0.03/0.24 WORST_CASE(?,O(n^1)) 0.03/0.24 0.03/0.24 Preprocessing Cost Relations 0.03/0.24 ===================================== 0.03/0.24 0.03/0.24 #### Computed strongly connected components 0.03/0.24 0. recursive : [f2/13] 0.03/0.24 1. non_recursive : [exit_location/1] 0.03/0.24 2. non_recursive : [f4/7] 0.03/0.24 3. non_recursive : [f2_loop_cont/8] 0.03/0.24 4. non_recursive : [f3/7] 0.03/0.24 0.03/0.24 #### Obtained direct recursion through partial evaluation 0.03/0.24 0. SCC is partially evaluated into f2/13 0.03/0.24 1. SCC is completely evaluated into other SCCs 0.03/0.24 2. SCC is completely evaluated into other SCCs 0.03/0.24 3. SCC is partially evaluated into f2_loop_cont/8 0.03/0.24 4. SCC is partially evaluated into f3/7 0.03/0.24 0.03/0.24 Control-Flow Refinement of Cost Relations 0.03/0.24 ===================================== 0.03/0.24 0.03/0.24 ### Specialization of cost equations f2/13 0.03/0.24 * CE 5 is refined into CE [8] 0.03/0.24 * CE 3 is refined into CE [9] 0.03/0.24 * CE 4 is refined into CE [10] 0.03/0.24 * CE 2 is refined into CE [11] 0.03/0.24 0.03/0.24 0.03/0.24 ### Cost equations --> "Loop" of f2/13 0.03/0.24 * CEs [11] --> Loop 8 0.03/0.24 * CEs [8] --> Loop 9 0.03/0.24 * CEs [9] --> Loop 10 0.03/0.24 * CEs [10] --> Loop 11 0.03/0.24 0.03/0.24 ### Ranking functions of CR f2(A,B,C,D,E,F,I,J,K,L,M,N,O) 0.03/0.24 * RF of phase [8]: [A,B] 0.03/0.24 0.03/0.24 #### Partial ranking functions of CR f2(A,B,C,D,E,F,I,J,K,L,M,N,O) 0.03/0.24 * Partial RF of phase [8]: 0.03/0.24 - RF of loop [8:1]: 0.03/0.24 A 0.03/0.24 B 0.03/0.24 0.03/0.24 0.03/0.24 ### Specialization of cost equations f2_loop_cont/8 0.03/0.24 * CE 7 is refined into CE [12] 0.03/0.24 * CE 6 is refined into CE [13] 0.03/0.24 0.03/0.24 0.03/0.24 ### Cost equations --> "Loop" of f2_loop_cont/8 0.03/0.24 * CEs [12] --> Loop 12 0.03/0.24 * CEs [13] --> Loop 13 0.03/0.24 0.03/0.24 ### Ranking functions of CR f2_loop_cont(A,B,C,D,E,F,G,H) 0.03/0.24 0.03/0.24 #### Partial ranking functions of CR f2_loop_cont(A,B,C,D,E,F,G,H) 0.03/0.24 0.03/0.24 0.03/0.24 ### Specialization of cost equations f3/7 0.03/0.24 * CE 1 is refined into CE [14,15,16,17,18,19] 0.03/0.24 0.03/0.24 0.03/0.24 ### Cost equations --> "Loop" of f3/7 0.03/0.24 * CEs [15] --> Loop 14 0.03/0.24 * CEs [14] --> Loop 15 0.03/0.24 * CEs [19] --> Loop 16 0.03/0.24 * CEs [16] --> Loop 17 0.03/0.24 * CEs [17] --> Loop 18 0.03/0.24 * CEs [18] --> Loop 19 0.03/0.24 0.03/0.24 ### Ranking functions of CR f3(A,B,C,D,E,F,I) 0.03/0.24 0.03/0.24 #### Partial ranking functions of CR f3(A,B,C,D,E,F,I) 0.03/0.24 0.03/0.24 0.03/0.24 Computing Bounds 0.03/0.24 ===================================== 