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 : [evalSequentialSinglebb1in/4,evalSequentialSinglebb2in/4,evalSequentialSinglebbin/4] 0.03/0.23 1. recursive : [evalSequentialSinglebb4in/4,evalSequentialSinglebb5in/4] 0.03/0.23 2. non_recursive : [evalSequentialSinglestop/3] 0.03/0.23 3. non_recursive : [evalSequentialSinglereturnin/3] 0.03/0.23 4. non_recursive : [exit_location/1] 0.03/0.23 5. non_recursive : [evalSequentialSinglebb5in_loop_cont/4] 0.03/0.23 6. non_recursive : [evalSequentialSinglebb1in_loop_cont/4] 0.03/0.23 7. non_recursive : [evalSequentialSingleentryin/3] 0.03/0.23 8. non_recursive : [evalSequentialSinglestart/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 evalSequentialSinglebb1in/4 0.03/0.23 1. SCC is partially evaluated into evalSequentialSinglebb5in/4 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 completely evaluated into other SCCs 0.03/0.23 5. SCC is partially evaluated into evalSequentialSinglebb5in_loop_cont/4 0.03/0.23 6. SCC is partially evaluated into evalSequentialSinglebb1in_loop_cont/4 0.03/0.23 7. SCC is partially evaluated into evalSequentialSingleentryin/3 0.03/0.23 8. SCC is partially evaluated into evalSequentialSinglestart/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 evalSequentialSinglebb1in/4 0.03/0.23 * CE 5 is refined into CE [14] 0.03/0.23 * CE 3 is refined into CE [15] 0.03/0.23 * CE 6 is refined into CE [16] 0.03/0.23 * CE 4 is refined into CE [17] 0.03/0.23 0.03/0.23 0.03/0.23 ### Cost equations --> "Loop" of evalSequentialSinglebb1in/4 0.03/0.23 * CEs [17] --> Loop 14 0.03/0.23 * CEs [14] --> Loop 15 0.03/0.23 * CEs [15] --> Loop 16 0.03/0.23 * CEs [16] --> Loop 17 0.03/0.23 0.03/0.23 ### Ranking functions of CR evalSequentialSinglebb1in(A,B,D,E) 0.03/0.23 * RF of phase [14]: [-A+B] 0.03/0.23 0.03/0.23 #### Partial ranking functions of CR evalSequentialSinglebb1in(A,B,D,E) 0.03/0.23 * Partial RF of phase [14]: 0.03/0.23 - RF of loop [14:1]: 0.03/0.23 -A+B 0.03/0.23 0.03/0.23 0.03/0.23 ### Specialization of cost equations evalSequentialSinglebb5in/4 0.03/0.23 * CE 11 is refined into CE [18] 0.03/0.23 * CE 10 is refined into CE [19] 0.03/0.23 * CE 9 is refined into CE [20] 0.03/0.23 0.03/0.23 0.03/0.23 ### Cost equations --> "Loop" of evalSequentialSinglebb5in/4 0.03/0.23 * CEs [20] --> Loop 18 0.03/0.23 * CEs [18] --> Loop 19 0.03/0.23 * CEs [19] --> Loop 20 0.03/0.23 0.03/0.23 ### Ranking functions of CR evalSequentialSinglebb5in(A,B,D,E) 0.03/0.23 * RF of phase [18]: [-A+B] 0.03/0.23 0.03/0.23 #### Partial ranking functions of CR evalSequentialSinglebb5in(A,B,D,E) 0.03/0.23 * Partial RF of phase [18]: 0.03/0.23 - RF of loop [18:1]: 0.03/0.23 -A+B 0.03/0.23 0.03/0.23 0.03/0.23 ### Specialization of cost equations evalSequentialSinglebb5in_loop_cont/4 0.03/0.23 * CE 13 is refined into CE [21] 0.03/0.23 * CE 12 is refined into CE [22] 0.03/0.23 0.03/0.23 