0.52/0.52 WORST_CASE(?,O(n^1)) 0.52/0.52 0.52/0.52 Preprocessing Cost Relations 0.52/0.52 ===================================== 0.52/0.52 0.52/0.52 #### Computed strongly connected components 0.52/0.52 0. recursive : [evalEx4bb1in/9,evalEx4bb2in/9,evalEx4bb3in/9] 0.52/0.52 1. recursive : [evalEx4bb2in_loop_cont/10,evalEx4bb4in/9] 0.52/0.52 2. non_recursive : [evalEx4stop/5] 0.52/0.52 3. non_recursive : [evalEx4returnin/5] 0.52/0.52 4. non_recursive : [exit_location/1] 0.52/0.52 5. non_recursive : [evalEx4bb4in_loop_cont/6] 0.52/0.52 6. non_recursive : [evalEx4entryin/5] 0.52/0.52 7. non_recursive : [evalEx4start/5] 0.52/0.52 0.52/0.52 #### Obtained direct recursion through partial evaluation 0.52/0.52 0. SCC is partially evaluated into evalEx4bb2in/9 0.52/0.52 1. SCC is partially evaluated into evalEx4bb4in/9 0.52/0.52 2. SCC is completely evaluated into other SCCs 0.52/0.52 3. SCC is completely evaluated into other SCCs 0.52/0.52 4. SCC is completely evaluated into other SCCs 0.52/0.52 5. SCC is partially evaluated into evalEx4bb4in_loop_cont/6 0.52/0.52 6. SCC is partially evaluated into evalEx4entryin/5 0.52/0.52 7. SCC is partially evaluated into evalEx4start/5 0.52/0.52 0.52/0.52 Control-Flow Refinement of Cost Relations 0.52/0.52 ===================================== 0.52/0.52 0.52/0.52 ### Specialization of cost equations evalEx4bb2in/9 0.52/0.52 * CE 13 is refined into CE [14] 0.52/0.52 * CE 10 is refined into CE [15] 0.52/0.52 * CE 12 is refined into CE [16] 0.52/0.52 * CE 11 is refined into CE [17] 0.52/0.52 0.52/0.52 0.52/0.52 ### Cost equations --> "Loop" of evalEx4bb2in/9 0.52/0.52 * CEs [17] --> Loop 14 0.52/0.52 * CEs [14] --> Loop 15 0.52/0.52 * CEs [15] --> Loop 16 0.52/0.52 * CEs [16] --> Loop 17 0.52/0.52 0.52/0.52 ### Ranking functions of CR evalEx4bb2in(A,B,C,D,F,G,H,I,J) 0.52/0.52 * RF of phase [14]: [D] 0.52/0.52 0.52/0.52 #### Partial ranking functions of CR evalEx4bb2in(A,B,C,D,F,G,H,I,J) 0.52/0.52 * Partial RF of phase [14]: 0.52/0.52 - RF of loop [14:1]: 0.52/0.52 D 0.52/0.52 0.52/0.52 0.52/0.52 ### Specialization of cost equations evalEx4bb4in/9 0.52/0.52 * CE 6 is refined into CE [18] 0.52/0.52 * CE 5 is refined into CE [19] 0.52/0.52 * CE 7 is refined into CE [20] 0.52/0.52 * CE 3 is refined into CE [21,22] 0.52/0.52 * CE 4 is refined into CE [23,24,25,26] 0.52/0.52 0.52/0.52 0.52/0.52 ### Cost equations --> "Loop" of evalEx4bb4in/9 0.52/0.52 * CEs [24] --> Loop 18 0.52/0.52 * CEs [23] --> Loop 19 0.52/0.52 * CEs [26] --> Loop 20 0.52/0.52 * CEs [25] --> Loop 21 0.52/0.52 * CEs [18] --> Loop 