0.03/0.18 MAYBE 0.03/0.18 0.03/0.18 Preprocessing Cost Relations 0.03/0.18 ===================================== 0.03/0.18 0.03/0.18 #### Computed strongly connected components 0.03/0.18 0. recursive : [f2/2] 0.03/0.18 1. non_recursive : [exit_location/1] 0.03/0.18 2. non_recursive : [f2_loop_cont/2] 0.03/0.18 3. recursive : [f3/5] 0.03/0.18 4. recursive : [f5/2] 0.03/0.18 5. non_recursive : [f5_loop_cont/2] 0.03/0.18 6. non_recursive : [f3_loop_cont/5] 0.03/0.18 7. non_recursive : [f0/4] 0.03/0.18 0.03/0.18 #### Obtained direct recursion through partial evaluation 0.03/0.18 0. SCC is partially evaluated into f2/2 0.03/0.18 1. SCC is completely evaluated into other SCCs 0.03/0.18 2. SCC is completely evaluated into other SCCs 0.03/0.18 3. SCC is partially evaluated into f3/5 0.03/0.18 4. SCC is partially evaluated into f5/2 0.03/0.18 5. SCC is completely evaluated into other SCCs 0.03/0.18 6. SCC is partially evaluated into f3_loop_cont/5 0.03/0.18 7. SCC is partially evaluated into f0/4 0.03/0.18 0.03/0.18 Control-Flow Refinement of Cost Relations 0.03/0.18 ===================================== 0.03/0.18 0.03/0.18 ### Specialization of cost equations f2/2 0.03/0.18 * CE 4 is refined into CE [12] 0.03/0.18 * CE 3 is refined into CE [13] 0.03/0.18 0.03/0.18 0.03/0.18 ### Cost equations --> "Loop" of f2/2 0.03/0.18 * CEs [13] --> Loop 12 0.03/0.18 * CEs [12] --> Loop 13 0.03/0.18 0.03/0.18 ### Ranking functions of CR f2(A,D) 0.03/0.18 0.03/0.18 #### Partial ranking functions of CR f2(A,D) 0.03/0.18 0.03/0.18 0.03/0.18 ### Specialization of cost equations f3/5 0.03/0.18 * CE 6 is refined into CE [14] 0.03/0.18 * CE 7 is refined into CE [15] 0.03/0.18 * CE 5 is refined into CE [16] 0.03/0.18 0.03/0.18 0.03/0.18 ### Cost equations --> "Loop" of f3/5 0.03/0.18 * CEs [16] --> Loop 14 0.03/0.18 * CEs [14] --> Loop 15 0.03/0.18 * CEs [15] --> Loop 16 0.03/0.18 0.03/0.18 ### Ranking functions of CR f3(A,B,D,E,F) 0.03/0.18 * RF of phase [14]: [B] 0.03/0.18 0.03/0.18 #### Partial ranking functions of CR f3(A,B,D,E,F) 0.03/0.18 * Partial RF of phase [14]: 0.03/0.18 - RF of loop [14:1]: 0.03/0.18 B 0.03/0.18 0.03/0.18 0.03/0.18 ### Specialization of cost equations f5/2 0.03/0.18 * CE 11 is refined into CE [17] 0.03/0.18 * CE 10 is refined into CE [18] 0.03/0.18 0.03/0.18 0.03/0.18 ### Cost equations --> "Loop" of f5/2 0.03/0.18 * CEs [18] --> Loop 17 0.03/0.18 * CEs [17] --> Loop 18 0.03/0.18 0.03/0.18 ### Ranking functions of CR f5(C,D) 0.03/0.18 0.03/0.18 #### Partial ranking functions of CR f5(C,D) 0.03/0.18 0.03/0.18 0.03/0.18 ### Specialization of cost equations f3_loop_cont/5 0.03/0.18 * CE 9 is refined into CE [19,20] 0.03/0.18 * CE 8 is refined into CE [21] 0.03/0.18 0.03/0.18 0.03/0.18 ### Cost equations --> "Loop" of f3_loop_cont/5 0.03/0.18 * CEs [19] --> Loop 19 0.03/0.18 * CEs [21] --> Loop 20 0.03/0.18 * CEs [20] --> Loop 21 0.03/0.18 0.03/0.18 ### Ranking functions of CR f3_loop_cont(A,B,C,D,E) 0.03/0.18 0.03/0.18 #### Partial ranking functions of CR f3_loop_cont(A,B,C,D,E) 0.03/0.18 0.03/0.18 0.03/0.18 ### Specialization of cost equations f0/4 0.03/0.18 * CE 1 is refined into CE [22,23] 0.03/0.18 * CE 2 is refined into CE [24,25,26,27,28,29] 0.03/0.18 0.03/0.18 0.03/0.18 ### Cost equations --> "Loop" of f0/4 0.03/0.18 * CEs [23] --> Loop 22 0.03/0.18 * CEs [27] --> Loop 23 0.03/0.18 * CEs [29] --> Loop 24 0.03/0.18 * CEs [22] --> Loop 25 0.03/0.18 * CEs [25,26] --> Loop 26 0.03/0.18 * CEs [24] --> Loop 27 0.03/0.18 * CEs [28] --> Loop 28 0.03/0.18 0.03/0.18 ### Ranking functions of CR f0(A,B,C,D) 0.03/0.18 0.03/0.18 #### Partial ranking functions of CR f0(A,B,C,D) 0.03/0.18 0.03/0.18 0.03/0.18 Computing Bounds 0.03/0.18 ===================================== 0.03/0.18 0.03/0.18 #### Cost of chains of f2(A,D): 0.03/0.18 * Chain [[12]]...: 1*it(12)+0 0.03/0.18 with precondition: [A>=0,D=2] 0.03/0.18 0.03/0.18 * Chain [[12],13]: 1*it(12)+0 0.03/0.18 with precondition: [D=2,A>=0] 0.03/0.18 0.03/0.18 * Chain [13]: 0 0.03/0.18 with precondition: [D=2,A>=0] 0.03/0.18 0.03/0.18 0.03/0.18 #### Cost of chains of f3(A,B,D,E,F): 0.03/0.18 * Chain [[14],16]: 1*it(14)+0 0.03/0.18 Such that:it(14) =< B 0.03/0.18 0.03/0.18 with precondition: [A=0,D=2,B>=1] 0.03/0.18 0.03/0.18 * Chain [[14],15]: 1*it(14)+0 0.03/0.18 Such that:it(14) =< B 0.03/0.18 0.03/0.18 with precondition: [A=0,D=3,E=0,F=0,B>=1] 0.03/0.18 0.03/0.18 * Chain [16]: 0 0.03/0.18 with precondition: [A=0,D=2] 0.03/0.18 0.03/0.18 * Chain [15]: 0 0.03/0.18 with precondition: [A=0,D=3,E=0,B=F,0>=B] 0.03/0.18 0.03/0.18 0.03/0.18 #### Cost of chains of f5(C,D): 0.03/0.18 * Chain [[17]]...: 1*it(17)+0 0.03/0.18 with precondition: [1>=C,D=2] 0.03/0.18 0.03/0.18 * Chain [[17],18]: 1*it(17)+0 0.03/0.18 with precondition: [D=2,1>=C] 0.03/0.18 0.03/0.18 * Chain [18]: 0 0.03/0.18 with precondition: [D=2,1>=C] 0.03/0.18 0.03/0.18 0.03/0.18 #### Cost of chains of f3_loop_cont(A,B,C,D,E): 0.03/0.18 * Chain [21]...: 1*s(3)+0 0.03/0.18 with precondition: [A=3,0>=D] 0.03/0.18 0.03/0.18 * Chain [20]: 0 0.03/0.18 with precondition: [A=2,0>=D] 0.03/0.18 0.03/0.18 * Chain [19]: 1*s(4)+0 0.03/0.18 with precondition: [A=3,0>=D] 0.03/0.18 0.03/0.18 0.03/0.18 #### Cost of chains of f0(A,B,C,D): 0.03/0.18 * Chain [28]: 1*s(5)+0 0.03/0.18 with precondition: [0>=B,0>=C] 0.03/0.18 0.03/0.18 * Chain [27]: 0 0.03/0.18 with precondition: [0>=C] 0.03/0.18 0.03/0.18 * Chain [26]: 2*s(6)+1*s(8)+0 0.03/0.18 Such that:aux(3) =< B 0.03/0.18 s(6) =< aux(3) 0.03/0.18 0.03/0.18 with precondition: [0>=C,B>=1] 0.03/0.18 0.03/0.18 * Chain [25]: 1*s(9)+0 0.03/0.18 with precondition: [C>=1] 0.03/0.18 0.03/0.18 * Chain [24]...: 1*s(10)+0 0.03/0.18 with precondition: [0>=B,0>=C] 0.03/0.18 0.03/0.18 * Chain [23]...: 1*s(11)+1*s(12)+0 0.03/0.18 Such that:s(11) =< B 0.03/0.18 0.03/0.18 with precondition: [0>=C,B>=1] 0.03/0.18 0.03/0.18 * Chain [22]...: 1*s(13)+0 0.03/0.18 with precondition: [C>=1] 0.03/0.18 0.03/0.18 0.03/0.18 Closed-form bounds of f0(A,B,C,D): 0.03/0.18 ------------------------------------- 0.03/0.18 * Chain [28] with precondition: [0>=B,0>=C] 0.03/0.18 - Upper bound: inf 0.03/0.18 - Complexity: infinity 0.03/0.18 * Chain [27] with precondition: [0>=C] 0.03/0.18 - Upper bound: 0 0.03/0.18 - Complexity: constant 0.03/0.18 * Chain [26] with precondition: [0>=C,B>=1] 0.03/0.18 - Upper bound: inf 0.03/0.18 - Complexity: infinity 0.03/0.18 * Chain [25] with precondition: [C>=1] 0.03/0.18 - Upper bound: inf 0.03/0.18 - Complexity: infinity 0.03/0.18 * Chain [24]... with precondition: [0>=B,0>=C] 0.03/0.18 - Upper bound: inf 0.03/0.18 - Complexity: infinity 0.03/0.18 * Chain [23]... with precondition: [0>=C,B>=1] 0.03/0.18 - Upper bound: inf 0.03/0.18 - Complexity: infinity 0.03/0.18 * Chain [22]... with precondition: [C>=1] 0.03/0.18 - Upper bound: inf 0.03/0.18 - Complexity: infinity 0.03/0.18 0.03/0.18 ### Maximum cost of f0(A,B,C,D): inf 0.03/0.18 Asymptotic class: infinity 0.03/0.18 * Total analysis performed in 121 ms. 0.03/0.18 0.03/0.28 EOF