0.03/0.31 WORST_CASE(?,O(n^1)) 0.03/0.31 0.03/0.31 Preprocessing Cost Relations 0.03/0.31 ===================================== 0.03/0.31 0.03/0.31 #### Computed strongly connected components 0.03/0.31 0. recursive : [evalSimpleSingle2bb1in/7,evalSimpleSingle2bb2in/7,evalSimpleSingle2bb3in/7,evalSimpleSingle2bb4in/7,evalSimpleSingle2bbin/7] 0.03/0.31 1. non_recursive : [evalSimpleSingle2stop/5] 0.03/0.31 2. non_recursive : [evalSimpleSingle2returnin/5] 0.03/0.31 3. non_recursive : [exit_location/1] 0.03/0.31 4. non_recursive : [evalSimpleSingle2bb4in_loop_cont/6] 0.03/0.31 5. non_recursive : [evalSimpleSingle2entryin/5] 0.03/0.31 6. non_recursive : [evalSimpleSingle2start/5] 0.03/0.31 0.03/0.31 #### Obtained direct recursion through partial evaluation 0.03/0.31 0. SCC is partially evaluated into evalSimpleSingle2bb4in/7 0.03/0.31 1. SCC is completely evaluated into other SCCs 0.03/0.31 2. SCC is completely evaluated into other SCCs 0.03/0.31 3. SCC is completely evaluated into other SCCs 0.03/0.31 4. SCC is partially evaluated into evalSimpleSingle2bb4in_loop_cont/6 0.03/0.31 5. SCC is partially evaluated into evalSimpleSingle2entryin/5 0.03/0.31 6. SCC is partially evaluated into evalSimpleSingle2start/5 0.03/0.31 0.03/0.31 Control-Flow Refinement of Cost Relations 0.03/0.31 ===================================== 0.03/0.31 0.03/0.31 ### Specialization of cost equations evalSimpleSingle2bb4in/7 0.03/0.31 * CE 6 is refined into CE [9] 0.03/0.31 * CE 3 is refined into CE [10] 0.03/0.31 * CE 5 is refined into CE [11] 0.03/0.31 * CE 4 is refined into CE [12] 0.03/0.31 0.03/0.31 0.03/0.31 ### Cost equations --> "Loop" of evalSimpleSingle2bb4in/7 0.03/0.31 * CEs [12] --> Loop 9 0.03/0.31 * CEs [11] --> Loop 10 0.03/0.31 * CEs [9] --> Loop 11 0.03/0.31 * CEs [10] --> Loop 12 0.03/0.31 0.03/0.31 ### Ranking functions of CR evalSimpleSingle2bb4in(A,B,C,D,F,G,H) 0.03/0.31 * RF of phase [9]: [-A+D,-B+D] 0.03/0.31 * RF of phase [10]: [-A+C,-B+C] 0.03/0.31 0.03/0.31 #### Partial ranking functions of CR evalSimpleSingle2bb4in(A,B,C,D,F,G,H) 0.03/0.31 * Partial RF of phase [9]: 0.03/0.31 - RF of loop [9:1]: 0.03/0.31 -A+D 0.03/0.31 -B+D 0.03/0.31 * Partial RF of phase [10]: 0.03/0.31 - RF of loop [10:1]: 0.03/0.31 -A+C 0.03/0.31 -B+C 0.03/0.31 0.03/0.31 0.03/0.31 ### Specialization of cost equations evalSimpleSingle2bb4in_loop_cont/6 0.03/0.31 * CE 8 is refined into CE [13] 0.03/0.31 * CE 7 is refined into CE [14] 0.03/0.31 0.03/0.31 0.03/0.31 ### Cost equations --> "Loop" of