0.03/0.30 WORST_CASE(?,O(n^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 : [f300/7] 0.03/0.30 1. non_recursive : [exit_location/1] 0.03/0.30 2. non_recursive : [f1/4] 0.03/0.30 3. non_recursive : [f300_loop_cont/5] 0.03/0.30 4. non_recursive : [f2/4] 0.03/0.30 0.03/0.30 #### Obtained direct recursion through partial evaluation 0.03/0.30 0. SCC is partially evaluated into f300/7 0.03/0.30 1. SCC is completely evaluated into other SCCs 0.03/0.30 2. SCC is completely evaluated into other SCCs 0.03/0.30 3. SCC is partially evaluated into f300_loop_cont/5 0.03/0.30 4. SCC is partially evaluated into f2/4 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 f300/7 0.03/0.30 * CE 6 is refined into CE [9] 0.03/0.30 * CE 5 is refined into CE [10] 0.03/0.30 * CE 3 is refined into CE [11] 0.03/0.30 * CE 4 is refined into CE [12] 0.03/0.30 * CE 2 is refined into CE [13] 0.03/0.30 0.03/0.30 0.03/0.30 ### Cost equations --> "Loop" of f300/7 0.03/0.30 * CEs [11] --> Loop 9 0.03/0.30 * CEs [12] --> Loop 10 0.03/0.30 * CEs [13] --> Loop 11 0.03/0.30 * CEs [9] --> Loop 12 0.03/0.30 * CEs [10] --> Loop 13 0.03/0.30 0.03/0.30 ### Ranking functions of CR f300(A,B,C,E,F,G,H) 0.03/0.30 * RF of phase [9]: [-A] 0.03/0.30 * RF of phase [10]: [-A,-B-1] 0.03/0.30 0.03/0.30 #### Partial ranking functions of CR f300(A,B,C,E,F,G,H) 0.03/0.30 * Partial RF of phase [9]: 0.03/0.30 - RF of loop [9:1]: 0.03/0.30 -A 0.03/0.30 * Partial RF of phase [10]: 0.03/0.30 - RF of loop [10:1]: 0.03/0.30 -A 0.03/0.30 -B-1 0.03/0.30 0.03/0.30 0.03/0.30 ### Specialization of cost equations f300_loop_cont/5 0.03/0.30 * CE 8 is refined into CE [14] 0.03/0.30 * CE 7 is refined into CE [15] 0.03/0.30 0.03/0.30 0.03/0.30 ### Cost equations --> "Loop" of f300_loop_cont/5 0.03/0.30 * CEs [14] --> Loop 14 0.03/0.30 * CEs [15] --> Loop 15 0.03/0.30 0.03/0.30 ### Ranking functions of CR f300_loop_cont(A,B,C,D,E) 0.03/0.30 0.03/0.30 #### Partial ranking functions of CR f300_loop_cont(A,B,C,D,E) 0.03/0.30 0.03/0.30 0.03/0.30 ### Specialization of cost equations f2/4 0.03/0.30 * CE 1 is refined into CE [16,17,18,19,20,21,22,23,24,25] 0.03/0.30 0.03/0.30 0.03/0.30 ### Cost equations --> "Loop" of f2/4 0.03/0.30 * CEs [21] --> Loop 16 0.03/0.30 * CEs [20,25] --> Loop 17 0.03/0.30 * CEs [19] --> Loop 18 0.03/0.30 * CEs [18,24] --> Loop 19 0.03/0.30 * CEs [23] --> Loop 20 0.03/0.30 * CEs [16,17] --> Loop 21 0.03/0.30 * CEs [22] --> Loop 22 0.03/0.30 0.03/0.30 ### Ranking functions of CR f2(A,B,C,E) 0.03/0.30 0.03/0.30 #### Partial ranking functions of CR f2(A,B,C,E) 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 f300(A,B,C,E,F,G,H): 0.03/0.30 * Chain [[10],13]: 1*it(10)+0 0.03/0.30 Such that:it(10) =< -B+G 0.03/0.30 0.03/0.30 with precondition: [E=2,F=0,A+G=B,0>=A+1,A>=B+1] 0.03/0.30 0.03/0.30 * Chain [[10],12]: 1*it(10)+0 0.03/0.30 Such that:it(10) =< -A 0.03/0.30 it(10) =< -B 0.03/0.30 0.03/0.30 with precondition: [E=3,0>=A+1,0>=B+2] 0.03/0.30 0.03/0.30 * Chain [[10],11,[9],13]: 1*it(9)+1*it(10)+1 0.03/0.30 Such that:it(10) =< -A-G+99 0.03/0.30 it(9) =< G 0.03/0.30 0.03/0.30 with precondition: [E=2,F=0,A+G=B+100,0>=B+2,B>=A] 0.03/0.30 0.03/0.30 * Chain [[10],11,[9],12]: 1*it(9)+1*it(10)+1 0.03/0.30 Such that:it(9) =< -A+B+100 0.03/0.30 it(10) =< -B 0.03/0.30 0.03/0.30 with precondition: [E=3,0>=B+2,B>=A] 