2.37/2.39 WORST_CASE(?,O(n^1)) 2.37/2.39 2.37/2.39 Preprocessing Cost Relations 2.37/2.39 ===================================== 2.37/2.39 2.37/2.39 #### Computed strongly connected components 2.37/2.39 0. recursive : [eval_Loopus2011_ex2_0/6,eval_Loopus2011_ex2_1/7,eval_Loopus2011_ex2_bb10_in/8,eval_Loopus2011_ex2_bb11_in/10,eval_Loopus2011_ex2_bb1_in/6,eval_Loopus2011_ex2_bb2_in/7,eval_Loopus2011_ex2_bb3_in/7,eval_Loopus2011_ex2_bb4_in/8,eval_Loopus2011_ex2_bb5_in/8,eval_Loopus2011_ex2_bb6_in/8,eval_Loopus2011_ex2_bb7_in/10,eval_Loopus2011_ex2_bb8_in/8,eval_Loopus2011_ex2_bb9_in/8] 2.37/2.39 1. non_recursive : [eval_Loopus2011_ex2_stop/1] 2.37/2.39 2. non_recursive : [eval_Loopus2011_ex2_bb12_in/1] 2.37/2.39 3. non_recursive : [eval_Loopus2011_ex2_bb1_in_loop_cont/2] 2.37/2.39 4. non_recursive : [eval_Loopus2011_ex2_bb0_in/3] 2.37/2.39 5. non_recursive : [eval_Loopus2011_ex2_start/3] 2.37/2.39 2.37/2.39 #### Obtained direct recursion through partial evaluation 2.37/2.39 0. SCC is partially evaluated into eval_Loopus2011_ex2_bb1_in/6 2.37/2.39 1. SCC is completely evaluated into other SCCs 2.37/2.39 2. SCC is completely evaluated into other SCCs 2.37/2.39 3. SCC is completely evaluated into other SCCs 2.37/2.39 4. SCC is partially evaluated into eval_Loopus2011_ex2_bb0_in/3 2.37/2.39 5. SCC is partially evaluated into eval_Loopus2011_ex2_start/3 2.37/2.39 2.37/2.39 Control-Flow Refinement of Cost Relations 2.37/2.39 ===================================== 2.37/2.39 2.37/2.39 ### Specialization of cost equations eval_Loopus2011_ex2_bb1_in/6 2.37/2.39 * CE 34 is refined into CE [56] 2.37/2.39 * CE 8 is refined into CE [57] 2.37/2.39 * CE 30 is discarded (unfeasible) 2.37/2.39 * CE 4 is discarded (unfeasible) 2.37/2.39 * CE 36 is discarded (unfeasible) 2.37/2.39 * CE 10 is discarded (unfeasible) 2.37/2.39 * CE 32 is discarded (unfeasible) 2.37/2.39 * CE 6 is discarded (unfeasible) 2.37/2.39 * CE 55 is refined into CE [58] 2.37/2.39 * CE 12 is discarded (unfeasible) 2.37/2.39 * CE 38 is discarded (unfeasible) 2.37/2.39 * CE 40 is discarded (unfeasible) 2.37/2.39 * CE 14 is discarded (unfeasible) 2.37/2.39 * CE 15 is refined into CE [59] 2.37/2.39 * CE 45 is discarded (unfeasible) 2.37/2.39 * CE 19 is refined into CE [60] 2.37/2.39 * CE 53 is discarded (unfeasible) 2.37/2.39 * CE 27 is discarded (unfeasible) 2.37/2.39 * CE 21 is discarded (unfeasible) 2.37/2.39 * CE 20 is refined into CE [61] 2.37/2.39 * CE 28 