0.03/0.55 WORST_CASE(?,O(n^1)) 0.03/0.55 0.03/0.55 Preprocessing Cost Relations 0.03/0.55 ===================================== 0.03/0.55 0.03/0.55 #### Computed strongly connected components 0.03/0.55 0. recursive : [evalfbb1in/6,evalfbb2in/6,evalfbb3in/6] 0.03/0.55 1. recursive : [evalfbb2in_loop_cont/9,evalfbb4in/8,evalfbb6in/8,evalfbbin/8] 0.03/0.55 2. non_recursive : [evalfstop/5] 0.03/0.55 3. non_recursive : [evalfreturnin/5] 0.03/0.55 4. non_recursive : [exit_location/1] 0.03/0.55 5. non_recursive : [evalfbb6in_loop_cont/6] 0.03/0.55 6. non_recursive : [evalfentryin/5] 0.03/0.55 7. non_recursive : [evalfstart/5] 0.03/0.55 0.03/0.55 #### Obtained direct recursion through partial evaluation 0.03/0.55 0. SCC is partially evaluated into evalfbb2in/6 0.03/0.55 1. SCC is partially evaluated into evalfbb6in/8 0.03/0.55 2. SCC is completely evaluated into other SCCs 0.03/0.55 3. SCC is completely evaluated into other SCCs 0.03/0.55 4. SCC is completely evaluated into other SCCs 0.03/0.55 5. SCC is partially evaluated into evalfbb6in_loop_cont/6 0.03/0.55 6. SCC is partially evaluated into evalfentryin/5 0.03/0.55 7. SCC is partially evaluated into evalfstart/5 0.03/0.55 0.03/0.55 Control-Flow Refinement of Cost Relations 0.03/0.55 ===================================== 0.03/0.55 0.03/0.55 ### Specialization of cost equations evalfbb2in/6 0.03/0.55 * CE 13 is refined into CE [14] 0.03/0.55 * CE 10 is refined into CE [15] 0.03/0.55 * CE 12 is refined into CE [16] 0.03/0.55 * CE 11 is refined into CE [17] 0.03/0.55 0.03/0.55 0.03/0.55 ### Cost equations --> "Loop" of evalfbb2in/6 0.03/0.55 * CEs [17] --> Loop 14 0.03/0.55 * CEs [14] --> Loop 15 0.03/0.55 * CEs [15] --> Loop 16 0.03/0.55 * CEs [16] --> Loop 17 0.03/0.55 0.03/0.55 ### Ranking functions of CR evalfbb2in(B,C,D,F,G,H) 0.03/0.55 * RF of phase [14]: [B-D] 0.03/0.55 0.03/0.55 #### Partial ranking functions of CR evalfbb2in(B,C,D,F,G,H) 0.03/0.55 * Partial RF of phase [14]: 0.03/0.55 - RF of loop [14:1]: 0.03/0.55 B-D 0.03/0.55 0.03/0.55 0.03/0.55 ### Specialization of cost equations evalfbb6in/8 0.03/0.55 * CE 6 is refined into CE [18] 0.03/0.55 * CE 3 is refined into CE [19,20] 0.03/0.55 * CE 7 is refined into CE [21] 0.03/0.55 * CE 5 is refined into CE [22,23] 0.03/0.55 * CE 4 is refined into CE [24,25] 0.03/0.55 0.03/0.55 0.03/0.55 ### Cost equations --> "Loop" of evalfbb6in/8 0.03/0.55 * CEs [25] --> Loop 18 0.03/0.55 * CEs [24] --> Loop 19 0.03/0.55 * CEs [23] --> Loop 20 0.03/0.55 * CEs [22] --> Loop 21 0.03/0.55 * CEs [18] --> Loop 22 0.03/0.55 * CEs [20] --> Loop 23 0.03/0.55 * CEs [19] --> Loop 24 0.03/0.55 * CEs [21] --> Loop 25 0.03/0.55 0.03/0.55 ### Ranking functions of CR