0.57/0.60 WORST_CASE(?,O(1)) 0.57/0.60 0.57/0.60 Preprocessing Cost Relations 0.57/0.60 ===================================== 0.57/0.60 0.57/0.60 #### Computed strongly connected components 0.57/0.60 0. recursive : [lbl111/13] 0.57/0.60 1. recursive : [lbl111_loop_cont/14,lbl91/13] 0.57/0.60 2. non_recursive : [exit_location/1] 0.57/0.60 3. non_recursive : [stop/7] 0.57/0.60 4. non_recursive : [lbl91_loop_cont/8] 0.57/0.60 5. non_recursive : [start/7] 0.57/0.60 6. non_recursive : [start0/7] 0.57/0.60 0.57/0.60 #### Obtained direct recursion through partial evaluation 0.57/0.60 0. SCC is partially evaluated into lbl111/13 0.57/0.60 1. SCC is partially evaluated into lbl91/13 0.57/0.60 2. SCC is completely evaluated into other SCCs 0.57/0.60 3. SCC is completely evaluated into other SCCs 0.57/0.60 4. SCC is partially evaluated into lbl91_loop_cont/8 0.57/0.60 5. SCC is partially evaluated into start/7 0.57/0.60 6. SCC is partially evaluated into start0/7 0.57/0.60 0.57/0.60 Control-Flow Refinement of Cost Relations 0.57/0.60 ===================================== 0.57/0.60 0.57/0.60 ### Specialization of cost equations lbl111/13 0.57/0.60 * CE 13 is refined into CE [19] 0.57/0.60 * CE 9 is refined into CE [20] 0.57/0.60 * CE 10 is refined into CE [21] 0.57/0.60 * CE 12 is refined into CE [22] 0.57/0.60 * CE 11 is refined into CE [23] 0.57/0.60 0.57/0.60 0.57/0.60 ### Cost equations --> "Loop" of lbl111/13 0.57/0.60 * CEs [22] --> Loop 15 0.57/0.60 * CEs [23] --> Loop 16 0.57/0.60 * CEs [19] --> Loop 17 0.57/0.60 * CEs [20] --> Loop 18 0.57/0.60 * CEs [21] --> Loop 19 0.57/0.60 0.57/0.60 ### Ranking functions of CR lbl111(A,B,C,D,E,F,G,H,I,J,K,L,M) 0.57/0.60 * RF of phase [15]: [-E/2+20] 0.57/0.60 * RF of phase [16]: [-E/2+20] 0.57/0.60 0.57/0.60 #### Partial ranking functions of CR lbl111(A,B,C,D,E,F,G,H,I,J,K,L,M) 0.57/0.60 * Partial RF of phase [15]: 0.57/0.60 - RF of loop [15:1]: 0.57/0.60 -E/2+20 0.57/0.60 * Partial RF of phase [16]: 0.57/0.60 - RF of loop [16:1]: 0.57/0.60 -E/2+20 0.57/0.60 0.57/0.60 0.57/0.60 ### Specialization of cost equations lbl91/13 0.57/0.60 * CE 18 is refined into CE [24] 0.57/0.60 * CE 16 is refined into CE [25] 0.57/0.60 * CE 17 is refined into CE [26] 0.57/0.60 0.57/0.60 0.57/0.60 ### Cost equations --> "Loop" of lbl91/13 0.57/0.60 * CEs [26] --> Loop 20 0.57/0.60 * CEs [24] --> Loop 21 0.57/0.60 * CEs [25] --> Loop 22 0.57/0.60 0.57/0.60 ### Ranking functions of CR lbl91(A,B,C,D,E,F,G,H,I,J,K,L,M) 0.57/0.60 * RF