0.03/0.26 WORST_CASE(?,O(n^2)) 0.03/0.26 0.03/0.26 Preprocessing Cost Relations 0.03/0.26 ===================================== 0.03/0.26 0.03/0.26 #### Computed strongly connected components 0.03/0.26 0. recursive : [l1/7] 0.03/0.26 1. non_recursive : [exit_location/1] 0.03/0.26 2. recursive : [l3/5] 0.03/0.26 3. recursive : [l2/3,l3_loop_cont/4] 0.03/0.26 4. non_recursive : [l2_loop_cont/2] 0.03/0.26 5. non_recursive : [l1_loop_cont/6] 0.03/0.26 6. non_recursive : [l0/5] 0.03/0.26 0.03/0.26 #### Obtained direct recursion through partial evaluation 0.03/0.26 0. SCC is partially evaluated into l1/7 0.03/0.26 1. SCC is completely evaluated into other SCCs 0.03/0.26 2. SCC is partially evaluated into l3/5 0.03/0.26 3. SCC is partially evaluated into l2/3 0.03/0.26 4. SCC is completely evaluated into other SCCs 0.03/0.26 5. SCC is partially evaluated into l1_loop_cont/6 0.03/0.26 6. SCC is partially evaluated into l0/5 0.03/0.26 0.03/0.26 Control-Flow Refinement of Cost Relations 0.03/0.26 ===================================== 0.03/0.26 0.03/0.26 ### Specialization of cost equations l1/7 0.03/0.26 * CE 4 is refined into CE [13] 0.03/0.26 * CE 3 is refined into CE [14] 0.03/0.26 * CE 2 is refined into CE [15] 0.03/0.26 0.03/0.26 0.03/0.26 ### Cost equations --> "Loop" of l1/7 0.03/0.26 * CEs [15] --> Loop 13 0.03/0.26 * CEs [13] --> Loop 14 0.03/0.26 * CEs [14] --> Loop 15 0.03/0.26 0.03/0.26 ### Ranking functions of CR l1(A,B,C,E,F,G,H) 0.03/0.26 * RF of phase [13]: [B] 0.03/0.26 0.03/0.26 #### Partial ranking functions of CR l1(A,B,C,E,F,G,H) 0.03/0.26 * Partial RF of phase [13]: 0.03/0.26 - RF of loop [13:1]: 0.03/0.26 B 0.03/0.26 0.03/0.26 0.03/0.26 ### Specialization of cost equations l3/5 0.03/0.26 * CE 12 is refined into CE [16] 0.03/0.26 * CE 11 is refined into CE [17] 0.03/0.26 * CE 10 is refined into CE [18] 0.03/0.26 0.03/0.26 0.03/0.26 ### Cost equations --> "Loop" of l3/5 0.03/0.26 * CEs [18] --> Loop 16 0.03/0.26 * CEs [16] --> Loop 17 0.03/0.26 * CEs [17] --> Loop 18 0.03/0.26 0.03/0.26 ### Ranking functions of CR l3(C,D,E,F,G) 0.03/0.26 * RF of phase [16]: [D] 0.03/0.26 0.03/0.26 #### Partial ranking functions of CR l3(C,D,E,F,G) 0.03/0.26 * Partial RF of phase [16]: 0.03/0.26 - RF of loop [16:1]: 0.03/0.26 D 0.03/0.26 0.03/0.26 0.03/0.26 ### Specialization of cost equations l2/3 0.03/0.26 * CE 7 is refined into CE [19,20] 0.03/0.26 * CE 9 is refined into CE [21] 0.03/0.26 * CE 8 is refined into CE [22] 0.03/0.26 0.03/0.26 