0.06/0.37 WORST_CASE(?,O(n^2)) 0.06/0.37 0.06/0.37 Preprocessing Cost Relations 0.06/0.37 ===================================== 0.06/0.37 0.06/0.37 #### Computed strongly connected components 0.06/0.37 0. recursive : [eval_hc_compute_2/5,eval_hc_compute_3/6,eval_hc_compute_bb2_in/4,eval_hc_compute_bb3_in/5] 0.06/0.37 1. recursive : [eval_hc_compute_6/3,eval_hc_compute_7/4,eval_hc_compute_bb5_in/3,eval_hc_compute_bb6_in/3,eval_hc_compute_bb7_in/4] 0.06/0.37 2. recursive : [eval_hc_compute_bb4_in/4,eval_hc_compute_bb5_in_loop_cont/6,eval_hc_compute_bb8_in/5] 0.06/0.37 3. recursive : [eval_hc_compute__critedge_in/4,eval_hc_compute_bb1_in/2,eval_hc_compute_bb2_in_loop_cont/5,eval_hc_compute_bb4_in_loop_cont/3] 0.06/0.37 4. non_recursive : [eval_hc_compute_stop/1] 0.06/0.37 5. non_recursive : [eval_hc_compute_bb9_in/1] 0.06/0.37 6. non_recursive : [eval_hc_compute_bb1_in_loop_cont/2] 0.06/0.37 7. non_recursive : [eval_hc_compute_bb0_in/2] 0.06/0.37 8. non_recursive : [eval_hc_compute_start/2] 0.06/0.37 0.06/0.37 #### Obtained direct recursion through partial evaluation 0.06/0.37 0. SCC is partially evaluated into eval_hc_compute_bb2_in/4 0.06/0.37 1. SCC is partially evaluated into eval_hc_compute_bb5_in/3 0.06/0.37 2. SCC is partially evaluated into eval_hc_compute_bb4_in/4 0.06/0.37 3. SCC is partially evaluated into eval_hc_compute_bb1_in/2 0.06/0.37 4. SCC is completely evaluated into other SCCs 0.06/0.37 5. SCC is completely evaluated into other SCCs 0.06/0.37 6. SCC is completely evaluated into other SCCs 0.06/0.37 7. SCC is partially evaluated into eval_hc_compute_bb0_in/2 0.06/0.37 8. SCC is partially evaluated into eval_hc_compute_start/2 0.06/0.37 0.06/0.37 Control-Flow Refinement of Cost Relations 0.06/0.37 ===================================== 0.06/0.37 0.06/0.37 ### Specialization of cost equations eval_hc_compute_bb2_in/4 0.06/0.37 * CE 5 is refined into CE [13] 0.06/0.37 * CE 7 is refined into CE [14] 0.06/0.37 * CE 6 is refined into CE [15] 0.06/0.37 0.06/0.37 0.06/0.37 ### Cost equations --> "Loop" of eval_hc_compute_bb2_in/4 0.06/0.37 * CEs [15] --> Loop 13 0.06/0.37 * CEs [13] --> Loop 14 0.06/0.37 * CEs [14] --> Loop 15 0.06/0.37 0.06/0.37 ### Ranking functions of CR eval_hc_compute_bb2_in(V_i_0_sink,B,C,D) 0.06/0.37 * RF of phase [13]: [V_i_0_sink-1] 0.06/0.37 0.06/0.37 #### Partial ranking functions of CR eval_hc_compute_bb2_in(V_i_0_sink,B,C,D) 0.06/0.37 * Partial RF of phase [13]: 0.06/0.37 - RF of loop [13:1]: 0.06/0.37 V_i_0_sink-1 0.06/0.37 0.06/0.37 0.06/0.37 ### Specialization of cost equations eval_hc_compute_bb5_in/3 0.06/0.37 * CE 10 is refined into CE [16] 0.06/0.37 * CE 12 is refined into CE [17] 0.06/0.37 * CE 11 is refined into CE [18] 0.06/0.37 0.06/0.37 0.06/0.37 ### Cost equations --> "Loop" of eval_hc_compute_bb5_in/3 0.06/0.37 * CEs [18] --> Loop 16 0.06/0.37 * CEs [16] --> Loop 17 0.06/0.37 * CEs [17] --> Loop 18 0.06/0.37 0.06/0.37 ### Ranking functions of CR eval_hc_compute_bb5_in(V_y_0,B,C) 0.06/0.37 * RF of phase [16]: [V_y_0] 0.06/0.37 0.06/0.37 #### Partial ranking functions of CR eval_hc_compute_bb5_in(V_y_0,B,C) 0.06/0.37 * Partial RF of phase [16]: 0.06/0.37 - RF of loop [16:1]: 0.06/0.37 V_y_0 0.06/0.37 0.06/0.37 0.06/0.37 ### Specialization of cost equations eval_hc_compute_bb4_in/4 0.06/0.37 * CE 9 is refined into CE [19] 0.06/0.37 * CE 8 is refined into CE [20,21,22] 0.06/0.37 0.06/0.37 0.06/0.37 ### Cost equations --> "Loop" of eval_hc_compute_bb4_in/4 0.06/0.37 * CEs [22] --> Loop 19 0.06/0.37 * CEs [20,21] --> Loop 20 0.06/0.37 * CEs [19] --> Loop 21 0.06/0.37 0.06/0.37 ### Ranking functions of CR eval_hc_compute_bb4_in(V_i_0,V_i_0_sink,V_x_0,B) 0.06/0.37 * RF of phase [19,20]: [V_x_0] 0.06/0.37 0.06/0.37 #### Partial ranking functions of CR eval_hc_compute_bb4_in(V_i_0,V_i_0_sink,V_x_0,B) 0.06/0.37 * Partial RF of phase [19,20]: 0.06/0.37 - RF of loop [19:1]: 0.06/0.37 V_x_0-1 0.06/0.37 - RF of loop [20:1]: 0.06/0.37 V_x_0 0.06/0.37 0.06/0.37 0.06/0.37 ### Specialization of cost equations eval_hc_compute_bb1_in/2 0.06/0.37 * CE 4 is refined into CE [23] 0.06/0.37 * CE 3 is refined into CE [24,25,26,27] 0.06/0.37 0.06/0.37 0.06/0.37 ### Cost equations --> "Loop" of eval_hc_compute_bb1_in/2 0.06/0.37 * CEs [27] --> Loop 22 0.06/0.37 * CEs [26] --> Loop 23 0.06/0.37 * CEs [25] --> Loop 24 0.06/0.37 * CEs [24] --> Loop 25 0.06/0.37 * CEs [23] --> Loop 26 0.06/0.37 0.06/0.37 ### Ranking functions of CR eval_hc_compute_bb1_in(V_i_0,B) 0.06/0.37 * RF of phase [22,23]: [V_i_0-1] 0.06/0.37 0.06/0.37 #### Partial ranking functions of CR eval_hc_compute_bb1_in(V_i_0,B) 0.06/0.37 * Partial RF of phase [22,23]: 0.06/0.37 - RF of loop [22:1]: 0.06/0.37 V_i_0/2-1 0.06/0.37 - RF of loop [23:1]: 0.06/0.37 V_i_0-1 0.06/0.37 0.06/0.37 0.06/0.37 ### Specialization of cost equations eval_hc_compute_bb0_in/2 0.06/0.37 * CE 2 is refined into CE [28,29,30,31] 0.06/0.37 0.06/0.37 0.06/0.37 ### Cost equations --> "Loop" of eval_hc_compute_bb0_in/2 0.06/0.37 * CEs [31] --> Loop 27 0.06/0.37 * CEs [30] --> Loop 28 0.06/0.37 * CEs [29] --> Loop 29 0.06/0.37 * CEs [28] --> Loop 30 0.06/0.37 0.06/0.37 ### Ranking functions of CR eval_hc_compute_bb0_in(V_num_values,B) 0.06/0.37 0.06/0.37 #### Partial ranking functions of CR eval_hc_compute_bb0_in(V_num_values,B) 