of phase [20]: [-E+40] 0.57/0.60 0.57/0.60 #### Partial ranking functions of CR lbl91(A,B,C,D,E,F,G,H,I,J,K,L,M) 0.57/0.60 * Partial RF of phase [20]: 0.57/0.60 - RF of loop [20:1]: 0.57/0.60 -E+40 0.57/0.60 0.57/0.60 0.57/0.60 ### Specialization of cost equations lbl91_loop_cont/8 0.57/0.60 * CE 15 is refined into CE [27] 0.57/0.60 * CE 14 is refined into CE [28] 0.57/0.60 0.57/0.60 0.57/0.60 ### Cost equations --> "Loop" of lbl91_loop_cont/8 0.57/0.60 * CEs [27] --> Loop 23 0.57/0.60 * CEs [28] --> Loop 24 0.57/0.60 0.57/0.60 ### Ranking functions of CR lbl91_loop_cont(A,B,C,D,E,F,G,H) 0.57/0.60 0.57/0.60 #### Partial ranking functions of CR lbl91_loop_cont(A,B,C,D,E,F,G,H) 0.57/0.60 0.57/0.60 0.57/0.60 ### Specialization of cost equations start/7 0.57/0.60 * CE 2 is refined into CE [29,30] 0.57/0.60 * CE 4 is discarded (unfeasible) 0.57/0.60 * CE 6 is refined into CE [31] 0.57/0.60 * CE 3 is refined into CE [32,33] 0.57/0.60 * CE 5 is discarded (unfeasible) 0.57/0.60 * CE 7 is refined into CE [34] 0.57/0.60 * CE 8 is refined into CE [35,36,37] 0.57/0.60 0.57/0.60 0.57/0.60 ### Cost equations --> "Loop" of start/7 0.57/0.60 * CEs [29,30,31] --> Loop 25 0.57/0.60 * CEs [32,33,34] --> Loop 26 0.57/0.60 * CEs [35,36,37] --> Loop 27 0.57/0.60 0.57/0.60 ### Ranking functions of CR start(A,B,C,D,E,F,G) 0.57/0.60 0.57/0.60 #### Partial ranking functions of CR start(A,B,C,D,E,F,G) 0.57/0.60 0.57/0.60 0.57/0.60 ### Specialization of cost equations start0/7 0.57/0.60 * CE 1 is refined into CE [38,39,40] 0.57/0.60 0.57/0.60 0.57/0.60 ### Cost equations --> "Loop" of start0/7 0.57/0.60 * CEs [40] --> Loop 28 0.57/0.60 * CEs [39] --> Loop 29 0.57/0.60 * CEs [38] --> Loop 30 0.57/0.60 0.57/0.60 ### Ranking functions of CR start0(A,B,C,D,E,F,G) 0.57/0.60 0.57/0.60 #### Partial ranking functions of CR start0(A,B,C,D,E,F,G) 0.57/0.60 0.57/0.60 0.57/0.60 Computing Bounds 0.57/0.60 ===================================== 0.57/0.60 0.57/0.60 #### Cost of chains of lbl111(A,B,C,D,E,F,G,H,I,J,K,L,M): 0.57/0.60 * Chain [[16],18]: 1*it(16)+0 0.57/0.60 Such that:it(16) =< -E/2+20 0.57/0.60 0.57/0.60 with precondition: [C=100,G=2,J=100,A=B,A=H,A=I,D=K,F=M,0>=A+1,41>=L,E>=2,L>=40,L>=E+2] 0.57/0.60 0.57/0.60 * Chain [[16],17]: 1*it(16)+0 0.57/0.60 Such that:it(16) =< -E/2+20 0.57/0.60 0.57/0.60 with precondition: [C=100,G=4,A=B,0>=A+1,39>=E,E>=2] 0.57/0.60 0.57/0.60 * Chain [[15],18]: 1*it(15)+0 0.57/0.60 Such that:it(15) =< -E/2+20 0.57/0.60 0.57/0.60 with precondition: [C=100,G=2,J=100,A=B,A=H,A=I,D=K,F=M,41>=L,A>=1,E>=2,L>=40,L>=E+2] 0.57/0.60 0.57/0.60 * Chain [[15],17]: 1*it(15)+0 0.57/0.60 Such that:it(15) =< -E/2+20 0.57/0.60 0.57/0.60 with precondition: [C=100,G=4,A=B,39>=E,A>=1,E>=2] 0.57/0.60 0.57/0.60 * Chain [19]: 0 0.57/0.60 with precondition: [A=0,B=0,C=100,E=2,G=3,H=0,I=0,J=100,L=3,K=D,M=F] 0.57/0.60 0.57/0.60 * Chain [17]: 0 0.57/0.60 with precondition: [C=100,G=4,B=A,E>=2] 0.57/0.60 0.57/0.60 0.57/0.60 #### Cost of chains of lbl91(A,B,C,D,E,F,G,H,I,J,K,L,M): 0.57/0.60 * Chain [[20],22]: 1*it(20)+0 0.57/0.60 Such that:it(20) =< -E+40 0.57/0.60 0.57/0.60 with precondition: [A=0,B=0,C=100,G=2,H=0,I=0,J=100,L=40,D=K,F=M,39>=E,E>=1] 0.57/0.60 0.57/0.60 * Chain [[20],21]: 1*it(20)+0 0.57/0.60 Such that:it(20) =< -E+40 0.57/0.60 0.57/0.60 with precondition: [A=0,B=0,C=100,G=4,39>=E,E>=1] 0.57/0.60 0.57/0.60 * Chain [22]: 0 0.57/0.60 with precondition: [A=0,B=0,C=100,E=40,G=2,H=0,I=0,J=100,L=40,K=D,M=F] 0.57/0.60 0.57/0.60 * Chain [21]: 0 0.57/0.60 with precondition: [G=4] 0.57/0.60 0.57/0.60 0.57/0.60 #### Cost of chains of lbl91_loop_cont(A,B,C,D,E,F,G,H): 0.57/0.60 * Chain [24]: 0 0.57/0.60 with precondition: [A=2] 0.57/0.60 0.57/0.60 * Chain [23]: 0 0.57/0.60 with precondition: [A=4] 0.57/0.60 0.57/0.60 0.57/0.60 #### Cost of chains of start(A,B,C,D,E,F,G): 0.57/0.60 * Chain [27]: 78 0.57/0.60 with precondition: [A=0,B=0,D=C,F=E] 0.57/0.60 0.57/0.60 * Chain [26]: 38 0.57/0.60 with precondition: [B=A,D=C,F=E,0>=B+1] 0.57/0.60 0.57/0.60 * Chain [25]: 38 0.57/0.60 with precondition: [B=A,D=C,F=E,B>=1] 0.57/0.60 0.57/0.60 0.57/0.60 #### Cost of chains of start0(A,B,C,D,E,F,G): 0.57/0.60 * Chain [30]: 78 0.57/0.60 with precondition: [B=0] 0.57/0.60 0.57/0.60 * Chain [29]: 38 0.57/0.60 with precondition: [0>=B+1] 0.57/0.60 0.57/0.60 * Chain [28]: 38 0.57/0.60 with precondition: [B>=1] 0.57/0.60 0.57/0.60 0.57/0.60 Closed-form bounds of start0(A,B,C,D,E,F,G): 0.57/0.60 ------------------------------------- 0.57/0.60 * Chain [30] with precondition: [B=0] 0.57/0.60 - Upper bound: 78 0.57/0.60 - Complexity: constant 0.57/0.60 * Chain [29] with precondition: [0>=B+1] 0.57/0.60 - Upper bound: 38 0.57/0.60 - Complexity: constant 0.57/0.60 * Chain [28] with precondition: [B>=1] 0.57/0.60 - Upper bound: 38 0.57/0.60 - Complexity: constant 0.57/0.60 0.57/0.60 ### Maximum cost of start0(A,B,C,D,E,F,G): 78 0.57/0.60 Asymptotic class: constant 0.57/0.60 * Total analysis performed in 505 ms. 0.57/0.60 0.60/0.70 EOF