0.03/0.35 WORST_CASE(?,O(n^1)) 0.03/0.35 0.03/0.66 Preprocessing Cost Relations 0.03/0.66 ===================================== 0.03/0.66 0.03/0.66 #### Computed strongly connected components 0.03/0.66 0. recursive : [f6/9] 0.03/0.66 1. non_recursive : [exit_location/1] 0.03/0.66 2. non_recursive : [f19/5] 0.03/0.66 3. non_recursive : [f15/5] 0.03/0.66 4. non_recursive : [f6_loop_cont/6] 0.03/0.66 5. non_recursive : [f0/5] 0.03/0.66 0.03/0.66 #### Obtained direct recursion through partial evaluation 0.03/0.66 0. SCC is partially evaluated into f6/9 0.03/0.66 1. SCC is completely evaluated into other SCCs 0.03/0.66 2. SCC is completely evaluated into other SCCs 0.03/0.66 3. SCC is partially evaluated into f15/5 0.03/0.66 4. SCC is partially evaluated into f6_loop_cont/6 0.03/0.66 5. SCC is partially evaluated into f0/5 0.03/0.66 0.03/0.66 Control-Flow Refinement of Cost Relations 0.03/0.66 ===================================== 0.03/0.66 0.03/0.66 ### Specialization of cost equations f6/9 0.03/0.66 * CE 7 is refined into CE [14] 0.03/0.66 * CE 6 is refined into CE [15] 0.03/0.66 * CE 5 is refined into CE [16] 0.03/0.66 * CE 4 is refined into CE [17] 0.03/0.66 * CE 2 is refined into CE [18] 0.03/0.66 * CE 3 is refined into CE [19] 0.03/0.66 0.03/0.66 0.03/0.66 ### Cost equations --> "Loop" of f6/9 0.03/0.66 * CEs [18] --> Loop 14 0.03/0.66 * CEs [19] --> Loop 15 0.03/0.66 * CEs [14] --> Loop 16 0.03/0.66 * CEs [15] --> Loop 17 0.03/0.66 * CEs [16] --> Loop 18 0.03/0.66 * CEs [17] --> Loop 19 0.03/0.66 0.03/0.66 ### Ranking functions of CR f6(A,B,C,D,E,F,G,H,I) 0.03/0.66 * RF of phase [14,15]: [-B+C] 0.03/0.66 0.03/0.66 #### Partial ranking functions of CR f6(A,B,C,D,E,F,G,H,I) 0.03/0.66 * Partial RF of phase [14,15]: 0.03/0.66 - RF of loop [14:1,15:1]: 0.03/0.66 -B+C 0.03/0.66 - RF of loop [15:1]: 0.03/0.66 -A/2+C-1/2 0.03/0.66 0.03/0.66 0.03/0.66 ### Specialization of cost equations f15/5 0.03/0.66 * CE 13 is refined into CE [20] 0.03/0.66 * CE 12 is refined into CE [21] 0.03/0.66 * CE 11 is refined into CE [22] 0.03/0.66 0.03/0.66 0.03/0.66 ### Cost equations --> "Loop" of f15/5 0.03/0.66 * CEs [20] --> Loop 20 0.03/0.66 * CEs [21] --> Loop 21 0.03/0.66 * CEs [22] --> Loop 22 0.03/0.66 0.03/0.66 ### Ranking functions of CR f15(A,B,C,D,E) 0.03/0.66 0.03/0.66 #### Partial ranking functions of CR f15(A,B,C,D,E) 0.03/0.66 0.03/0.66 0.03/0.66 ### Specialization of cost equations f6_loop_cont/6 0.03/0.66 * CE 10 is refined into CE [23] 0.03/0.66 * CE 