0.06/0.37 0.06/0.37 0.06/0.37 ### Specialization of cost equations eval_hc_compute_start/2 0.06/0.37 * CE 1 is refined into CE [32,33,34,35] 0.06/0.37 0.06/0.37 0.06/0.37 ### Cost equations --> "Loop" of eval_hc_compute_start/2 0.06/0.37 * CEs [35] --> Loop 31 0.06/0.37 * CEs [34] --> Loop 32 0.06/0.37 * CEs [33] --> Loop 33 0.06/0.37 * CEs [32] --> Loop 34 0.06/0.37 0.06/0.37 ### Ranking functions of CR eval_hc_compute_start(V_num_values,B) 0.06/0.37 0.06/0.37 #### Partial ranking functions of CR eval_hc_compute_start(V_num_values,B) 0.06/0.37 0.06/0.37 0.06/0.37 Computing Bounds 0.06/0.37 ===================================== 0.06/0.37 0.06/0.37 #### Cost of chains of eval_hc_compute_bb2_in(V_i_0_sink,B,C,D): 0.06/0.37 * Chain [[13],15]: 1*it(13)+0 0.06/0.37 Such that:it(13) =< V_i_0_sink 0.06/0.37 0.06/0.37 with precondition: [B=3,C=1,D=0,V_i_0_sink>=2] 0.06/0.37 0.06/0.37 * Chain [[13],14]: 1*it(13)+0 0.06/0.37 Such that:it(13) =< V_i_0_sink-D 0.06/0.37 0.06/0.37 with precondition: [B=3,C=D+1,C>=2,V_i_0_sink>=C+1] 0.06/0.37 0.06/0.37 * Chain [15]: 0 0.06/0.37 with precondition: [V_i_0_sink=1,B=3,C=1,D=0] 0.06/0.37 0.06/0.37 * Chain [14]: 0 0.06/0.37 with precondition: [B=3,V_i_0_sink=C,V_i_0_sink=D+1,V_i_0_sink>=2] 0.06/0.37 0.06/0.37 0.06/0.37 #### Cost of chains of eval_hc_compute_bb5_in(V_y_0,B,C): 0.06/0.37 * Chain [[16],18]: 1*it(16)+0 0.06/0.37 Such that:it(16) =< V_y_0 0.06/0.37 0.06/0.37 with precondition: [B=2,C=0,V_y_0>=1] 0.06/0.37 0.06/0.37 * Chain [[16],17]: 1*it(16)+0 0.06/0.37 Such that:it(16) =< V_y_0-C 0.06/0.37 0.06/0.37 with precondition: [B=2,C>=1,V_y_0>=C+1] 0.06/0.37 0.06/0.37 * Chain [17]: 0 0.06/0.37 with precondition: [B=2,V_y_0=C,V_y_0>=1] 0.06/0.37 0.06/0.37 0.06/0.37 #### Cost of chains of eval_hc_compute_bb4_in(V_i_0,V_i_0_sink,V_x_0,B): 0.06/0.37 * Chain [[19,20],21]: 2*it(19)+1*s(5)+1*s(6)+0 0.06/0.37 Such that:aux(5) =< V_x_0 0.06/0.37 it(19) =< aux(5) 0.06/0.37 aux(2) =< aux(5)+1 0.06/0.37 s(5) =< it(19)*aux(5) 0.06/0.37 s(6) =< it(19)*aux(2) 0.06/0.37 0.06/0.37 with precondition: [B=4,V_i_0>=1,V_x_0>=1] 0.06/0.37 0.06/0.37 * Chain [21]: 0 0.06/0.37 with precondition: [B=4,0>=V_x_0,V_i_0>=1] 0.06/0.37 0.06/0.37 0.06/0.37 #### Cost of chains of eval_hc_compute_bb1_in(V_i_0,B): 0.06/0.37 * Chain [[22,23],25,26]: 1*it(22)+6*it(23)+2*s(8)+1*s(10)+1*s(11)+1*s(34)+1*s(35)+1*s(38)+1*s(39)+1 0.06/0.37 Such that:it(22) =< V_i_0/2 0.06/0.37 aux(10) =< 1 0.06/0.37 aux(11) =< V_i_0 0.06/0.37 s(8) =< aux(10) 0.06/0.37 s(9) =< aux(10)+1 0.06/0.37 s(10) =< s(8)*aux(10) 0.06/0.37 s(11) =< s(8)*s(9) 0.06/0.37 it(22) =< aux(11) 0.06/0.37 it(23) =< aux(11) 0.06/0.37 