0.03/0.30 WORST_CASE(?,O(1)) 0.03/0.30 0.03/0.30 Preprocessing Cost Relations 0.03/0.30 ===================================== 0.03/0.30 0.03/0.30 #### Computed strongly connected components 0.03/0.30 0. recursive : [f15/6,f16/6] 0.03/0.30 1. non_recursive : [exit_location/1] 0.03/0.30 2. recursive : [f23/4] 0.03/0.30 3. non_recursive : [f7/6] 0.03/0.30 4. non_recursive : [f23_loop_cont/7] 0.03/0.30 5. non_recursive : [f15_loop_cont/7] 0.03/0.30 6. non_recursive : [f0/6] 0.03/0.30 0.03/0.30 #### Obtained direct recursion through partial evaluation 0.03/0.30 0. SCC is partially evaluated into f15/6 0.03/0.30 1. SCC is completely evaluated into other SCCs 0.03/0.30 2. SCC is partially evaluated into f23/4 0.03/0.30 3. SCC is completely evaluated into other SCCs 0.03/0.30 4. SCC is partially evaluated into f23_loop_cont/7 0.03/0.30 5. SCC is partially evaluated into f15_loop_cont/7 0.03/0.30 6. SCC is partially evaluated into f0/6 0.03/0.30 0.03/0.30 Control-Flow Refinement of Cost Relations 0.03/0.30 ===================================== 0.03/0.30 0.03/0.30 ### Specialization of cost equations f15/6 0.03/0.30 * CE 4 is refined into CE [16] 0.03/0.30 * CE 3 is discarded (unfeasible) 0.03/0.30 * CE 7 is refined into CE [17] 0.03/0.30 * CE 8 is refined into CE [18] 0.03/0.30 * CE 6 is refined into CE [19] 0.03/0.30 * CE 5 is discarded (unfeasible) 0.03/0.30 0.03/0.30 0.03/0.30 ### Cost equations --> "Loop" of f15/6 0.03/0.30 * CEs [19] --> Loop 15 0.03/0.30 * CEs [16] --> Loop 16 0.03/0.30 * CEs [17] --> Loop 17 0.03/0.30 * CEs [18] --> Loop 18 0.03/0.30 0.03/0.30 ### Ranking functions of CR f15(A,B,E,H,I,J) 0.03/0.30 * RF of phase [15]: [A-B,-B+100] 0.03/0.30 0.03/0.30 #### Partial ranking functions of CR f15(A,B,E,H,I,J) 0.03/0.30 * Partial RF of phase [15]: 0.03/0.30 - RF of loop [15:1]: 0.03/0.30 A-B 0.03/0.30 -B+100 0.03/0.30 0.03/0.30 0.03/0.30 ### Specialization of cost equations f23/4 0.03/0.30 * CE 13 is refined into CE [20] 0.03/0.30 * CE 12 is refined into CE [21] 0.03/0.30 * CE 11 is refined into CE [22] 0.03/0.30 0.03/0.30 0.03/0.30 ### Cost equations --> "Loop" of f23/4 0.03/0.30 * CEs [22] --> Loop 19 0.03/0.30 * CEs [20] --> Loop 20 0.03/0.30 * CEs [21] --> Loop 21 0.03/0.30 0.03/0.30 ### Ranking functions of CR f23(B,E,H,I) 0.03/0.30 * RF of phase [19]: [B-E] 0.03/0.30 0.03/0.30 #### Partial ranking functions of CR f23(B,E,H,I) 0.03/0.30 * Partial RF of phase [19]: 0.03/0.30 - RF of loop [19:1]: 0.03/0.30 B-E 0.03/0.30 0.03/0.30 0.03/0.30 ### Specialization of cost equations f23_loop_cont/7 0.03/0.30 * CE 15 is refined into CE [23] 0.03/0.30 * CE 14 is refined into CE [24] 0.03/0.30 0.03/0.30 0.03/0.30 ### Cost equations --> "Loop" of f23_loop_cont/7 0.03/0.30 * CEs [23] --> Loop 22 0.03/0.30 * CEs [24] --> Loop 23 0.03/0.30 0.03/0.30 ### Ranking functions of CR f23_loop_cont(A,B,C,D,E,F,G) 0.03/0.30 0.03/0.30 #### Partial ranking functions of CR f23_loop_cont(A,B,C,D,E,F,G) 0.03/0.30 0.03/0.30 0.03/0.30 ### Specialization of cost equations f15_loop_cont/7 0.03/0.30 * CE 10 is refined into CE [25,26,27,28] 0.03/0.30 * CE 9 is refined into CE [29] 0.03/0.30 0.03/0.30 0.03/0.30 ### Cost equations --> "Loop" of f15_loop_cont/7 0.03/0.30 * CEs [25,28] --> Loop 24 0.03/0.30 * CEs [26] --> Loop 