evalfbb6in(A,B,C,D,F,G,H,I) 0.03/0.55 * RF of phase [18,20]: [-A+B-1] 0.03/0.55 0.03/0.55 #### Partial ranking functions of CR evalfbb6in(A,B,C,D,F,G,H,I) 0.03/0.55 * Partial RF of phase [18,20]: 0.03/0.55 - RF of loop [18:1]: 0.03/0.55 -A+B-2 0.03/0.55 - RF of loop [20:1]: 0.03/0.55 -A+B-1 0.03/0.55 0.03/0.55 0.03/0.55 ### Specialization of cost equations evalfbb6in_loop_cont/6 0.03/0.55 * CE 8 is refined into CE [26] 0.03/0.55 * CE 9 is refined into CE [27] 0.03/0.55 0.03/0.55 0.03/0.55 ### Cost equations --> "Loop" of evalfbb6in_loop_cont/6 0.03/0.55 * CEs [26] --> Loop 26 0.03/0.55 * CEs [27] --> Loop 27 0.03/0.55 0.03/0.55 ### Ranking functions of CR evalfbb6in_loop_cont(A,B,C,D,E,F) 0.03/0.55 0.03/0.55 #### Partial ranking functions of CR evalfbb6in_loop_cont(A,B,C,D,E,F) 0.03/0.55 0.03/0.55 0.03/0.55 ### Specialization of cost equations evalfentryin/5 0.03/0.55 * CE 2 is refined into CE [28,29,30,31,32,33,34,35,36] 0.03/0.55 0.03/0.55 0.03/0.55 ### Cost equations --> "Loop" of evalfentryin/5 0.03/0.55 * CEs [32,35] --> Loop 28 0.03/0.55 * CEs [31,34] --> Loop 29 0.03/0.55 * CEs [30] --> Loop 30 0.03/0.55 * CEs [36] --> Loop 31 0.03/0.55 * CEs [28,33] --> Loop 32 0.03/0.55 * CEs [29] --> Loop 33 0.03/0.55 0.03/0.55 ### Ranking functions of CR evalfentryin(A,B,C,D,F) 0.03/0.55 0.03/0.55 #### Partial ranking functions of CR evalfentryin(A,B,C,D,F) 0.03/0.55 0.03/0.55 0.03/0.55 ### Specialization of cost equations evalfstart/5 0.03/0.55 * CE 1 is refined into CE [37,38,39,40,41,42] 0.03/0.55 0.03/0.55 0.03/0.55 ### Cost equations --> "Loop" of evalfstart/5 0.03/0.55 * CEs [42] --> Loop 34 0.03/0.55 * CEs [41] --> Loop 35 0.03/0.55 * CEs [40] --> Loop 36 0.03/0.55 * CEs [39] --> Loop 37 0.03/0.55 * CEs [38] --> Loop 38 0.03/0.55 * CEs [37] --> Loop 39 0.03/0.55 0.03/0.55 ### Ranking functions of CR evalfstart(A,B,C,D,F) 0.03/0.55 0.03/0.55 #### Partial ranking functions of CR evalfstart(A,B,C,D,F) 0.03/0.55 0.03/0.55 0.03/0.55 Computing Bounds 0.03/0.55 ===================================== 0.03/0.55 0.03/0.55 #### Cost of chains of evalfbb2in(B,C,D,F,G,H): 0.03/0.55 * Chain [[14],17]: 1*it(14)+0 0.03/0.55 Such that:it(14) =< -C+G 0.03/0.55 0.03/0.55 with precondition: [F=2,B=H,B+C=D+G,C>=0,B>=D+1] 0.03/0.55 0.03/0.55 * Chain [[14],16]: 1*it(14)+0 0.03/0.55 Such that:it(14) =< -D+H 0.03/0.55 0.03/0.55 with precondition: [F=2,D+G=C+H,C>=0,G>=C+1,B+C>=D+G+1] 0.03/0.55 0.03/0.55 * Chain [[14],15]: 1*it(14)+0 0.03/0.55 Such that:it(14) =< B-D 0.03/0.55 0.03/0.55 with precondition: [F=3,C>=0,B>=D+1] 0.03/0.55 0.03/0.55 * Chain [17]: 0 0.03/0.55 with precondition: [F=2,D=B,C=G,D=H,C>=0] 0.03/0.55 0.03/0.55 * Chain [16]: 0 0.03/0.55 with precondition: [F=2,C=G,D=H,C>=0,B>=D+1] 0.03/0.55 0.03/0.55 * Chain [15]: 0 0.03/0.55 with precondition: [F=3,C>=0,B>=D] 0.03/0.55 0.03/0.55 0.03/0.55 #### Cost of chains of evalfbb6in(A,B,C,D,F,G,H,I): 0.03/0.55 * Chain [[18,20],25]: 3*it(18)+0 0.03/0.55 Such that:aux(3) =< -A+B 0.03/0.55 it(18) =< aux(3) 0.03/0.55 0.03/0.55 with precondition: [F=3,A>=0,B>=A+2] 0.03/0.55 0.03/0.55 * Chain [[18,20],24]: 3*it(18)+0 0.03/0.55 Such that:aux(4) =< -A+B 0.03/0.55 it(18) =< aux(4) 0.03/0.55 0.03/0.55 with precondition: [F=3,A>=0,B>=A+2] 0.03/0.55 0.03/0.55 * Chain [[18,20],23]: 4*it(18)+0 0.03/0.55 Such that:aux(5) =< -A+B 0.03/0.55 it(18) =< aux(5) 0.03/0.55 0.03/0.55 with precondition: [F=3,A>=0,B>=A+3] 0.03/0.55 0.03/0.55 * Chain [[18,20],21,25]: 3*it(18)+1 0.03/0.55 Such that:aux(6) =< -A+B 0.03/0.55 it(18) =< aux(6) 0.03/0.55 0.03/0.55 with precondition: [F=3,A>=0,B>=A+2] 0.03/0.55 0.03/0.55 * Chain [[18,20],21,22]: 3*it(18)+1 0.03/0.55 Such that:aux(7) =< -A+G 0.03/0.55 it(18) =< aux(7) 0.03/0.55 0.03/0.55 with precondition: [F=4,H=0,B=G,B=I,A>=0,B>=A+2] 0.03/0.55 0.03/0.55 * Chain [[18,20],19,25]: 4*it(18)+1 0.03/0.55 Such that:aux(8) =< -A+B 0.03/0.55 it(18) =< aux(8) 0.03/0.55 0.03/0.55 with precondition: [F=3,A>=0,B>=A+3] 0.03/0.55 0.03/0.55 * Chain [[18,20],19,24]: 4*it(18)+1 0.03/0.55 Such that:aux(9) =< -A+B 0.03/0.55 it(18) =< aux(9) 0.03/0.55 0.03/0.55 with precondition: [F=3,A>=0,B>=A+3] 0.03/0.55 0.03/0.55 * Chain [[18,20],19,21,25]: 4*it(18)+2 0.03/0.55 Such that:aux(10) =< -A+B 0.03/0.55 it(18) =< aux(10) 0.03/0.55 0.03/0.55 with precondition: [F=3,A>=0,B>=A+3] 0.03/0.55 0.03/0.55 * Chain [[18,20],19,21,22]: 4*it(18)+2 0.03/0.55 Such that:aux(11) =< -A+G 0.03/0.55 it(18) =< aux(11) 0.03/0.55 0.03/0.55 with precondition: [F=4,H=0,B=G,B=I,A>=0,B>=A+3] 0.03/0.55 0.03/0.55 * Chain [25]: 0 0.03/0.55 with precondition: [F=3,A>=0] 0.03/0.55 0.03/0.55 * Chain [24]: 0 0.03/0.55 with precondition: [F=3,A>=0,B>=A+1] 0.03/0.55 0.03/0.55 * Chain [23]: 1*s(4)+0 0.03/0.55 Such that:s(4) =< -A+B 0.03/0.55 0.03/0.55 with precondition: [F=3,A>=0,B>=A+2] 0.03/0.55 0.03/0.55 * Chain [22]: 0 0.03/0.55 with precondition: [F=4,H=C,I=D,A=G,A>=0,A>=B] 0.03/0.55 0.03/0.55 * Chain [21,25]: 1 0.03/0.55 with precondition: [F=3,B=A+1,B>=1] 0.03/0.55 0.03/0.55 * Chain [21,22]: 1 0.03/0.55 with precondition: [F=4,H=0,B=A+1,B=G,B=I,B>=1] 0.03/0.55 0.03/0.55 * Chain [19,25]: 1*s(5)+1 0.03/0.55 Such that:s(5) =< -A+B 0.03/0.55 0.03/0.55 with precondition: [F=3,A>=0,B>=A+2] 0.03/0.55 0.03/0.55 * Chain [19,24]: 1*s(5)+1 0.03/0.55 Such that:s(5) =< -A+B 0.03/0.55 0.03/0.55 with precondition: [F=3,A>=0,B>=A+2] 0.03/0.55 0.03/0.55 * Chain [19,21,25]: 1*s(5)+2 0.03/0.55 Such