s(38) =< it(23)*aux(10) 0.06/0.37 s(39) =< it(23)*s(9) 0.06/0.37 s(20) =< aux(11)+1 0.06/0.37 s(34) =< it(23)*aux(11) 0.06/0.37 s(35) =< it(23)*s(20) 0.06/0.37 0.06/0.37 with precondition: [B=5,V_i_0>=2] 0.06/0.37 0.06/0.37 * Chain [[22,23],24,26]: 1*it(22)+9*it(23)+2*s(34)+2*s(35)+1*s(38)+1*s(39)+1 0.06/0.37 Such that:s(28) =< 1 0.06/0.37 it(22) =< V_i_0/2 0.06/0.37 aux(13) =< V_i_0 0.06/0.37 it(22) =< aux(13) 0.06/0.37 it(23) =< aux(13) 0.06/0.37 s(20) =< aux(13)+1 0.06/0.37 s(34) =< it(23)*aux(13) 0.06/0.37 s(35) =< it(23)*s(20) 0.06/0.37 s(30) =< s(28)+1 0.06/0.37 s(38) =< it(23)*s(28) 0.06/0.37 s(39) =< it(23)*s(30) 0.06/0.37 0.06/0.37 with precondition: [B=5,V_i_0>=3] 0.06/0.37 0.06/0.37 * Chain [26]: 0 0.06/0.37 with precondition: [B=5,0>=V_i_0] 0.06/0.37 0.06/0.37 * Chain [25,26]: 2*s(8)+1*s(10)+1*s(11)+1 0.06/0.37 Such that:s(7) =< 1 0.06/0.37 s(8) =< s(7) 0.06/0.37 s(9) =< s(7)+1 0.06/0.37 s(10) =< s(8)*s(7) 0.06/0.37 s(11) =< s(8)*s(9) 0.06/0.37 0.06/0.37 with precondition: [V_i_0=1,B=5] 0.06/0.37 0.06/0.37 * Chain [24,26]: 3*s(41)+1*s(45)+1*s(46)+1 0.06/0.37 Such that:aux(12) =< V_i_0 0.06/0.37 s(41) =< aux(12) 0.06/0.37 s(44) =< aux(12)+1 0.06/0.37 s(45) =< s(41)*aux(12) 0.06/0.37 s(46) =< s(41)*s(44) 0.06/0.37 0.06/0.37 with precondition: [B=5,V_i_0>=2] 0.06/0.37 0.06/0.37 0.06/0.37 #### Cost of chains of eval_hc_compute_bb0_in(V_num_values,B): 0.06/0.37 * Chain [30]: 2*s(66)+1*s(68)+1*s(69)+1 0.06/0.37 Such that:s(65) =< 1 0.06/0.37 s(66) =< s(65) 0.06/0.37 s(67) =< s(65)+1 0.06/0.37 s(68) =< s(66)*s(65) 0.06/0.37 s(69) =< s(66)*s(67) 0.06/0.37 0.06/0.37 with precondition: [V_num_values=1] 0.06/0.37 0.06/0.37 * Chain [29]: 0 0.06/0.37 with precondition: [0>=V_num_values] 0.06/0.37 0.06/0.37 * Chain [28]: 1*s(71)+9*s(73)+2*s(75)+2*s(76)+2*s(77)+1*s(79)+1*s(80)+1*s(81)+1*s(82)+1 0.06/0.37 Such that:s(70) =< 1 0.06/0.37 s(72) =< V_num_values 0.06/0.37 s(71) =< V_num_values/2 0.06/0.37 s(73) =< s(72) 0.06/0.37 s(74) =< s(72)+1 0.06/0.37 s(75) =< s(73)*s(72) 0.06/0.37 s(76) =< s(73)*s(74) 0.06/0.37 s(77) =< s(70) 0.06/0.37 s(78) =< s(70)+1 0.06/0.37 s(79) =< s(77)*s(70) 0.06/0.37 s(80) =< s(77)*s(78) 0.06/0.37 s(71) =< s(72) 0.06/0.37 s(81) =< s(73)*s(70) 0.06/0.37 s(82) =< s(73)*s(78) 0.06/0.37 0.06/0.37 with precondition: [V_num_values>=2] 0.06/0.37 0.06/0.37 * Chain [27]: 1*s(84)+9*s(86)+2*s(88)+2*s(89)+1*s(91)+1*s(92)+1 0.06/0.37 Such that:s(83) =< 1 0.06/0.37 s(85) =< V_num_values 0.06/0.37 s(84) =< V_num_values/2 0.06/0.37 s(84) =< s(85) 0.06/0.37 s(86) =< s(85) 0.06/0.37 s(87) =< s(85)+1 0.06/0.37 s(88) =< s(86)*s(85) 0.06/0.37 s(89) =< s(86)*s(87) 0.06/0.37 s(90) =< s(83)+1 