0.03/0.28 WORST_CASE(?,O(n^1)) 0.03/0.28 0.03/0.28 Preprocessing Cost Relations 0.03/0.28 ===================================== 0.03/0.28 0.03/0.28 #### Computed strongly connected components 0.03/0.28 0. recursive : [f2/5] 0.03/0.28 1. recursive : [f2_loop_cont/8,f300/7] 0.03/0.28 2. non_recursive : [exit_location/1] 0.03/0.28 3. non_recursive : [f1/4] 0.03/0.28 4. non_recursive : [f300_loop_cont/5] 0.03/0.28 5. non_recursive : [f3/4] 0.03/0.28 0.03/0.28 #### Obtained direct recursion through partial evaluation 0.03/0.28 0. SCC is partially evaluated into f2/5 0.03/0.28 1. SCC is partially evaluated into f300/7 0.03/0.28 2. SCC is completely evaluated into other SCCs 0.03/0.28 3. SCC is completely evaluated into other SCCs 0.03/0.28 4. SCC is partially evaluated into f300_loop_cont/5 0.03/0.28 5. SCC is partially evaluated into f3/4 0.03/0.28 0.03/0.28 Control-Flow Refinement of Cost Relations 0.03/0.28 ===================================== 0.03/0.28 0.03/0.28 ### Specialization of cost equations f2/5 0.03/0.28 * CE 10 is refined into CE [11] 0.03/0.28 * CE 9 is refined into CE [12] 0.03/0.28 * CE 8 is refined into CE [13] 0.03/0.28 0.03/0.28 0.03/0.28 ### Cost equations --> "Loop" of f2/5 0.03/0.28 * CEs [13] --> Loop 11 0.03/0.28 * CEs [11] --> Loop 12 0.03/0.28 * CEs [12] --> Loop 13 0.03/0.28 0.03/0.28 ### Ranking functions of CR f2(A,B,E,F,G) 0.03/0.28 * RF of phase [11]: [A-30] 0.03/0.28 0.03/0.28 #### Partial ranking functions of CR f2(A,B,E,F,G) 0.03/0.28 * Partial RF of phase [11]: 0.03/0.28 - RF of loop [11:1]: 0.03/0.28 A-30 0.03/0.28 0.03/0.28 0.03/0.28 ### Specialization of cost equations f300/7 0.03/0.28 * CE 4 is refined into CE [14] 0.03/0.28 * CE 2 is refined into CE [15,16] 0.03/0.28 * CE 5 is refined into CE [17] 0.03/0.28 * CE 3 is refined into CE [18,19] 0.03/0.28 0.03/0.28 0.03/0.28 ### Cost equations --> "Loop" of f300/7 0.03/0.28 * CEs [19] --> Loop 14 0.03/0.28 * CEs [18] --> Loop 15 0.03/0.28 * CEs [14] --> Loop 16 0.03/0.28 * CEs [16] --> Loop 17 0.03/0.28 * CEs [15] --> Loop 18 0.03/0.28 * CEs [17] --> Loop 19 0.03/0.28 0.03/0.28 ### Ranking functions of CR f300(A,B,C,E,F,G,H) 0.03/0.28 * RF of phase [14]: [B-20] 0.03/0.28 0.03/0.28 #### Partial ranking functions of CR f300(A,B,C,E,F,G,H) 0.03/0.28 * Partial RF of phase [14]: 0.03/0.28 - RF of loop [14:1]: 0.03/0.28 B-20 0.03/0.28 0.03/0.28 0.03/0.28 ### Specialization of cost equations f300_loop_cont/5 0.03/0.28 * CE 6 is refined into CE [20] 0.03/0.28 * CE 7 is refined into CE [21] 0.03/0.28 0.03/0.28 0.03/0.28 ### Cost equations --> "Loop" of f300_loop_cont/5 0.03/0.28 * CEs [20] --> Loop 20 0.03/0.28 * CEs [21] --> Loop 21 0.03/0.28 0.03/0.28 ### Ranking functions of CR f300_loop_cont(A,B,C,D,E) 0.03/0.28 0.03/0.28 #### Partial ranking functions of CR f300_loop_cont(A,B,C,D,E) 0.03/0.28 0.03/0.28 0.03/0.28 ### Specialization