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. recursive : [evalaaron2bb3in/6,evalaaron2bb4in/6,evalaaron2bb5in/6,evalaaron2bb6in/6] 0.03/0.21 1. non_recursive : [evalaaron2stop/4] 0.03/0.21 2. non_recursive : [evalaaron2returnin/4] 0.03/0.21 3. non_recursive : [exit_location/1] 0.03/0.21 4. non_recursive : [evalaaron2bb6in_loop_cont/5] 0.03/0.21 5. non_recursive : [evalaaron2entryin/4] 0.03/0.21 6. non_recursive : [evalaaron2start/4] 0.03/0.21 0.03/0.21 #### Obtained direct recursion through partial evaluation 0.03/0.21 0. SCC is partially evaluated into evalaaron2bb6in/6 0.03/0.21 1. SCC is completely evaluated into other SCCs 0.03/0.21 2. SCC is completely evaluated into other SCCs 0.03/0.21 3. SCC is completely evaluated into other SCCs 0.03/0.21 4. SCC is partially evaluated into evalaaron2bb6in_loop_cont/5 0.03/0.21 5. SCC is partially evaluated into evalaaron2entryin/4 0.03/0.21 6. SCC is partially evaluated into evalaaron2start/4 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 evalaaron2bb6in/6 0.03/0.21 * CE 8 is refined into CE [11] 0.03/0.21 * CE 6 is refined into CE [12] 0.03/0.21 * CE 7 is discarded (unfeasible) 0.03/0.21 * CE 5 is refined into CE [13] 0.03/0.21 * CE 4 is refined into CE [14] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of evalaaron2bb6in/6 0.03/0.21 * CEs [13] --> Loop 11 0.03/0.21 * CEs [14] --> Loop 12 0.03/0.21 * CEs [11] --> Loop 13 0.03/0.21 * CEs [12] --> Loop 14 0.03/0.21 0.03/0.21 ### Ranking functions of CR evalaaron2bb6in(A,B,C,E,F,G) 0.03/0.21 * RF of phase [11,12]: [-B+C+1] 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR evalaaron2bb6in(A,B,C,E,F,G) 0.03/0.21 * Partial RF of phase [11,12]: 0.03/0.21 - RF of loop [11:1,12:1]: 0.03/0.21 -B+C+1 0.03/0.21 0.03/0.21 0.03/0.21 ### Specialization of cost equations evalaaron2bb6in_loop_cont/5 0.03/0.21 * CE 10 is refined into CE [15] 0.03/0.21 * CE 9 is refined into CE [16] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of evalaaron2bb6in_loop_cont/5 0.03/0.21 * CEs [15] --> Loop 15 0.03/0.21 * CEs [16] --> Loop 16 0.03/0.21 0.03/0.21 ### Ranking functions of CR evalaaron2bb6in_loop_cont(A,B,C,D,E) 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR evalaaron2bb6in_loop_cont(A,B,C,D,E) 0.03/0.21 0.03/0.21 0.03/0.21 ### Specialization of cost equations evalaaron2entryin/4 0.03/0.21 * CE 3 is refined into CE [17,18,19,20] 0.03/0.21 * CE 2 is refined into CE [21] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of evalaaron2entryin/4 0.03/0.21 * CEs [18,20] --> Loop 17 0.03/0.21 * CEs [17] --> 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 evalaaron2entryin(A,B,C,E) 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR evalaaron2entryin(A,B,C,E) 0.03/0.21 0.03/0.21 0.03/0.21 ### Specialization of cost equations evalaaron2start/4 0.03/0.21 * CE 1 is refined into CE [22,23,24,25] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of evalaaron2start/4 0.03/0.21 * CEs [25] --> Loop 21 