0.03/0.30 MAYBE 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 : [l2/9] 0.03/0.30 1. recursive : [l1/9,l2_loop_cont/10] 0.03/0.30 2. non_recursive : [exit_location/1] 0.03/0.30 3. recursive : [l3/2] 0.03/0.30 4. non_recursive : [l3_loop_cont/2] 0.03/0.30 5. non_recursive : [l1_loop_cont/6] 0.03/0.30 6. non_recursive : [l0/5] 0.03/0.30 0.03/0.30 #### Obtained direct recursion through partial evaluation 0.03/0.30 0. SCC is partially evaluated into l2/9 0.03/0.30 1. SCC is partially evaluated into l1/9 0.03/0.30 2. SCC is completely evaluated into other SCCs 0.03/0.30 3. SCC is partially evaluated into l3/2 0.03/0.30 4. SCC is completely evaluated into other SCCs 0.03/0.30 5. SCC is partially evaluated into l1_loop_cont/6 0.03/0.30 6. SCC is partially evaluated into l0/5 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 l2/9 0.03/0.30 * CE 10 is refined into CE [13] 0.03/0.30 * CE 9 is refined into CE [14] 0.03/0.30 * CE 8 is refined into CE [15] 0.03/0.30 0.03/0.30 0.03/0.30 ### Cost equations --> "Loop" of l2/9 0.03/0.30 * CEs [15] --> Loop 13 0.03/0.30 * CEs [13] --> Loop 14 0.03/0.30 * CEs [14] --> Loop 15 0.03/0.30 0.03/0.30 ### Ranking functions of CR l2(A,B,C,D,E,F,G,H,I) 0.03/0.30 * RF of phase [13]: [B-C] 0.03/0.30 0.03/0.30 #### Partial ranking functions of CR l2(A,B,C,D,E,F,G,H,I) 0.03/0.30 * Partial RF of phase [13]: 0.03/0.30 - RF of loop [13:1]: 0.03/0.30 B-C 0.03/0.30 0.03/0.30 0.03/0.30 ### Specialization of cost equations l1/9 0.03/0.30 * CE 4 is refined into CE [16] 0.03/0.30 * CE 2 is refined into CE [17,18] 0.03/0.30 * CE 5 is refined into CE [19] 0.03/0.30 * CE 3 is refined into CE [20] 0.03/0.30 0.03/0.30 0.03/0.30 ### Cost equations --> "Loop" of l1/9 0.03/0.30 * CEs [20] --> Loop 16 0.03/0.30 * CEs [16] --> Loop 17 0.03/0.30 * CEs [17,18] --> Loop 18 0.03/0.30 * CEs [19] --> Loop 19 0.03/0.30 0.03/0.30 ### Ranking functions of CR l1(A,B,C,D,E,F,G,H,I) 0.03/0.30 * RF of phase [16]: [B] 0.03/0.30 0.03/0.30 #### Partial ranking functions of CR l1(A,B,C,D,E,F,G,H,I) 0.03/0.30 * Partial RF of phase [16]: 0.03/0.30 - RF of loop [16:1]: 0.03/0.30 B 0.03/0.30 0.03/0.30 0.03/0.30 ### Specialization of cost equations l3/2 0.03/0.30 * CE 12 is refined into CE [21] 0.03/0.30 * CE 11 is refined into CE [22] 0.03/0.30 0.03/0.30 0.03/0.30 ### Cost equations --> "Loop" of l3/2 0.03/0.30 * CEs [22] --> Loop 20 0.03/0.30 * CEs [21] --> Loop 21 0.03/0.30 0.03/0.30 ### Ranking functions of CR l3(A,E) 0.03/0.30 * RF of phase [20]: [A] 0.03/0.30 0.03/0.30 #### Partial ranking functions of CR l3(A,E) 0.03/0.30 * Partial RF of phase [20]: 0.03/0.30 - RF of loop [20:1]: 0.03/0.30 A 0.03/0.30 0.03/0.30 0.03/0.30 ### Specialization of cost equations l1_loop_cont/6 0.03/0.30 * CE 7 is refined into CE [23,24] 0.03/0.30 * CE 6 is refined into CE [25] 0.03/0.30 0.03/0.30 0.03/0.30 ### Cost equations --> "Loop" of l1_loop_cont/6 0.03/0.30 * CEs [24] --> Loop 22 0.03/0.30 * CEs [23] --> Loop 23 0.03/0.30 * CEs [25] --> Loop 24 0.03/0.30 0.03/0.30 ### Ranking functions of CR l1_loop_cont(A,B,C,D,E,F) 0.03/0.30 0.03/0.30 #### Partial ranking functions of CR l1_loop_cont(A,B,C,D,E,F) 0.03/0.30 0.03/0.30 0.03/0.30 ### Specialization of cost equations l0/5 0.03/0.30 * CE 1 is refined into CE [26,27,28,29,30,31] 0.03/0.30 0.03/0.30 0.03/0.30 ### Cost equations --> "Loop" of l0/5 0.03/0.30 * CEs [28] --> Loop 25 0.03/0.30 * CEs [27,29,30] --> Loop 26 0.03/0.30 * CEs [31] --> Loop 