03/0.19 WORST_CASE(?,O(n^1)) 0.03/0.19 0.03/0.19 Preprocessing Cost Relations 0.03/0.19 ===================================== 0.03/0.19 0.03/0.19 #### Computed strongly connected components 0.03/0.19 0. recursive : [eval2/3] 0.03/0.19 1. recursive : [eval3/3] 0.03/0.19 2. recursive : [eval1/3,eval2_loop_cont/4,eval3_loop_cont/4] 0.03/0.19 3. non_recursive : [exit_location/1] 0.03/0.19 4. non_recursive : [eval1_loop_cont/2] 0.03/0.19 5. non_recursive : [start/3] 0.03/0.19 0.03/0.19 #### Obtained direct recursion through partial evaluation 0.03/0.19 0. SCC is partially evaluated into eval2/3 0.03/0.19 1. SCC is partially evaluated into eval3/3 0.03/0.19 2. SCC is partially evaluated into eval1/3 0.03/0.19 3. SCC is completely evaluated into other SCCs 0.03/0.19 4. SCC is completely evaluated into other SCCs 0.03/0.19 5. SCC is partially evaluated into start/3 0.03/0.19 0.03/0.19 Control-Flow Refinement of Cost Relations 0.03/0.19 ===================================== 0.03/0.19 0.03/0.19 ### Specialization of cost equations eval2/3 0.03/0.19 * CE 9 is refined into CE [13] 0.03/0.19 * CE 8 is refined into CE [14] 0.03/0.19 * CE 7 is refined into CE [15] 0.03/0.19 0.03/0.19 0.03/0.19 ### Cost equations --> "Loop" of eval2/3 0.03/0.19 * CEs [15] --> Loop 13 0.03/0.19 * CEs [13] --> Loop 14 0.03/0.19 * CEs [14] --> Loop 15 0.03/0.19 0.03/0.19 ### Ranking functions of CR eval2(A,C,D) 0.03/0.19 * RF of phase [13]: [A] 0.03/0.19 0.03/0.19 #### Partial ranking functions of CR eval2(A,C,D) 0.03/0.19 * Partial RF of phase [13]: 0.03/0.19 - RF of loop [13:1]: 0.03/0.19 A 0.03/0.19 0.03/0.19 0.03/0.19 ### Specialization of cost equations eval3/3 0.03/0.19 * CE 12 is refined into CE [16] 0.03/0.19 * CE 11 is refined into CE [17] 0.03/0.19 * CE 10 is refined into CE [18] 0.03/0.19 0.03/0.19 0.03/0.19 ### Cost equations --> "Loop" of eval3/3 0.03/0.19 * CEs [18] --> Loop 16 0.03/0.19 * CEs [16] --> Loop 17 0.03/0.19 * CEs [17] --> Loop 18 0.03/0.19 0.03/0.19 ### Ranking functions of CR eval3(B,C,D) 0.03/0.19 * RF of phase [16]: [B] 0.03/0.19 0.03/0.19 #### Partial ranking functions of CR eval3(B,C,D) 0.03/0.19 * Partial RF of phase [16]: 0.03/0.19 - RF of loop [16:1]: 0.03/0.19 B 0.03/0.19 0.03/0.19 0.03/0.19 ### Specialization of cost equations eval1/3 0.03/0.19 * CE 2 is refined into CE [19,20] 0.03/0.19 * CE 4 is refined into CE [21,22] 0.03/0.19 * CE 6 is refined into CE [23] 0.03/0.19 * CE 3 is refined into CE [24] 0.03/0.19 * CE 5 is refined into CE [25] 0.03/0.19 0.03/0.19 0.03/0.19 ### Cost equations --> "Loop" of eval1/3 0.03/0.19 * CEs [25] --> Loop 19 0.03/0.19 * CEs [24] --> Loop 20 0.03/0.19 * CEs [19,20] --> Loop 21 0.03/0.19 * CEs [21,22] --> Loop 22 0.03/0.19 * CEs [23] --> Loop 23 0.03/0.19 0.03/0.19 ### Ranking functions of CR eval1(A,B,C) 0.03/0.19 0.03/0.19 #### Partial ranking functions of CR eval1(A,B,C) 0.03/0.19 0.03/0.19 0.03/0.19 ### Specialization of cost equations start/3 