22 0.52/0.52 * CEs [19] --> Loop 23 0.52/0.52 * CEs [20] --> Loop 24 0.52/0.52 * CEs [22] --> Loop 25 0.52/0.52 * CEs [21] --> Loop 26 0.52/0.52 0.52/0.52 ### Ranking functions of CR evalEx4bb4in(A,B,C,D,F,G,H,I,J) 0.52/0.52 * RF of phase [18]: [B-1] 0.52/0.52 0.52/0.52 #### Partial ranking functions of CR evalEx4bb4in(A,B,C,D,F,G,H,I,J) 0.52/0.52 * Partial RF of phase [18]: 0.52/0.52 - RF of loop [18:1]: 0.52/0.53 B-1 0.52/0.53 0.52/0.53 0.52/0.53 ### Specialization of cost equations evalEx4bb4in_loop_cont/6 0.52/0.53 * CE 8 is refined into CE [27] 0.52/0.53 * CE 9 is refined into CE [28] 0.52/0.53 0.52/0.53 0.52/0.53 ### Cost equations --> "Loop" of evalEx4bb4in_loop_cont/6 0.52/0.53 * CEs [27] --> Loop 27 0.52/0.53 * CEs [28] --> Loop 28 0.52/0.53 0.52/0.53 ### Ranking functions of CR evalEx4bb4in_loop_cont(A,B,C,D,E,F) 0.52/0.53 0.52/0.53 #### Partial ranking functions of CR evalEx4bb4in_loop_cont(A,B,C,D,E,F) 0.52/0.53 0.52/0.53 0.52/0.53 ### Specialization of cost equations evalEx4entryin/5 0.52/0.53 * CE 2 is refined into CE [29,30,31,32,33,34,35,36,37,38] 0.52/0.53 0.52/0.53 0.52/0.53 ### Cost equations --> "Loop" of evalEx4entryin/5 0.52/0.53 * CEs [32,34,37] --> Loop 29 0.52/0.53 * CEs [31,33,36] --> Loop 30 0.52/0.53 * CEs [30,35] --> Loop 31 0.52/0.53 * CEs [29,38] --> Loop 32 0.52/0.53 0.52/0.53 ### Ranking functions of CR evalEx4entryin(A,B,C,D,F) 0.52/0.53 0.52/0.53 #### Partial ranking functions of CR evalEx4entryin(A,B,C,D,F) 0.52/0.53 0.52/0.53 0.52/0.53 ### Specialization of cost equations evalEx4start/5 0.52/0.53 * CE 1 is refined into CE [39,40,41,42] 0.52/0.53 0.52/0.53 0.52/0.53 ### Cost equations --> "Loop" of evalEx4start/5 0.52/0.53 * CEs [42] --> Loop 33 0.52/0.53 * CEs [41] --> Loop 34 0.52/0.53 * CEs [40] --> Loop 35 0.52/0.53 * CEs [39] --> Loop 36 0.52/0.53 0.52/0.53 ### Ranking functions of CR evalEx4start(A,B,C,D,F) 0.52/0.53 0.52/0.53 #### Partial ranking functions of CR evalEx4start(A,B,C,D,F) 0.52/0.53 0.52/0.53 0.52/0.53 Computing Bounds 0.52/0.53 ===================================== 0.52/0.53 0.52/0.53 #### Cost of chains of evalEx4bb2in(A,B,C,D,F,G,H,I,J): 0.52/0.53 * Chain [[14],17]: 1*it(14)+0 0.52/0.53 Such that:it(14) =< D 0.52/0.53 0.52/0.53 with precondition: [A=1,F=2,G=1,H=0,I=1,J=0,1>=C,D>=1] 0.52/0.53 0.52/0.53 * Chain [[14],16]: 1*it(14)+0 0.52/0.53 Such that:it(14) =< D-J 0.52/0.53 0.52/0.53 with precondition: [A=1,F=2,G=1,I=1,H=J,1>=C,H>=1,D>=H+1] 0.52/0.53 0.52/0.53 * Chain [[14],15]: 1*it(14)+0 0.52/0.53 Such that:it(14) =< D 0.52/0.53 0.52/0.53 with