0.03/0.23 ### Cost equations --> "Loop" of evalSequentialSinglebb5in_loop_cont/4 0.03/0.23 * CEs [21] --> Loop 21 0.03/0.23 * CEs [22] --> Loop 22 0.03/0.23 0.03/0.23 ### Ranking functions of CR evalSequentialSinglebb5in_loop_cont(A,B,C,D) 0.03/0.23 0.03/0.23 #### Partial ranking functions of CR evalSequentialSinglebb5in_loop_cont(A,B,C,D) 0.03/0.23 0.03/0.23 0.03/0.23 ### Specialization of cost equations evalSequentialSinglebb1in_loop_cont/4 0.03/0.23 * CE 8 is refined into CE [23,24,25,26] 0.03/0.23 * CE 7 is refined into CE [27] 0.03/0.23 0.03/0.23 0.03/0.23 ### Cost equations --> "Loop" of evalSequentialSinglebb1in_loop_cont/4 0.03/0.23 * CEs [23] --> Loop 23 0.03/0.23 * CEs [24,26] --> Loop 24 0.03/0.23 * CEs [25] --> Loop 25 0.03/0.23 * CEs [27] --> Loop 26 0.03/0.23 0.03/0.23 ### Ranking functions of CR evalSequentialSinglebb1in_loop_cont(A,B,C,D) 0.03/0.23 0.03/0.23 #### Partial ranking functions of CR evalSequentialSinglebb1in_loop_cont(A,B,C,D) 0.03/0.23 0.03/0.23 0.03/0.23 ### Specialization of cost equations evalSequentialSingleentryin/3 0.03/0.23 * CE 2 is refined into CE [28,29,30,31,32,33,34,35,36,37] 0.03/0.23 0.03/0.23 0.03/0.23 ### Cost equations --> "Loop" of evalSequentialSingleentryin/3 0.03/0.23 * CEs [36,37] --> Loop 27 0.03/0.23 * CEs [29,30,31,34,35] --> Loop 28 0.03/0.23 * CEs [32,33] --> Loop 29 0.03/0.23 * CEs [28] --> Loop 30 0.03/0.23 0.03/0.23 ### Ranking functions of CR evalSequentialSingleentryin(A,B,D) 0.03/0.23 0.03/0.23 #### Partial ranking functions of CR evalSequentialSingleentryin(A,B,D) 0.03/0.23 0.03/0.23 0.03/0.23 ### Specialization of cost equations evalSequentialSinglestart/3 0.03/0.23 * CE 1 is refined into CE [38,39,40,41] 0.03/0.23 0.03/0.23 0.03/0.23 ### Cost equations --> "Loop" of evalSequentialSinglestart/3 0.03/0.23 * CEs [41] --> Loop 31 0.03/0.23 * CEs [40] --> Loop 32 0.03/0.23 * CEs [39] --> Loop 33 0.03/0.23 * CEs [38] --> Loop 34 0.03/0.23 0.03/0.23 ### Ranking functions of CR evalSequentialSinglestart(A,B,D) 0.03/0.23 0.03/0.23 #### Partial ranking functions of CR evalSequentialSinglestart(A,B,D) 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 evalSequentialSinglebb1in(A,B,D,E): 0.03/0.23 * Chain [[14],17]: 1*it(14)+0 0.03/0.23 Such that:it(14) =< -A+B 0.03/0.23 0.03/0.23 with precondition: [D=3,A>=0,B>=A+1] 0.03/0.23 0.03/0.23 * Chain [[14],16]: 1*it(14)+0 0.03/0.23 Such that:it(14) =< -A+E 0.03/0.23 0.03/0.23 with precondition: [D=4,A>=0,E>=A+1,B>=E+1] 0.03/0.23 0.03/0.23 * Chain [[14],15]: 1*it(14)+0 0.03/0.23 Such that:it(14) =< -A+E 0.03/0.23 0.03/0.23 with precondition: [D=4,B=E,A>=0,B>=A+1] 0.03/0.23 0.03/0.23 * Chain [17]: 0 0.03/0.23 with precondition: [D=3,A>=0] 0.03/0.23 0.03/0.23 * Chain [16]: 0 0.03/0.23 with precondition: [D=4,A=E,A>=0,B>=A+1] 0.03/0.23 0.03/0.23 * Chain [15]: 0 0.03/0.23 with precondition: [D=4,A=E,A>=0,A>=B] 0.03/0.23 0.03/0.23 0.03/0.23 #### Cost