0.03/0.46 WORST_CASE(?,O(n^2)) 0.03/0.46 0.03/0.46 Preprocessing Cost Relations 0.03/0.46 ===================================== 0.03/0.46 0.03/0.46 #### Computed strongly connected components 0.03/0.46 0. recursive : [lbl72/7] 0.03/0.46 1. recursive : [lbl62/8,lbl72_loop_cont/9] 0.03/0.46 2. non_recursive : [exit_location/1] 0.03/0.46 3. non_recursive : [stop/7] 0.03/0.46 4. non_recursive : [lbl62_loop_cont/8] 0.03/0.46 5. non_recursive : [start/7] 0.03/0.46 6. non_recursive : [start0/7] 0.03/0.46 0.03/0.46 #### Obtained direct recursion through partial evaluation 0.03/0.46 0. SCC is partially evaluated into lbl72/7 0.03/0.46 1. SCC is partially evaluated into lbl62/8 0.03/0.46 2. SCC is completely evaluated into other SCCs 0.03/0.46 3. SCC is completely evaluated into other SCCs 0.03/0.46 4. SCC is partially evaluated into lbl62_loop_cont/8 0.03/0.46 5. SCC is partially evaluated into start/7 0.03/0.46 6. SCC is partially evaluated into start0/7 0.03/0.46 0.03/0.46 Control-Flow Refinement of Cost Relations 0.03/0.46 ===================================== 0.03/0.46 0.03/0.46 ### Specialization of cost equations lbl72/7 0.03/0.46 * CE 13 is refined into CE [14] 0.03/0.46 * CE 12 is refined into CE [15] 0.03/0.46 * CE 11 is refined into CE [16] 0.03/0.46 0.03/0.46 0.03/0.46 ### Cost equations --> "Loop" of lbl72/7 0.03/0.46 * CEs [14] --> Loop 14 0.03/0.46 * CEs [15] --> Loop 15 0.03/0.46 * CEs [16] --> Loop 16 0.03/0.46 0.03/0.46 ### Ranking functions of CR lbl72(A,B,D,F,G,H,I) 0.03/0.46 0.03/0.46 #### Partial ranking functions of CR lbl72(A,B,D,F,G,H,I) 0.03/0.46 0.03/0.46 0.03/0.46 ### Specialization of cost equations lbl62/8 0.03/0.46 * CE 8 is refined into CE [17] 0.03/0.46 * CE 4 is refined into CE [18] 0.03/0.46 * CE 6 is refined into CE [19] 0.03/0.46 * CE 7 is refined into CE [20] 0.03/0.46 * CE 5 is refined into CE [21] 0.03/0.46 0.03/0.46 0.03/0.46 ### Cost equations --> "Loop" of lbl62/8 0.03/0.46 * CEs [20] --> Loop 17 0.03/0.46 * CEs [21] --> Loop 18 0.03/0.46 * CEs [17] --> Loop 19 0.03/0.46 * CEs [18] --> Loop 20 0.03/0.46 * CEs [19] --> Loop 21 0.03/0.46 0.03/0.46 ### Ranking functions of CR lbl62(A,B,D,F,G,H,I,J) 0.03/0.46 0.03/0.46 #### Partial ranking functions of CR lbl62(A,B,D,F,G,H,I,J) 0.03/0.46 * Partial RF of phase [17,18]: 0.03/0.46 - RF of loop [17:1]: 0.03/0.46 B depends on loops [18:1] 0.03/0.46 - RF of loop [18:1]: 0.03/0.46 -B+1 depends on loops [17:1] 0.03/0.46 D-1 0.03/0.46 0.03/0.46 0.03/0.46 ### Specialization of cost equations lbl62_loop_cont/8 0.03/0.46 * CE 9 is refined into CE [22] 0.03/0.46 * CE 10 is refined into CE [23] 0.03/0.46 0.03/0.46 0.03/0.46 ### Cost equations --> "Loop" of lbl62_loop_cont/8 0.03/0.46 * CEs [22] --> Loop 22 0.03/0.46 * CEs [23] --> Loop 23 0.03/0.46 0.03/0.46 ### Ranking functions of CR lbl62_loop_cont(A,B,C,D,E,F,G,H) 0.03/0.46 0.03/0.46 #### Partial ranking functions of CR lbl62_loop_cont(A,B,C,D,E,F,G,H) 0.03/0.46 0.03/0.46 0.03/0.46 ### Specialization