0.03/0.26 ### Cost equations --> "Loop" of l2/3 0.03/0.26 * CEs [22] --> Loop 19 0.03/0.26 * CEs [19,20] --> Loop 20 0.03/0.26 * CEs [21] --> Loop 21 0.03/0.26 0.03/0.26 ### Ranking functions of CR l2(C,D,E) 0.03/0.26 * RF of phase [19]: [C] 0.03/0.26 0.03/0.26 #### Partial ranking functions of CR l2(C,D,E) 0.03/0.26 * Partial RF of phase [19]: 0.03/0.26 - RF of loop [19:1]: 0.03/0.26 C 0.03/0.26 0.03/0.26 0.03/0.26 ### Specialization of cost equations l1_loop_cont/6 0.03/0.26 * CE 5 is refined into CE [23] 0.03/0.26 * CE 6 is refined into CE [24,25,26] 0.03/0.26 0.03/0.26 0.03/0.26 ### Cost equations --> "Loop" of l1_loop_cont/6 0.03/0.26 * CEs [23] --> Loop 22 0.03/0.26 * CEs [26] --> Loop 23 0.03/0.26 * CEs [25] --> Loop 24 0.03/0.26 * CEs [24] --> Loop 25 0.03/0.26 0.03/0.26 ### Ranking functions of CR l1_loop_cont(A,B,C,D,E,F) 0.03/0.26 0.03/0.26 #### Partial ranking functions of CR l1_loop_cont(A,B,C,D,E,F) 0.03/0.26 0.03/0.26 0.03/0.26 ### Specialization of cost equations l0/5 0.03/0.26 * CE 1 is refined into CE [27,28,29,30,31,32] 0.03/0.26 0.03/0.26 0.03/0.26 ### Cost equations --> "Loop" of l0/5 0.03/0.26 * CEs [29] --> Loop 26 0.03/0.26 * CEs [27,28,32] --> Loop 27 0.03/0.26 * CEs [30] --> Loop 28 0.03/0.26 * CEs [31] --> Loop 29 0.03/0.26 0.03/0.26 ### Ranking functions of CR l0(A,B,C,D,E) 0.03/0.26 0.03/0.26 #### Partial ranking functions of CR l0(A,B,C,D,E) 0.03/0.26 0.03/0.26 0.03/0.26 Computing Bounds 0.03/0.26 ===================================== 0.03/0.26 0.03/0.26 #### Cost of chains of l1(A,B,C,E,F,G,H): 0.03/0.26 * Chain [[13],15]: 1*it(13)+0 0.03/0.26 Such that:it(13) =< -A+F 0.03/0.26 0.03/0.26 with precondition: [E=2,G=0,A+B=F,A+B=H,A>=0,B>=1] 0.03/0.26 0.03/0.26 * Chain [[13],14]: 1*it(13)+0 0.03/0.26 Such that:it(13) =< B 0.03/0.26 0.03/0.26 with precondition: [E=3,A>=0,B>=1] 0.03/0.26 0.03/0.26 * Chain [15]: 0 0.03/0.26 with precondition: [E=2,A=F,B=G,A=H,0>=B,A>=0] 0.03/0.26 0.03/0.26 * Chain [14]: 0 0.03/0.26 with precondition: [E=3,A>=0] 0.03/0.26 0.03/0.26 0.03/0.26 #### Cost of chains of l3(C,D,E,F,G): 0.03/0.26 * Chain [[16],18]: 1*it(16)+0 0.03/0.26 Such that:it(16) =< D 0.03/0.26 0.03/0.26 with precondition: [E=2,G=0,C=F+1,D>=1,C>=D] 0.03/0.26 0.03/0.26 * Chain [[16],17]: 1*it(16)+0 0.03/0.26 Such that:it(16) =< D 0.03/0.26 0.03/0.26 with precondition: [E=3,D>=1,C>=D] 0.03/0.26 0.03/0.26 * Chain [17]: 0 0.03/0.26 with precondition: [E=3,C>=1,C>=D] 0.03/0.26 0.03/0.26 0.03/0.26 #### Cost of chains of