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 : [evalEx6bb1in/6,evalEx6bb2in/6,evalEx6bb3in/6,evalEx6bbin/6] 0.03/0.19 1. non_recursive : [evalEx6stop/4] 0.03/0.19 2. non_recursive : [evalEx6returnin/4] 0.03/0.19 3. non_recursive : [exit_location/1] 0.03/0.19 4. non_recursive : [evalEx6bb3in_loop_cont/5] 0.03/0.19 5. non_recursive : [evalEx6entryin/4] 0.03/0.19 6. non_recursive : [evalEx6start/4] 0.03/0.19 0.03/0.19 #### Obtained direct recursion through partial evaluation 0.03/0.19 0. SCC is partially evaluated into evalEx6bb3in/6 0.03/0.19 1. SCC is completely evaluated into other SCCs 0.03/0.19 2. SCC is completely evaluated into other SCCs 0.03/0.19 3. SCC is completely evaluated into other SCCs 0.03/0.19 4. SCC is partially evaluated into evalEx6bb3in_loop_cont/5 0.03/0.19 5. SCC is partially evaluated into evalEx6entryin/4 0.03/0.19 6. SCC is partially evaluated into evalEx6start/4 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 evalEx6bb3in/6 0.03/0.19 * CE 6 is refined into CE [9] 0.03/0.19 * CE 5 is refined into CE [10] 0.03/0.19 * CE 3 is refined into CE [11] 0.03/0.19 * CE 4 is refined into CE [12] 0.03/0.19 0.03/0.19 0.03/0.19 ### Cost equations --> "Loop" of evalEx6bb3in/6 0.03/0.19 * CEs [11] --> Loop 9 0.03/0.19 * CEs [12] --> Loop 10 0.03/0.19 * CEs [9] --> Loop 11 0.03/0.19 * CEs [10] --> Loop 12 0.03/0.19 0.03/0.19 ### Ranking functions of CR evalEx6bb3in(A,B,C,D,E,F) 0.03/0.19 0.03/0.19 #### Partial ranking functions of CR evalEx6bb3in(A,B,C,D,E,F) 0.03/0.19 * Partial RF of phase [9,10]: 0.03/0.19 - RF of loop [9:1]: 0.03/0.19 A-B depends on loops [10:1] 0.03/0.19 -B+C 0.03/0.19 - RF of loop [10:1]: 0.03/0.19 -A+B+1 depends on loops [9:1] 0.03/0.19 -A+C 0.03/0.19 0.03/0.19 0.03/0.19 ### Specialization of cost equations evalEx6bb3in_loop_cont/5 0.03/0.19 * CE 8 is refined into CE [13] 0.03/0.19 * CE 7 is refined into CE [14] 0.03/0.19 0.03/0.19 0.03/0.19 ### Cost equations --> "Loop" of evalEx6bb3in_loop_cont/5 0.03/0.19 * CEs [13] --> Loop 13 0.03/0.19 * CEs [14] --> Loop 14 0.03/0.19 0.03/0.19 ### Ranking functions of CR evalEx6bb3in_loop_cont(A,B,C,D,E) 0.03/0.19 0.03/0.19 #### Partial ranking functions of CR evalEx6bb3in_loop_cont(A,B,C,D,E) 0.03/0.19 0.03/0.19 0.03/0.19 ### Specialization of cost equations evalEx6entryin/4 0.03/0.19 * CE 2 is refined into CE [15,16,17,18] 0.03/0.19 0.03/0.19 0.03/0.19 ### Cost equations --> "Loop" of evalEx6entryin/4 0.03/0.19 * CEs [15] --> Loop 15 0.03/0.19 * CEs [16,18] --> Loop 16 0.03/0.19 * CEs [17] --> Loop 17 0.03/0.19 0.03/0.19 ### Ranking functions of CR evalEx6entryin(A,B,C,D) 0.03/0.19 0.03/0.19 #### Partial ranking functions of CR evalEx6entryin(A,B,C,D) 0.03/0.19 0.03/0.19 0.03/0.19 ### Specialization of cost equations evalEx6start/4 0.03/0.19 * CE 1 is refined into CE [19,20,21] 0.03/0.19 0.03/0.19 0.03/0.19 ### Cost equations --> "Loop" of evalEx6start/4 0.03/0.19 * CEs [21] --> Loop 18 0.03/0.19 * CEs [20] --> Loop 19 0.03/0.19 * CEs [19] --> Loop 20 0.03/0.19 0.03/0.19 ### Ranking functions of CR evalEx6start(A,B,C,D) 0.03/0.19 0.03/0.19 #### Partial ranking functions of CR evalEx6start(A,B,C,D) 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 evalEx6bb3in(A,B,C,D,E,F): 0.03/0.19 * Chain [[9,10],12]: 1*it(9)+1*it(10)+0 0.03/0.19 Such that:it(10) =< -A+C 0.03/0.19 it(10) =< -A+E 0.03/0.19 it(9) =< -B+F 0.03/0.19 0.03/0.19 with precondition: [D=2,C=F,E>=A,C>=B+1,E>=C] 0.03/0.19 0.03/0.19 * Chain [[9,10],11]: 1*it(9)+1*it(10)+0 0.03/0.19 Such that:it(10) =< -A+C 0.03/0.19 it(9) =< -B+C 0.03/0.19 0.03/0.19 with precondition: [D=3,C>=B+1] 0.03/0.19 0.03/0.19 * Chain [12]: 0 0.03/0.19 with precondition: [D=2,E=A,B=F,B>=C] 0.03/0.19 0.03/0.19 * Chain [11]: 0 0.03/0.19 with precondition: [D=3] 0.03/0.19 0.03/0.19 0.03/0.19 #### Cost of chains of evalEx6bb3in_loop_cont(A,B,C,D,E): 0.03/0.19 * Chain [14]: 0 0.03/0.19 with precondition: [A=2] 0.03/0.19 0.03/0.19 * Chain [13]: 0 0.03/0.19 with precondition: [A=3] 0.03/0.19 0.03/0.19 0.03/0.19 #### Cost of chains of evalEx6entryin(A,B,C,D): 0.03/0.19 * Chain [17]: 0 0.03/0.19 with precondition: [] 0.03/0.19 0.03/0.19 * Chain [16]: 2*s(1)+2*s(2)+0 0.03/0.19 Such that:aux(5) =< -A+C 0.03/0.19 aux(6) =< -B+C 0.03/0.19 s(2) =< aux(5) 0.03/0.19 s(1) =< aux(6) 0.03/0.19 0.03/0.19 with precondition: [C>=A+1] 0.03/0.19 0.03/0.19 * Chain [15]: 0 0.03/0.19 with precondition: [A>=C] 0.03/0.19 0.03/0.19 0.03/0.19 #### Cost of chains of evalEx6start(A,B,C,D): 0.03/0.19 * Chain [20]: 0 0.03/0.19 with precondition: [] 0.03/0.19 0.03/0.19 * Chain [19]: 2*s(7)+2*s(8)+0 0.03/0.19 Such that:s(5) =< -A+C 0.03/0.19 s(6) =< -B+C 0.03/0.19 s(7) =< s(5) 0.03/0.19 s(8) =< s(6) 0.03/0.19 0.03/0.19 with precondition: [C>=A+1] 0.03/0.19 0.03/0.19 * Chain [18]: 0 0.03/0.19 with precondition: [A>=C] 0.03/0.19 0.03/0.19 0.03/0.19 Closed-form bounds of evalEx6start(A,B,C,D): 0.03/0.19 ------------------------------------- 0.03/0.19 * Chain [20] with precondition: [] 0.03/0.19 - Upper bound: 0 0.03/0.19 - Complexity: constant 0.03/0.19 * Chain [19] with precondition: [C>=A+1] 0.03/0.19 - Upper bound: -2*A+2*C+nat(-B+C)*2 0.03/0.19 - Complexity: n 0.03/0.19 * Chain [18] with precondition: [A>=C] 0.03/0.19 - Upper bound: 0 0.03/0.19 - Complexity: constant 0.03/0.19 0.03/0.19 ### Maximum cost of evalEx6start(A,B,C,D): nat(-B+C)*2+nat(-A+C)*2 0.03/0.19 Asymptotic class: n 0.03/0.19 * Total analysis performed in 129 ms. 0.03/0.19 0.03/0.29 EOF