0.63/0.68 WORST_CASE(?,O(n^2)) 0.63/0.68 0.63/0.68 Preprocessing Cost Relations 0.63/0.68 ===================================== 0.63/0.68 0.63/0.68 #### Computed strongly connected components 0.63/0.68 0. recursive : [eval_start_10/9,eval_start_11/9,eval_start_8/9,eval_start_9/9,eval_start_bb2_in/9,eval_start_bb3_in/9,eval_start_bb4_in/9] 0.63/0.68 1. recursive : [eval_start_15/15,eval_start_16/15,eval_start_bb1_in/15,eval_start_bb2_in_loop_cont/16,eval_start_bb5_in/15] 0.63/0.68 2. non_recursive : [eval_start_stop/9] 0.63/0.68 3. non_recursive : [eval_start_bb6_in/9] 0.63/0.68 4. non_recursive : [exit_location/1] 0.63/0.68 5. non_recursive : [eval_start_bb1_in_loop_cont/10] 0.63/0.68 6. non_recursive : [eval_start_5/9] 0.63/0.68 7. non_recursive : [eval_start_4/9] 0.63/0.68 8. non_recursive : [eval_start_3/9] 0.63/0.68 9. non_recursive : [eval_start_2/9] 0.63/0.68 10. non_recursive : [eval_start_1/9] 0.63/0.68 11. non_recursive : [eval_start_0/9] 0.63/0.68 12. non_recursive : [eval_start_bb0_in/9] 0.63/0.68 13. non_recursive : [eval_start_start/9] 0.63/0.68 0.63/0.68 #### Obtained direct recursion through partial evaluation 0.63/0.68 0. SCC is partially evaluated into eval_start_bb2_in/9 0.63/0.68 1. SCC is partially evaluated into eval_start_bb1_in/15 0.63/0.68 2. SCC is completely evaluated into other SCCs 0.63/0.68 3. SCC is completely evaluated into other SCCs 0.63/0.68 4. SCC is completely evaluated into other SCCs 0.63/0.68 5. SCC is partially evaluated into eval_start_bb1_in_loop_cont/10 0.63/0.68 6. SCC is partially evaluated into eval_start_5/9 0.63/0.68 7. SCC is completely evaluated into other SCCs 0.63/0.68 8. SCC is completely evaluated into other SCCs 0.63/0.68 9. SCC is completely evaluated into other SCCs 0.63/0.68 10. SCC is completely evaluated into other SCCs 0.63/0.68 11. SCC is completely evaluated into other SCCs 0.63/0.68 12. SCC is completely evaluated into other SCCs 0.63/0.68 13. SCC is partially evaluated into eval_start_start/9 0.63/0.68 0.63/0.68 Control-Flow Refinement of Cost Relations 0.63/0.68 ===================================== 0.63/0.68 0.63/0.68 ### Specialization of cost equations eval_start_bb2_in/9 0.63/0.68 * CE 12 is refined into CE [13] 0.63/0.68 * CE 11 is refined into CE [14] 0.63/0.68 * CE 10 is refined into CE [15] 0.63/0.68 * CE 9 is refined into CE [16] 0.63/0.68 0.63/0.68 0.63/0.68 ### Cost equations --> "Loop" of eval_start_bb2_in/9 0.63/0.68 * CEs [15] --> Loop 13 0.63/0.68 * CEs [16] --> Loop 14 0.63/0.68 * CEs [13] --> Loop 15 0.63/0.68 * CEs [14] --> Loop 16 0.63/0.68 0.63/0.68 ### Ranking functions of CR eval_start_bb2_in(V__1,V_1,V_3,V_i_0_sink,B,C,D,E,F) 0.63/0.68 * RF of phase [13,14]: [V__1-V_i_0_sink-1] 0.63/0.68 0.63/0.68 #### Partial ranking functions of CR eval_start_bb2_in(V__1,V_1,V_3,V_i_0_sink,B,C,D,E,F) 0.63/0.68 * Partial RF of phase [13,14]: 0.63/0.68 - RF of loop [13:1]: 0.63/0.68 V__1-1 0.63/0.68 - RF of loop [13:1,14:1]: 0.63/0.68 V__1-V_i_0_sink-1 0.63/0.68 0.63/0.68 0.63/0.68 ### Specialization of cost equations eval_start_bb1_in/15 0.63/0.68 * CE 5 is refined into CE [17] 0.63/0.68 * CE 3 is refined into CE [18,19] 0.63/0.68 * CE 6 is refined into CE [20] 0.63/0.68 * CE 4 is refined into CE [21,22] 0.63/0.68 0.63/0.68 0.63/0.68 ### Cost equations --> "Loop" of eval_start_bb1_in/15 0.63/0.68 * CEs [22] --> Loop 17 0.63/0.68 * CEs [21] --> Loop 18 0.63/0.68 * CEs [17] --> Loop 19 0.63/0.68 * CEs [19] --> Loop 20 0.63/0.68 * CEs [18] --> Loop 21 0.63/0.68 * CEs [20] --> Loop 22 0.63/0.68 0.63/0.68 ### Ranking functions of CR eval_start_bb1_in(V__0,V__1,V_1,V_3,V_7,V_i_0,V_i_0_sink,B,C,D,E,F,G,H,I) 0.63/0.68 * RF of phase [17]: [V__0-V_i_0-1] 0.63/0.68 0.63/0.68 #### Partial ranking functions of CR eval_start_bb1_in(V__0,V__1,V_1,V_3,V_7,V_i_0,V_i_0_sink,B,C,D,E,F,G,H,I) 0.63/0.68 * Partial RF of phase [17]: 0.63/0.68 - RF of loop [17:1]: 0.63/0.68 V__0-V_i_0-1 0.63/0.68 0.63/0.68 0.63/0.68 ### Specialization of cost equations eval_start_bb1_in_loop_cont/10 0.63/0.68 * CE 7 is refined into CE [23] 0.63/0.68 * CE 8 is refined into CE [24] 0.63/0.68 0.63/0.68 0.63/0.68 ### Cost equations --> "Loop" of eval_start_bb1_in_loop_cont/10 0.63/0.68 * CEs [23] --> Loop 23 0.63/0.68 * CEs [24] --> Loop 24 0.63/0.68 0.63/0.68 ### Ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J) 0.63/0.68 0.63/0.68 #### Partial ranking functions of CR eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J) 0.63/0.68 0.63/0.68 0.63/0.68 ### Specialization of cost equations eval_start_5/9 0.63/0.68 * CE 2 is refined into CE [25,26,27,28,29,30,31,32,33] 0.63/0.68 0.63/0.68 0.63/0.68 ### Cost equations --> "Loop" of eval_start_5/9 0.63/0.68 * CEs [29] --> Loop 25 0.63/0.68 * CEs [28,32,33] --> Loop 26 0.63/0.68 * CEs [27] --> Loop 27 0.63/0.68 * CEs [31] --> Loop 28 0.63/0.68 * CEs [25,30] --> Loop 29 0.63/0.68 * CEs [26] --> Loop 30 0.63/0.68 0.63/0.68 ### Ranking functions of CR eval_start_5(V__0,V__1,V_1,V_3,V_7,V_i_0,V_i_0_sink,V_n,B) 0.63/0.68 0.63/0.68 #### Partial ranking functions of CR eval_start_5(V__0,V__1,V_1,V_3,V_7,V_i_0,V_i_0_sink,V_n,B) 