l2(C,D,E): 0.03/0.26 * Chain [[19],21]: 1*it(19)+1*s(3)+0 0.03/0.26 Such that:aux(3) =< C 0.03/0.26 it(19) =< aux(3) 0.03/0.26 s(3) =< it(19)*aux(3) 0.03/0.26 0.03/0.26 with precondition: [E=3,C>=1] 0.03/0.26 0.03/0.26 * Chain [[19],20]: 2*it(19)+1*s(3)+0 0.03/0.26 Such that:aux(4) =< C 0.03/0.26 it(19) =< aux(4) 0.03/0.26 s(3) =< it(19)*aux(4) 0.03/0.26 0.03/0.26 with precondition: [E=3,C>=2] 0.03/0.26 0.03/0.26 * Chain [21]: 0 0.03/0.26 with precondition: [E=3] 0.03/0.26 0.03/0.26 * Chain [20]: 1*s(4)+0 0.03/0.26 Such that:s(4) =< C 0.03/0.26 0.03/0.26 with precondition: [E=3,C>=1] 0.03/0.26 0.03/0.26 0.03/0.26 #### Cost of chains of l1_loop_cont(A,B,C,D,E,F): 0.03/0.26 * Chain [25]: 0 0.03/0.26 with precondition: [A=2] 0.03/0.26 0.03/0.26 * Chain [24]: 2*s(10)+1*s(11)+0 0.03/0.26 Such that:s(9) =< D 0.03/0.26 s(10) =< s(9) 0.03/0.26 s(11) =< s(10)*s(9) 0.03/0.26 0.03/0.26 with precondition: [A=2,D>=1] 0.03/0.26 0.03/0.26 * Chain [23]: 2*s(13)+1*s(14)+0 0.03/0.26 Such that:s(12) =< D 0.03/0.26 s(13) =< s(12) 0.03/0.26 s(14) =< s(13)*s(12) 0.03/0.26 0.03/0.26 with precondition: [A=2,D>=2] 0.03/0.26 0.03/0.26 * Chain [22]: 0 0.03/0.26 with precondition: [A=3] 0.03/0.26 0.03/0.26 0.03/0.26 #### Cost of chains of l0(A,B,C,D,E): 0.03/0.26 * Chain [29]: 0 0.03/0.26 with precondition: [] 0.03/0.26 0.03/0.26 * Chain [28]: 0 0.03/0.26 with precondition: [0>=B] 0.03/0.26 0.03/0.26 * Chain [27]: 5*s(15)+1*s(19)+0 0.03/0.26 Such that:aux(7) =< B 0.03/0.26 s(15) =< aux(7) 0.03/0.26 s(19) =< s(15)*aux(7) 0.03/0.26 0.03/0.26 with precondition: [B>=1] 0.03/0.26 0.03/0.26 * Chain [26]: 3*s(21)+1*s(24)+0 0.03/0.26 Such that:aux(8) =< B 0.03/0.26 s(21) =< aux(8) 0.03/0.26 s(24) =< s(21)*aux(8) 0.03/0.26 0.03/0.26 with precondition: [B>=2] 0.03/0.26 0.03/0.26 0.03/0.26 Closed-form bounds of l0(A,B,C,D,E): 0.03/0.26 ------------------------------------- 0.03/0.26 * Chain [29] with precondition: [] 0.03/0.26 - Upper bound: 0 0.03/0.26 - Complexity: constant 0.03/0.26 * Chain [28] with precondition: [0>=B] 0.03/0.26 - Upper bound: 0 0.03/0.26 - Complexity: constant 0.03/0.26 * Chain [27] with precondition: [B>=1] 0.03/0.26 - Upper bound: 5*B+B*B 0.03/0.26 - Complexity: n^2 0.03/0.26 * Chain [26] with precondition: [B>=2] 0.03/0.26 - Upper bound: 3*B+B*B 0.03/0.26 - Complexity: n^2 0.03/0.26 0.03/0.26 ### Maximum cost of l0(A,B,C,D,E): nat(B)*nat(B)+nat(B)*5 0.03/0.26 Asymptotic class: n^2 0.03/0.26 * Total analysis performed in 199 ms. 0.03/0.26 0.03/0.36 EOF