0.03/0.21 WORST_CASE(?,O(n^1)) 0.03/0.21 0.03/0.21 Preprocessing Cost Relations 0.03/0.21 ===================================== 0.03/0.21 0.03/0.21 #### Computed strongly connected components 0.03/0.21 0. non_recursive : [f1/6] 0.03/0.21 1. recursive : [f300/7] 0.03/0.21 2. non_recursive : [exit_location/1] 0.03/0.21 3. non_recursive : [f300_loop_cont/7] 0.03/0.21 4. non_recursive : [f2/6] 0.03/0.21 0.03/0.21 #### Obtained direct recursion through partial evaluation 0.03/0.21 0. SCC is completely evaluated into other SCCs 0.03/0.21 1. SCC is partially evaluated into f300/7 0.03/0.21 2. SCC is completely evaluated into other SCCs 0.03/0.21 3. SCC is partially evaluated into f300_loop_cont/7 0.03/0.21 4. SCC is partially evaluated into f2/6 0.03/0.21 0.03/0.21 Control-Flow Refinement of Cost Relations 0.03/0.21 ===================================== 0.03/0.21 0.03/0.21 ### Specialization of cost equations f300/7 0.03/0.21 * CE 6 is refined into CE [9] 0.03/0.21 * CE 3 is refined into CE [10] 0.03/0.21 * CE 4 is refined into CE [11] 0.03/0.21 * CE 5 is refined into CE [12] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of f300/7 0.03/0.21 * CEs [11] --> Loop 9 0.03/0.21 * CEs [12] --> Loop 10 0.03/0.21 * CEs [9] --> Loop 11 0.03/0.21 * CEs [10] --> Loop 12 0.03/0.21 0.03/0.21 ### Ranking functions of CR f300(B,D,E,G,H,I,J) 0.03/0.21 * RF of phase [9]: [-D-1] 0.03/0.21 * RF of phase [10]: [-D-1,-E-1] 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR f300(B,D,E,G,H,I,J) 0.03/0.21 * Partial RF of phase [9]: 0.03/0.21 - RF of loop [9:1]: 0.03/0.21 -D-1 0.03/0.21 * Partial RF of phase [10]: 0.03/0.21 - RF of loop [10:1]: 0.03/0.21 -D-1 0.03/0.21 -E-1 0.03/0.21 0.03/0.21 0.03/0.21 ### Specialization of cost equations f300_loop_cont/7 0.03/0.21 * CE 8 is refined into CE [13] 0.03/0.21 * CE 7 is refined into CE [14] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of f300_loop_cont/7 0.03/0.21 * CEs [13] --> Loop 13 0.03/0.21 * CEs [14] --> Loop 14 0.03/0.21 0.03/0.21 ### Ranking functions of CR f300_loop_cont(A,B,C,D,E,F,G) 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR f300_loop_cont(A,B,C,D,E,F,G) 0.03/0.21 0.03/0.21 0.03/0.21 ### Specialization of cost equations f2/6 0.03/0.21 * CE 2 is refined into CE [15,16,17,18,19,20] 0.03/0.21 * CE 1 is refined into CE [21] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of f2/6 0.03/0.21 * CEs [17] --> Loop 15 0.03/0.21 * CEs [18] --> Loop 16 0.03/0.21 * CEs [16] --> Loop 17 0.03/0.21 * CEs [15,20] --> Loop 18 0.03/0.21 * CEs [19] --> Loop 19 0.03/0.21 * CEs [21] --> Loop 20 0.03/0.21 0.03/0.21 ### Ranking functions of CR f2(A,B,C,D,E,G) 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR f2(A,B,C,D,E,G) 0.03/0.21 0.03/0.21 0.03/0.21 Computing Bounds 0.03/0.21 ===================================== 