9 is refined into CE [24] 0.03/0.66 * CE 8 is refined into CE [25,26,27] 0.03/0.66 0.03/0.66 0.03/0.66 ### Cost equations --> "Loop" of f6_loop_cont/6 0.03/0.66 * CEs [23] --> Loop 23 0.03/0.66 * CEs [24] --> Loop 24 0.03/0.66 * CEs [27] --> Loop 25 0.03/0.66 * CEs [26] --> Loop 26 0.03/0.66 * CEs [25] --> Loop 27 0.03/0.66 0.03/0.66 ### Ranking functions of CR f6_loop_cont(A,B,C,D,E,F) 0.03/0.66 0.03/0.66 #### Partial ranking functions of CR f6_loop_cont(A,B,C,D,E,F) 0.03/0.66 0.03/0.66 0.03/0.66 ### Specialization of cost equations f0/5 0.03/0.66 * CE 1 is refined into CE [28,29,30,31,32,33,34,35,36] 0.03/0.66 0.03/0.66 0.03/0.66 ### Cost equations --> "Loop" of f0/5 0.03/0.66 * CEs [31,34] --> Loop 28 0.03/0.66 * CEs [30,32,36] --> Loop 29 0.03/0.66 * CEs [29] --> Loop 30 0.03/0.66 * CEs [33] --> Loop 31 0.03/0.66 * CEs [28] --> Loop 32 0.03/0.66 * CEs [35] --> Loop 33 0.03/0.66 0.03/0.66 ### Ranking functions of CR f0(A,B,C,D,E) 0.03/0.66 0.03/0.66 #### Partial ranking functions of CR f0(A,B,C,D,E) 0.03/0.66 0.03/0.66 0.03/0.66 Computing Bounds 0.03/0.66 ===================================== 0.03/0.66 0.03/0.66 #### Cost of chains of f6(A,B,C,D,E,F,G,H,I): 0.03/0.66 * Chain [[14,15],19]: 1*it(14)+1*it(15)+0 0.03/0.66 Such that:it(15) =< -A/2+F/2 0.03/0.66 aux(3) =< -B+H 0.03/0.66 it(14) =< aux(3) 0.03/0.66 it(15) =< aux(3) 0.03/0.66 0.03/0.66 with precondition: [E=2,C=G,C=H,D=I,A>=0,F>=A,2*B>=A,C>=B+1,C>=F+1,A+2*C>=2*B+F] 0.03/0.66 0.03/0.66 * Chain [[14,15],18]: 1*it(14)+1*it(15)+0 0.03/0.66 Such that:it(15) =< -A/2+F/2 0.03/0.66 aux(4) =< -B+H 0.03/0.66 it(14) =< aux(4) 0.03/0.66 it(15) =< aux(4) 0.03/0.66 0.03/0.66 with precondition: [E=2,C=G,C=H,D=I,A>=0,F>=A,2*B>=A,C>=B+1,F>=C+1,A+2*C>=2*B+F] 0.03/0.67 0.03/0.67 * Chain [[14,15],17]: 1*it(14)+1*it(15)+0 0.03/0.67 Such that:it(15) =< -A/2+H/2 0.03/0.67 aux(5) =< -B+H 0.03/0.67 it(14) =< aux(5) 0.03/0.67 it(15) =< aux(5) 0.03/0.67 0.03/0.67 with precondition: [E=3,I=1,C=F,C=G,C=H,A>=0,C>=2,C>=A,2*B>=A,C>=B+1,A+C>=2*B] 0.03/0.67 0.03/0.67 * Chain [[14,15],16]: 2*it(14)+0 0.03/0.67 Such that:aux(6) =< -B+C 0.03/0.67 it(14) =< aux(6) 0.03/0.67 0.03/0.67 with precondition: [E=4,A>=0,2*B>=A,C>=B+1] 0.03/0.67 0.03/0.67 * Chain [18]: 0 0.03/0.67 with precondition: [E=2,I=D,A=F,B=G,C=H,A>=0,2*B>=A,A>=C+1,B>=C] 0.03/0.67 0.03/0.67 * Chain [17]: 0 0.03/0.67 with precondition: [E=3,I=1,A=C,A=F,B=G,A=H,A>=0,B>=A] 0.03/0.67 0.03/0.67 * Chain [16]: 0 0.03/0.67 with precondition: [E=4,A>=0,2*B>=A] 