0.63/0.68 0.63/0.68 0.63/0.68 ### Specialization of cost equations eval_start_start/9 0.63/0.68 * CE 1 is refined into CE [34,35,36,37,38,39] 0.63/0.68 0.63/0.68 0.63/0.68 ### Cost equations --> "Loop" of eval_start_start/9 0.63/0.68 * CEs [39] --> Loop 31 0.63/0.68 * CEs [38] --> Loop 32 0.63/0.68 * CEs [37] --> Loop 33 0.63/0.68 * CEs [36] --> Loop 34 0.63/0.68 * CEs [35] --> Loop 35 0.63/0.68 * CEs [34] --> Loop 36 0.63/0.68 0.63/0.68 ### Ranking functions of CR eval_start_start(V__0,V__1,V_1,V_3,V_7,V_i_0,V_i_0_sink,V_n,B) 0.63/0.68 0.63/0.68 #### Partial ranking functions of CR eval_start_start(V__0,V__1,V_1,V_3,V_7,V_i_0,V_i_0_sink,V_n,B) 0.63/0.68 0.63/0.68 0.63/0.68 Computing Bounds 0.63/0.68 ===================================== 0.63/0.68 0.63/0.68 #### Cost of chains of eval_start_bb2_in(V__1,V_1,V_3,V_i_0_sink,B,C,D,E,F): 0.63/0.68 * Chain [[13,14],16]: 1*it(13)+1*it(14)+0 0.63/0.68 Such that:it(13) =< V__1-C 0.63/0.68 aux(3) =< V__1-V_i_0_sink 0.63/0.68 it(13) =< aux(3) 0.63/0.68 it(14) =< aux(3) 0.63/0.68 0.63/0.68 with precondition: [B=2,C=D,C=F+1,V_i_0_sink>=0,V__1>=V_i_0_sink+2,C>=V_i_0_sink+1,V__1>=C] 0.63/0.68 0.63/0.68 * Chain [[13,14],15]: 2*it(13)+0 0.63/0.68 Such that:aux(4) =< V__1-V_i_0_sink 0.63/0.68 it(13) =< aux(4) 0.63/0.68 0.63/0.68 with precondition: [B=3,V_i_0_sink>=0,V__1>=V_i_0_sink+2] 0.63/0.68 0.63/0.68 * Chain [16]: 0 0.63/0.68 with precondition: [B=2,E=V_3,V__1=V_i_0_sink+1,V__1=C,V__1=D,V__1=F+1,V__1>=1] 0.63/0.68 0.63/0.68 * Chain [15]: 0 0.63/0.68 with precondition: [B=3,V_i_0_sink>=0,V__1>=V_i_0_sink+1] 0.63/0.68 0.63/0.68 0.63/0.68 #### Cost of chains of eval_start_bb1_in(V__0,V__1,V_1,V_3,V_7,V_i_0,V_i_0_sink,B,C,D,E,F,G,H,I): 0.63/0.68 * Chain [[17],22]: 1*it(17)+1*s(7)+1*s(8)+0 0.63/0.68 Such that:aux(8) =< V__0-V_i_0 0.63/0.68 it(17) =< aux(8) 0.63/0.68 s(7) =< aux(8) 0.63/0.68 s(9) =< it(17)*aux(8) 0.63/0.68 s(7) =< s(9) 0.63/0.68 s(8) =< s(9) 0.63/0.68 0.63/0.68 with precondition: [B=3,V_i_0>=0,V__0>=V_i_0+2] 0.63/0.68 0.63/0.68 * Chain [[17],21]: 1*it(17)+1*s(7)+1*s(8)+0 0.63/0.68 Such that:aux(9) =< V__0-V_i_0 0.63/0.68 it(17) =< aux(9) 0.63/0.68 s(7) =< aux(9) 0.63/0.68 s(9) =< it(17)*aux(9) 0.63/0.68 s(7) =< s(9) 0.63/0.68 s(8) =< s(9) 0.63/0.68 0.63/0.68 with precondition: [B=3,V_i_0>=0,V__0>=V_i_0+2] 0.63/0.68 0.63/0.68 * Chain [[17],20]: 3*it(17)+1*s(7)+1*s(8)+0 0.63/0.68 Such that:aux(10) =< V__0-V_i_0 0.63/0.68 it(17) =< aux(10) 0.63/0.68 s(7) =< aux(10) 0.63/0.68 s(9) =< it(17)*aux(10) 0.63/0.68 s(7) =< s(9) 0.63/0.68 