0.03/0.48 WORST_CASE(?,O(1)) 0.03/0.48 0.03/0.48 Preprocessing Cost Relations 0.03/0.48 ===================================== 0.03/0.48 0.03/0.48 #### Computed strongly connected components 0.03/0.48 0. recursive : [f10/9,f9/9] 0.03/0.48 1. non_recursive : [exit_location/1] 0.03/0.48 2. recursive : [f16/9] 0.03/0.48 3. non_recursive : [f28/8] 0.03/0.48 4. non_recursive : [f16_loop_cont/9] 0.03/0.48 5. non_recursive : [f9_loop_cont/9] 0.03/0.48 6. non_recursive : [f0/8] 0.03/0.48 0.03/0.48 #### Obtained direct recursion through partial evaluation 0.03/0.48 0. SCC is partially evaluated into f9/9 0.03/0.48 1. SCC is completely evaluated into other SCCs 0.03/0.48 2. SCC is partially evaluated into f16/9 0.03/0.48 3. SCC is completely evaluated into other SCCs 0.03/0.48 4. SCC is partially evaluated into f16_loop_cont/9 0.03/0.48 5. SCC is partially evaluated into f9_loop_cont/9 0.03/0.48 6. SCC is partially evaluated into f0/8 0.03/0.48 0.03/0.48 Control-Flow Refinement of Cost Relations 0.03/0.48 ===================================== 0.03/0.48 0.03/0.48 ### Specialization of cost equations f9/9 0.03/0.48 * CE 2 is refined into CE [17] 0.03/0.48 * CE 3 is refined into CE [18] 0.03/0.48 * CE 7 is refined into CE [19] 0.03/0.48 * CE 6 is refined into CE [20] 0.03/0.48 * CE 4 is refined into CE [21] 0.03/0.48 * CE 5 is refined into CE [22] 0.03/0.48 0.03/0.48 0.03/0.48 ### Cost equations --> "Loop" of f9/9 0.03/0.48 * CEs [21] --> Loop 17 0.03/0.48 * CEs [22] --> Loop 18 0.03/0.48 * CEs [17] --> Loop 19 0.03/0.48 * CEs [18] --> Loop 20 0.03/0.48 * CEs [19] --> Loop 21 0.03/0.48 * CEs [20] --> Loop 22 0.03/0.48 0.03/0.48 ### Ranking functions of CR f9(A,B,C,D,I,J,K,L,M) 0.03/0.48 * RF of phase [17,18]: [-A+10,-B+10] 0.03/0.48 0.03/0.48 #### Partial ranking functions of CR f9(A,B,C,D,I,J,K,L,M) 0.03/0.48 * Partial RF of phase [17,18]: 0.03/0.48 - RF of loop [17:1,18:1]: 0.03/0.48 -A+10 0.03/0.48 -B+10 0.03/0.48 0.03/0.48 0.03/0.48 ### Specialization of cost equations f16/9 0.03/0.48 * CE 14 is refined into CE [23] 0.03/0.48 * CE 10 is refined into CE [24] 0.03/0.48 * CE 13 is refined into CE [25] 0.03/0.48 * CE 12 is refined into CE [26] 0.03/0.48 * CE 11 is refined into CE [27] 0.03/0.48 0.03/0.48 0.03/0.48 ### Cost equations --> "Loop" of f16/9 0.03/0.48 * CEs [26] --> Loop 23 0.03/0.48 * CEs [27] --> Loop 24 0.03/0.48 * CEs [23] --> Loop 25 0.03/0.48 * CEs [24] --> Loop 26 0.03/0.48 * CEs [25] --> Loop 27 0.03/0.48 0.03/0.48 ### Ranking functions of CR f16(A,E,F,G,I,J,K,L,M) 0.03/0.48 * RF of phase [23,24]: [-A+10] 0.03/0.48 