is discarded (unfeasible) 2.37/2.39 * CE 46 is refined into CE [62] 2.37/2.39 * CE 54 is discarded (unfeasible) 2.37/2.39 * CE 41 is refined into CE [63] 2.37/2.39 * CE 48 is discarded (unfeasible) 2.37/2.39 * CE 47 is discarded (unfeasible) 2.37/2.39 * CE 22 is discarded (unfeasible) 2.37/2.39 * CE 7 is refined into CE [64] 2.37/2.39 * CE 3 is discarded (unfeasible) 2.37/2.39 * CE 9 is discarded (unfeasible) 2.37/2.39 * CE 5 is discarded (unfeasible) 2.37/2.39 * CE 33 is refined into CE [65] 2.37/2.39 * CE 29 is discarded (unfeasible) 2.37/2.39 * CE 35 is discarded (unfeasible) 2.37/2.39 * CE 31 is discarded (unfeasible) 2.37/2.39 * CE 11 is discarded (unfeasible) 2.37/2.39 * CE 13 is discarded (unfeasible) 2.37/2.39 * CE 37 is discarded (unfeasible) 2.37/2.39 * CE 39 is discarded (unfeasible) 2.37/2.39 * CE 17 is refined into CE [66] 2.37/2.39 * CE 25 is discarded (unfeasible) 2.37/2.39 * CE 18 is refined into CE [67] 2.37/2.39 * CE 26 is discarded (unfeasible) 2.37/2.39 * CE 43 is discarded (unfeasible) 2.37/2.39 * CE 51 is discarded (unfeasible) 2.37/2.39 * CE 44 is refined into CE [68] 2.37/2.39 * CE 52 is discarded (unfeasible) 2.37/2.39 * CE 42 is refined into CE [69] 2.37/2.39 * CE 50 is discarded (unfeasible) 2.37/2.39 * CE 49 is discarded (unfeasible) 2.37/2.39 * CE 16 is refined into CE [70] 2.37/2.39 * CE 24 is discarded (unfeasible) 2.37/2.39 * CE 23 is discarded (unfeasible) 2.37/2.39 2.37/2.39 2.37/2.39 ### Cost equations --> "Loop" of eval_Loopus2011_ex2_bb1_in/6 2.37/2.39 * CEs [64] --> Loop 56 2.37/2.39 * CEs [65] --> Loop 57 2.37/2.39 * CEs [68] --> Loop 58 2.37/2.39 * CEs [66] --> Loop 59 2.37/2.39 * CEs [69] --> Loop 60 2.37/2.39 * CEs [70] --> Loop 61 2.37/2.39 * CEs [67] --> Loop 62 2.37/2.39 * CEs [57] --> Loop 63 2.37/2.39 * CEs [56] --> Loop 64 2.37/2.39 * CEs [58] --> Loop 65 2.37/2.39 * CEs [62] --> Loop 66 2.37/2.39 * CEs [59] --> Loop 67 2.37/2.39 * CEs [63] --> Loop 68 2.37/2.39 * CEs [60] --> Loop 69 2.37/2.39 * CEs [61] --> Loop 70 2.37/2.39 2.37/2.39 ### Ranking functions of CR eval_Loopus2011_ex2_bb1_in(V_r,V_d_0,V_f_0,V_c_0,V__0,B) 2.37/2.39 * RF of phase [58]: [V__0/4-3/4] 2.37/2.39 * RF of phase [59]: [-V__0/4+63] 2.37/2.39 2.37/2.39 #### Partial ranking functions of CR eval_Loopus2011_ex2_bb1_in(V_r,V_d_0,V_f_0,V_c_0,V__0,B) 2.37/2.39 * Partial RF of phase [58]: 2.37/2.39 - RF of loop [58:1]: 2.37/2.39 V__0/4-3/4 2.37/2.39 * Partial RF of phase [59]: 2.37/2.39 - RF