25 0.03/0.30 * CEs [27] --> Loop 26 0.03/0.30 * CEs [29] --> Loop 27 0.03/0.30 0.03/0.30 ### Ranking functions of CR f15_loop_cont(A,B,C,D,E,F,G) 0.03/0.30 0.03/0.30 #### Partial ranking functions of CR f15_loop_cont(A,B,C,D,E,F,G) 0.03/0.30 0.03/0.30 0.03/0.30 ### Specialization of cost equations f0/6 0.03/0.30 * CE 1 is refined into CE [30] 0.03/0.30 * CE 2 is refined into CE [31,32,33,34,35,36,37,38,39,40] 0.03/0.30 0.03/0.30 0.03/0.30 ### Cost equations --> "Loop" of f0/6 0.03/0.30 * CEs [30,31,32,33,34,35,36,37,38,39,40] --> Loop 28 0.03/0.30 0.03/0.30 ### Ranking functions of CR f0(A,B,C,D,E,H) 0.03/0.30 0.03/0.30 #### Partial ranking functions of CR f0(A,B,C,D,E,H) 0.03/0.30 0.03/0.30 0.03/0.30 Computing Bounds 0.03/0.30 ===================================== 0.03/0.30 0.03/0.30 #### Cost of chains of f15(A,B,E,H,I,J): 0.03/0.30 * Chain [[15],18]: 1*it(15)+0 0.03/0.30 Such that:it(15) =< A-B 0.03/0.30 0.03/0.30 with precondition: [H=3,100>=A,B>=0,A>=B+1] 0.03/0.30 0.03/0.30 * Chain [[15],17]: 1*it(15)+0 0.03/0.30 Such that:it(15) =< -B+I+1 0.03/0.30 0.03/0.30 with precondition: [H=4,J=0,A=I+1,100>=A,B>=0,A>=B+1] 0.03/0.30 0.03/0.30 * Chain [[15],16]: 1*it(15)+0 0.03/0.30 Such that:it(15) =< -B+I+1 0.03/0.30 0.03/0.30 with precondition: [H=4,J=0,100>=A,B>=0,I>=B,A>=I+2] 0.03/0.30 0.03/0.30 * Chain [18]: 0 0.03/0.30 with precondition: [H=3,100>=A,A>=1,B>=0] 0.03/0.30 0.03/0.30 * Chain [16]: 0 0.03/0.30 with precondition: [H=4,J=0,B=I+1,100>=A,B>=0,A>=B+1] 0.03/0.30 0.03/0.30 0.03/0.30 #### Cost of chains of f23(B,E,H,I): 0.03/0.30 * Chain [[19],21]: 1*it(19)+0 0.03/0.30 Such that:it(19) =< B-E 0.03/0.30 0.03/0.30 with precondition: [H=2,B=I,B>=E+1] 0.03/0.30 0.03/0.30 * Chain [[19],20]: 1*it(19)+0 0.03/0.30 Such that:it(19) =< B-E 0.03/0.30 0.03/0.30 with precondition: [H=3,B>=E+1] 0.03/0.30 0.03/0.30 * Chain [21]: 0 0.03/0.30 with precondition: [H=2,E=I,E>=B] 0.03/0.30 0.03/0.30 * Chain [20]: 0 0.03/0.30 with precondition: [H=3] 0.03/0.30 0.03/0.30 0.03/0.30 #### Cost of chains of f23_loop_cont(A,B,C,D,E,F,G): 0.03/0.30 * Chain [23]: 0 0.03/0.30 with precondition: [A=2,D=B,100>=D,D>=1] 0.03/0.30 0.03/0.30 * Chain [22]: 0 0.03/0.30 with precondition: [A=3,D=B,100>=D,D>=1] 0.03/0.30 0.03/0.30 0.03/0.30 #### Cost of chains of f15_loop_cont(A,B,C,D,E,F,G): 0.03/0.30 * Chain [27]: 0 0.03/0.30 with precondition: [A=3,D=B,100>=D,D>=1] 0.03/0.30 0.03/0.30 * Chain [26]: 0 0.03/0.30 with precondition: [A=4,D=B,100>=D,D>=1] 0.03/0.30 0.03/0.30 * Chain [25]: 0 0.03/0.30 with precondition: [A=4,D=B,100>=D,D>=1,F>=C] 0.03/0.30 0.03/0.30 * Chain [24]: 2*s(1)+0 0.03/0.30 Such that:aux(1) =< C-F 0.03/0.30 s(1) =< aux(1) 0.03/0.30 0.03/0.30 with precondition: [A=4,D=B,100>=D,D>=1,C>=F+1] 0.03/0.30 0.03/0.30 0.03/0.30 #### Cost of chains of f0(A,B,C,D,E,H): 0.03/0.30 * Chain [28]: 894 0.03/0.30 with precondition: [] 0.03/0.30 0.03/0.30 0.03/0.30 Closed-form bounds of f0(A,B,C,D,E,H): 0.03/0.30 ------------------------------------- 0.03/0.30 * Chain [28] with precondition: [] 0.03/0.30 - Upper bound: 894 0.03/0.30 - Complexity: constant 0.03/0.30 0.03/0.30 ### Maximum cost of f0(A,B,C,D,E,H): 894 0.03/0.30 Asymptotic class: constant 0.03/0.30 * Total analysis performed in 232 ms. 0.03/0.30 0.03/0.40 EOF