that:s(5) =< -A+B 0.03/0.55 0.03/0.55 with precondition: [F=3,A>=0,B>=A+2] 0.03/0.55 0.03/0.55 * Chain [19,21,22]: 1*s(5)+2 0.03/0.55 Such that:s(5) =< -A+G 0.03/0.55 0.03/0.55 with precondition: [F=4,H=0,B=G,B=I,A>=0,B>=A+2] 0.03/0.55 0.03/0.55 0.03/0.55 #### Cost of chains of evalfbb6in_loop_cont(A,B,C,D,E,F): 0.03/0.55 * Chain [27]: 0 0.03/0.55 with precondition: [A=3] 0.03/0.55 0.03/0.55 * Chain [26]: 0 0.03/0.55 with precondition: [A=4] 0.03/0.55 0.03/0.55 0.03/0.55 #### Cost of chains of evalfentryin(A,B,C,D,F): 0.03/0.55 * Chain [33]: 0 0.03/0.55 with precondition: [] 0.03/0.55 0.03/0.55 * Chain [32]: 1 0.03/0.55 with precondition: [B=1] 0.03/0.55 0.03/0.55 * Chain [31]: 0 0.03/0.55 with precondition: [0>=B] 0.03/0.55 0.03/0.55 * Chain [30]: 0 0.03/0.55 with precondition: [B>=1] 0.03/0.55 0.03/0.55 * Chain [29]: 17*s(28)+2 0.03/0.55 Such that:aux(15) =< B 0.03/0.55 s(28) =< aux(15) 0.03/0.55 0.03/0.55 with precondition: [B>=2] 0.03/0.55 0.03/0.55 * Chain [28]: 20*s(32)+2 0.03/0.55 Such that:aux(16) =< B 0.03/0.55 s(32) =< aux(16) 0.03/0.55 0.03/0.55 with precondition: [B>=3] 0.03/0.55 0.03/0.55 0.03/0.55 #### Cost of chains of evalfstart(A,B,C,D,F): 0.03/0.55 * Chain [39]: 0 0.03/0.55 with precondition: [] 0.03/0.55 0.03/0.55 * Chain [38]: 1 0.03/0.55 with precondition: [B=1] 0.03/0.55 0.03/0.55 * Chain [37]: 0 0.03/0.55 with precondition: [0>=B] 0.03/0.55 0.03/0.55 * Chain [36]: 0 0.03/0.55 with precondition: [B>=1] 0.03/0.55 0.03/0.55 * Chain [35]: 17*s(36)+2 0.03/0.55 Such that:s(35) =< B 0.03/0.55 s(36) =< s(35) 0.03/0.55 0.03/0.55 with precondition: [B>=2] 0.03/0.55 0.03/0.55 * Chain [34]: 20*s(38)+2 0.03/0.55 Such that:s(37) =< B 0.03/0.55 s(38) =< s(37) 0.03/0.55 0.03/0.55 with precondition: [B>=3] 0.03/0.55 0.03/0.55 0.03/0.55 Closed-form bounds of evalfstart(A,B,C,D,F): 0.03/0.55 ------------------------------------- 0.03/0.55 * Chain [39] with precondition: [] 0.03/0.55 - Upper bound: 0 0.03/0.55 - Complexity: constant 0.03/0.55 * Chain [38] with precondition: [B=1] 0.03/0.55 - Upper bound: 1 0.03/0.55 - Complexity: constant 0.03/0.55 * Chain [37] with precondition: [0>=B] 0.03/0.55 - Upper bound: 0 0.03/0.55 - Complexity: constant 0.03/0.55 * Chain [36] with precondition: [B>=1] 0.03/0.55 - Upper bound: 0 0.03/0.55 - Complexity: constant 0.03/0.55 * Chain [35] with precondition: [B>=2] 0.03/0.55 - Upper bound: 17*B+2 0.03/0.55 - Complexity: n 0.03/0.55 * Chain [34] with precondition: [B>=3] 0.03/0.55 - Upper bound: 20*B+2 0.03/0.55 - Complexity: n 0.03/0.55 0.03/0.55 ### Maximum cost of evalfstart(A,B,C,D,F): nat(B)*20+1+1 0.03/0.55 Asymptotic class: n 0.03/0.55 * Total analysis performed in 471 ms. 0.03/0.55 0.55/0.66 EOF