0.06/0.37 s(91) =< s(86)*s(83) 0.06/0.37 s(92) =< s(86)*s(90) 0.06/0.37 0.06/0.37 with precondition: [V_num_values>=3] 0.06/0.37 0.06/0.37 0.06/0.37 #### Cost of chains of eval_hc_compute_start(V_num_values,B): 0.06/0.37 * Chain [34]: 2*s(94)+1*s(96)+1*s(97)+1 0.06/0.37 Such that:s(93) =< 1 0.06/0.37 s(94) =< s(93) 0.06/0.37 s(95) =< s(93)+1 0.06/0.37 s(96) =< s(94)*s(93) 0.06/0.37 s(97) =< s(94)*s(95) 0.06/0.37 0.06/0.37 with precondition: [V_num_values=1] 0.06/0.37 0.06/0.37 * Chain [33]: 0 0.06/0.37 with precondition: [0>=V_num_values] 0.06/0.37 0.06/0.37 * Chain [32]: 1*s(100)+9*s(101)+2*s(103)+2*s(104)+2*s(105)+1*s(107)+1*s(108)+1*s(109)+1*s(110)+1 0.06/0.37 Such that:s(98) =< 1 0.06/0.37 s(99) =< V_num_values 0.06/0.37 s(100) =< V_num_values/2 0.06/0.37 s(101) =< s(99) 0.06/0.37 s(102) =< s(99)+1 0.06/0.37 s(103) =< s(101)*s(99) 0.06/0.37 s(104) =< s(101)*s(102) 0.06/0.37 s(105) =< s(98) 0.06/0.37 s(106) =< s(98)+1 0.06/0.37 s(107) =< s(105)*s(98) 0.06/0.37 s(108) =< s(105)*s(106) 0.06/0.37 s(100) =< s(99) 0.06/0.37 s(109) =< s(101)*s(98) 0.06/0.37 s(110) =< s(101)*s(106) 0.06/0.37 0.06/0.37 with precondition: [V_num_values>=2] 0.06/0.37 0.06/0.37 * Chain [31]: 1*s(113)+9*s(114)+2*s(116)+2*s(117)+1*s(119)+1*s(120)+1 0.06/0.37 Such that:s(111) =< 1 0.06/0.37 s(112) =< V_num_values 0.06/0.37 s(113) =< V_num_values/2 0.06/0.37 s(113) =< s(112) 0.06/0.37 s(114) =< s(112) 0.06/0.37 s(115) =< s(112)+1 0.06/0.37 s(116) =< s(114)*s(112) 0.06/0.37 s(117) =< s(114)*s(115) 0.06/0.37 s(118) =< s(111)+1 0.06/0.37 s(119) =< s(114)*s(111) 0.06/0.37 s(120) =< s(114)*s(118) 0.06/0.37 0.06/0.37 with precondition: [V_num_values>=3] 0.06/0.37 0.06/0.37 0.06/0.37 Closed-form bounds of eval_hc_compute_start(V_num_values,B): 0.06/0.37 ------------------------------------- 0.06/0.37 * Chain [34] with precondition: [V_num_values=1] 0.06/0.37 - Upper bound: 6 0.06/0.37 - Complexity: constant 0.06/0.37 * Chain [33] with precondition: [0>=V_num_values] 0.06/0.37 - Upper bound: 0 0.06/0.37 - Complexity: constant 0.06/0.37 * Chain [32] with precondition: [V_num_values>=2] 0.06/0.37 - Upper bound: V_num_values/2+(14*V_num_values+6+4*V_num_values*V_num_values) 0.06/0.37 - Complexity: n^2 0.06/0.37 * Chain [31] with precondition: [V_num_values>=3] 0.06/0.37 - Upper bound: V_num_values/2+(14*V_num_values+1+4*V_num_values*V_num_values) 0.06/0.37 - Complexity: n^2 0.06/0.37 0.06/0.37 ### Maximum cost of eval_hc_compute_start(V_num_values,B): nat(V_num_values)*4*nat(V_num_values)+nat(V_num_values)*14+nat(V_num_values/2)+6 0.06/0.37 Asymptotic class: n^2 0.06/0.37 * Total analysis performed in 273 ms. 0.06/0.37 0.06/0.48 EOF