0.03/0.22 WORST_CASE(?,O(n^1)) 0.03/0.22 0.03/0.22 Preprocessing Cost Relations 0.03/0.22 ===================================== 0.03/0.22 0.03/0.22 #### Computed strongly connected components 0.03/0.22 0. recursive : [evalwisebb3in/5,evalwisebb4in/5,evalwisebb5in/5,evalwisebb6in/5] 0.03/0.22 1. non_recursive : [evalwisestop/3] 0.03/0.22 2. non_recursive : [evalwisereturnin/3] 0.03/0.22 3. non_recursive : [exit_location/1] 0.03/0.22 4. non_recursive : [evalwisebb6in_loop_cont/4] 0.03/0.22 5. non_recursive : [evalwiseentryin/3] 0.03/0.22 6. non_recursive : [evalwisestart/3] 0.03/0.22 0.03/0.22 #### Obtained direct recursion through partial evaluation 0.03/0.22 0. SCC is partially evaluated into evalwisebb6in/5 0.03/0.22 1. SCC is completely evaluated into other SCCs 0.03/0.22 2. SCC is completely evaluated into other SCCs 0.03/0.22 3. SCC is completely evaluated into other SCCs 0.03/0.22 4. SCC is partially evaluated into evalwisebb6in_loop_cont/4 0.03/0.22 5. SCC is partially evaluated into evalwiseentryin/3 0.03/0.22 6. SCC is partially evaluated into evalwisestart/3 0.03/0.22 0.03/0.22 Control-Flow Refinement of Cost Relations 0.03/0.22 ===================================== 0.03/0.22 0.03/0.22 ### Specialization of cost equations evalwisebb6in/5 0.03/0.22 * CE 8 is refined into CE [11] 0.03/0.22 * CE 7 is refined into CE [12] 0.03/0.22 * CE 5 is refined into CE [13] 0.03/0.22 * CE 6 is refined into CE [14] 0.03/0.22 0.03/0.22 0.03/0.22 ### Cost equations --> "Loop" of evalwisebb6in/5 0.03/0.22 * CEs [13] --> Loop 11 0.03/0.22 * CEs [14] --> Loop 12 0.03/0.22 * CEs [11] --> Loop 13 0.03/0.22 * CEs [12] --> Loop 14 0.03/0.22 0.03/0.22 ### Ranking functions of CR evalwisebb6in(A,B,C,D,E) 0.03/0.22 * RF of phase [11]: [A-B-2] 0.03/0.22 * RF of phase [12]: [-A+B-2] 0.03/0.22 0.03/0.22 #### Partial ranking functions of CR evalwisebb6in(A,B,C,D,E) 0.03/0.22 * Partial RF of phase [11]: 0.03/0.22 - RF of loop [11:1]: 0.03/0.22 A-B-2 0.03/0.22 * Partial RF of phase [12]: 0.03/0.22 - RF of loop [12:1]: 0.03/0.22 -A+B-2 0.03/0.22 0.03/0.22 0.03/0.22 ### Specialization of cost equations evalwisebb6in_loop_cont/4 0.03/0.22 * CE 10 is refined into CE [15] 0.03/0.22 * CE 9 is refined into CE [16] 0.03/0.22 0.03/0.22 0.03/0.22 ### Cost equations --> "Loop" of evalwisebb6in_loop_cont/4 0.03/0.22 * CEs [15] --> Loop 15 0.03/0.22 * CEs [16] --> Loop 16 0.03/0.22 0.03/0.22 ### Ranking functions of CR evalwisebb6in_loop_cont(A,B,C,D) 0.03/0.22 0.03/0.22 #### Partial ranking functions of CR evalwisebb6in_loop_cont(A,B,C,D) 0.03/0.22 0.03/0.22 0.03/0.22 ### Specialization of cost equations evalwiseentryin/3 0.03/0.22 * CE 4 is refined into CE [17,18,19,20,21,22] 0.03/0.22 * CE 3 is refined into CE [23] 0.03/0.22 * CE 2 is refined into CE [24] 0.03/0.22 0.03/0.22 0.03/0.22 ### Cost equations --> "Loop" of evalwiseentryin/3 0.03/0.22 * CEs [19,21] --> Loop 17 0.03/0.22 * CEs [17,22] --> Loop 18 0.03/0.22 * CEs [18] --> Loop 19 0.03/0.22 * CEs [20] --> Loop 20 0.03/0.22 * CEs [23] --> Loop 21 0.03/0.22 * CEs [24] --> Loop 22 0.03/0.22 0.03/0.22 ### Ranking functions of CR evalwiseentryin(A,B,C) 0.03/0.22 0.03/0.22 #### Partial ranking functions of CR evalwiseentryin(A,B,C) 0.03/0.22 0.03/0.22 0.03/0.22 ### Specialization of cost equations evalwisestart/3 0.03/0.22 * CE 1 is refined into CE [25,26,27,28,29,30] 0.03/0.22 0.03/0.22 0.03/0.22 ### Cost equations --> "Loop" of evalwisestart/3 0.03/0.22 * CEs [30] --> Loop 23 0.03/0.22 * CEs [29] --> Loop 24 0.03/0.22 * CEs [28] --> Loop 25 0.03/0.22 * CEs [27] --> Loop 26 0.03/0.22 * CEs [26] --> Loop 27 0.03/0.22 * CEs [25] --> Loop 28 0.03/0.22 0.03/0.22 ### Ranking