of cost equations f3/4 0.03/0.28 * CE 1 is refined into CE [22,23,24,25,26,27,28,29,30,31,32] 0.03/0.28 0.03/0.28 0.03/0.28 ### Cost equations --> "Loop" of f3/4 0.03/0.28 * CEs [29] --> Loop 22 0.03/0.28 * CEs [28] --> Loop 23 0.03/0.28 * CEs [27,30] --> Loop 24 0.03/0.28 * CEs [26] --> Loop 25 0.03/0.28 * CEs [32] --> Loop 26 0.03/0.28 * CEs [25] --> Loop 27 0.03/0.28 * CEs [24,31] --> Loop 28 0.03/0.28 * CEs [22] --> Loop 29 0.03/0.28 * CEs [23] --> Loop 30 0.03/0.28 0.03/0.28 ### Ranking functions of CR f3(A,B,C,E) 0.03/0.28 0.03/0.28 #### Partial ranking functions of CR f3(A,B,C,E) 0.03/0.28 0.03/0.28 0.03/0.28 Computing Bounds 0.03/0.28 ===================================== 0.03/0.28 0.03/0.28 #### Cost of chains of f2(A,B,E,F,G): 0.03/0.28 * Chain [[11],13]: 1*it(11)+0 0.03/0.28 Such that:it(11) =< A 0.03/0.28 0.03/0.28 with precondition: [E=2,F=30,B=G+1,A>=31,B>=21] 0.03/0.28 0.03/0.28 * Chain [[11],12]: 1*it(11)+0 0.03/0.28 Such that:it(11) =< A 0.03/0.28 0.03/0.28 with precondition: [E=3,A>=31,B>=21] 0.03/0.28 0.03/0.28 * Chain [13]: 0 0.03/0.28 with precondition: [E=2,A=F,B=G+1,30>=A,B>=21] 0.03/0.28 0.03/0.28 * Chain [12]: 0 0.03/0.28 with precondition: [E=3,B>=21] 0.03/0.28 0.03/0.28 0.03/0.28 #### Cost of chains of f300(A,B,C,E,F,G,H): 0.03/0.28 * Chain [[14],19]: 1*it(14)+0 0.03/0.28 Such that:it(14) =< B 0.03/0.28 0.03/0.28 with precondition: [E=3,30>=A,B>=21] 0.03/0.28 0.03/0.28 * Chain [[14],17]: 1*it(14)+0 0.03/0.28 Such that:it(14) =< B 0.03/0.28 0.03/0.28 with precondition: [E=3,30>=A,B>=22] 0.03/0.28 0.03/0.28 * Chain [[14],16]: 1*it(14)+0 0.03/0.28 Such that:it(14) =< B 0.03/0.28 0.03/0.28 with precondition: [E=4,G=20,A=F,30>=A,B>=21] 0.03/0.28 0.03/0.28 * Chain [19]: 0 0.03/0.28 with precondition: [E=3] 0.03/0.28 0.03/0.28 * Chain [18]: 1*s(1)+0 0.03/0.28 Such that:s(1) =< A 0.03/0.28 0.03/0.28 with precondition: [E=3,A>=31,B>=21] 0.03/0.28 0.03/0.28 * Chain [17]: 0 0.03/0.28 with precondition: [E=3,B>=21] 0.03/0.28 0.03/0.28 * Chain [16]: 0 0.03/0.28 with precondition: [E=4,F=A,B=G,20>=B] 0.03/0.28 0.03/0.28 * Chain [15,[14],19]: 1*it(14)+1*s(2)+1 0.03/0.28 Such that:s(2) =< A 0.03/0.28 it(14) =< B 0.03/0.28 0.03/0.28 with precondition: [E=3,A>=31,B>=22] 0.03/0.28 0.03/0.28 * Chain [15,[14],17]: 1*it(14)+1*s(2)+1 0.03/0.28 Such that:s(2) =< A 0.03/0.28 it(14) =< B 0.03/0.28 0.03/0.28 with precondition: [E=3,A>=31,B>=23] 0.03/0.28 0.03/0.28 * Chain [15,[14],16]: 1*it(14)+1*s(2)+1 0.03/0.28 Such that:s(2) =< A 0.03/0.28 it(14) =< B 0.03/0.28 0.03/0.28 with precondition: [E=4,F=30,G=20,A>=31,B>=22] 0.03/0.28 0.03/0.28 * Chain [15,19]: 1*s(2)+1 0.03/0.28 Such that:s(2) =< A 0.03/0.28 0.03/0.28 with precondition: [E=3,A>=31,B>=21] 0.03/0.28 0.03/0.28 * Chain [15,17]: 1*s(2)+1 0.03/0.28 Such that:s(2) =< A 0.03/0.28 0.03/0.28 with precondition: [E=3,A>=31,B>=22] 0.03/0.28 0.03/0.28 * Chain [15,16]: 1*s(2)+1 0.03/0.28 Such that:s(2) =< A 0.03/0.28 0.03/0.28 with precondition: [B=21,E=4,F=30,G=20,A>=31] 0.03/0.28 0.03/0.28 0.03/0.28 #### Cost of chains of f300_loop_cont(A,B,C,D,E): 0.03/0.28 * Chain [21]: 0 0.03/0.28 with precondition: [A=3] 0.03/0.28 0.03/0.28 * Chain [20]: 0 0.03/0.28 with precondition: [A=4] 0.03/0.28 0.03/0.28 0.03/0.28 #### Cost of chains of f3(A,B,C,E): 0.03/0.28 * Chain [30]: 0 0.03/0.28 with precondition: [] 0.03/0.28 0.03/0.28 * Chain [29]: 1*s(8)+1 0.03/0.28 Such that:s(8) =< A 0.03/0.28 0.03/0.28 with precondition: [B=21,A>=31] 0.03/0.28 0.03/0.28 * Chain [28]: 2*s(9)+0 0.03/0.28 Such that:aux(3) =< B 0.03/0.28 s(9) =< aux(3) 0.03/0.28 0.03/0.28 with precondition: [30>=A,B>=21] 0.03/0.28 0.03/0.28 * Chain [27]: 1*s(11)+0 0.03/0.28 Such that:s(11) =< B 0.03/0.28 0.03/0.28 with precondition: [30>=A,B>=22] 0.03/0.28 0.03/0.28 * Chain [26]: 0 0.03/0.28 with precondition: [20>=B] 0.03/0.28 0.03/0.28 * Chain [25]: 2*s(13)+1 0.03/0.28 Such that:s(12) =< A 0.03/0.28 s(13) =< s(12) 0.03/0.28 0.03/0.28 with precondition: [A>=31,B>=21] 0.03/0.28 0.03/0.28 * Chain [24]: 2*s(14)+3*s(16)+1 0.03/0.28 Such that:aux(4) =< A 0.03/0.28 aux(5) =< B 0.03/0.28 s(16) =< aux(4) 0.03/0.28 s(14) =< aux(5) 0.03/0.28 0.03/0.28 with precondition: [A>=31,B>=22] 0.03/0.28 0.03/0.28 * Chain [23]: 1*s(19)+1*s(20)+1 0.03/0.28 Such that:s(19) =< A 0.03/0.28 s(20) =< B 0.03/0.28 0.03/0.28 with precondition: [A>=31,B>=23] 0.03/0.28 0.03/0.28 * Chain [22]: 0 0.03/0.28 with precondition: [B>=21] 0.03/0.28 0.03/0.28 0.03/0.28 Closed-form bounds of f3(A,B,C,E): 0.03/0.28 ------------------------------------- 0.03/0.28 * Chain [30] with precondition: [] 0.03/0.28 - Upper bound: 0 0.03/0.28 - Complexity: constant 0.03/0.28 * Chain [29] with precondition: [B=21,A>=31] 0.03/0.28 - Upper bound: A+1 0.03/0.28 - Complexity: n 0.03/0.28 * Chain [28] with precondition: [30>=A,B>=21] 0.03/0.28 - Upper bound: 2*B 0.03/0.28 - Complexity: n 0.03/0.28 * Chain [27] with precondition: [30>=A,B>=22] 0.03/0.28 - Upper bound: B 0.03/0.28 - Complexity: n 0.03/0.28 * Chain [26] with precondition: [20>=B] 0.03/0.28 - Upper bound: 0 0.03/0.28 - Complexity: constant 0.03/0.28 * Chain [25] with precondition: [A>=31,B>=21] 0.03/0.28 - Upper bound: 2*A+1 0.03/0.28 - Complexity: n 0.03/0.28 * Chain [24] with precondition: [A>=31,B>=22] 0.03/0.28 - Upper bound: 3*A+2*B+1 0.03/0.28 - Complexity: n 0.03/0.28 * Chain [23] with precondition: [A>=31,B>=23] 0.03/0.28 - Upper bound: A+B+1 0.03/0.28 - Complexity: n 0.03/0.28 * Chain [22] with precondition: [B>=21] 0.03/0.28 - Upper bound: 0 0.03/0.28 - Complexity: constant 0.03/0.28 0.03/0.28 ### Maximum cost of f3(A,B,C,E): max([nat(B)*2,nat(A)+1+max([nat(B),nat(B)*2+nat(A)+nat(A)])]) 0.03/0.28 Asymptotic class: n 0.03/0.28 * Total analysis performed in 217 ms. 0.03/0.28 0.03/0.38 EOF