27 0.03/0.30 * CEs [26] --> Loop 28 0.03/0.30 0.03/0.30 ### Ranking functions of CR l0(A,B,C,D,E) 0.03/0.30 0.03/0.30 #### Partial ranking functions of CR l0(A,B,C,D,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 l2(A,B,C,D,E,F,G,H,I): 0.03/0.30 * Chain [[13],15]: 1*it(13)+0 0.03/0.30 Such that:it(13) =< B-C 0.03/0.30 0.03/0.30 with precondition: [E=2,B=G+1,B=H,A+I=F,B>=C+1] 0.03/0.30 0.03/0.30 * Chain [[13],14]: 1*it(13)+0 0.03/0.30 Such that:it(13) =< B-C 0.03/0.30 0.03/0.30 with precondition: [E=3,B>=C+1] 0.03/0.30 0.03/0.30 * Chain [14]: 0 0.03/0.30 with precondition: [E=3,B>=C] 0.03/0.30 0.03/0.30 0.03/0.30 #### Cost of chains of l1(A,B,C,D,E,F,G,H,I): 0.03/0.30 * Chain [[16],19]: 1*it(16)+1*s(3)+0 0.03/0.30 Such that:aux(3) =< B 0.03/0.30 it(16) =< aux(3) 0.03/0.30 s(3) =< it(16)*aux(3) 0.03/0.30 0.03/0.30 with precondition: [E=3,B>=1] 0.03/0.30 0.03/0.30 * Chain [[16],18]: 2*it(16)+1*s(3)+0 0.03/0.30 Such that:aux(4) =< B 0.03/0.30 it(16) =< aux(4) 0.03/0.30 s(3) =< it(16)*aux(4) 0.03/0.30 0.03/0.30 with precondition: [E=3,B>=2] 0.03/0.30 0.03/0.30 * Chain [[16],17]: 1*it(16)+1*s(3)+0 0.03/0.30 Such that:aux(5) =< B 0.03/0.30 it(16) =< aux(5) 0.03/0.30 s(3) =< it(16)*aux(5) 0.03/0.30 0.03/0.30 with precondition: [E=4,G=0,H=1,B>=1] 0.03/0.30 0.03/0.30 * Chain [19]: 0 0.03/0.30 with precondition: [E=3] 0.03/0.30 0.03/0.30 * Chain [18]: 1*s(4)+0 0.03/0.30 Such that:s(4) =< B 0.03/0.30 0.03/0.30 with precondition: [E=3,B>=1] 0.03/0.30 0.03/0.30 * Chain [17]: 0 0.03/0.30 with precondition: [E=4,F=A,H=C,I=D,B=G,0>=B] 0.03/0.30 0.03/0.30 0.03/0.30 #### Cost of chains of l3(A,E): 0.03/0.30 * Chain [[20],21]: 1*it(20)+0 0.03/0.30 Such that:it(20) =< A 0.03/0.30 0.03/0.30 with precondition: [E=3,A>=1] 0.03/0.30 0.03/0.30 * Chain [21]: 0 0.03/0.30 with precondition: [E=3] 0.03/0.30 0.03/0.30 0.03/0.30 #### Cost of chains of l1_loop_cont(A,B,C,D,E,F): 0.03/0.30 * Chain [24]: 0 0.03/0.30 with precondition: [A=3] 0.03/0.30 0.03/0.30 * Chain [23]: 0 0.03/0.30 with precondition: [A=4] 0.03/0.30 0.03/0.30 * Chain [22]: 1*s(9)+0 0.03/0.30 Such that:s(9) =< B 0.03/0.30 0.03/0.30 with precondition: [A=4,B>=1] 0.03/0.30 0.03/0.30 0.03/0.30 #### Cost of chains of l0(A,B,C,D,E): 0.03/0.30 * Chain [28]: 0 0.03/0.30 with precondition: [] 0.03/0.30 0.03/0.30 * Chain [27]: 0 0.03/0.30 with precondition: [0>=B] 0.03/0.30 0.03/0.30 * Chain [26]: 4*s(11)+3*s(12)+1*s(19)+0 0.03/0.30 Such that:aux(7) =< B 0.03/0.30 s(11) =< aux(7) 0.03/0.30 s(12) =< s(11)*aux(7) 0.03/0.30 0.03/0.30 with precondition: [B>=1] 0.03/0.30 0.03/0.30 * Chain [25]: 2*s(21)+1*s(22)+0 0.03/0.30 Such that:s(20) =< B 0.03/0.30 s(21) =< s(20) 0.03/0.30 s(22) =< s(21)*s(20) 0.03/0.30 0.03/0.30 with precondition: [B>=2] 0.03/0.30 0.03/0.30 0.03/0.30 Closed-form bounds of l0(A,B,C,D,E): 0.03/0.30 ------------------------------------- 0.03/0.30 * Chain [28] with precondition: [] 0.03/0.30 - Upper bound: 0 0.03/0.30 - Complexity: constant 0.03/0.30 * Chain [27] with precondition: [0>=B] 0.03/0.30 - Upper bound: 0 0.03/0.30 - Complexity: constant 0.03/0.30 * Chain [26] with precondition: [B>=1] 0.03/0.30 - Upper bound: inf 0.03/0.30 - Complexity: infinity 0.03/0.30 * Chain [25] with precondition: [B>=2] 0.03/0.30 - Upper bound: 2*B+B*B 0.03/0.30 - Complexity: n^2 0.03/0.30 0.03/0.30 ### Maximum cost of l0(A,B,C,D,E): inf 0.03/0.30 Asymptotic class: infinity 0.03/0.30 * Total analysis performed in 232 ms. 0.03/0.30 0.03/0.40 EOF