functions of CR evalwisestart(A,B,C) 0.03/0.22 0.03/0.22 #### Partial ranking functions of CR evalwisestart(A,B,C) 0.03/0.22 0.03/0.22 0.03/0.22 Computing Bounds 0.03/0.22 ===================================== 0.03/0.22 0.03/0.22 #### Cost of chains of evalwisebb6in(A,B,C,D,E): 0.03/0.22 * Chain [[12],14]: 1*it(12)+0 0.03/0.22 Such that:it(12) =< -A+E 0.03/0.22 0.03/0.22 with precondition: [C=2,B=D+2,B=E,A>=0,B>=A+3] 0.03/0.22 0.03/0.22 * Chain [[12],13]: 1*it(12)+0 0.03/0.22 Such that:it(12) =< -A+B 0.03/0.22 0.03/0.22 with precondition: [C=3,A>=0,B>=A+3] 0.03/0.22 0.03/0.22 * Chain [[11],14]: 1*it(11)+0 0.03/0.22 Such that:it(11) =< -B+E 0.03/0.22 0.03/0.22 with precondition: [C=2,A=D,A=E+2,B>=0,A>=B+3] 0.03/0.22 0.03/0.22 * Chain [[11],13]: 1*it(11)+0 0.03/0.22 Such that:it(11) =< A-B 0.03/0.22 0.03/0.22 with precondition: [C=3,B>=0,A>=B+3] 0.03/0.22 0.03/0.22 * Chain [14]: 0 0.03/0.22 with precondition: [C=2,A=D,B=E,A>=0,B>=0,B+2>=A,A+2>=B] 0.03/0.22 0.03/0.22 * Chain [13]: 0 0.03/0.22 with precondition: [C=3,A>=0,B>=0] 0.03/0.22 0.03/0.22 0.03/0.22 #### Cost of chains of evalwisebb6in_loop_cont(A,B,C,D): 0.03/0.22 * Chain [16]: 0 0.03/0.22 with precondition: [A=2] 0.03/0.22 0.03/0.22 * Chain [15]: 0 0.03/0.22 with precondition: [A=3] 0.03/0.22 0.03/0.22 0.03/0.22 #### Cost of chains of evalwiseentryin(A,B,C): 0.03/0.22 * Chain [22]: 0 0.03/0.22 with precondition: [0>=A+1] 0.03/0.22 0.03/0.22 * Chain [21]: 0 0.03/0.22 with precondition: [0>=B+1] 0.03/0.22 0.03/0.22 * Chain [20]: 0 0.03/0.22 with precondition: [A>=0,B>=0] 0.03/0.22 0.03/0.22 * Chain [19]: 0 0.03/0.22 with precondition: [A>=0,B>=0,B+2>=A,A+2>=B] 0.03/0.22 0.03/0.22 * Chain [18]: 2*s(1)+0 0.03/0.22 Such that:aux(1) =< -A+B 0.03/0.22 s(1) =< aux(1) 0.03/0.22 0.03/0.22 with precondition: [A>=0,B>=A+3] 0.03/0.22 0.03/0.22 * Chain [17]: 2*s(3)+0 0.03/0.22 Such that:aux(2) =< A-B 0.03/0.22 s(3) =< aux(2) 0.03/0.22 0.03/0.22 with precondition: [B>=0,A>=B+3] 0.03/0.22 0.03/0.22 0.03/0.22 #### Cost of chains of evalwisestart(A,B,C): 0.03/0.22 * Chain [28]: 0 0.03/0.22 with precondition: [0>=A+1] 0.03/0.22 0.03/0.22 * Chain [27]: 0 0.03/0.22 with precondition: [0>=B+1] 0.03/0.22 0.03/0.22 * Chain [26]: 0 0.03/0.22 with precondition: [A>=0,B>=0] 0.03/0.22 0.03/0.22 * Chain [25]: 0 0.03/0.22 with precondition: [A>=0,B>=0,B+2>=A,A+2>=B] 0.03/0.22 0.03/0.22 * Chain [24]: 2*s(6)+0 0.03/0.22 Such that:s(5) =< -A+B 0.03/0.22 s(6) =< s(5) 0.03/0.22 0.03/0.22 with precondition: [A>=0,B>=A+3] 0.03/0.22 0.03/0.22 * Chain [23]: 2*s(8)+0 0.03/0.22 Such that:s(7) =< A-B 0.03/0.22 s(8) =< s(7) 0.03/0.22 0.03/0.22 with precondition: [B>=0,A>=B+3] 0.03/0.22 0.03/0.22 0.03/0.22 Closed-form bounds of evalwisestart(A,B,C): 0.03/0.22 ------------------------------------- 0.03/0.22 * Chain [28] with precondition: [0>=A+1] 0.03/0.22 - Upper bound: 0 0.03/0.22 - Complexity: constant 0.03/0.22 * Chain [27] with precondition: [0>=B+1] 0.03/0.22 - Upper bound: 0 0.03/0.22 - Complexity: constant 0.03/0.22 * Chain [26] with precondition: [A>=0,B>=0] 0.03/0.22 - Upper bound: 0 0.03/0.22 - Complexity: constant 0.03/0.22 * Chain [25] with precondition: [A>=0,B>=0,B+2>=A,A+2>=B] 0.03/0.22 - Upper bound: 0 0.03/0.22 - Complexity: constant 0.03/0.22 * Chain [24] with precondition: [A>=0,B>=A+3] 0.03/0.22 - Upper bound: -2*A+2*B 0.03/0.22 - Complexity: n 0.03/0.22 * Chain [23] with precondition: [B>=0,A>=B+3] 0.03/0.22 - Upper bound: 2*A-2*B 0.03/0.22 - Complexity: n 0.03/0.22 0.03/0.22 ### Maximum cost of evalwisestart(A,B,C): max([nat(-A+B)*2,nat(A-B)*2]) 0.03/0.22 Asymptotic class: n 0.03/0.22 * Total analysis performed in 158 ms. 0.03/0.22 0.03/0.32 EOF