0.03/0.30 0.03/0.30 * Chain [[10],11,12]: 1*it(10)+1 0.03/0.30 Such that:it(10) =< -B 0.03/0.30 0.03/0.30 with precondition: [E=3,0>=B+2,B>=A] 0.03/0.30 0.03/0.30 * Chain [[9],13]: 1*it(9)+0 0.03/0.30 Such that:it(9) =< -A 0.03/0.30 0.03/0.30 with precondition: [E=2,F=0,A+G=B,0>=A+1,B>=0] 0.03/0.30 0.03/0.30 * Chain [[9],12]: 1*it(9)+0 0.03/0.30 Such that:it(9) =< -A 0.03/0.30 0.03/0.30 with precondition: [E=3,0>=A+1,B>=0] 0.03/0.30 0.03/0.30 * Chain [13]: 0 0.03/0.30 with precondition: [E=2,G=B,A=F,A>=0] 0.03/0.30 0.03/0.30 * Chain [12]: 0 0.03/0.30 with precondition: [E=3] 0.03/0.30 0.03/0.30 * Chain [11,[9],13]: 1*it(9)+1 0.03/0.30 Such that:it(9) =< -A+99 0.03/0.30 0.03/0.30 with precondition: [B+1=0,E=2,F=0,A+G=99,0>=A+1] 0.03/0.30 0.03/0.30 * Chain [11,[9],12]: 1*it(9)+1 0.03/0.30 Such that:it(9) =< -A+99 0.03/0.30 0.03/0.30 with precondition: [B+1=0,E=3,0>=A+1] 0.03/0.30 0.03/0.30 * Chain [11,12]: 1 0.03/0.30 with precondition: [B+1=0,E=3,0>=A+1] 0.03/0.30 0.03/0.30 0.03/0.30 #### Cost of chains of f300_loop_cont(A,B,C,D,E): 0.03/0.30 * Chain [15]: 0 0.03/0.30 with precondition: [A=2] 0.03/0.30 0.03/0.30 * Chain [14]: 0 0.03/0.30 with precondition: [A=3] 0.03/0.30 0.03/0.30 0.03/0.30 #### Cost of chains of f2(A,B,C,E): 0.03/0.30 * Chain [22]: 0 0.03/0.30 with precondition: [] 0.03/0.30 0.03/0.30 * Chain [21]: 2*s(5)+1 0.03/0.30 Such that:aux(2) =< -A+99 0.03/0.30 s(5) =< aux(2) 0.03/0.30 0.03/0.30 with precondition: [B+1=0,0>=A+1] 0.03/0.30 0.03/0.30 * Chain [20]: 1*s(7)+0 0.03/0.30 Such that:s(7) =< -A 0.03/0.30 s(7) =< -B 0.03/0.30 0.03/0.30 with precondition: [0>=A+1,0>=B+2] 0.03/0.30 0.03/0.30 * Chain [19]: 2*s(8)+0 0.03/0.30 Such that:aux(3) =< -A 0.03/0.30 s(8) =< aux(3) 0.03/0.30 0.03/0.30 with precondition: [0>=A+1,B>=0] 0.03/0.30 0.03/0.30 * Chain [18]: 1*s(10)+0 0.03/0.30 Such that:s(10) =< -A 0.03/0.30 0.03/0.30 with precondition: [0>=A+1,A>=B+1] 0.03/0.30 0.03/0.30 * Chain [17]: 3*s(11)+2*s(12)+1 0.03/0.30 Such that:aux(4) =< -A+B+100 0.03/0.30 aux(5) =< -B 0.03/0.30 s(12) =< aux(4) 0.03/0.30 s(11) =< aux(5) 0.03/0.30 0.03/0.30 with precondition: [0>=B+2,B>=A] 0.03/0.30 0.03/0.30 * Chain [16]: 0 0.03/0.30 with precondition: [A>=0] 0.03/0.30 0.03/0.30 0.03/0.30 Closed-form bounds of f2(A,B,C,E): 0.03/0.30 ------------------------------------- 0.03/0.30 * Chain [22] with precondition: [] 0.03/0.30 - Upper bound: 0 0.03/0.30 - Complexity: constant 0.03/0.30 * Chain [21] with precondition: [B+1=0,0>=A+1] 0.03/0.30 - Upper bound: -2*A+199 0.03/0.30 - Complexity: n 0.03/0.30 * Chain [20] with precondition: [0>=A+1,0>=B+2] 0.03/0.30 - Upper bound: -A 0.03/0.30 - Complexity: n 0.03/0.30 * Chain [19] with precondition: [0>=A+1,B>=0] 0.03/0.30 - Upper bound: -2*A 0.03/0.30 - Complexity: n 0.03/0.30 * Chain [18] with precondition: [0>=A+1,A>=B+1] 0.03/0.30 - Upper bound: -A 0.03/0.30 - Complexity: n 0.03/0.30 * Chain [17] with precondition: [0>=B+2,B>=A] 0.03/0.30 - Upper bound: -2*A-B+201 0.03/0.30 - Complexity: n 0.03/0.30 * Chain [16] with precondition: [A>=0] 0.03/0.30 - Upper bound: 0 0.03/0.30 - Complexity: constant 0.03/0.30 0.03/0.30 ### Maximum cost of f2(A,B,C,E): max([max([nat(-A+99)*2+1,nat(-B)*3+1+nat(-A+B+100)*2]),nat(-A)*2]) 0.03/0.30 Asymptotic class: n 0.03/0.30 * Total analysis performed in 232 ms. 0.03/0.30 0.03/0.40 EOF