0.04/0.44 WORST_CASE(?,O(n^1)) 0.04/0.44 0.04/0.44 Preprocessing Cost Relations 0.04/0.44 ===================================== 0.04/0.44 0.04/0.44 #### Computed strongly connected components 0.04/0.44 0. recursive : [evalwcet1bb1in/8,evalwcet1bb4in/8,evalwcet1bb5in/8,evalwcet1bb6in/8,evalwcet1bbin/8] 0.04/0.44 1. non_recursive : [evalwcet1stop/5] 0.04/0.44 2. non_recursive : [evalwcet1returnin/5] 0.04/0.44 3. non_recursive : [exit_location/1] 0.04/0.44 4. non_recursive : [evalwcet1bbin_loop_cont/6] 0.04/0.44 5. non_recursive : [evalwcet1entryin/5] 0.04/0.44 6. non_recursive : [evalwcet1start/5] 0.04/0.44 0.04/0.44 #### Obtained direct recursion through partial evaluation 0.04/0.44 0. SCC is partially evaluated into evalwcet1bbin/8 0.04/0.44 1. SCC is completely evaluated into other SCCs 0.04/0.44 2. SCC is completely evaluated into other SCCs 0.04/0.44 3. SCC is completely evaluated into other SCCs 0.04/0.44 4. SCC is partially evaluated into evalwcet1bbin_loop_cont/6 0.04/0.44 5. SCC is partially evaluated into evalwcet1entryin/5 0.04/0.44 6. SCC is partially evaluated into evalwcet1start/5 0.04/0.44 0.04/0.44 Control-Flow Refinement of Cost Relations 0.04/0.44 ===================================== 0.04/0.44 0.04/0.44 ### Specialization of cost equations evalwcet1bbin/8 0.04/0.44 * CE 12 is refined into CE [15] 0.04/0.44 * CE 10 is refined into CE [16] 0.04/0.44 * CE 7 is refined into CE [17] 0.04/0.44 * CE 6 is refined into CE [18] 0.04/0.44 * CE 11 is refined into CE [19] 0.04/0.44 * CE 5 is refined into CE [20] 0.04/0.44 * CE 8 is refined into CE [21] 0.04/0.44 * CE 4 is discarded (unfeasible) 0.04/0.44 * CE 9 is refined into CE [22] 0.04/0.44 0.04/0.44 0.04/0.44 ### Cost equations --> "Loop" of evalwcet1bbin/8 0.04/0.44 * CEs [20] --> Loop 15 0.04/0.44 * CEs [21] --> Loop 16 0.04/0.44 * CEs [22] --> Loop 17 0.04/0.44 * CEs [15] --> Loop 18 0.04/0.44 * CEs [16] --> Loop 19 0.04/0.44 * CEs [17] --> Loop 20 0.04/0.44 * CEs [19] --> Loop 21 0.04/0.44 * CEs [18] --> Loop 22 0.04/0.44 0.04/0.44 ### Ranking functions of CR evalwcet1bbin(A,B,C,D,F,G,H,I) 0.04/0.44 * RF of phase [15,16,17]: [C-1] 0.04/0.44 0.04/0.44 #### Partial ranking functions of CR evalwcet1bbin(A,B,C,D,F,G,H,I) 0.04/0.44 * Partial RF of phase [15,16,17]: 0.04/0.44 - RF of loop [15:1]: 0.04/0.44 A-B-1 depends on loops [16:1,17:1] 0.04/0.44 - RF of loop [15:1,16:1,17:1]: 0.04/0.44 C-1 0.04/0.44 - RF of loop [16:1]: 0.04/0.44 B-1 depends on loops [15:1] 0.04/0.44 0.04/0.44 0.04/0.44 ### Specialization of cost equations evalwcet1bbin_loop_cont/6 0.04/0.44 * CE 14 is refined into CE [23] 0.04/0.44 * CE 13 is