of loop [59:1]: 2.37/2.39 -V__0/4+63 2.37/2.39 2.37/2.39 2.37/2.39 ### Specialization of cost equations eval_Loopus2011_ex2_bb0_in/3 2.37/2.39 * CE 2 is refined into CE [71,72,73,74,75,76,77,78,79,80,81,82,83] 2.37/2.39 2.37/2.39 2.37/2.39 ### Cost equations --> "Loop" of eval_Loopus2011_ex2_bb0_in/3 2.37/2.39 * CEs [80] --> Loop 71 2.37/2.39 * CEs [83] --> Loop 72 2.37/2.39 * CEs [79] --> Loop 73 2.37/2.39 * CEs [78] --> Loop 74 2.37/2.39 * CEs [77] --> Loop 75 2.37/2.39 * CEs [82] --> Loop 76 2.37/2.39 * CEs [76] --> Loop 77 2.37/2.39 * CEs [75] --> Loop 78 2.37/2.39 * CEs [74] --> Loop 79 2.37/2.39 * CEs [73] --> Loop 80 2.37/2.39 * CEs [72] --> Loop 81 2.37/2.39 * CEs [71] --> Loop 82 2.37/2.39 * CEs [81] --> Loop 83 2.37/2.39 2.37/2.39 ### Ranking functions of CR eval_Loopus2011_ex2_bb0_in(V_r,V_s,B) 2.37/2.39 2.37/2.39 #### Partial ranking functions of CR eval_Loopus2011_ex2_bb0_in(V_r,V_s,B) 2.37/2.39 2.37/2.39 2.37/2.39 ### Specialization of cost equations eval_Loopus2011_ex2_start/3 2.37/2.39 * CE 1 is refined into CE [84,85,86,87,88,89,90,91,92,93,94,95,96] 2.37/2.39 2.37/2.39 2.37/2.39 ### Cost equations --> "Loop" of eval_Loopus2011_ex2_start/3 2.37/2.39 * CEs [96] --> Loop 84 2.37/2.39 * CEs [95] --> Loop 85 2.37/2.39 * CEs [94] --> Loop 86 2.37/2.39 * CEs [93] --> Loop 87 2.37/2.39 * CEs [92] --> Loop 88 2.37/2.39 * CEs [91] --> Loop 89 2.37/2.39 * CEs [90] --> Loop 90 2.37/2.39 * CEs [89] --> Loop 91 2.37/2.39 * CEs [88] --> Loop 92 2.37/2.39 * CEs [87] --> Loop 93 2.37/2.39 * CEs [86] --> Loop 94 2.37/2.39 * CEs [85] --> Loop 95 2.37/2.39 * CEs [84] --> Loop 96 2.37/2.39 2.37/2.39 ### Ranking functions of CR eval_Loopus2011_ex2_start(V_r,V_s,B) 2.37/2.39 2.37/2.39 #### Partial ranking functions of CR eval_Loopus2011_ex2_start(V_r,V_s,B) 2.37/2.39 2.37/2.39 2.37/2.39 Computing Bounds 2.37/2.39 ===================================== 2.37/2.39 2.37/2.39 #### Cost of chains of eval_Loopus2011_ex2_bb1_in(V_r,V_d_0,V_f_0,V_c_0,V__0,B): 2.37/2.39 * Chain [[58],67]: 1*it(58)+0 2.37/2.39 Such that:it(58) =< V__0/4 2.37/2.39 2.37/2.39 with precondition: [V_f_0=0,V_c_0=4,B=2,1>=V_d_0,V_d_0>=0,V__0>=4] 2.37/2.39 2.37/2.39 * Chain [[58],66]: 1*it(58)+0 2.37/2.39 Such that:it(58) =< V__0/4 2.37/2.39 2.37/2.39 with precondition: [V_f_0=0,V_c_0=4,B=2,1>=V_d_0,V_d_0>=0,V__0>=4] 2.37/2.39 2.37/2.39 * Chain [[58],61,63]: 1*it(58)+1 2.37/2.39 Such that:it(58) =< V__0/4 2.37/2.39 2.37/2.39 with precondition: [V_f_0=0,V_c_0=4,B=2,1>=V_d_0,V_d_0>=0,V__0>=4] 2.37/2.39 2.37/2.39 * Chain [[58],61,57,65]: 1*it(58)+2 2.37/2.39 Such that:it(58) =< V__0/4 2.37/2.39 2.37/2.39 with precondition: [V_f_0=0,V_c_0=4,B=2,1>=V_d_0,V_d_0>=0,V__0>=4] 2.37/2.39 2.37/2.39 * Chain [[58],61,56,65]: 1*it(58)+2 2.37/2.39 Such that:it(58) =< V__0/4 2.37/2.39 2.37/2.39 with precondition: [V_f_0=0,V_c_0=4,B=2,1>=V_d_0,V_d_0>=0,V__0>=4] 2.37/2.39 2.37/2.39 * Chain [70]: 0 2.37/2.39 with precondition: [V_d_0=0,V_f_0=0,V_c_0=4,B=2,V__0>=252] 2.37/2.39 2.37/2.39 * Chain [67]: 0 2.37/2.39 with precondition: [V_f_0=0,V_c_0=4,B=2,2>=V_d_0,V_d_0>=0] 2.37/2.39 2.37/2.39 * Chain [66]: 0 2.37/2.39 with precondition: [V_f_0=0,V_c_0=4,B=2,1>=V_d_0,3>=V__0,V_d_0>=0] 2.37/2.39 2.37/2.39 * Chain [62,[59],69]: 1*it(59)+1 2.37/2.39 Such that:it(59) =< -V__0/4+62 2.37/2.39 2.37/2.39 with precondition: [V_d_0=0,V_f_0=0,V_c_0=4,B=2,247>=V__0] 2.37/2.39 2.37/2.39 * Chain [62,[59],68]: 1*it(59)+1 2.37/2.39 Such that:it(59) =< -V__0/4 2.37/2.39 2.37/2.39 with precondition: [V_d_0=0,V_f_0=0,V_c_0=4,B=2,0>=V__0+7] 2.37/2.39 2.37/2.39 * Chain [62,[59],67]: 1*it(59)+1 2.37/2.39 Such that:it(59) =< -V__0/4+62 2.37/2.39 2.37/2.39 with precondition: [V_d_0=0,V_f_0=0,V_c_0=4,B=2,247>=V__0] 2.37/2.39 2.37/2.39 * Chain [62,[59],60,64]: 1*it(59)+2 2.37/2.39 Such that:it(59) =< -V__0/4 2.37/2.39 2.37/2.39 with precondition: [V_d_0=0,V_f_0=0,V_c_0=4,B=2,0>=V__0+6] 2.37/2.39 2.37/2.39 * Chain [62,[59],60,63]: 1*it(59)+2 2.37/2.39 Such that:it(59) =< -V__0/4+62 2.37/2.39 2.37/2.39 with precondition: [V_d_0=0,V_f_0=0,V_c_0=4,B=2,247>=V__0] 2.37/2.39 2.37/2.39 * Chain [62,[59],60,57,65]: 1*it(59)+3 2.37/2.39 Such that:it(59) =< -V__0/4+62 2.37/2.39 2.37/2.39 with precondition: [V_d_0=0,V_f_0=0,V_c_0=4,B=2,247>=V__0] 2.37/2.39 2.37/2.39 * Chain [62,[59],60,56,65]: 1*it(59)+3 2.37/2.39 Such that:it(59) =< -V__0/4+62 2.37/2.39 2.37/2.39 with precondition: [V_d_0=0,V_f_0=0,V_c_0=4,B=2,247>=V__0] 2.37/2.39 2.37/2.39 * Chain [62,69]: 1 2.37/2.39 with precondition: [V_d_0=0,V_f_0=0,V_c_0=4,B=2,251>=V__0,V__0>=248] 2.37/2.39 2.37/2.39 * Chain [62,68]: 1 2.37/2.39 with precondition: [V_d_0=0,V_f_0=0,V_c_0=4,B=2,0>=V__0+3] 2.37/2.39 2.37/2.39 * Chain [62,67]: 1 2.37/2.39 with precondition: [V_d_0=0,V_f_0=0,V_c_0=4,B=2,251>=V__0] 2.37/2.39 2.37/2.39 * Chain [62,60,64]: 2 2.37/2.39 with precondition: [V_d_0=0,V_f_0=0,V_c_0=4,V__0+2=0,B=2] 2.37/2.39 2.37/2.39 * Chain [62,60,63]: 2 2.37/2.39 