precondition: [A=1,F=3,1>=C,D>=1] 0.52/0.53 0.52/0.53 * Chain [17]: 0 0.52/0.53 with precondition: [A=1,F=2,C=G,D=H,C=I,D=J,1>=C,0>=D] 0.52/0.53 0.52/0.53 * Chain [16]: 0 0.52/0.53 with precondition: [A=1,F=2,C=G,D=H,C=I,D=J,1>=C,D>=1] 0.52/0.53 0.52/0.53 * Chain [15]: 0 0.52/0.53 with precondition: [A=1,F=3,1>=C] 0.52/0.53 0.52/0.53 0.52/0.53 #### Cost of chains of evalEx4bb4in(A,B,C,D,F,G,H,I,J): 0.52/0.53 * Chain [[18],26]: 2*it(18)+0 0.52/0.53 Such that:aux(3) =< B 0.52/0.53 it(18) =< aux(3) 0.52/0.53 0.52/0.53 with precondition: [A=1,F=3,B>=2] 0.52/0.53 0.52/0.53 * Chain [[18],25]: 3*it(18)+0 0.52/0.53 Such that:aux(4) =< B 0.52/0.53 it(18) =< aux(4) 0.52/0.53 0.52/0.53 with precondition: [A=1,F=3,B>=2] 0.52/0.53 0.52/0.53 * Chain [[18],24]: 2*it(18)+0 0.52/0.53 Such that:aux(5) =< B 0.52/0.53 it(18) =< aux(5) 0.52/0.53 0.52/0.53 with precondition: [A=1,F=3,B>=2] 0.52/0.53 0.52/0.53 * Chain [[18],20,24]: 2*it(18)+1 0.52/0.53 Such that:aux(6) =< B 0.52/0.53 it(18) =< aux(6) 0.52/0.53 0.52/0.53 with precondition: [A=1,F=3,B>=2] 0.52/0.53 0.52/0.53 * Chain [[18],20,23]: 2*it(18)+1 0.52/0.53 Such that:aux(1) =< B 0.52/0.53 aux(2) =< B-H 0.52/0.53 it(18) =< aux(1) 0.52/0.53 it(18) =< aux(2) 0.52/0.53 0.52/0.53 with precondition: [A=1,F=4,G=0,I=0,H=J,H>=1,B>=H+1] 0.52/0.53 0.52/0.53 * Chain [[18],19,26]: 3*it(18)+1 0.52/0.53 Such that:aux(7) =< B 0.52/0.53 it(18) =< aux(7) 0.52/0.53 0.52/0.53 with precondition: [A=1,F=3,B>=2] 0.52/0.53 0.52/0.53 * Chain [[18],19,24]: 3*it(18)+1 0.52/0.53 Such that:aux(8) =< B 0.52/0.53 it(18) =< aux(8) 0.52/0.53 0.52/0.53 with precondition: [A=1,F=3,B>=2] 0.52/0.53 0.52/0.53 * Chain [[18],19,21,24]: 3*it(18)+2 0.52/0.53 Such that:aux(9) =< B 0.52/0.53 it(18) =< aux(9) 0.52/0.53 0.52/0.53 with precondition: [A=1,F=3,B>=2] 0.52/0.53 0.52/0.53 * Chain [[18],19,21,23]: 3*it(18)+2 0.52/0.53 Such that:aux(10) =< B 0.52/0.53 it(18) =< aux(10) 0.52/0.53 0.52/0.53 with precondition: [A=1,F=4,G=0,H=0,I=0,J=0,B>=2] 0.52/0.53 0.52/0.53 * Chain [26]: 0 0.52/0.53 with precondition: [A=1,F=3] 0.52/0.53 0.52/0.53 * Chain [25]: 1*s(4)+0 0.52/0.53 Such that:s(4) =< B 0.52/0.53 0.52/0.53 with precondition: [A=1,F=3,B>=1] 0.52/0.53 0.52/0.53 * Chain [24]: 0 0.52/0.53 with precondition: [F=3,1>=A,A>=0] 0.52/0.53 0.52/0.53 * Chain [21,24]: 1 0.52/0.53 with precondition: [A=1,F=3,0>=B] 0.52/0.53 0.52/0.53 * Chain [21,23]: 1 0.52/0.53 with precondition: [A=1,F=4,G=0,I=0,B=H,B=J,0>=B] 0.52/0.53 0.52/0.53 * Chain [20,24]: 1 0.52/0.53 with precondition: [A=1,F=3,B>=1] 0.52/0.53 0.52/0.53 * Chain [20,23]: 1 0.52/0.53 