s(8) =< s(9) 0.63/0.68 0.63/0.68 with precondition: [B=3,V_i_0>=0,V__0>=V_i_0+3] 0.63/0.68 0.63/0.68 * Chain [[17],19]: 1*it(17)+1*s(7)+1*s(8)+0 0.63/0.68 Such that:aux(11) =< V__0-V_i_0 0.63/0.68 it(17) =< aux(11) 0.63/0.68 s(7) =< aux(11) 0.63/0.68 s(9) =< it(17)*aux(11) 0.63/0.68 s(7) =< s(9) 0.63/0.68 s(8) =< s(9) 0.63/0.68 0.63/0.68 with precondition: [B=4,C=D,C=E,C=G,C=H,C=I+1,V_i_0>=0,C>=V_i_0+1,V__0>=C+1] 0.63/0.68 0.63/0.68 * Chain [[17],18,22]: 1*it(17)+1*s(7)+1*s(8)+1 0.63/0.68 Such that:aux(12) =< V__0-V_i_0 0.63/0.68 it(17) =< aux(12) 0.63/0.68 s(7) =< aux(12) 0.63/0.68 s(9) =< it(17)*aux(12) 0.63/0.68 s(7) =< s(9) 0.63/0.68 s(8) =< s(9) 0.63/0.68 0.63/0.68 with precondition: [B=3,V_i_0>=0,V__0>=V_i_0+2] 0.63/0.68 0.63/0.68 * Chain [[17],18,19]: 1*it(17)+1*s(7)+1*s(8)+1 0.63/0.68 Such that:aux(13) =< V__0-V_i_0 0.63/0.68 it(17) =< aux(13) 0.63/0.68 s(7) =< aux(13) 0.63/0.68 s(9) =< it(17)*aux(13) 0.63/0.68 s(7) =< s(9) 0.63/0.68 s(8) =< s(9) 0.63/0.68 0.63/0.68 with precondition: [B=4,C=D,C=E,C=G,C=H,C=I+1,V_i_0>=0,C>=V_i_0+2,V__0>=C] 0.63/0.68 0.63/0.68 * Chain [22]: 0 0.63/0.68 with precondition: [B=3,V_i_0>=0] 0.63/0.68 0.63/0.68 * Chain [21]: 0 0.63/0.68 with precondition: [B=3,V_i_0>=0,V__0>=V_i_0+1] 0.63/0.68 0.63/0.68 * Chain [20]: 2*s(11)+0 0.63/0.68 Such that:s(10) =< V__0-V_i_0 0.63/0.68 s(11) =< s(10) 0.63/0.68 0.63/0.68 with precondition: [B=3,V_i_0>=0,V__0>=V_i_0+2] 0.63/0.68 0.63/0.68 * Chain [19]: 0 0.63/0.68 with precondition: [B=4,D=V__1,E=V_1,F=V_3,G=V_7,I=V_i_0_sink,V__0=C,V_i_0=H,V_i_0>=0,V_i_0>=V__0] 0.63/0.68 0.63/0.68 * Chain [18,22]: 1 0.63/0.68 with precondition: [B=3,V_i_0+1=V__0,V_i_0>=0] 0.63/0.68 0.63/0.68 * Chain [18,19]: 1 0.63/0.68 with precondition: [B=4,V_i_0+1=V__0,V_i_0+1=C,V_i_0+1=D,V_i_0+1=E,V_3=F,V_i_0+1=G,V_i_0+1=H,V_i_0=I,V_i_0>=0] 0.63/0.68 0.63/0.68 0.63/0.68 #### Cost of chains of eval_start_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J): 0.63/0.68 * Chain [24]: 0 0.63/0.68 with precondition: [A=3] 0.63/0.68 0.63/0.68 * Chain [23]: 0 0.63/0.68 with precondition: [A=4] 0.63/0.68 0.63/0.68 0.63/0.68 #### Cost of chains of eval_start_5(V__0,V__1,V_1,V_3,V_7,V_i_0,V_i_0_sink,V_n,B): 0.63/0.68 * Chain [30]: 0 0.63/0.68 with precondition: [] 0.63/0.68 0.63/0.68 * Chain [29]: 1 0.63/0.68 with precondition: [V_n=1] 0.63/0.68 0.63/0.68 * Chain [28]: 0 0.63/0.68 with precondition: [0>=V_n] 0.63/0.68 0.63/0.68 * Chain [27]: 0 0.63/0.68 with precondition: [V_n>=1] 0.63/0.68 0.63/0.68 * Chain [26]: 7*s(30)+5*s(31)+5*s(33)+1 0.63/0.68 Such