evalSimpleSingle2bb4in_loop_cont/6 0.03/0.31 * CEs [13] --> Loop 13 0.03/0.31 * CEs [14] --> Loop 14 0.03/0.31 0.03/0.31 ### Ranking functions of CR evalSimpleSingle2bb4in_loop_cont(A,B,C,D,E,F) 0.03/0.31 0.03/0.31 #### Partial ranking functions of CR evalSimpleSingle2bb4in_loop_cont(A,B,C,D,E,F) 0.03/0.31 0.03/0.31 0.03/0.31 ### Specialization of cost equations evalSimpleSingle2entryin/5 0.03/0.31 * CE 2 is refined into CE [15,16,17,18,19,20,21,22] 0.03/0.31 0.03/0.31 0.03/0.31 ### Cost equations --> "Loop" of evalSimpleSingle2entryin/5 0.03/0.31 * CEs [16,21] --> Loop 15 0.03/0.31 * CEs [18,20] --> Loop 16 0.03/0.31 * CEs [17,22] --> Loop 17 0.03/0.31 * CEs [15,19] --> Loop 18 0.03/0.31 0.03/0.31 ### Ranking functions of CR evalSimpleSingle2entryin(A,B,C,D,F) 0.03/0.31 0.03/0.31 #### Partial ranking functions of CR evalSimpleSingle2entryin(A,B,C,D,F) 0.03/0.31 0.03/0.31 0.03/0.31 ### Specialization of cost equations evalSimpleSingle2start/5 0.03/0.31 * CE 1 is refined into CE [23,24,25,26] 0.03/0.31 0.03/0.31 0.03/0.31 ### Cost equations --> "Loop" of evalSimpleSingle2start/5 0.03/0.31 * CEs [26] --> Loop 19 0.03/0.31 * CEs [25] --> Loop 20 0.03/0.31 * CEs [24] --> Loop 21 0.03/0.31 * CEs [23] --> Loop 22 0.03/0.31 0.03/0.31 ### Ranking functions of CR evalSimpleSingle2start(A,B,C,D,F) 0.03/0.31 0.03/0.31 #### Partial ranking functions of CR evalSimpleSingle2start(A,B,C,D,F) 0.03/0.31 0.03/0.31 0.03/0.31 Computing Bounds 0.03/0.31 ===================================== 0.03/0.31 0.03/0.31 #### Cost of chains of evalSimpleSingle2bb4in(A,B,C,D,F,G,H): 0.03/0.31 * Chain [[10],[9],12]: 1*it(9)+1*it(10)+0 0.03/0.31 Such that:it(10) =< -A+C 0.03/0.31 it(9) =< -C+H 0.03/0.31 0.03/0.31 with precondition: [F=2,A=B,G=H,A>=0,C>=A+1,G>=C+1,D>=G] 0.03/0.31 0.03/0.31 * Chain [[10],[9],11]: 1*it(9)+1*it(10)+0 0.03/0.31 Such that:it(10) =< -A+C 0.03/0.31 it(9) =< -C+D 0.03/0.31 0.03/0.31 with precondition: [F=3,A=B,A>=0,C>=A+1,D>=C+1] 0.03/0.31 0.03/0.31 * Chain [[10],12]: 1*it(10)+0 0.03/0.31 Such that:it(10) =< -A+G 0.03/0.31 0.03/0.31 with precondition: [F=2,A=B,G=H,A>=0,G>=A+1,C>=G] 0.03/0.31 0.03/0.31 * Chain [[10],11]: 1*it(10)+0 0.03/0.31 Such that:it(10) =< -A+C 0.03/0.31 0.03/0.31 with precondition: [F=3,A=B,A>=0,C>=A+1] 0.03/0.31 0.03/0.31 * Chain [[9],12]: 1*it(9)+0 0.03/0.31 Such that:it(9) =< -A+H 0.03/0.31 0.03/0.31 with precondition: [F=2,A=B,G=H,A>=0,G>=A+1,A>=C,D>=G] 0.03/0.31 0.03/0.31 * Chain [[9],11]: 1*it(9)+0 0.03/0.31 Such that:it(9) =< -A+D 0.03/0.31 0.03/0.31 with precondition: [F=3,A=B,A>=0,D>=A+1,A>=C] 0.03/0.31 0.03/0.31 * Chain [12]: 0 0.03/0.31 with precondition: [F=2,B=A,B=G,B=H,B>=0] 0.03/0.31 0.03/0.31 * Chain [11]: 0 0.03/0.31 with precondition: [F=3,B=A,B>=0] 0.03/0.31 0.03/0.31 0.03/0.31 #### Cost of chains of evalSimpleSingle2bb4in_loop_cont(A,B,C,D,E,F): 0.03/0.31 * Chain [14]: 0 0.03/0.31 with precondition: [A=2] 0.03/0.31 0.03/0.31 * Chain [13]: 0 0.03/0.31 with precondition: [A=3] 0.03/0.31 0.03/0.31 0.03/0.31 #### Cost of chains of evalSimpleSingle2entryin(A,B,C,D,F): 0.03/0.31 * Chain [18]: 0 0.03/0.31 with precondition: [] 0.03/0.31 0.03/0.31 * Chain [17]: 2*s(1)+0 0.03/0.31 Such that:aux(1) =< D 0.03/0.31 s(1) =< aux(1) 0.03/0.31 0.03/0.31 with precondition: [0>=C,D>=1] 0.03/0.31 0.03/0.31 * Chain [16]: 2*s(3)+0 0.03/0.31 Such that:aux(2) =< C 0.03/0.31 s(3) =< aux(2) 0.03/0.31 0.03/0.31 with precondition: [C>=1] 0.03/0.31 0.03/0.31 * Chain [15]: 2*s(5)+2*s(6)+0 0.03/0.31 Such that:aux(3) =< -C+D 0.03/0.31 aux(4) =< C 0.03/0.31 s(6) =< aux(3) 0.03/0.31 s(5) =< aux(4) 0.03/0.31 0.03/0.31 with precondition: [C>=1,D>=C+1] 0.03/0.31 0.03/0.31 0.03/0.31 #### Cost of chains of evalSimpleSingle2start(A,B,C,D,F): 0.03/0.31 * Chain [22]: 0 0.03/0.31 with precondition: [] 0.03/0.31 0.03/0.31 * Chain [21]: 2*s(10)+0 0.03/0.31 Such that:s(9) =< D 0.03/0.31 s(10) =< s(9) 0.03/0.31 0.03/0.31 with precondition: [0>=C,D>=1] 0.03/0.31 0.03/0.31 * Chain [20]: 2*s(12)+0 0.03/0.31 Such that:s(11) =< C 0.03/0.31 s(12) =< s(11) 0.03/0.31 0.03/0.31 with precondition: [C>=1] 0.03/0.31 0.03/0.31 * Chain [19]: 2*s(15)+2*s(16)+0 0.03/0.31 Such that:s(13) =< -C+D 0.03/0.31 s(14) =< C 0.03/0.31 s(15) =< s(13) 0.03/0.31 s(16) =< s(14) 0.03/0.31 0.03/0.31 with precondition: [C>=1,D>=C+1] 0.03/0.31 0.03/0.31 0.03/0.31 Closed-form bounds of evalSimpleSingle2start(A,B,C,D,F): 0.03/0.31 ------------------------------------- 0.03/0.31 * Chain [22] with precondition: [] 0.03/0.31 - Upper bound: 0 0.03/0.31 - Complexity: constant 0.03/0.31 * Chain [21] with precondition: [0>=C,D>=1] 0.03/0.31 - Upper bound: 2*D 0.03/0.31 - Complexity: n 0.03/0.31 * Chain [20] with precondition: [C>=1] 0.03/0.31 - Upper bound: 2*C 0.03/0.31 - Complexity: n 0.03/0.31 * Chain [19] with precondition: [C>=1,D>=C+1] 0.03/0.31 - Upper bound: 2*D 0.03/0.31 - Complexity: n 0.03/0.31 0.03/0.31 ### Maximum cost of evalSimpleSingle2start(A,B,C,D,F): max([nat(D)*2,nat(-C+D)*2+nat(C)*2]) 0.03/0.31 Asymptotic class: n 0.03/0.31 * Total analysis performed in 238 ms. 0.03/0.31 0.03/0.41 EOF