0.71/0.70 WORST_CASE(?,O(n^2)) 0.71/0.70 0.71/0.70 Preprocessing Cost Relations 0.71/0.70 ===================================== 0.71/0.70 0.71/0.70 #### Computed strongly connected components 0.71/0.70 0. recursive : [eval_p3_15/7,eval_p3_16/7,eval_p3_bb3_in/7,eval_p3_bb4_in/7] 0.71/0.70 1. recursive : [eval_p3_bb1_in/12,eval_p3_bb2_in/12,eval_p3_bb3_in_loop_cont/13,eval_p3_bb5_in/12,eval_p3_bb6_in/12] 0.71/0.70 2. non_recursive : [eval_p3_stop/9] 0.71/0.70 3. non_recursive : [eval_p3_bb7_in/9] 0.71/0.70 4. non_recursive : [exit_location/1] 0.71/0.70 5. non_recursive : [eval_p3_bb1_in_loop_cont/10] 0.71/0.70 6. non_recursive : [eval_p3_7/9] 0.71/0.70 7. non_recursive : [eval_p3_6/9] 0.71/0.70 8. non_recursive : [eval_p3_5/9] 0.71/0.70 9. non_recursive : [eval_p3_4/9] 0.71/0.70 10. non_recursive : [eval_p3_3/9] 0.71/0.70 11. non_recursive : [eval_p3_2/9] 0.71/0.70 12. non_recursive : [eval_p3_1/9] 0.71/0.70 13. non_recursive : [eval_p3_0/9] 0.71/0.70 14. non_recursive : [eval_p3_bb0_in/9] 0.71/0.70 15. non_recursive : [eval_p3_start/9] 0.71/0.70 0.71/0.70 #### Obtained direct recursion through partial evaluation 0.71/0.70 0. SCC is partially evaluated into eval_p3_bb3_in/7 0.71/0.70 1. SCC is partially evaluated into eval_p3_bb1_in/12 0.71/0.70 2. SCC is completely evaluated into other SCCs 0.71/0.71 3. SCC is completely evaluated into other SCCs 0.71/0.71 4. SCC is completely evaluated into other SCCs 0.71/0.71 5. SCC is partially evaluated into eval_p3_bb1_in_loop_cont/10 0.71/0.71 6. SCC is partially evaluated into eval_p3_7/9 0.71/0.71 7. SCC is completely evaluated into other SCCs 0.71/0.71 8. SCC is completely evaluated into other SCCs 0.71/0.71 9. SCC is completely evaluated into other SCCs 0.71/0.71 10. SCC is completely evaluated into other SCCs 0.71/0.71 11. SCC is completely evaluated into other SCCs 0.71/0.71 12. SCC is completely evaluated into other SCCs 0.71/0.71 13. SCC is completely evaluated into other SCCs 0.71/0.71 14. SCC is completely evaluated into other SCCs 0.71/0.71 15. SCC is partially evaluated into eval_p3_start/9 0.71/0.71 0.71/0.71 Control-Flow Refinement of Cost Relations 0.71/0.71 ===================================== 0.71/0.71 0.71/0.71 ### Specialization of cost equations eval_p3_bb3_in/7 0.71/0.71 * CE 13 is refined into CE [14] 0.71/0.71 * CE 12 is refined into CE [15] 0.71/0.71 * CE 11 is refined into CE [16] 0.71/0.71 0.71/0.71 0.71/0.71 ### Cost equations --> "Loop" of eval_p3_bb3_in/7 0.71/0.71 * CEs [16] --> Loop 14 0.71/0.71 * CEs [14] --> Loop 15 0.71/0.71 * CEs [15] --> Loop 16 0.71/0.71 0.71/0.71 ### Ranking functions of CR eval_p3_bb3_in(V__1,V__3,V_12,B,C,D,E) 0.71/0.71 * RF of phase [14]: [V__1] 0.71/0.71 0.71/0.71 #### Partial ranking functions of CR eval_p3_bb3_in(V__1,V__3,V_12,B,C,D,E) 0.71/0.71 * Partial RF of phase [14]: 0.71/0.71 - RF of loop [14:1]: 0.71/0.71 V__1 0.71/0.71 0.71/0.71 0.71/0.71 ### Specialization of cost equations eval_p3_bb1_in/12 0.71/0.71 * CE 7 is refined into CE [17] 0.71/0.71 * CE 6 is refined into CE [18,19] 0.71/0.71 * CE 8 is refined into CE [20] 0.71/0.71 * CE 5 is refined into CE [21,22] 0.71/0.71 * CE 3 is refined into CE [23] 0.71/0.71 * CE 4 is refined into CE [24] 0.71/0.71 0.71/0.71 0.71/0.71 ### Cost equations --> "Loop" of eval_p3_bb1_in/12 0.71/0.71 * CEs [22] --> Loop 17 0.71/0.71 * CEs [23] --> Loop 18 0.71/0.71 * CEs [21] --> Loop 19 0.71/0.71 * CEs [24] --> Loop 20 0.71/0.71 * CEs [17] --> Loop 21 0.71/0.71 * CEs [19] --> Loop 22 0.71/0.71 * CEs [18] --> Loop 23 0.71/0.71 * CEs [20] --> Loop 24 0.71/0.71 0.71/0.71 ### Ranking functions of CR eval_p3_bb1_in(V__0,V__01,V__1,V__3,V_12,V_z,B,C,D,E,F,G) 0.71/0.71 * RF of phase [17,18,19,20]: [V__0] 0.71/0.71 0.71/0.71 #### Partial ranking functions of CR eval_p3_bb1_in(V__0,V__01,V__1,V__3,V_12,V_z,B,C,D,E,F,G) 0.71/0.71 * Partial RF of phase [17,18,19,20]: 0.71/0.71 - RF of loop [17:1]: 0.71/0.71 V__01 depends on loops [18:1,20:1] 0.71/0.71 - RF of loop [17:1,18:1,19:1,20:1]: 0.71/0.71 V__0 0.71/0.71 0.71/0.71 0.71/0.71 ### Specialization of cost equations eval_p3_bb1_in_loop_cont/10 0.71/0.71 * CE 9 is refined into CE [25] 0.71/0.71 * CE 10 is refined into CE [26] 0.71/0.71 0.71/0.71 0.71/0.71 ### Cost equations --> "Loop" of eval_p3_bb1_in_loop_cont/10 0.71/0.71 * CEs [25] --> Loop 25 0.71/0.71 * CEs [26] --> Loop 26 0.71/0.71 0.71/0.71 ### Ranking functions of CR eval_p3_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J) 0.71/0.71 0.71/0.71 #### Partial ranking functions of CR eval_p3_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J) 0.71/0.71 0.71/0.71 0.71/0.71 ### Specialization of cost equations eval_p3_7/9 0.71/0.71 * CE 2 is refined into CE [27,28,29,30,31,32] 0.71/0.71 0.71/0.71 0.71/0.71 ### Cost equations --> "Loop" of eval_p3_7/9 0.71/0.71 * CEs [30] --> Loop 27 0.71/0.71 * CEs [29] --> Loop 28 0.71/0.71 * CEs [28,31] --> Loop 29 0.71/0.71 * CEs [32] --> Loop 30 0.71/0.71 * CEs [27] --> Loop 31 0.71/0.71 0.71/0.71 ### Ranking functions of CR eval_p3_7(V__0,V__01,V__1,V__3,V_12,V_x,V_y,V_z,B) 0.71/0.71 0.71/0.71 #### Partial ranking functions of CR eval_p3_7(V__0,V__01,V__1,V__3,V_12,V_x,V_y,V_z,B) 0.71/0.71 0.71/0.71 0.71/0.71 ### Specialization of cost equations eval_p3_start/9 0.71/0.71 * CE 1 is refined into CE [33,34,35,36,37] 0.71/0.71 0.71/0.71 0.71/0.71 ### Cost equations --> "Loop" of eval_p3_start/9 0.71/0.71 * CEs [37] --> Loop 32 0.71/0.71 * CEs [36] --> Loop 33 0.71/0.71 * CEs [35] --> Loop 34 0.71/0.71 * CEs [34] --> Loop 35 0.71/0.71 * CEs [33] --> Loop 36 0.71/0.71 0.71/0.71 ### Ranking functions of CR eval_p3_start(V__0,V__01,V__1,V__3,V_12,V_x,V_y,V_z,B) 0.71/0.71 0.71/0.71 #### Partial ranking functions of CR eval_p3_start(V__0,V__01,V__1,V__3,V_12,V_x,V_y,V_z,B) 0.71/0.71 0.71/0.71 0.71/0.71 Computing Bounds 0.71/0.71 ===================================== 0.71/0.71 0.71/0.71 #### Cost of chains of eval_p3_bb3_in(V__1,V__3,V_12,B,C,D,E): 0.71/0.71 * Chain [[14],16]: 1*it(14)+0 0.71/0.71 Such that:it(14) =< V__1-C 0.71/0.71 0.71/0.71 with precondition: [B=2,C=D,C=E,C>=0,V__1>=C+1] 0.71/0.71 0.71/0.71 * Chain [[14],15]: 1*it(14)+0 0.71/0.71 Such that:it(14) =< V__1 0.71/0.71 0.71/0.71 with precondition: [B=3,V__1>=1] 0.71/0.71 0.71/0.71 * Chain [16]: 0 0.71/0.71 with precondition: [B=2,E=V_12,V__1=C,V__1=D] 0.71/0.71 0.71/0.71 * Chain [15]: 0 0.71/0.71 with precondition: [B=3] 0.71/0.71 0.71/0.71 0.71/0.71 #### Cost of chains of eval_p3_bb1_in(V__0,V__01,V__1,V__3,V_12,V_z,B,C,D,E,F,G): 0.71/0.71 * Chain [[17,18,19,20],24]: 1*it(17)+3*it(18)+1*s(3)+0 0.71/0.71 Such that:aux(10) =< V__01 0.71/0.71 aux(6) =< V_z 0.71/0.71 aux(11) =< V__0 0.71/0.71 it(17) =< aux(11) 0.71/0.71 it(18) =< aux(11) 0.71/0.71 aux(7) =< aux(6) 0.71/0.71 aux(4) =< max([aux(10),aux(6)])+it(18) 0.71/0.71 aux(1) =< it(18)*aux(7) 0.71/0.71 s(3) =< it(18)+aux(1)+aux(10) 0.71/0.71 it(17) =< it(18)+aux(1)+aux(10) 0.71/0.71 s(3) =< it(17)*aux(4) 0.71/0.71 0.71/0.71 with precondition: [B=3,V__0>=1] 0.71/0.71 0.71/0.71 * Chain [[17,18,19,20],23]: 1*it(17)+3*it(18)+1*s(3)+0 0.71/0.71 Such that:aux(10) =< V__01 0.71/0.71 aux(6) =< V_z 0.71/0.71 aux(12) =< V__0 0.71/0.71 it(17) =< aux(12) 0.71/0.71 it(18) =< aux(12) 0.71/0.71 aux(7) =< aux(6) 0.71/0.71 aux(4) =< max([aux(10),aux(6)])+it(18) 0.71/0.71 aux(1) =< it(18)*aux(7) 0.71/0.71 s(3) =< it(18)+aux(1)+aux(10) 0.71/0.71 it(17) =< it(18)+aux(1)+aux(10) 0.71/0.71 s(3) =< it(17)*aux(4) 0.71/0.71 0.71/0.71 with precondition: [B=3,V__0>=2] 0.71/0.71 0.71/0.71 * Chain [[17,18,19,20],22]: 1*it(17)+3*it(18)+1*s(3)+1*s(5)+0 0.71/0.71 Such that:it([22]) =< 1 0.71/0.71 aux(18) =< V_z 0.71/0.71 aux(24) =< V__0 0.71/0.71 aux(25) =< V__01 0.71/0.71 it(17) =< aux(24) 0.71/0.71 it(18) =< aux(24) 0.71/0.71 it([22]) =< aux(24) 0.71/0.71 aux(19) =< aux(18) 0.71/0.71 aux(16) =< max([aux(25),aux(18)])+it(18) 0.71/0.71 aux(22) =< aux(16) 0.71/0.71 aux(13) =< it(18)*aux(19) 0.71/0.71 it([22]) =< it(18)+aux(13)+aux(25) 0.71/0.71 s(3) =< it(18)+aux(13)+aux(25) 0.71/0.71 