0.03/0.29 WORST_CASE(?,O(n^1)) 0.03/0.29 0.03/0.29 Preprocessing Cost Relations 0.03/0.29 ===================================== 0.03/0.29 0.03/0.29 #### Computed strongly connected components 0.03/0.29 0. non_recursive : [end/5] 0.03/0.29 1. recursive : [eval3/5] 0.03/0.29 2. recursive : [eval11/4,eval5/4,eval7/4,eval9/4] 0.03/0.29 3. non_recursive : [exit_location/1] 0.03/0.29 4. non_recursive : [eval5_loop_cont/2] 0.03/0.29 5. non_recursive : [eval3_loop_cont/6] 0.03/0.29 6. non_recursive : [eval1/5] 0.03/0.29 7. non_recursive : [eval0/5] 0.03/0.29 0.03/0.29 #### Obtained direct recursion through partial evaluation 0.03/0.29 0. SCC is completely evaluated into other SCCs 0.03/0.29 1. SCC is partially evaluated into eval3/5 0.03/0.29 2. SCC is partially evaluated into eval5/4 0.03/0.29 3. SCC is completely evaluated into other SCCs 0.03/0.29 4. SCC is completely evaluated into other SCCs 0.03/0.29 5. SCC is partially evaluated into eval3_loop_cont/6 0.03/0.29 6. SCC is partially evaluated into eval1/5 0.03/0.29 7. SCC is partially evaluated into eval0/5 0.03/0.29 0.03/0.29 Control-Flow Refinement of Cost Relations 0.03/0.29 ===================================== 0.03/0.29 0.03/0.29 ### Specialization of cost equations eval3/5 0.03/0.29 * CE 5 is refined into CE [13] 0.03/0.29 * CE 6 is refined into CE [14] 0.03/0.29 * CE 4 is refined into CE [15] 0.03/0.29 0.03/0.29 0.03/0.29 ### Cost equations --> "Loop" of eval3/5 0.03/0.29 * CEs [15] --> Loop 13 0.03/0.29 * CEs [13] --> Loop 14 0.03/0.29 * CEs [14] --> Loop 15 0.03/0.29 0.03/0.29 ### Ranking functions of CR eval3(A,C,E,F,G) 0.03/0.29 * RF of phase [13]: [-A/11+101/11] 0.03/0.29 0.03/0.29 #### Partial ranking functions of CR eval3(A,C,E,F,G) 0.03/0.29 * Partial RF of phase [13]: 0.03/0.29 - RF of loop [13:1]: 0.03/0.29 -A/11+101/11 0.03/0.29 0.03/0.29 0.03/0.29 ### Specialization of cost equations eval5/4 0.03/0.29 * CE 12 is refined into CE [16] 0.03/0.29 * CE 10 is refined into CE [17] 0.03/0.29 * CE 11 is refined into CE [18] 0.03/0.29 * CE 9 is refined into CE [19] 0.03/0.29 0.03/0.29 0.03/0.29 ### Cost equations --> "Loop" of eval5/4 0.03/0.29 * CEs [17] --> Loop 16 0.03/0.29 * CEs [18] --> Loop 17 0.03/0.29 * CEs [19] --> Loop 18 0.03/0.29 * CEs [16] --> Loop 19 0.03/0.29 0.03/0.29 ### Ranking functions of CR eval5(A,C,D,E) 0.03/0.29 0.03/0.29 #### Partial ranking functions of CR eval5(A,C,D,E) 0.03/0.29 * Partial RF of phase [16,17]: 0.03/0.29 - RF of loop [16:1]: 0.03/0.29 -A+111 depends on loops [17:1] 0.03/0.29 - RF of loop [17:1]: 0.03/0.29 A/9-110/9 depends on loops [16:1] 0.03/0.29 C-1 