0.03/0.24 0.03/0.24 #### Cost of chains of f2(A,B,C,D,E,F,I,J,K,L,M,N,O): 0.03/0.24 * Chain [[8],11]: 1*it(8)+0 0.03/0.24 Such that:it(8) =< A 0.03/0.24 0.03/0.24 with precondition: [I=2,J=0,L=1,N+1=0,A+K=B,A+M=B+1,A>=1,B>=A+1] 0.03/0.24 0.03/0.24 * Chain [[8],10]: 1*it(8)+0 0.03/0.24 Such that:it(8) =< A-J 0.03/0.24 0.03/0.24 with precondition: [I=2,M=1,A=B+J,A+1=B+L,A=B+N+1,0>=K,B>=1,A>=B] 0.03/0.24 0.03/0.24 * Chain [[8],9]: 1*it(8)+0 0.03/0.24 Such that:it(8) =< A 0.03/0.24 it(8) =< B 0.03/0.24 0.03/0.24 with precondition: [I=3,A>=1,B>=1] 0.03/0.24 0.03/0.24 * Chain [11]: 0 0.03/0.24 with precondition: [I=2,L=C,M=D,N=E,A=J,B=K,0>=A,B>=1] 0.03/0.24 0.03/0.24 * Chain [10]: 0 0.03/0.24 with precondition: [I=2,J=A,L=C,M=D,N=E,0>=B,0>=K] 0.03/0.24 0.03/0.24 * Chain [9]: 0 0.03/0.24 with precondition: [I=3] 0.03/0.24 0.03/0.24 0.03/0.24 #### Cost of chains of f2_loop_cont(A,B,C,D,E,F,G,H): 0.03/0.24 * Chain [13]: 0 0.03/0.24 with precondition: [A=2] 0.03/0.24 0.03/0.24 * Chain [12]: 0 0.03/0.24 with precondition: [A=3] 0.03/0.24 0.03/0.24 0.03/0.24 #### Cost of chains of f3(A,B,C,D,E,F,I): 0.03/0.24 * Chain [19]: 0 0.03/0.24 with precondition: [] 0.03/0.24 0.03/0.24 * Chain [18]: 0 0.03/0.24 with precondition: [0>=A,B>=1] 0.03/0.24 0.03/0.24 * Chain [17]: 0 0.03/0.24 with precondition: [0>=B] 0.03/0.24 0.03/0.24 * Chain [16]: 1*s(1)+0 0.03/0.24 Such that:s(1) =< A 0.03/0.24 s(1) =< B 0.03/0.24 0.03/0.24 with precondition: [A>=1,B>=1] 0.03/0.24 0.03/0.24 * Chain [15]: 1*s(2)+0 0.03/0.24 Such that:s(2) =< A 0.03/0.24 0.03/0.24 with precondition: [A>=1,B>=A+1] 0.03/0.24 0.03/0.24 * Chain [14]: 1*s(3)+0 0.03/0.24 Such that:s(3) =< B 0.03/0.24 0.03/0.24 with precondition: [B>=1,A>=B] 0.03/0.24 0.03/0.24 0.03/0.24 Closed-form bounds of f3(A,B,C,D,E,F,I): 0.03/0.24 ------------------------------------- 0.03/0.24 * Chain [19] with precondition: [] 0.03/0.24 - Upper bound: 0 0.03/0.24 - Complexity: constant 0.03/0.24 * Chain [18] with precondition: [0>=A,B>=1] 0.03/0.24 - Upper bound: 0 0.03/0.24 - Complexity: constant 0.03/0.24 * Chain [17] with precondition: [0>=B] 0.03/0.24 - Upper bound: 0 0.03/0.24 - Complexity: constant 0.03/0.24 * Chain [16] with precondition: [A>=1,B>=1] 0.03/0.24 - Upper bound: A 0.03/0.24 - Complexity: n 0.03/0.24 * Chain [15] with precondition: [A>=1,B>=A+1] 0.03/0.24 - Upper bound: A 0.03/0.24 - Complexity: n 0.03/0.24 * Chain [14] with precondition: [B>=1,A>=B] 0.03/0.24 - Upper bound: B 0.03/0.24 - Complexity: n 0.03/0.24 0.03/0.24 ### Maximum cost of f3(A,B,C,D,E,F,I): max([nat(A),nat(B)]) 0.03/0.24 Asymptotic class: n 0.03/0.24 * Total analysis performed in 175 ms. 0.03/0.24 0.03/0.34 EOF