of cost equations start/7 0.03/0.46 * CE 3 is refined into CE [24,25,26,27,28] 0.03/0.46 * CE 2 is refined into CE [29] 0.03/0.46 0.03/0.46 0.03/0.46 ### Cost equations --> "Loop" of start/7 0.03/0.46 * CEs [26,28] --> Loop 24 0.03/0.46 * CEs [27] --> Loop 25 0.03/0.46 * CEs [29] --> Loop 26 0.03/0.46 * CEs [24,25] --> Loop 27 0.03/0.46 0.03/0.46 ### Ranking functions of CR start(A,B,C,D,E,F,G) 0.03/0.46 0.03/0.46 #### Partial ranking functions of CR start(A,B,C,D,E,F,G) 0.03/0.46 0.03/0.46 0.03/0.46 ### Specialization of cost equations start0/7 0.03/0.46 * CE 1 is refined into CE [30,31,32,33] 0.03/0.46 0.03/0.46 0.03/0.46 ### Cost equations --> "Loop" of start0/7 0.03/0.46 * CEs [33] --> Loop 28 0.03/0.46 * CEs [32] --> Loop 29 0.03/0.46 * CEs [31] --> Loop 30 0.03/0.46 * CEs [30] --> Loop 31 0.03/0.46 0.03/0.46 ### Ranking functions of CR start0(A,B,C,D,E,F,G) 0.03/0.46 0.03/0.46 #### Partial ranking functions of CR start0(A,B,C,D,E,F,G) 0.03/0.46 0.03/0.46 0.03/0.46 Computing Bounds 0.03/0.46 ===================================== 0.03/0.46 0.03/0.46 #### Cost of chains of lbl72(A,B,D,F,G,H,I): 0.03/0.46 * Chain [16]: 0 0.03/0.46 with precondition: [B=0,D=0,G=2,H=0,I=0,F=A,F>=1] 0.03/0.46 0.03/0.46 * Chain [15]: 0 0.03/0.46 with precondition: [B=0,G=3,F=A,F=H+1,D=I,D>=1,F>=D+1] 0.03/0.46 0.03/0.46 * Chain [14]: 0 0.03/0.46 with precondition: [B=0,G=4,F=A,D>=0,F>=D+1] 0.03/0.46 0.03/0.46 0.03/0.46 #### Cost of chains of lbl62(A,B,D,F,G,H,I,J): 0.03/0.46 * Chain [[17,18],21]: 1*it(17)+1*it(18)+0 0.03/0.46 Such that:it(18) =< D 0.03/0.46 aux(23) =< B 0.03/0.46 aux(24) =< J 0.03/0.46 aux(17) =< aux(24) 0.03/0.46 aux(17) =< aux(24) 0.03/0.46 aux(18) =< it(18)*aux(17) 0.03/0.46 aux(1) =< it(18)*aux(17) 0.03/0.46 aux(12) =< it(18)*aux(24) 0.03/0.46 aux(1) =< it(18)*aux(24) 0.03/0.46 aux(3) =< aux(18) 0.03/0.46 aux(3) =< aux(12) 0.03/0.46 it(17) =< aux(1)+aux(23) 0.03/0.46 it(17) =< aux(3)+aux(23) 0.03/0.46 0.03/0.46 with precondition: [G=2,A=F,A=H,A=J,A>=2,B>=0,D>=1,A>=B+1,A>=D,B+D>=2] 0.03/0.46 0.03/0.46 * Chain [[17,18],20]: 1*it(17)+1*it(18)+0 0.03/0.46 Such that:it(18) =< D 0.03/0.46 aux(25) =< B 0.03/0.46 aux(26) =< F 0.03/0.46 aux(17) =< aux(26) 0.03/0.46 aux(17) =< aux(26) 0.03/0.46 aux(18) =< it(18)*aux(17) 0.03/0.46 aux(1) =< it(18)*aux(17) 0.03/0.46 aux(12) =< it(18)*aux(26) 0.03/0.46 aux(1) =< it(18)*aux(26) 0.03/0.46 aux(3) =< aux(18) 0.03/0.46 aux(3) =< aux(12) 0.03/0.46 it(17) =< aux(1)+aux(25) 0.03/0.46 it(17) =< aux(3)+aux(25) 0.03/0.46 0.03/0.46 with precondition: [G=4,A=F,A>=2,B>=0,D>=1,A>=B+1,A>=D,B+D>=2] 0.03/0.46 0.03/0.46 * Chain [[17,18],19]: 1*it(17)+1*it(18)+0 0.03/0.46 Such that:aux(4) =< A 0.03/0.46 it(18) =< D 0.03/0.46 aux(27) =< B 0.03/0.46 aux(28) =< F 0.03/0.46 aux(4) =< aux(27) 0.03/0.46 aux(17) =< aux(28) 0.03/0.46 aux(17) =< aux(28) 0.03/0.46 aux(18) =< it(18)*aux(17) 0.03/0.46 aux(1) =< it(18)*aux(17) 0.03/0.46 aux(12) =< it(18)*aux(28) 0.03/0.46 aux(1) =< it(18)*aux(28) 0.03/0.46 