0.03/0.67 0.03/0.67 0.03/0.67 #### Cost of chains of f15(A,B,C,D,E): 0.03/0.67 * Chain [22]: 0 0.03/0.67 with precondition: [C+1=A] 0.03/0.67 0.03/0.67 * Chain [21]: 0 0.03/0.67 with precondition: [C>=A] 0.03/0.67 0.03/0.67 * Chain [20]: 0 0.03/0.67 with precondition: [A>=C+2] 0.03/0.67 0.03/0.67 0.03/0.67 #### Cost of chains of f6_loop_cont(A,B,C,D,E,F): 0.03/0.67 * Chain [27]: 0 0.03/0.67 with precondition: [A=2,D+1=B] 0.03/0.67 0.03/0.67 * Chain [26]: 0 0.03/0.67 with precondition: [A=2,D>=B] 0.03/0.67 0.03/0.67 * Chain [25]: 0 0.03/0.67 with precondition: [A=2,B>=D+2] 0.03/0.67 0.03/0.67 * Chain [24]: 0 0.03/0.67 with precondition: [A=3] 0.03/0.67 0.03/0.67 * Chain [23]: 0 0.03/0.67 with precondition: [A=4] 0.03/0.67 0.03/0.67 0.03/0.67 #### Cost of chains of f0(A,B,C,D,E): 0.03/0.67 * Chain [33]: 0 0.03/0.67 with precondition: [] 0.03/0.67 0.03/0.67 * Chain [32]: 0 0.03/0.67 with precondition: [C+1=0] 0.03/0.67 0.03/0.67 * Chain [31]: 0 0.03/0.67 with precondition: [C=0] 0.03/0.67 0.03/0.67 * Chain [30]: 0 0.03/0.67 with precondition: [0>=C+2] 0.03/0.67 0.03/0.67 * Chain [29]: 1*s(1)+4*s(3)+1*s(4)+0 0.03/0.67 Such that:s(4) =< C/2 0.03/0.67 s(1) =< C/2+1/2 0.03/0.67 aux(7) =< C 0.03/0.67 s(3) =< aux(7) 0.03/0.67 s(1) =< aux(7) 0.03/0.67 s(4) =< aux(7) 0.03/0.67 0.03/0.67 with precondition: [C>=1] 0.03/0.67 0.03/0.67 * Chain [28]: 3*s(9)+1*s(12)+0 0.03/0.67 Such that:s(12) =< C/2 0.03/0.67 aux(9) =< C 0.03/0.67 s(9) =< aux(9) 0.03/0.67 s(12) =< aux(9) 0.03/0.67 0.03/0.67 with precondition: [C>=2] 0.03/0.67 0.03/0.67 0.03/0.67 Closed-form bounds of f0(A,B,C,D,E): 0.03/0.67 ------------------------------------- 0.03/0.67 * Chain [33] with precondition: [] 0.03/0.67 - Upper bound: 0 0.03/0.67 - Complexity: constant 0.03/0.67 * Chain [32] with precondition: [C+1=0] 0.03/0.67 - Upper bound: 0 0.03/0.67 - Complexity: constant 0.03/0.67 * Chain [31] with precondition: [C=0] 0.03/0.67 - Upper bound: 0 0.03/0.67 - Complexity: constant 0.03/0.67 * Chain [30] with precondition: [0>=C+2] 0.03/0.67 - Upper bound: 0 0.03/0.67 - Complexity: constant 0.03/0.67 * Chain [29] with precondition: [C>=1] 0.03/0.67 - Upper bound: 5*C+1/2 0.03/0.67 - Complexity: n 0.03/0.67 * Chain [28] with precondition: [C>=2] 0.03/0.67 - Upper bound: 7/2*C 0.03/0.67 - Complexity: n 0.03/0.67 0.03/0.67 ### Maximum cost of f0(A,B,C,D,E): nat(C)*3+nat(C/2)+(nat(C/2+1/2)+nat(C)) 0.03/0.67 Asymptotic class: n 0.03/0.67 * Total analysis performed in 285 ms. 0.03/0.67 0.03/0.67 EOF