0.03/0.21 0.03/0.21 #### Cost of chains of f300(B,D,E,G,H,I,J): 0.03/0.21 * Chain [[10],12]: 1*it(10)+0 0.03/0.21 Such that:it(10) =< -E+J 0.03/0.21 0.03/0.21 with precondition: [G=2,I+1=0,D+J+1=E,0>=D+2,D>=E] 0.03/0.21 0.03/0.21 * Chain [[10],11]: 1*it(10)+0 0.03/0.21 Such that:it(10) =< -D 0.03/0.21 it(10) =< -E 0.03/0.21 0.03/0.21 with precondition: [G=3,0>=D+2,0>=E+2] 0.03/0.21 0.03/0.21 * Chain [[9],12]: 1*it(9)+0 0.03/0.21 Such that:it(9) =< -E+J 0.03/0.21 0.03/0.21 with precondition: [G=2,I+1=0,D+J+1=E,0>=D+2,E>=0] 0.03/0.21 0.03/0.21 * Chain [[9],11]: 1*it(9)+0 0.03/0.21 Such that:it(9) =< -D 0.03/0.21 0.03/0.21 with precondition: [G=3,0>=D+2,E>=0] 0.03/0.21 0.03/0.21 * Chain [12]: 0 0.03/0.21 with precondition: [G=2,J=E,D=I,D+1>=0] 0.03/0.21 0.03/0.21 * Chain [11]: 0 0.03/0.21 with precondition: [G=3] 0.03/0.21 0.03/0.21 0.03/0.21 #### Cost of chains of f300_loop_cont(A,B,C,D,E,F,G): 0.03/0.21 * Chain [14]: 0 0.03/0.21 with precondition: [A=2,B>=2,D>=2] 0.03/0.21 0.03/0.21 * Chain [13]: 0 0.03/0.21 with precondition: [A=3,B>=2,D>=2] 0.03/0.21 0.03/0.21 0.03/0.21 #### Cost of chains of f2(A,B,C,D,E,G): 0.03/0.21 * Chain [20]: 0 0.03/0.21 with precondition: [1>=A] 0.03/0.21 0.03/0.21 * Chain [19]: 1*s(1)+0 0.03/0.21 Such that:s(1) =< -D 0.03/0.21 s(1) =< -E 0.03/0.21 0.03/0.21 with precondition: [0>=D+2,0>=E+2,A>=2,C>=2] 0.03/0.21 0.03/0.21 * Chain [18]: 2*s(2)+0 0.03/0.21 Such that:aux(1) =< -D 0.03/0.21 s(2) =< aux(1) 0.03/0.21 0.03/0.21 with precondition: [0>=D+2,A>=2,C>=2,E>=0] 0.03/0.21 0.03/0.21 * Chain [17]: 1*s(4)+0 0.03/0.21 Such that:s(4) =< -D 0.03/0.21 0.03/0.21 with precondition: [0>=D+2,A>=2,C>=2,D>=E] 0.03/0.21 0.03/0.21 * Chain [16]: 0 0.03/0.21 with precondition: [A>=2,C>=2] 0.03/0.21 0.03/0.21 * Chain [15]: 0 0.03/0.21 with precondition: [A>=2,C>=2,D+1>=0] 0.03/0.21 0.03/0.21 0.03/0.21 Closed-form bounds of f2(A,B,C,D,E,G): 0.03/0.21 ------------------------------------- 0.03/0.21 * Chain [20] with precondition: [1>=A] 0.03/0.21 - Upper bound: 0 0.03/0.21 - Complexity: constant 0.03/0.21 * Chain [19] with precondition: [0>=D+2,0>=E+2,A>=2,C>=2] 0.03/0.21 - Upper bound: -D 0.03/0.21 - Complexity: n 0.03/0.21 * Chain [18] with precondition: [0>=D+2,A>=2,C>=2,E>=0] 0.03/0.21 - Upper bound: -2*D 0.03/0.21 - Complexity: n 0.03/0.21 * Chain [17] with precondition: [0>=D+2,A>=2,C>=2,D>=E] 0.03/0.21 - Upper bound: -D 0.03/0.21 - Complexity: n 0.03/0.21 * Chain [16] with precondition: [A>=2,C>=2] 0.03/0.21 - Upper bound: 0 0.03/0.21 - Complexity: constant 0.03/0.21 * Chain [15] with precondition: [A>=2,C>=2,D+1>=0] 0.03/0.21 - Upper bound: 0 0.03/0.21 - Complexity: constant 0.03/0.21 0.03/0.21 ### Maximum cost of f2(A,B,C,D,E,G): nat(-D)*2 0.03/0.21 Asymptotic class: n 0.03/0.21 * Total analysis performed in 152 ms. 0.03/0.21 0.03/0.32 EOF