0.03/0.19 * CE 1 is refined into CE [26,27,28] 0.03/0.19 0.03/0.19 0.03/0.19 ### Cost equations --> "Loop" of start/3 0.03/0.19 * CEs [28] --> Loop 24 0.03/0.19 * CEs [27] --> Loop 25 0.03/0.19 * CEs [26] --> Loop 26 0.03/0.19 0.03/0.19 ### Ranking functions of CR start(A,B,C) 0.03/0.19 0.03/0.19 #### Partial ranking functions of CR start(A,B,C) 0.03/0.19 0.03/0.19 0.03/0.19 Computing Bounds 0.03/0.19 ===================================== 0.03/0.19 0.03/0.19 #### Cost of chains of eval2(A,C,D): 0.03/0.19 * Chain [[13],15]: 1*it(13)+0 0.03/0.19 Such that:it(13) =< A 0.03/0.19 0.03/0.19 with precondition: [C=2,D=0,A>=1] 0.03/0.19 0.03/0.19 * Chain [[13],14]: 1*it(13)+0 0.03/0.19 Such that:it(13) =< A 0.03/0.19 0.03/0.19 with precondition: [C=3,A>=1] 0.03/0.19 0.03/0.19 * Chain [14]: 0 0.03/0.19 with precondition: [C=3] 0.03/0.19 0.03/0.19 0.03/0.19 #### Cost of chains of eval3(B,C,D): 0.03/0.19 * Chain [[16],18]: 1*it(16)+0 0.03/0.19 Such that:it(16) =< B 0.03/0.19 0.03/0.19 with precondition: [C=2,D=0,B>=1] 0.03/0.19 0.03/0.19 * Chain [[16],17]: 1*it(16)+0 0.03/0.19 Such that:it(16) =< B 0.03/0.19 0.03/0.19 with precondition: [C=3,B>=1] 0.03/0.19 0.03/0.19 * Chain [17]: 0 0.03/0.19 with precondition: [C=3,B>=0] 0.03/0.19 0.03/0.19 0.03/0.19 #### Cost of chains of eval1(A,B,C): 0.03/0.19 * Chain [23]: 0 0.03/0.19 with precondition: [C=3] 0.03/0.19 0.03/0.19 * Chain [22]: 1*s(1)+0 0.03/0.19 Such that:s(1) =< B 0.03/0.19 0.03/0.19 with precondition: [C=3,A>=1,B>=A] 0.03/0.19 0.03/0.19 * Chain [21]: 1*s(2)+0 0.03/0.19 Such that:s(2) =< A 0.03/0.19 0.03/0.19 with precondition: [C=3,B>=1,A>=B+1] 0.03/0.19 0.03/0.19 * Chain [20,23]: 1*s(3)+1 0.03/0.19 Such that:s(3) =< A 0.03/0.19 0.03/0.19 with precondition: [C=3,B>=1,A>=B+1] 0.03/0.19 0.03/0.19 * Chain [19,23]: 1*s(4)+1 0.03/0.19 Such that:s(4) =< B 0.03/0.19 0.03/0.19 with precondition: [C=3,A>=1,B>=A] 0.03/0.19 0.03/0.19 0.03/0.19 #### Cost of chains of start(A,B,C): 0.03/0.19 * Chain [26]: 0 0.03/0.19 with precondition: [] 0.03/0.19 0.03/0.19 * Chain [25]: 2*s(10)+1 0.03/0.19 Such that:s(9) =< B 0.03/0.19 s(10) =< s(9) 0.03/0.19 0.03/0.19 with precondition: [A>=1,B>=A] 0.03/0.19 0.03/0.19 * Chain [24]: 2*s(12)+1 0.03/0.19 Such that:s(11) =< A 0.03/0.19 s(12) =< s(11) 0.03/0.19 0.03/0.19 with precondition: [B>=1,A>=B+1] 0.03/0.19 0.03/0.19 0.03/0.19 Closed-form bounds of start(A,B,C): 0.03/0.19 ------------------------------------- 0.03/0.19 * Chain [26] with precondition: [] 0.03/0.19 - Upper bound: 0 0.03/0.19 - Complexity: constant 0.03/0.19 * Chain [25] with precondition: [A>=1,B>=A] 0.03/0.19 - Upper bound: 2*B+1 0.03/0.19 - Complexity: n 0.03/0.19 * Chain [24] with precondition: [B>=1,A>=B+1] 0.03/0.19 - Upper bound: 2*A+1 0.03/0.19 - Complexity: n 0.03/0.19 0.03/0.19 ### Maximum cost of start(A,B,C): max([nat(A)*2+1,nat(B)*2+1]) 0.03/0.19 Asymptotic class: n 0.03/0.19 * Total analysis performed in 132 ms. 0.03/0.19 0.03/0.29 EOF