0.03/0.29 0.03/0.29 0.03/0.29 ### Specialization of cost equations eval3_loop_cont/6 0.03/0.29 * CE 8 is refined into CE [20,21,22] 0.03/0.29 * CE 7 is refined into CE [23] 0.03/0.29 0.03/0.29 0.03/0.29 ### Cost equations --> "Loop" of eval3_loop_cont/6 0.03/0.29 * CEs [22] --> Loop 20 0.03/0.29 * CEs [21] --> Loop 21 0.03/0.29 * CEs [20] --> Loop 22 0.03/0.29 * CEs [23] --> Loop 23 0.03/0.29 0.03/0.29 ### Ranking functions of CR eval3_loop_cont(A,B,C,D,E,F) 0.03/0.29 0.03/0.29 #### Partial ranking functions of CR eval3_loop_cont(A,B,C,D,E,F) 0.03/0.29 0.03/0.29 0.03/0.29 ### Specialization of cost equations eval1/5 0.03/0.29 * CE 2 is refined into CE [24] 0.03/0.29 * CE 3 is refined into CE [25,26,27,28,29] 0.03/0.29 0.03/0.29 0.03/0.29 ### Cost equations --> "Loop" of eval1/5 0.03/0.29 * CEs [24] --> Loop 24 0.03/0.29 * CEs [25,26,28,29] --> Loop 25 0.03/0.29 * CEs [27] --> Loop 26 0.03/0.29 0.03/0.29 ### Ranking functions of CR eval1(A,B,C,D,E) 0.03/0.29 0.03/0.29 #### Partial ranking functions of CR eval1(A,B,C,D,E) 0.03/0.29 0.03/0.29 0.03/0.29 ### Specialization of cost equations eval0/5 0.03/0.29 * CE 1 is refined into CE [30,31,32] 0.03/0.29 0.03/0.29 0.03/0.29 ### Cost equations --> "Loop" of eval0/5 0.03/0.29 * CEs [32] --> Loop 27 0.03/0.29 * CEs [31] --> Loop 28 0.03/0.29 * CEs [30] --> Loop 29 0.03/0.29 0.03/0.29 ### Ranking functions of CR eval0(A,B,C,D,E) 0.03/0.29 0.03/0.29 #### Partial ranking functions of CR eval0(A,B,C,D,E) 0.03/0.29 0.03/0.29 0.03/0.29 Computing Bounds 0.03/0.29 ===================================== 0.03/0.29 0.03/0.29 #### Cost of chains of eval3(A,C,E,F,G): 0.03/0.29 * Chain [[13],15]: 1*it(13)+0 0.03/0.29 Such that:it(13) =< -A/11+101/11 0.03/0.29 0.03/0.29 with precondition: [E=2,100>=A,C>=1] 0.03/0.29 0.03/0.29 * Chain [[13],14]: 1*it(13)+0 0.03/0.29 Such that:it(13) =< -A/11+101/11 0.03/0.29 0.03/0.29 with precondition: [E=3,A+11*G=11*C+F,111>=F,C>=1,F>=101,F>=A+11] 0.03/0.29 0.03/0.29 * Chain [15]: 0 0.03/0.29 with precondition: [E=2,C>=1,11*C+89>=A] 0.03/0.29 0.03/0.29 0.03/0.29 #### Cost of chains of eval5(A,C,D,E): 0.03/0.29 * Chain [[16,17],19]: 1*it(16)+1*it(17)+0 0.03/0.29 Such that:aux(1) =< -A+111 0.03/0.29 it(17) =< C 0.03/0.29 it(16) =< it(17)*9+aux(1) 0.03/0.29 0.03/0.29 with precondition: [E=2,C>=2] 0.03/0.29 0.03/0.29 * Chain [[16,17],18,19]: 1*it(16)+1*it(17)+1 0.03/0.29 Such that:aux(1) =< -A+111 0.03/0.29 it(17) =< C 0.03/0.29 it(16) =< it(17)*9+aux(1) 0.03/0.29 0.03/0.29 with precondition: [E=2,C>=2] 0.03/0.29 0.03/0.29 * Chain [19]: 0 0.03/0.29 with precondition: [E=2] 0.03/0.29 0.03/0.29 * Chain [18,19]: 1 0.03/0.29 with precondition: [C=2,E=2,A>=111] 0.03/0.29 0.03/0.29 0.03/0.29 #### Cost of chains of eval3_loop_cont(A,B,C,D,E,F): 0.03/0.29 * Chain [23]: 0 0.03/0.29 with precondition: [A=2,100>=C] 0.03/0.29 0.03/0.29 * Chain [22]: 1 0.03/0.29 with precondition: [A=3,D=2,100>=C,B>=111] 0.03/0.29 0.03/0.29 * Chain [21]: 0 0.03/0.29 with precondition: [A=3,100>=C] 0.03/0.29 0.03/0.29 * Chain [20]: 2*s(9)+2*s(10)+1 0.03/0.29 Such that:s(7) =< -B+111 0.03/0.29 s(8) =< D 0.03/0.29 s(9) =< s(8) 0.03/0.29 s(10) =< s(9)*9+s(7) 0.03/0.29 0.03/0.29 with precondition: [A=3,100>=C,D>=2] 0.03/0.29 0.03/0.29 0.03/0.29 #### Cost of chains of eval1(A,B,C,D,E): 0.03/0.29 * Chain [26]: 1*s(11)+1 0.03/0.29 Such that:s(11) =< 1/11 0.03/0.29 0.03/0.29 with precondition: [A=100,B=100,C=1] 0.03/0.29 0.03/0.29 * Chain [25]: 2*s(12)+1*s(14)+2*s(17)+2*s(18)+1 0.03/0.29 Such that:s(15) =< 10 0.03/0.29 aux(7) =< -B+122 0.03/0.29 s(14) =< -B/11+101/11 0.03/0.29 s(16) =< -B/11+122/11 0.03/0.29 aux(8) =< -A/11+101/11 0.03/0.29 s(12) =< aux(8) 0.03/0.29 s(15) =< aux(7) 0.03/0.29 s(16) =< aux(7) 0.03/0.29 s(17) =< s(16) 0.03/0.29 s(18) =< s(17)*9+s(15) 0.03/0.29 0.03/0.29 with precondition: [C=1,B=A,100>=B] 0.03/0.29 0.03/0.29 * Chain [24]: 0 0.03/0.29 with precondition: [C=1,B=A,B>=101] 0.03/0.29 0.03/0.29 0.03/0.29 #### Cost of chains of eval0(A,B,C,D,E): 0.03/0.29 * Chain [29]: 1*s(19)+1 0.03/0.29 Such that:s(19) =< 1/11 0.03/0.29 0.03/0.29 with precondition: [B=100] 0.03/0.29 0.03/0.29 * Chain [28]: 3*s(22)+2*s(26)+2*s(27)+1 0.03/0.29 Such that:s(20) =< 10 0.03/0.29 s(21) =< -B+122 0.03/0.29 s(23) =< -B/11+122/11 0.03/0.29 aux(9) =< -B/11+101/11 0.03/0.29 s(22) =< aux(9) 0.03/0.29 s(20) =< s(21) 0.03/0.29 s(23) =< s(21) 0.03/0.29 s(26) =< s(23) 0.03/0.29 s(27) =< s(26)*9+s(20) 0.03/0.29 0.03/0.29 with precondition: [100>=B] 0.03/0.29 0.03/0.29 * Chain [27]: 0 0.03/0.29 with precondition: [B>=101] 0.03/0.29 0.03/0.29 0.03/0.29 Closed-form bounds of eval0(A,B,C,D,E): 0.03/0.29 ------------------------------------- 0.03/0.29 * Chain [29] with precondition: [B=100] 0.03/0.29 - Upper bound: 12/11 0.03/0.29 - Complexity: constant 0.03/0.29 * Chain [28] with precondition: [100>=B] 0.03/0.29 - Upper bound: -23/11*B+2974/11 0.03/0.29 - Complexity: n 0.03/0.29 * Chain [27] with precondition: [B>=101] 0.03/0.29 - Upper bound: 0 0.03/0.29 - Complexity: constant 0.03/0.29 0.03/0.29 ### Maximum cost of eval0(A,B,C,D,E): max([12/11,nat(-B/11+101/11)*3+21+nat(-B/11+122/11)*20]) 0.03/0.29 Asymptotic class: n 0.03/0.29 * Total analysis performed in 223 ms. 0.03/0.29 0.03/0.39 EOF