0.03/0.21 * CEs [24] --> Loop 22 0.03/0.21 * CEs [23] --> Loop 23 0.03/0.21 * CEs [22] --> Loop 24 0.03/0.21 0.03/0.21 ### Ranking functions of CR evalaaron2start(A,B,C,E) 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR evalaaron2start(A,B,C,E) 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 evalaaron2bb6in(A,B,C,E,F,G): 0.03/0.21 * Chain [[11,12],14]: 2*it(11)+0 0.03/0.21 Such that:aux(1) =< -B+C+1 0.03/0.21 aux(2) =< -B+C+F-G 0.03/0.21 it(11) =< aux(1) 0.03/0.21 it(11) =< aux(2) 0.03/0.21 0.03/0.21 with precondition: [E=2,F>=B,C>=G,F>=G+1,A+G+1>=F,C+F>=A+B+G+1] 0.03/0.21 0.03/0.21 * Chain [[11,12],13]: 2*it(11)+0 0.03/0.21 Such that:aux(2) =< A-B+C+1 0.03/0.21 aux(1) =< -B+C+1 0.03/0.21 it(11) =< aux(1) 0.03/0.21 it(11) =< aux(2) 0.03/0.21 0.03/0.21 with precondition: [E=3,A>=0,C>=B] 0.03/0.21 0.03/0.21 * Chain [14]: 0 0.03/0.21 with precondition: [E=2,B=F,C=G,A>=0,B>=C+1] 0.03/0.21 0.03/0.21 * Chain [13]: 0 0.03/0.21 with precondition: [E=3,A>=0] 0.03/0.21 0.03/0.21 0.03/0.21 #### Cost of chains of evalaaron2bb6in_loop_cont(A,B,C,D,E): 0.03/0.21 * Chain [16]: 0 0.03/0.21 with precondition: [A=2,B>=0] 0.03/0.21 0.03/0.21 * Chain [15]: 0 0.03/0.21 with precondition: [A=3,B>=0] 0.03/0.21 0.03/0.21 0.03/0.21 #### Cost of chains of evalaaron2entryin(A,B,C,E): 0.03/0.21 * Chain [20]: 0 0.03/0.21 with precondition: [0>=A+1] 0.03/0.21 0.03/0.21 * Chain [19]: 0 0.03/0.21 with precondition: [A>=0] 0.03/0.21 0.03/0.21 * Chain [18]: 0 0.03/0.21 with precondition: [A>=0,C>=B+1] 0.03/0.21 0.03/0.21 * Chain [17]: 4*s(3)+0 0.03/0.21 Such that:aux(3) =< A+B-C+1 0.03/0.21 aux(4) =< B-C+1 0.03/0.21 s(3) =< aux(4) 0.03/0.21 s(3) =< aux(3) 0.03/0.21 0.03/0.21 with precondition: [A>=0,B>=C] 0.03/0.21 0.03/0.21 0.03/0.21 #### Cost of chains of evalaaron2start(A,B,C,E): 0.03/0.21 * Chain [24]: 0 0.03/0.21 with precondition: [0>=A+1] 0.03/0.21 0.03/0.21 * Chain [23]: 0 0.03/0.21 with precondition: [A>=0] 0.03/0.21 0.03/0.21 * Chain [22]: 0 0.03/0.21 with precondition: [A>=0,C>=B+1] 0.03/0.21 0.03/0.21 * Chain [21]: 4*s(9)+0 0.03/0.21 Such that:s(7) =< A+B-C+1 0.03/0.21 s(8) =< B-C+1 0.03/0.21 s(9) =< s(8) 0.03/0.21 s(9) =< s(7) 0.03/0.21 0.03/0.21 with precondition: [A>=0,B>=C] 0.03/0.21 0.03/0.21 0.03/0.21 Closed-form bounds of evalaaron2start(A,B,C,E): 0.03/0.21 ------------------------------------- 0.03/0.21 * Chain [24] with precondition: [0>=A+1] 0.03/0.21 - Upper bound: 0 0.03/0.21 - Complexity: constant 0.03/0.21 * Chain [23] with precondition: [A>=0] 0.03/0.21 - Upper bound: 0 0.03/0.21 - Complexity: constant 0.03/0.21 * Chain [22] with precondition: [A>=0,C>=B+1] 0.03/0.21 - Upper bound: 0 0.03/0.21 - Complexity: constant 0.03/0.21 * Chain [21] with precondition: [A>=0,B>=C] 0.03/0.21 - Upper bound: 4*B-4*C+4 0.03/0.21 - Complexity: n 0.03/0.21 0.03/0.21 ### Maximum cost of evalaaron2start(A,B,C,E): nat(B-C+1)*4 0.03/0.21 Asymptotic class: n 0.03/0.21 * Total analysis performed in 147 ms. 0.03/0.21 0.03/0.31 EOF