that:aux(15) =< V_n 0.63/0.68 s(30) =< aux(15) 0.63/0.68 s(31) =< aux(15) 0.63/0.68 s(32) =< s(30)*aux(15) 0.63/0.68 s(31) =< s(32) 0.63/0.68 s(33) =< s(32) 0.63/0.68 0.63/0.68 with precondition: [V_n>=2] 0.63/0.68 0.63/0.68 * Chain [25]: 3*s(45)+1*s(46)+1*s(48)+0 0.63/0.68 Such that:s(44) =< V_n 0.63/0.68 s(45) =< s(44) 0.63/0.68 s(46) =< s(44) 0.63/0.68 s(47) =< s(45)*s(44) 0.63/0.68 s(46) =< s(47) 0.63/0.68 s(48) =< s(47) 0.63/0.68 0.63/0.68 with precondition: [V_n>=3] 0.63/0.68 0.63/0.68 0.63/0.68 #### Cost of chains of eval_start_start(V__0,V__1,V_1,V_3,V_7,V_i_0,V_i_0_sink,V_n,B): 0.63/0.68 * Chain [36]: 0 0.63/0.68 with precondition: [] 0.63/0.68 0.63/0.68 * Chain [35]: 1 0.63/0.68 with precondition: [V_n=1] 0.63/0.68 0.63/0.68 * Chain [34]: 0 0.63/0.68 with precondition: [0>=V_n] 0.63/0.68 0.63/0.68 * Chain [33]: 0 0.63/0.68 with precondition: [V_n>=1] 0.63/0.68 0.63/0.68 * Chain [32]: 7*s(50)+5*s(51)+5*s(53)+1 0.63/0.68 Such that:s(49) =< V_n 0.63/0.68 s(50) =< s(49) 0.63/0.68 s(51) =< s(49) 0.63/0.68 s(52) =< s(50)*s(49) 0.63/0.68 s(51) =< s(52) 0.63/0.68 s(53) =< s(52) 0.63/0.68 0.63/0.68 with precondition: [V_n>=2] 0.63/0.68 0.63/0.68 * Chain [31]: 3*s(55)+1*s(56)+1*s(58)+0 0.63/0.68 Such that:s(54) =< V_n 0.63/0.68 s(55) =< s(54) 0.63/0.68 s(56) =< s(54) 0.63/0.68 s(57) =< s(55)*s(54) 0.63/0.68 s(56) =< s(57) 0.63/0.68 s(58) =< s(57) 0.63/0.68 0.63/0.68 with precondition: [V_n>=3] 0.63/0.68 0.63/0.68 0.63/0.68 Closed-form bounds of eval_start_start(V__0,V__1,V_1,V_3,V_7,V_i_0,V_i_0_sink,V_n,B): 0.63/0.68 ------------------------------------- 0.63/0.68 * Chain [36] with precondition: [] 0.63/0.68 - Upper bound: 0 0.63/0.68 - Complexity: constant 0.63/0.68 * Chain [35] with precondition: [V_n=1] 0.63/0.68 - Upper bound: 1 0.63/0.68 - Complexity: constant 0.63/0.68 * Chain [34] with precondition: [0>=V_n] 0.63/0.68 - Upper bound: 0 0.63/0.68 - Complexity: constant 0.63/0.68 * Chain [33] with precondition: [V_n>=1] 0.63/0.68 - Upper bound: 0 0.63/0.68 - Complexity: constant 0.63/0.68 * Chain [32] with precondition: [V_n>=2] 0.63/0.68 - Upper bound: 12*V_n+1+5*V_n*V_n 0.63/0.68 - Complexity: n^2 0.63/0.68 * Chain [31] with precondition: [V_n>=3] 0.63/0.68 - Upper bound: 4*V_n+V_n*V_n 0.63/0.68 - Complexity: n^2 0.63/0.68 0.63/0.68 ### Maximum cost of eval_start_start(V__0,V__1,V_1,V_3,V_7,V_i_0,V_i_0_sink,V_n,B): max([1,nat(V_n)*8+1+nat(V_n)*4*nat(V_n)+(nat(V_n)*nat(V_n)+nat(V_n)*4)]) 0.63/0.68 Asymptotic class: n^2 0.63/0.68 * Total analysis performed in 580 ms. 0.63/0.68 0.68/0.78 EOF