refined into CE [24] 0.04/0.44 0.04/0.44 0.04/0.44 ### Cost equations --> "Loop" of evalwcet1bbin_loop_cont/6 0.04/0.44 * CEs [23] --> Loop 23 0.04/0.44 * CEs [24] --> Loop 24 0.04/0.44 0.04/0.44 ### Ranking functions of CR evalwcet1bbin_loop_cont(A,B,C,D,E,F) 0.04/0.44 0.04/0.44 #### Partial ranking functions of CR evalwcet1bbin_loop_cont(A,B,C,D,E,F) 0.04/0.44 0.04/0.44 0.04/0.44 ### Specialization of cost equations evalwcet1entryin/5 0.04/0.44 * CE 3 is refined into CE [25,26,27,28,29,30,31,32] 0.04/0.44 * CE 2 is refined into CE [33] 0.04/0.44 0.04/0.44 0.04/0.44 ### Cost equations --> "Loop" of evalwcet1entryin/5 0.04/0.44 * CEs [30] --> Loop 25 0.04/0.44 * CEs [27,28,29,32] --> Loop 26 0.04/0.44 * CEs [31] --> Loop 27 0.04/0.44 * CEs [33] --> Loop 28 0.04/0.44 * CEs [25,26] --> Loop 29 0.04/0.44 0.04/0.44 ### Ranking functions of CR evalwcet1entryin(A,B,C,D,F) 0.04/0.44 0.04/0.44 #### Partial ranking functions of CR evalwcet1entryin(A,B,C,D,F) 0.04/0.44 0.04/0.44 0.04/0.44 ### Specialization of cost equations evalwcet1start/5 0.04/0.44 * CE 1 is refined into CE [34,35,36,37,38] 0.04/0.44 0.04/0.44 0.04/0.44 ### Cost equations --> "Loop" of evalwcet1start/5 0.04/0.44 * CEs [38] --> Loop 30 0.04/0.44 * CEs [37] --> Loop 31 0.04/0.44 * CEs [36] --> Loop 32 0.04/0.44 * CEs [35] --> Loop 33 0.04/0.44 * CEs [34] --> Loop 34 0.04/0.44 0.04/0.44 ### Ranking functions of CR evalwcet1start(A,B,C,D,F) 0.04/0.44 0.04/0.44 #### Partial ranking functions of CR evalwcet1start(A,B,C,D,F) 0.04/0.44 0.04/0.44 0.04/0.44 Computing Bounds 0.04/0.44 ===================================== 0.04/0.44 0.04/0.44 #### Cost of chains of evalwcet1bbin(A,B,C,D,F,G,H,I): 0.04/0.44 * Chain [[15,16,17],22]: 3*it(15)+0 0.04/0.44 Such that:aux(6) =< -B+G 0.04/0.44 aux(5) =< -B+G+1 0.04/0.44 it(15) =< aux(5) 0.04/0.44 it(15) =< aux(6) 0.04/0.44 0.04/0.44 with precondition: [F=2,H=1,I=0,A=G+1,A=B+C,B>=0,A>=B+2] 0.04/0.44 0.04/0.44 * Chain [[15,16,17],21]: 3*it(15)+0 0.04/0.44 Such that:aux(7) =< C 0.04/0.44 it(15) =< aux(7) 0.04/0.44 0.04/0.44 with precondition: [F=2,H=1,I=0,1>=G,B>=0,C>=2,G>=0,A>=B+C,C+G>=B+1] 0.04/0.44 0.04/0.44 * Chain [[15,16,17],20]: 3*it(15)+0 0.04/0.44 Such that:aux(8) =< C 0.04/0.44 it(15) =< aux(8) 0.04/0.44 0.04/0.44 with precondition: [F=2,H=1,G+1=I,B>=0,C>=2,G>=0,A>=G+2,A>=B+C,C+G>=B+1,B+C>=G+1] 0.04/0.44 0.04/0.44 * Chain [[15,16,17],19]: 3*it(15)+0 0.04/0.44 Such that:aux(9) =< C 0.04/0.44 it(15) =< aux(9) 0.04/0.44 0.04/0.44 with precondition: [F=2,H=1,G=I+1,B>=0,C>=2,G>=2,A>=B+C,C+G>=B+1,B+C>=G+1] 0.04/0.44 0.04/0.44 * Chain [[15,16,17],18]: 3*it(15)+0 0.04/0.44 Such that:aux(10) =< C 