0.03/0.22 WORST_CASE(?,O(n^1)) 0.03/0.22 0.03/0.22 Preprocessing Cost Relations 0.03/0.22 ===================================== 0.03/0.22 0.03/0.22 #### Computed strongly connected components 0.03/0.22 0. recursive : [f2/7] 0.03/0.22 1. non_recursive : [exit_location/1] 0.03/0.22 2. non_recursive : [f300/4] 0.03/0.22 3. non_recursive : [f2_loop_cont/5] 0.03/0.22 4. non_recursive : [f1/4] 0.03/0.22 0.03/0.22 #### Obtained direct recursion through partial evaluation 0.03/0.22 0. SCC is partially evaluated into f2/7 0.03/0.22 1. SCC is completely evaluated into other SCCs 0.03/0.22 2. SCC is completely evaluated into other SCCs 0.03/0.22 3. SCC is partially evaluated into f2_loop_cont/5 0.03/0.22 4. SCC is partially evaluated into f1/4 0.03/0.22 0.03/0.22 Control-Flow Refinement of Cost Relations 0.03/0.22 ===================================== 0.03/0.22 0.03/0.22 ### Specialization of cost equations f2/7 0.03/0.22 * CE 5 is refined into CE [8] 0.03/0.22 * CE 4 is refined into CE [9] 0.03/0.22 * CE 3 is refined into CE [10] 0.03/0.22 * CE 2 is refined into CE [11] 0.03/0.22 0.03/0.22 0.03/0.22 ### Cost equations --> "Loop" of f2/7 0.03/0.22 * CEs [10] --> Loop 8 0.03/0.22 * CEs [11] --> Loop 9 0.03/0.22 * CEs [8] --> Loop 10 0.03/0.22 * CEs [9] --> Loop 11 0.03/0.22 0.03/0.22 ### Ranking functions of CR f2(A,B,C,E,F,G,H) 0.03/0.22 * RF of phase [8]: [-B+3] 0.03/0.22 * RF of phase [9]: [-A+2] 0.03/0.22 0.03/0.22 #### Partial ranking functions of CR f2(A,B,C,E,F,G,H) 0.03/0.22 * Partial RF of phase [8]: 0.03/0.22 - RF of loop [8:1]: 0.03/0.22 -B+3 0.03/0.22 * Partial RF of phase [9]: 0.03/0.22 - RF of loop [9:1]: 0.03/0.22 -A+2 0.03/0.22 0.03/0.22 0.03/0.22 ### Specialization of cost equations f2_loop_cont/5 0.03/0.22 * CE 7 is refined into CE [12] 0.03/0.22 * CE 6 is refined into CE [13] 0.03/0.22 0.03/0.22 0.03/0.22 ### Cost equations --> "Loop" of f2_loop_cont/5 0.03/0.22 * CEs [12] --> Loop 12 0.03/0.22 * CEs [13] --> Loop 13 0.03/0.22 0.03/0.22 ### Ranking functions of CR f2_loop_cont(A,B,C,D,E) 0.03/0.22 0.03/0.22 #### Partial ranking functions of CR f2_loop_cont(A,B,C,D,E) 0.03/0.22 0.03/0.22 0.03/0.22 ### Specialization of cost equations f1/4 0.03/0.22 * CE 1 is refined into CE [14,15,16,17,18,19,20,21] 0.03/0.22 0.03/0.22 0.03/0.22 ### Cost equations --> "Loop" of f1/4 0.03/0.22 * CEs [17] --> Loop 14 0.03/0.22 * CEs [16,21] --> Loop 15 0.03/0.22 * CEs [15,20] --> Loop 16 0.03/0.22 * CEs [14] --> Loop 17 0.03/0.22 * CEs [19] --> Loop 18 0.03/0.22 * CEs [18] --> Loop 19 0.03/0.22 0.03/0.22 ### Ranking functions of CR f1(A,B,C,E) 0.03/0.22 0.03/0.22 #### Partial ranking functions of CR f1(A,B,C,E) 0.03/0.22 0.03/0.22 0.03/0.22 Computing Bounds 0.03/0.22 ===================================== 0.03/0.22 0.03/0.22 #### Cost of chains of f2(A,B,C,E,F,G,H): 0.03/0.22 * Chain [[9],[8],11]: 1*it(8)+1*it(9)+0 0.03/0.22 Such that:it(9) =< -A+2 0.03/0.22 it(8) =< F 0.03/0.22 0.03/0.22 with precondition: [E=2,G=3,A+3=B+F,1>=A,A>=B] 0.03/0.22 0.03/0.22 * Chain [[9],[8],10]: 1*it(8)+1*it(9)+0 0.03/0.22 Such that:it(9) =< -A+2 0.03/0.22 it(8) =< A-B+1 0.03/0.22 0.03/0.22 with precondition: [E=3,1>=A,A>=B] 0.03/0.22 0.03/0.22 * Chain [[9],11]: 1*it(9)+0 0.03/0.22 Such that:it(9) =< -A+2 0.03/0.22 0.03/0.22 with precondition: [E=2,F=2,A+G=B+2,1>=A,B>=A+1] 0.03/0.22 0.03/0.22 * Chain [[9],10]: 1*it(9)+0 0.03/0.22 Such that:it(9) =< -A+2 0.03/0.22 0.03/0.22 with precondition: [E=3,1>=A] 0.03/0.22 0.03/0.22 * Chain [[8],11]: 1*it(8)+0 0.03/0.22 Such that:it(8) =< -A+F 0.03/0.22 0.03/0.22 with precondition: [E=2,G=3,A+3=B+F,2>=B,A>=2] 0.03/0.22 0.03/0.22 * Chain [[8],10]: 1*it(8)+0 0.03/0.22 Such that:it(8) =< -B+3 0.03/0.22 0.03/0.22 with precondition: [E=3,2>=B,A>=2] 0.03/0.22 0.03/0.22 * Chain [11]: 0 0.03/0.22 with precondition: [E=2,A=F,B=G,A>=2,B>=3] 0.03/0.22 0.03/0.22 * Chain [10]: 0 0.03/0.22 with precondition: [E=3] 0.03/0.22 0.03/0.22 0.03/0.22 #### Cost of chains of f2_loop_cont(A,B,C,D,E): 0.03/0.22 * Chain [13]: 0 0.03/0.22 with precondition: [A=2] 0.03/0.22 0.03/0.22 * Chain [12]: 0 0.03/0.22 with precondition: [A=3] 0.03/0.22 0.03/0.22 0.03/0.22 #### Cost of chains of f1(A,B,C,E): 0.03/0.22 * Chain [19]: 0 0.03/0.22 with precondition: [] 0.03/0.22 0.03/0.22 * Chain [18]: 1*s(1)+0 0.03/0.22 Such that:s(1) =< -A+2 0.03/0.22 0.03/0.22 with precondition: [1>=A] 0.03/0.22 0.03/0.22 * Chain [17]: 1*s(2)+0 0.03/0.22 Such that:s(2) =< -A+2 0.03/0.22 0.03/0.22 with precondition: [1>=A,B>=A+1] 0.03/0.22 0.03/0.22 * Chain [16]: 2*s(3)+1*s(4)+1*s(6)+0 0.03/0.22 Such that:s(6) =< A-B+1 0.03/0.22 s(4) =< A-B+3 0.03/0.22 aux(1) =< -A+2 0.03/0.22 s(3) =< aux(1) 0.03/0.22 0.03/0.22 with precondition: [1>=A,A>=B] 0.03/0.22 0.03/0.22 * Chain [15]: 2*s(7)+0 0.03/0.22 Such that:aux(2) =< -B+3 0.03/0.22 s(7) =< aux(2) 0.03/0.22 0.03/0.22 with precondition: [2>=B,A>=2] 0.03/0.22 0.03/0.22 * Chain [14]: 0 0.03/0.22 with precondition: [A>=2,B>=3] 0.03/0.22 0.03/0.22 0.03/0.22 Closed-form bounds of f1(A,B,C,E): 0.03/0.22 ------------------------------------- 0.03/0.22 * Chain [19] with precondition: [] 0.03/0.22 - Upper bound: 0 0.03/0.22 - Complexity: constant 0.03/0.22 * Chain [18] with precondition: [1>=A] 0.03/0.22 - Upper bound: -A+2 0.03/0.22 - Complexity: n 0.03/0.22 * Chain [17] with precondition: [1>=A,B>=A+1] 0.03/0.22 - Upper bound: -A+2 0.03/0.22 - Complexity: n 0.03/0.22 * Chain [16] with precondition: [1>=A,A>=B] 0.03/0.22 - Upper bound: -2*B+8 0.03/0.22 - Complexity: n 0.03/0.22 * Chain [15] with precondition: [2>=B,A>=2] 0.03/0.22 - Upper bound: -2*B+6 0.03/0.22 - Complexity: n 0.03/0.22 * Chain [14] with precondition: [A>=2,B>=3] 0.03/0.22 - Upper bound: 0 0.03/0.22 - Complexity: constant 0.03/0.22 0.03/0.22 ### Maximum cost of f1(A,B,C,E): max([nat(-B+3)*2,nat(A-B+1)+nat(-A+2)+nat(A-B+3)+nat(-A+2)]) 0.03/0.22 Asymptotic class: n 0.03/0.22 * Total analysis performed in 161 ms. 0.03/0.22 0.03/0.32 EOF