0.03/0.48 #### Partial ranking functions of CR f16(A,E,F,G,I,J,K,L,M) 0.03/0.48 * Partial RF of phase [23,24]: 0.03/0.48 - RF of loop [23:1,24:1]: 0.03/0.48 -A+10 0.03/0.48 0.03/0.48 0.03/0.48 ### Specialization of cost equations f16_loop_cont/9 0.03/0.48 * CE 16 is refined into CE [28] 0.03/0.48 * CE 15 is refined into CE [29] 0.03/0.48 0.03/0.48 0.03/0.48 ### Cost equations --> "Loop" of f16_loop_cont/9 0.03/0.48 * CEs [28] --> Loop 28 0.03/0.48 * CEs [29] --> Loop 29 0.03/0.48 0.03/0.48 ### Ranking functions of CR f16_loop_cont(A,B,C,D,E,F,G,H,I) 0.03/0.48 0.03/0.48 #### Partial ranking functions of CR f16_loop_cont(A,B,C,D,E,F,G,H,I) 0.03/0.48 0.03/0.48 0.03/0.48 ### Specialization of cost equations f9_loop_cont/9 0.03/0.48 * CE 9 is refined into CE [30,31,32,33,34,35] 0.03/0.48 * CE 8 is refined into CE [36] 0.03/0.48 0.03/0.48 0.03/0.48 ### Cost equations --> "Loop" of f9_loop_cont/9 0.03/0.48 * CEs [33] --> Loop 30 0.03/0.48 * CEs [32] --> Loop 31 0.03/0.48 * CEs [30,31,35] --> Loop 32 0.03/0.48 * CEs [34] --> Loop 33 0.03/0.48 * CEs [36] --> Loop 34 0.03/0.48 0.03/0.48 ### Ranking functions of CR f9_loop_cont(A,B,C,D,E,F,G,H,I) 0.03/0.48 0.03/0.48 #### Partial ranking functions of CR f9_loop_cont(A,B,C,D,E,F,G,H,I) 0.03/0.48 0.03/0.48 0.03/0.48 ### Specialization of cost equations f0/8 0.03/0.48 * CE 1 is refined into CE [37,38,39,40,41,42,43,44,45,46,47,48,49,50] 0.03/0.48 0.03/0.48 0.03/0.48 ### Cost equations --> "Loop" of f0/8 0.03/0.48 * CEs [37,38,39,40,41,42,43,44,45,46,47,48,49,50] --> Loop 35 0.03/0.48 0.03/0.48 ### Ranking functions of CR f0(A,B,C,D,E,F,G,I) 0.03/0.48 0.03/0.48 #### Partial ranking functions of CR f0(A,B,C,D,E,F,G,I) 0.03/0.48 0.03/0.48 0.03/0.48 Computing Bounds 0.03/0.48 ===================================== 0.03/0.48 0.03/0.48 #### Cost of chains of f9(A,B,C,D,I,J,K,L,M): 0.03/0.48 * Chain [[17,18],22]: 2*it(17)+0 0.03/0.48 Such that:aux(5) =< -B+10 0.03/0.48 aux(6) =< -B+K 0.03/0.48 it(17) =< aux(5) 0.03/0.48 it(17) =< aux(6) 0.03/0.48 0.03/0.48 with precondition: [I=4,J=0,L=0,M=0,A=B,10>=K,A>=0,K>=A+1] 0.03/0.48 0.03/0.48 * Chain [[17,18],21]: 2*it(17)+0 0.03/0.48 Such that:aux(7) =< -A+10 0.03/0.48 it(17) =< aux(7) 0.03/0.48 0.03/0.48 with precondition: [I=3,A=B,9>=A,A>=0] 0.03/0.48 0.03/0.48 * Chain [[17,18],20]: 2*it(17)+0 0.03/0.48 Such that:aux(8) =< -B+10 0.03/0.48 it(17) =< aux(8) 0.03/0.48 0.03/0.48 with precondition: [I=4,J=0,K=10,A=B,L=M,9>=A,0>=L+1,A>=0] 0.03/0.48 0.03/0.48 * Chain [[17,18],19]: 2*it(17)+0 0.03/0.48 Such that:aux(9) =< -B+10 0.03/0.48 it(17) =< aux(9) 