aux(3) =< aux(18) 0.03/0.46 aux(3) =< aux(12) 0.03/0.46 it(17) =< aux(1)+aux(27) 0.03/0.46 it(17) =< aux(3)+aux(4) 0.03/0.46 0.03/0.46 with precondition: [G=4,A=F,A>=2,B>=0,D>=1,A>=B+1,A>=D,B+D>=2] 0.03/0.46 0.03/0.46 * Chain [21]: 0 0.03/0.46 with precondition: [B=0,D=1,G=2,F=A,F=H,F=J,F>=1] 0.03/0.46 0.03/0.46 * Chain [20]: 0 0.03/0.46 with precondition: [B=0,G=4,F=A,D>=1,F>=D] 0.03/0.46 0.03/0.46 * Chain [19]: 0 0.03/0.46 with precondition: [G=4,F=A,B>=0,D>=1,F>=B+1,F>=D] 0.03/0.46 0.03/0.46 0.03/0.46 #### Cost of chains of lbl62_loop_cont(A,B,C,D,E,F,G,H): 0.03/0.46 * Chain [23]: 0 0.03/0.46 with precondition: [A=2,F>=1] 0.03/0.46 0.03/0.46 * Chain [22]: 0 0.03/0.46 with precondition: [A=4,F>=1] 0.03/0.46 0.03/0.46 0.03/0.46 #### Cost of chains of start(A,B,C,D,E,F,G): 0.03/0.46 * Chain [27]: 0 0.03/0.46 with precondition: [A=1,F=1,C=B,E=D] 0.03/0.46 0.03/0.46 * Chain [26]: 0 0.03/0.46 with precondition: [F=A,C=B,E=D,0>=F] 0.03/0.46 0.03/0.46 * Chain [25]: 0 0.03/0.46 with precondition: [F=A,C=B,E=D,F>=1] 0.03/0.46 0.03/0.46 * Chain [24]: 3*s(20)+3*s(28)+0 0.03/0.46 Such that:aux(34) =< F 0.03/0.46 s(20) =< aux(34) 0.03/0.46 s(23) =< aux(34) 0.03/0.46 s(23) =< aux(34) 0.03/0.46 s(24) =< s(20)*s(23) 0.03/0.46 s(25) =< s(20)*s(23) 0.03/0.46 s(26) =< s(20)*aux(34) 0.03/0.46 s(25) =< s(20)*aux(34) 0.03/0.46 s(27) =< s(24) 0.03/0.46 s(27) =< s(26) 0.03/0.46 s(28) =< s(25)+aux(34) 0.03/0.46 s(28) =< s(27)+aux(34) 0.03/0.46 0.03/0.46 with precondition: [F=A,C=B,E=D,F>=2] 0.03/0.46 0.03/0.46 0.03/0.46 #### Cost of chains of start0(A,B,C,D,E,F,G): 0.03/0.46 * Chain [31]: 0 0.03/0.46 with precondition: [A=1] 0.03/0.46 0.03/0.46 * Chain [30]: 0 0.03/0.46 with precondition: [0>=A] 0.03/0.46 0.03/0.46 * Chain [29]: 0 0.03/0.46 with precondition: [A>=1] 0.03/0.46 0.03/0.46 * Chain [28]: 3*s(42)+3*s(48)+0 0.03/0.46 Such that:s(41) =< A 0.03/0.46 s(42) =< s(41) 0.03/0.46 s(43) =< s(41) 0.03/0.46 s(43) =< s(41) 0.03/0.46 s(44) =< s(42)*s(43) 0.03/0.46 s(45) =< s(42)*s(43) 0.03/0.46 s(46) =< s(42)*s(41) 0.03/0.46 s(45) =< s(42)*s(41) 0.03/0.46 s(47) =< s(44) 0.03/0.46 s(47) =< s(46) 0.03/0.46 s(48) =< s(45)+s(41) 0.03/0.46 s(48) =< s(47)+s(41) 0.03/0.46 0.03/0.46 with precondition: [A>=2] 0.03/0.46 0.03/0.46 0.03/0.46 Closed-form bounds of start0(A,B,C,D,E,F,G): 0.03/0.46 ------------------------------------- 0.03/0.46 * Chain [31] with precondition: [A=1] 0.03/0.46 - Upper bound: 0 0.03/0.46 - Complexity: constant 0.03/0.46 * Chain [30] with precondition: [0>=A] 0.03/0.46 - Upper bound: 0 0.03/0.46 - Complexity: constant 0.03/0.46 * Chain [29] with precondition: [A>=1] 0.03/0.46 - Upper bound: 0 0.03/0.46 - Complexity: constant 0.03/0.46 * Chain [28] with precondition: [A>=2] 0.03/0.46 - Upper bound: 3*A*A+6*A 0.03/0.46 - Complexity: n^2 0.03/0.46 0.03/0.46 ### Maximum cost of start0(A,B,C,D,E,F,G): nat(A)*3*nat(A)+nat(A)*6 0.03/0.46 Asymptotic class: n^2 0.03/0.46 * Total analysis performed in 378 ms. 0.03/0.46 0.03/0.56 EOF