with precondition: [V_d_0=0,V_f_0=0,V_c_0=4,B=2,251>=V__0,V__0+2>=0] 2.37/2.39 2.37/2.39 * Chain [62,60,57,65]: 3 2.37/2.39 with precondition: [V_d_0=0,V_f_0=0,V_c_0=4,B=2,251>=V__0,V__0+1>=0] 2.37/2.39 2.37/2.39 * Chain [62,60,56,65]: 3 2.37/2.39 with precondition: [V_d_0=0,V_f_0=0,V_c_0=4,B=2,251>=V__0,V__0+2>=0] 2.37/2.39 2.37/2.39 2.37/2.39 #### Cost of chains of eval_Loopus2011_ex2_bb0_in(V_r,V_s,B): 2.37/2.39 * Chain [83]: 0 2.37/2.39 with precondition: [] 2.37/2.39 2.37/2.39 * Chain [82]: 2 2.37/2.39 with precondition: [V_s+2=0] 2.37/2.39 2.37/2.39 * Chain [81]: 1 2.37/2.39 with precondition: [251>=V_s] 2.37/2.39 2.37/2.39 * Chain [80]: 3 2.37/2.39 with precondition: [251>=V_s,V_s+2>=0] 2.37/2.39 2.37/2.39 * Chain [79]: 3 2.37/2.39 with precondition: [251>=V_s,V_s+1>=0] 2.37/2.39 2.37/2.39 * Chain [78]: 1 2.37/2.39 with precondition: [251>=V_s,V_s>=248] 2.37/2.39 2.37/2.39 * Chain [77]: 5*s(12)+3 2.37/2.39 Such that:s(11) =< -V_s/4+62 2.37/2.39 s(12) =< s(11) 2.37/2.39 2.37/2.39 with precondition: [247>=V_s] 2.37/2.39 2.37/2.39 * Chain [76]: 0 2.37/2.39 with precondition: [3>=V_s] 2.37/2.39 2.37/2.39 * Chain [75]: 1 2.37/2.39 with precondition: [0>=V_s+3] 2.37/2.39 2.37/2.39 * Chain [74]: 1*s(13)+2 2.37/2.39 Such that:s(13) =< -V_s/4 2.37/2.39 2.37/2.39 with precondition: [0>=V_s+6] 2.37/2.39 2.37/2.39 * Chain [73]: 1*s(14)+1 2.37/2.39 Such that:s(14) =< -V_s/4 2.37/2.39 2.37/2.39 with precondition: [0>=V_s+7] 2.37/2.39 2.37/2.39 * Chain [72]: 5*s(16)+2 2.37/2.39 Such that:s(15) =< V_s/4 2.37/2.39 s(16) =< s(15) 2.37/2.39 2.37/2.39 with precondition: [V_s>=4] 2.37/2.39 2.37/2.39 * Chain [71]: 0 2.37/2.39 with precondition: [V_s>=252] 2.37/2.39 2.37/2.39 2.37/2.39 #### Cost of chains of eval_Loopus2011_ex2_start(V_r,V_s,B): 2.37/2.39 * Chain [96]: 0 2.37/2.39 with precondition: [] 2.37/2.39 2.37/2.39 * Chain [95]: 2 2.37/2.39 with precondition: [V_s+2=0] 2.37/2.39 2.37/2.39 * Chain [94]: 1 2.37/2.39 with precondition: [251>=V_s] 2.37/2.39 2.37/2.39 * Chain [93]: 3 2.37/2.39 with precondition: [251>=V_s,V_s+2>=0] 2.37/2.39 2.37/2.39 * Chain [92]: 3 2.37/2.39 with precondition: [251>=V_s,V_s+1>=0] 2.37/2.39 2.37/2.39 * Chain [91]: 1 2.37/2.39 with precondition: [251>=V_s,V_s>=248] 2.37/2.39 2.37/2.39 * Chain [90]: 5*s(18)+3 2.37/2.39 Such that:s(17) =< -V_s/4+62 2.37/2.39 s(18) =< s(17) 2.37/2.39 2.37/2.39 with precondition: [247>=V_s] 2.37/2.39 2.37/2.39 * Chain [89]: 0 2.37/2.39 with precondition: [3>=V_s] 2.37/2.39 2.37/2.39 * Chain [88]: 1 2.37/2.39 with precondition: [0>=V_s+3] 2.37/2.39 2.37/2.39 * Chain [87]: 1*s(19)+2 2.37/2.39 Such that:s(19) =< -V_s/4 2.37/2.39 2.37/2.39 with precondition: [0>=V_s+6] 2.37/2.39 2.37/2.39 * Chain [86]: 1*s(20)+1 2.37/2.39 Such that:s(20) =< -V_s/4 2.37/2.39 2.37/2.39 with precondition: [0>=V_s+7] 2.37/2.39 2.37/2.39 * Chain [85]: 5*s(22)+2 2.37/2.39 Such that:s(21) =< V_s/4 2.37/2.39 s(22) =< s(21) 2.37/2.39 2.37/2.39 with precondition: [V_s>=4] 2.37/2.39 2.37/2.39 * Chain [84]: 0 2.37/2.39 with precondition: [V_s>=252] 2.37/2.39 2.37/2.39 2.37/2.39 Closed-form bounds of eval_Loopus2011_ex2_start(V_r,V_s,B): 2.37/2.39 ------------------------------------- 2.37/2.39 * Chain [96] with precondition: [] 2.37/2.39 - Upper bound: 0 2.37/2.39 - Complexity: constant 2.37/2.39 * Chain [95] with precondition: [V_s+2=0] 2.37/2.39 - Upper bound: 2 2.37/2.39 - Complexity: constant 2.37/2.39 * Chain [94] with precondition: [251>=V_s] 2.37/2.39 - Upper bound: 1 2.37/2.39 - Complexity: constant 2.37/2.39 * Chain [93] with precondition: [251>=V_s,V_s+2>=0] 2.37/2.39 - Upper bound: 3 2.37/2.39 - Complexity: constant 2.37/2.39 * Chain [92] with precondition: [251>=V_s,V_s+1>=0] 2.37/2.39 - Upper bound: 3 2.37/2.39 - Complexity: constant 2.37/2.39 * Chain [91] with precondition: [251>=V_s,V_s>=248] 2.37/2.39 - Upper bound: 1 2.37/2.39 - Complexity: constant 2.37/2.39 * Chain [90] with precondition: [247>=V_s] 2.37/2.39 - Upper bound: -5/4*V_s+313 2.37/2.39 - Complexity: n 2.37/2.39 * Chain [89] with precondition: [3>=V_s] 2.37/2.39 - Upper bound: 0 2.37/2.39 - Complexity: constant 2.37/2.39 * Chain [88] with precondition: [0>=V_s+3] 2.37/2.39 - Upper bound: 1 2.37/2.39 - Complexity: constant 2.37/2.39 * Chain [87] with precondition: [0>=V_s+6] 2.37/2.39 - Upper bound: -V_s/4+2 2.37/2.39 - Complexity: n 2.37/2.39 * Chain [86] with precondition: [0>=V_s+7] 2.37/2.39 - Upper bound: -V_s/4+1 2.37/2.39 - Complexity: n 2.37/2.39 * Chain [85] with precondition: [V_s>=4] 2.37/2.39 - Upper bound: 5/4*V_s+2 2.37/2.39 - Complexity: n 2.37/2.39 * Chain [84] with precondition: [V_s>=252] 2.37/2.39 - Upper bound: 0 2.37/2.39 - Complexity: constant 2.37/2.39 2.37/2.39 ### Maximum cost of eval_Loopus2011_ex2_start(V_r,V_s,B): max([max([3,nat(-V_s/4+62)*5+3,nat(V_s/4)*5+2]),nat(-V_s/4)+2]) 2.37/2.39 Asymptotic class: n 2.37/2.39 * Total analysis performed in 2236 ms. 2.37/2.39 2.41/2.50 EOF