0.03/0.48 0.03/0.48 with precondition: [I=4,J=0,K=10,A=B,L=M,9>=A,A>=0,L>=1] 0.03/0.48 0.03/0.48 * Chain [22]: 0 0.03/0.48 with precondition: [C=0,I=4,J=0,L=0,M=0,B=A,B=K,B>=0] 0.03/0.48 0.03/0.48 * Chain [21]: 0 0.03/0.48 with precondition: [I=3,B=A,B>=0] 0.03/0.48 0.03/0.48 0.03/0.48 #### Cost of chains of f16(A,E,F,G,I,J,K,L,M): 0.03/0.48 * Chain [[23,24],27]: 2*it(23)+0 0.03/0.48 Such that:aux(10) =< -A+10 0.03/0.48 aux(11) =< -A+J 0.03/0.48 it(23) =< aux(10) 0.03/0.48 it(23) =< aux(11) 0.03/0.48 0.03/0.48 with precondition: [I=2,L=0,M=0,J=K,9>=J,J>=A+1] 0.03/0.48 0.03/0.48 * Chain [[23,24],26]: 2*it(23)+0 0.03/0.48 Such that:aux(12) =< -A+10 0.03/0.48 it(23) =< aux(12) 0.03/0.48 0.03/0.48 with precondition: [I=2,J=10,K=9,L=M,9>=A] 0.03/0.48 0.03/0.48 * Chain [[23,24],25]: 2*it(23)+0 0.03/0.48 Such that:aux(13) =< -A+10 0.03/0.48 it(23) =< aux(13) 0.03/0.48 0.03/0.48 with precondition: [I=3,9>=A] 0.03/0.48 0.03/0.48 * Chain [27]: 0 0.03/0.48 with precondition: [I=2,L=0,M=0,A=J,A=K,9>=A] 0.03/0.48 0.03/0.48 * Chain [26]: 0 0.03/0.48 with precondition: [I=2,K=E,L=F,M=G,A=J,A>=10] 0.03/0.48 0.03/0.48 * Chain [25]: 0 0.03/0.48 with precondition: [I=3] 0.03/0.48 0.03/0.48 0.03/0.48 #### Cost of chains of f16_loop_cont(A,B,C,D,E,F,G,H,I): 0.03/0.48 * Chain [29]: 0 0.03/0.48 with precondition: [A=2] 0.03/0.48 0.03/0.48 * Chain [28]: 0 0.03/0.48 with precondition: [A=3] 0.03/0.48 0.03/0.48 0.03/0.48 #### Cost of chains of f9_loop_cont(A,B,C,D,E,F,G,H,I): 0.03/0.48 * Chain [34]: 0 0.03/0.48 with precondition: [A=3] 0.03/0.48 0.03/0.48 * Chain [33]: 0 0.03/0.48 with precondition: [A=4] 0.03/0.48 0.03/0.48 * Chain [32]: 4*s(2)+0 0.03/0.48 Such that:aux(14) =< -B+10 0.03/0.48 s(2) =< aux(14) 0.03/0.48 0.03/0.48 with precondition: [A=4,9>=B] 0.03/0.48 0.03/0.48 * Chain [31]: 2*s(7)+0 0.03/0.48 Such that:s(6) =< -B+9 0.03/0.48 s(5) =< -B+10 0.03/0.48 s(7) =< s(5) 0.03/0.48 s(7) =< s(6) 0.03/0.48 0.03/0.48 with precondition: [A=4,8>=B] 0.03/0.48 0.03/0.48 * Chain [30]: 0 0.03/0.48 with precondition: [A=4,B>=10] 0.03/0.48 0.03/0.48 0.03/0.48 #### Cost of chains of f0(A,B,C,D,E,F,G,I): 0.03/0.48 * Chain [35]: 440 0.03/0.48 with precondition: [] 0.03/0.48 0.03/0.48 0.03/0.48 Closed-form bounds of f0(A,B,C,D,E,F,G,I): 0.03/0.48 ------------------------------------- 0.03/0.48 * Chain [35] with precondition: [] 0.03/0.48 - Upper bound: 440 0.03/0.48 - Complexity: constant 0.03/0.48 0.03/0.48 ### Maximum cost of f0(A,B,C,D,E,F,G,I): 440 0.03/0.48 Asymptotic class: constant 0.03/0.48 * Total analysis performed in 400 ms. 0.03/0.48 0.03/0.59 EOF