it(17) =< it(18)+aux(13)+aux(25) 0.71/0.71 s(5) =< it(18)+aux(13)+aux(25) 0.71/0.71 s(5) =< it([22])*aux(22) 0.71/0.71 s(3) =< it(17)*aux(16) 0.71/0.71 0.71/0.71 with precondition: [B=3,V__0>=2] 0.71/0.71 0.71/0.71 * Chain [[17,18,19,20],21]: 1*it(17)+3*it(18)+1*s(3)+0 0.71/0.71 Such that:aux(10) =< V__01 0.71/0.71 aux(6) =< V_z 0.71/0.71 aux(26) =< V__0 0.71/0.71 it(17) =< aux(26) 0.71/0.71 it(18) =< aux(26) 0.71/0.71 aux(7) =< aux(6) 0.71/0.71 aux(4) =< max([aux(10),aux(6)])+it(18) 0.71/0.71 aux(1) =< it(18)*aux(7) 0.71/0.71 s(3) =< it(18)+aux(1)+aux(10) 0.71/0.71 it(17) =< it(18)+aux(1)+aux(10) 0.71/0.71 s(3) =< it(17)*aux(4) 0.71/0.71 0.71/0.71 with precondition: [B=4,C=0,D=F,V__0>=1] 0.71/0.71 0.71/0.71 * Chain [24]: 0 0.71/0.71 with precondition: [B=3] 0.71/0.71 0.71/0.71 * Chain [23]: 0 0.71/0.71 with precondition: [B=3,V__0>=1] 0.71/0.71 0.71/0.71 * Chain [22]: 1*s(4)+0 0.71/0.71 Such that:s(4) =< V__01 0.71/0.71 0.71/0.71 with precondition: [B=3,V__0>=1,V__01>=1] 0.71/0.71 0.71/0.71 * Chain [21]: 0 0.71/0.71 with precondition: [B=4,D=V__01,E=V__1,F=V__3,G=V_12,V__0=C,0>=V__0] 0.71/0.71 0.71/0.71 0.71/0.71 #### Cost of chains of eval_p3_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J): 0.71/0.71 * Chain [26]: 0 0.71/0.71 with precondition: [A=3] 0.71/0.71 0.71/0.71 * Chain [25]: 0 0.71/0.71 with precondition: [A=4] 0.71/0.71 0.71/0.71 0.71/0.71 #### Cost of chains of eval_p3_7(V__0,V__01,V__1,V__3,V_12,V_x,V_y,V_z,B): 0.71/0.71 * Chain [31]: 0 0.71/0.71 with precondition: [] 0.71/0.71 0.71/0.71 * Chain [30]: 0 0.71/0.71 with precondition: [0>=V_x] 0.71/0.71 0.71/0.71 * Chain [29]: 2*s(39)+6*s(40)+2*s(44)+0 0.71/0.71 Such that:aux(30) =< V_x 0.71/0.71 aux(31) =< V_y 0.71/0.71 aux(32) =< V_z 0.71/0.71 s(39) =< aux(30) 0.71/0.71 s(40) =< aux(30) 0.71/0.71 s(41) =< aux(32) 0.71/0.71 s(42) =< max([aux(31),aux(32)])+s(40) 0.71/0.71 s(43) =< s(40)*s(41) 0.71/0.71 s(44) =< s(40)+s(43)+aux(31) 0.71/0.71 s(39) =< s(40)+s(43)+aux(31) 0.71/0.71 s(44) =< s(39)*s(42) 0.71/0.71 0.71/0.71 with precondition: [V_x>=1] 0.71/0.71 0.71/0.71 * Chain [28]: 1*s(54)+0 0.71/0.71 Such that:s(54) =< V_y 0.71/0.71 0.71/0.71 with precondition: [V_x>=1,V_y>=1] 0.71/0.71 0.71/0.71 * Chain [27]: 2*s(59)+6*s(60)+2*s(65)+1*s(66)+0 0.71/0.71 Such that:s(55) =< 1 0.71/0.71 s(56) =< V_x 0.71/0.71 s(57) =< V_y 0.71/0.71 s(58) =< V_z 0.71/0.71 s(59) =< s(56) 0.71/0.71 s(60) =< s(56) 0.71/0.71 s(55) =< s(56) 0.71/0.71 s(61) =< s(58) 0.71/0.71 s(62) =< max([s(57),s(58)])+s(60) 0.71/0.71 s(63) =< s(62) 0.71/0.71 s(64) =< s(60)*s(61) 0.71/0.71 s(55) =< s(60)+s(64)+s(57) 0.71/0.71 s(65) =< s(60)+s(64)+s(57) 0.71/0.71 s(59) =< s(60)+s(64)+s(57) 