0.04/0.44 it(15) =< aux(10) 0.04/0.44 0.04/0.44 with precondition: [F=3,B>=0,C>=2,A>=B+C] 0.04/0.44 0.04/0.44 * Chain [22]: 0 0.04/0.44 with precondition: [C=1,F=2,H=1,I=0,A=B+1,A=G+1,A>=1] 0.04/0.44 0.04/0.44 * Chain [21]: 0 0.04/0.44 with precondition: [C=1,F=2,H=1,I=0,B=G,1>=B,B>=0,A>=B+1] 0.04/0.44 0.04/0.44 * Chain [18]: 0 0.04/0.44 with precondition: [F=3,B>=0,C>=1,A>=B+C] 0.04/0.44 0.04/0.44 0.04/0.44 #### Cost of chains of evalwcet1bbin_loop_cont(A,B,C,D,E,F): 0.04/0.44 * Chain [24]: 0 0.04/0.44 with precondition: [A=2,B>=1] 0.04/0.44 0.04/0.44 * Chain [23]: 0 0.04/0.44 with precondition: [A=3,B>=1] 0.04/0.44 0.04/0.44 0.04/0.44 #### Cost of chains of evalwcet1entryin(A,B,C,D,F): 0.04/0.44 * Chain [29]: 0 0.04/0.44 with precondition: [A=1] 0.04/0.44 0.04/0.44 * Chain [28]: 0 0.04/0.44 with precondition: [0>=A] 0.04/0.44 0.04/0.45 * Chain [27]: 0 0.04/0.45 with precondition: [A>=1] 0.04/0.45 0.04/0.45 * Chain [26]: 12*s(3)+0 0.04/0.45 Such that:aux(12) =< A 0.04/0.45 s(3) =< aux(12) 0.04/0.45 0.04/0.45 with precondition: [A>=2] 0.04/0.45 0.04/0.45 * Chain [25]: 3*s(11)+0 0.04/0.45 Such that:s(10) =< A 0.04/0.45 s(11) =< s(10) 0.04/0.45 0.04/0.45 with precondition: [A>=3] 0.04/0.45 0.04/0.45 0.04/0.45 #### Cost of chains of evalwcet1start(A,B,C,D,F): 0.04/0.45 * Chain [34]: 0 0.04/0.45 with precondition: [A=1] 0.04/0.45 0.04/0.45 * Chain [33]: 0 0.04/0.45 with precondition: [0>=A] 0.04/0.45 0.04/0.45 * Chain [32]: 0 0.04/0.45 with precondition: [A>=1] 0.04/0.45 0.04/0.45 * Chain [31]: 12*s(13)+0 0.04/0.45 Such that:s(12) =< A 0.04/0.45 s(13) =< s(12) 0.04/0.45 0.04/0.45 with precondition: [A>=2] 0.04/0.45 0.04/0.45 * Chain [30]: 3*s(15)+0 0.04/0.45 Such that:s(14) =< A 0.04/0.45 s(15) =< s(14) 0.04/0.45 0.04/0.45 with precondition: [A>=3] 0.04/0.45 0.04/0.45 0.04/0.45 Closed-form bounds of evalwcet1start(A,B,C,D,F): 0.04/0.45 ------------------------------------- 0.04/0.45 * Chain [34] with precondition: [A=1] 0.04/0.45 - Upper bound: 0 0.04/0.45 - Complexity: constant 0.04/0.45 * Chain [33] with precondition: [0>=A] 0.04/0.45 - Upper bound: 0 0.04/0.45 - Complexity: constant 0.04/0.45 * Chain [32] with precondition: [A>=1] 0.04/0.45 - Upper bound: 0 0.04/0.45 - Complexity: constant 0.04/0.45 * Chain [31] with precondition: [A>=2] 0.04/0.45 - Upper bound: 12*A 0.04/0.45 - Complexity: n 0.04/0.45 * Chain [30] with precondition: [A>=3] 0.04/0.45 - Upper bound: 3*A 0.04/0.45 - Complexity: n 0.04/0.45 0.04/0.45 ### Maximum cost of evalwcet1start(A,B,C,D,F): nat(A)*12 0.04/0.45 Asymptotic class: n 0.04/0.45 * Total analysis performed in 368 ms. 0.04/0.45 0.04/0.55 EOF