of chains of evalSequentialSinglebb5in(A,B,D,E): 0.03/0.23 * Chain [[18],20]: 1*it(18)+0 0.03/0.23 Such that:it(18) =< -A+E 0.03/0.23 0.03/0.23 with precondition: [D=2,B=E,B>=A+1] 0.03/0.23 0.03/0.23 * Chain [[18],19]: 1*it(18)+0 0.03/0.23 Such that:it(18) =< -A+B 0.03/0.23 0.03/0.23 with precondition: [D=3,B>=A+1] 0.03/0.23 0.03/0.23 * Chain [20]: 0 0.03/0.23 with precondition: [D=2,A=E,A>=B] 0.03/0.23 0.03/0.23 * Chain [19]: 0 0.03/0.23 with precondition: [D=3] 0.03/0.23 0.03/0.23 0.03/0.23 #### Cost of chains of evalSequentialSinglebb5in_loop_cont(A,B,C,D): 0.03/0.23 * Chain [22]: 0 0.03/0.23 with precondition: [A=2] 0.03/0.23 0.03/0.23 * Chain [21]: 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 evalSequentialSinglebb1in_loop_cont(A,B,C,D): 0.03/0.23 * Chain [26]: 0 0.03/0.23 with precondition: [A=3] 0.03/0.23 0.03/0.23 * Chain [25]: 0 0.03/0.23 with precondition: [A=4] 0.03/0.23 0.03/0.23 * Chain [24]: 2*s(1)+0 0.03/0.23 Such that:aux(1) =< -B+C 0.03/0.23 s(1) =< aux(1) 0.03/0.23 0.03/0.23 with precondition: [A=4,C>=B+1] 0.03/0.23 0.03/0.23 * Chain [23]: 0 0.03/0.23 with precondition: [A=4,B>=C] 0.03/0.23 0.03/0.23 0.03/0.23 #### Cost of chains of evalSequentialSingleentryin(A,B,D): 0.03/0.23 * Chain [30]: 0 0.03/0.23 with precondition: [] 0.03/0.23 0.03/0.23 * Chain [29]: 0 0.03/0.23 with precondition: [0>=B] 0.03/0.23 0.03/0.23 * Chain [28]: 5*s(3)+0 0.03/0.23 Such that:aux(2) =< B 0.03/0.23 s(3) =< aux(2) 0.03/0.23 0.03/0.23 with precondition: [B>=1] 0.03/0.23 0.03/0.23 * Chain [27]: 4*s(8)+0 0.03/0.23 Such that:aux(4) =< B 0.03/0.23 s(8) =< aux(4) 0.03/0.23 0.03/0.23 with precondition: [B>=2] 0.03/0.23 0.03/0.23 0.03/0.23 #### Cost of chains of evalSequentialSinglestart(A,B,D): 0.03/0.23 * Chain [34]: 0 0.03/0.23 with precondition: [] 0.03/0.23 0.03/0.23 * Chain [33]: 0 0.03/0.23 with precondition: [0>=B] 0.03/0.23 0.03/0.23 * Chain [32]: 5*s(13)+0 0.03/0.23 Such that:s(12) =< B 0.03/0.23 s(13) =< s(12) 0.03/0.23 0.03/0.23 with precondition: [B>=1] 0.03/0.23 0.03/0.23 * Chain [31]: 4*s(15)+0 0.03/0.23 Such that:s(14) =< B 0.03/0.23 s(15) =< s(14) 0.03/0.23 0.03/0.23 with precondition: [B>=2] 0.03/0.23 0.03/0.23 0.03/0.23 Closed-form bounds of evalSequentialSinglestart(A,B,D): 0.03/0.23 ------------------------------------- 0.03/0.23 * Chain [34] with precondition: [] 0.03/0.23 - Upper bound: 0 0.03/0.23 - Complexity: constant 0.03/0.23 * Chain [33] with precondition: [0>=B] 0.03/0.23 - Upper bound: 0 0.03/0.23 - Complexity: constant 0.03/0.23 * Chain [32] with precondition: [B>=1] 0.03/0.23 - Upper bound: 5*B 0.03/0.23 - Complexity: n 0.03/0.23 * Chain [31] with precondition: [B>=2] 0.03/0.23 - Upper bound: 4*B 0.03/0.23 - Complexity: n 0.03/0.23 0.03/0.23 ### Maximum cost of evalSequentialSinglestart(A,B,D): nat(B)*5 0.03/0.23 Asymptotic class: n 0.03/0.23 * Total analysis performed in 165 ms. 0.03/0.23 0.03/0.33 EOF