with precondition: [A=1,F=4,G=0,I=0,B=H,B=J,B>=1] 0.52/0.53 0.52/0.53 * Chain [19,26]: 1*s(5)+1 0.52/0.53 Such that:s(5) =< B 0.52/0.53 0.52/0.53 with precondition: [A=1,F=3,B>=1] 0.52/0.53 0.52/0.53 * Chain [19,24]: 1*s(5)+1 0.52/0.53 Such that:s(5) =< B 0.52/0.53 0.52/0.53 with precondition: [A=1,F=3,B>=1] 0.52/0.53 0.52/0.53 * Chain [19,21,24]: 1*s(5)+2 0.52/0.53 Such that:s(5) =< B 0.52/0.53 0.52/0.53 with precondition: [A=1,F=3,B>=1] 0.52/0.53 0.52/0.53 * Chain [19,21,23]: 1*s(5)+2 0.52/0.53 Such that:s(5) =< B 0.52/0.53 0.52/0.53 with precondition: [A=1,F=4,G=0,H=0,I=0,J=0,B>=1] 0.52/0.53 0.52/0.53 0.52/0.53 #### Cost of chains of evalEx4bb4in_loop_cont(A,B,C,D,E,F): 0.52/0.53 * Chain [28]: 0 0.52/0.53 with precondition: [A=3] 0.52/0.53 0.52/0.53 * Chain [27]: 0 0.52/0.53 with precondition: [A=4] 0.52/0.53 0.52/0.53 0.52/0.53 #### Cost of chains of evalEx4entryin(A,B,C,D,F): 0.52/0.53 * Chain [32]: 0 0.52/0.53 with precondition: [] 0.52/0.53 0.52/0.53 * Chain [31]: 1 0.52/0.53 with precondition: [0>=A] 0.52/0.53 0.52/0.53 * Chain [30]: 5*s(25)+2 0.52/0.53 Such that:aux(13) =< A 0.52/0.53 s(25) =< aux(13) 0.52/0.53 0.52/0.53 with precondition: [A>=1] 0.52/0.53 0.52/0.53 * Chain [29]: 23*s(28)+2 0.52/0.53 Such that:aux(15) =< A 0.52/0.53 s(28) =< aux(15) 0.52/0.53 0.52/0.53 with precondition: [A>=2] 0.52/0.53 0.52/0.53 0.52/0.53 #### Cost of chains of evalEx4start(A,B,C,D,F): 0.52/0.53 * Chain [36]: 0 0.52/0.53 with precondition: [] 0.52/0.53 0.52/0.53 * Chain [35]: 1 0.52/0.53 with precondition: [0>=A] 0.52/0.53 0.52/0.53 * Chain [34]: 5*s(35)+2 0.52/0.53 Such that:s(34) =< A 0.52/0.53 s(35) =< s(34) 0.52/0.53 0.52/0.53 with precondition: [A>=1] 0.52/0.53 0.52/0.53 * Chain [33]: 23*s(37)+2 0.52/0.53 Such that:s(36) =< A 0.52/0.53 s(37) =< s(36) 0.52/0.53 0.52/0.53 with precondition: [A>=2] 0.52/0.53 0.52/0.53 0.52/0.53 Closed-form bounds of evalEx4start(A,B,C,D,F): 0.52/0.53 ------------------------------------- 0.52/0.53 * Chain [36] with precondition: [] 0.52/0.53 - Upper bound: 0 0.52/0.53 - Complexity: constant 0.52/0.53 * Chain [35] with precondition: [0>=A] 0.52/0.53 - Upper bound: 1 0.52/0.53 - Complexity: constant 0.52/0.53 * Chain [34] with precondition: [A>=1] 0.52/0.53 - Upper bound: 5*A+2 0.52/0.53 - Complexity: n 0.52/0.53 * Chain [33] with precondition: [A>=2] 0.52/0.53 - Upper bound: 23*A+2 0.52/0.53 - Complexity: n 0.52/0.53 0.52/0.53 ### Maximum cost of evalEx4start(A,B,C,D,F): nat(A)*23+1+1 0.52/0.53 Asymptotic class: n 0.52/0.53 * Total analysis performed in 445 ms. 0.52/0.53 0.52/0.63 EOF