0.71/0.71 s(66) =< s(60)+s(64)+s(57) 0.71/0.71 s(66) =< s(55)*s(63) 0.71/0.71 s(65) =< s(59)*s(62) 0.71/0.71 0.71/0.71 with precondition: [V_x>=2] 0.71/0.71 0.71/0.71 0.71/0.71 #### Cost of chains of eval_p3_start(V__0,V__01,V__1,V__3,V_12,V_x,V_y,V_z,B): 0.71/0.71 * Chain [36]: 0 0.71/0.71 with precondition: [] 0.71/0.71 0.71/0.71 * Chain [35]: 0 0.71/0.71 with precondition: [0>=V_x] 0.71/0.71 0.71/0.71 * Chain [34]: 2*s(70)+6*s(71)+2*s(75)+0 0.71/0.71 Such that:s(67) =< V_x 0.71/0.71 s(68) =< V_y 0.71/0.71 s(69) =< V_z 0.71/0.71 s(70) =< s(67) 0.71/0.71 s(71) =< s(67) 0.71/0.71 s(72) =< s(69) 0.71/0.71 s(73) =< max([s(68),s(69)])+s(71) 0.71/0.71 s(74) =< s(71)*s(72) 0.71/0.71 s(75) =< s(71)+s(74)+s(68) 0.71/0.71 s(70) =< s(71)+s(74)+s(68) 0.71/0.71 s(75) =< s(70)*s(73) 0.71/0.71 0.71/0.71 with precondition: [V_x>=1] 0.71/0.71 0.71/0.71 * Chain [33]: 1*s(76)+0 0.71/0.71 Such that:s(76) =< V_y 0.71/0.71 0.71/0.71 with precondition: [V_x>=1,V_y>=1] 0.71/0.71 0.71/0.71 * Chain [32]: 2*s(81)+6*s(82)+2*s(87)+1*s(88)+0 0.71/0.71 Such that:s(77) =< 1 0.71/0.71 s(78) =< V_x 0.71/0.71 s(79) =< V_y 0.71/0.71 s(80) =< V_z 0.71/0.71 s(81) =< s(78) 0.71/0.71 s(82) =< s(78) 0.71/0.71 s(77) =< s(78) 0.71/0.71 s(83) =< s(80) 0.71/0.71 s(84) =< max([s(79),s(80)])+s(82) 0.71/0.71 s(85) =< s(84) 0.71/0.71 s(86) =< s(82)*s(83) 0.71/0.71 s(77) =< s(82)+s(86)+s(79) 0.71/0.71 s(87) =< s(82)+s(86)+s(79) 0.71/0.71 s(81) =< s(82)+s(86)+s(79) 0.71/0.71 s(88) =< s(82)+s(86)+s(79) 0.71/0.71 s(88) =< s(77)*s(85) 0.71/0.71 s(87) =< s(81)*s(84) 0.71/0.71 0.71/0.71 with precondition: [V_x>=2] 0.71/0.71 0.71/0.71 0.71/0.71 Closed-form bounds of eval_p3_start(V__0,V__01,V__1,V__3,V_12,V_x,V_y,V_z,B): 0.71/0.71 ------------------------------------- 0.71/0.71 * Chain [36] with precondition: [] 0.71/0.71 - Upper bound: 0 0.71/0.71 - Complexity: constant 0.71/0.71 * Chain [35] with precondition: [0>=V_x] 0.71/0.71 - Upper bound: 0 0.71/0.71 - Complexity: constant 0.71/0.71 * Chain [34] with precondition: [V_x>=1] 0.71/0.71 - Upper bound: 2*V_x*nat(V_z)+10*V_x+nat(V_y)*2 0.71/0.71 - Complexity: n^2 0.71/0.71 * Chain [33] with precondition: [V_x>=1,V_y>=1] 0.71/0.71 - Upper bound: V_y 0.71/0.71 - Complexity: n 0.71/0.71 * Chain [32] with precondition: [V_x>=2] 0.71/0.71 - Upper bound: 11*V_x+max([nat(V_y),nat(V_z)])+2*V_x*nat(V_z)+nat(V_y)*2 0.71/0.71 - Complexity: n^2 0.71/0.71 0.71/0.71 ### Maximum cost of eval_p3_start(V__0,V__01,V__1,V__3,V_12,V_x,V_y,V_z,B): nat(V_x)*2*nat(V_z)+nat(V_x)*10+nat(V_y)+(nat(V_x)+max([nat(V_y),nat(V_z)]))+nat(V_y) 0.71/0.71 Asymptotic class: n^2 0.71/0.71 * Total analysis performed in 595 ms. 0.71/0.71 0.71/0.81 EOF