/export/starexec/sandbox2/solver/bin/starexec_run_C /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(n^1)) Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. recursive : [eval_Loopus2015_original_bb3_in/8,eval_Loopus2015_original_bb4_in/8] 1. recursive : [eval_Loopus2015_original_1/6,eval_Loopus2015_original_2/7,eval_Loopus2015_original_3/8,eval_Loopus2015_original_4/9,eval_Loopus2015_original_bb1_in/5,eval_Loopus2015_original_bb2_in/5,eval_Loopus2015_original_bb3_in_loop_cont/6] 2. non_recursive : [eval_Loopus2015_original_stop/1] 3. non_recursive : [eval_Loopus2015_original_bb5_in/1] 4. non_recursive : [eval_Loopus2015_original_bb1_in_loop_cont/2] 5. non_recursive : [eval_Loopus2015_original_bb0_in/2] 6. non_recursive : [eval_Loopus2015_original_start/2] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into eval_Loopus2015_original_bb3_in/8 1. SCC is partially evaluated into eval_Loopus2015_original_bb1_in/5 2. SCC is completely evaluated into other SCCs 3. SCC is completely evaluated into other SCCs 4. SCC is completely evaluated into other SCCs 5. SCC is partially evaluated into eval_Loopus2015_original_bb0_in/2 6. SCC is partially evaluated into eval_Loopus2015_original_start/2 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations eval_Loopus2015_original_bb3_in/8 * CE 9 is refined into CE [10] * CE 8 is refined into CE [11] ### Cost equations --> "Loop" of eval_Loopus2015_original_bb3_in/8 * CEs [11] --> Loop 9 * CEs [10] --> Loop 10 ### Ranking functions of CR eval_Loopus2015_original_bb3_in(V_i_0,V_end_0,V_beg_0,V_2,V__end_0,V_4,V_k_0,B) * RF of phase [9]: [V__end_0-V_k_0,V_i_0-V_k_0+1] #### Partial ranking functions of CR eval_Loopus2015_original_bb3_in(V_i_0,V_end_0,V_beg_0,V_2,V__end_0,V_4,V_k_0,B) * Partial RF of phase [9]: - RF of loop [9:1]: V__end_0-V_k_0 V_i_0-V_k_0+1 ### Specialization of cost equations eval_Loopus2015_original_bb1_in/5 * CE 7 is refined into CE [12] * CE 6 is refined into CE [13] * CE 3 is refined into CE [14] * CE 4 is refined into CE [15,16] * CE 5 is refined into CE [17] ### Cost equations --> "Loop" of eval_Loopus2015_original_bb1_in/5 * CEs [13] --> Loop 11 * CEs [16] --> Loop 12 * CEs [15] --> Loop 13 * CEs [14] --> Loop 14 * CEs [17] --> Loop 15 * CEs [12] --> Loop 16 ### Ranking functions of CR eval_Loopus2015_original_bb1_in(V_len,V_i_0,V_end_0,V_beg_0,B) * RF of phase [11,12,13,14,15]: [V_len-V_i_0] #### Partial ranking functions of CR eval_Loopus2015_original_bb1_in(V_len,V_i_0,V_end_0,V_beg_0,B) * Partial RF of phase [11,12,13,14,15]: - RF of loop [11:1,12:1,13:1,14:1,15:1]: V_len-V_i_0 - RF of loop [12:1]: V_end_0-V_beg_0 depends on loops [15:1] V_i_0-V_beg_0 depends on loops [11:1,15:1] V_len/2-V_beg_0/2-1/2 - RF of loop [12:1,13:1,14:1,15:1]: V_len-V_end_0 - RF of loop [13:1,14:1]: V_len-V_beg_0 ### Specialization of cost equations eval_Loopus2015_original_bb0_in/2 * CE 2 is refined into CE [18,19] ### Cost equations --> "Loop" of eval_Loopus2015_original_bb0_in/2 * CEs [19] --> Loop 17 * CEs [18] --> Loop 18 ### Ranking functions of CR eval_Loopus2015_original_bb0_in(V_len,B) #### Partial ranking functions of CR eval_Loopus2015_original_bb0_in(V_len,B) ### Specialization of cost equations eval_Loopus2015_original_start/2 * CE 1 is refined into CE [20,21] ### Cost equations --> "Loop" of eval_Loopus2015_original_start/2 * CEs [21] --> Loop 19 * CEs [20] --> Loop 20 ### Ranking functions of CR eval_Loopus2015_original_start(V_len,B) #### Partial ranking functions of CR eval_Loopus2015_original_start(V_len,B) Computing Bounds ===================================== #### Cost of chains of eval_Loopus2015_original_bb3_in(V_i_0,V_end_0,V_beg_0,V_2,V__end_0,V_4,V_k_0,B): * Chain [[9],10]: 1*it(9)+0 Such that:it(9) =< V__end_0-V_k_0 with precondition: [B=2,V_beg_0>=0,V_4>=1,V_i_0>=V_end_0,V__end_0>=V_end_0,V_end_0>=V_beg_0,V_k_0>=V_beg_0,V_i_0+1>=V__end_0,V__end_0>=V_k_0+1] * Chain [10]: 0 with precondition: [B=2,V_k_0=V__end_0,V_beg_0>=0,V_4>=1,V_i_0>=V_end_0,V_k_0>=V_end_0,V_end_0>=V_beg_0,V_i_0+1>=V_k_0] #### Cost of chains of eval_Loopus2015_original_bb1_in(V_len,V_i_0,V_end_0,V_beg_0,B): * Chain [[11,12,13,14,15],16]: 1*it(11)+1*it(12)+2*it(13)+1*it(15)+1*s(5)+1*s(6)+0 Such that:aux(14) =< V_len it(12) =< V_len/2-V_beg_0/2 aux(23) =< V_len-V_i_0 aux(24) =< V_len-V_end_0 aux(25) =< V_len-V_beg_0 aux(26) =< V_i_0-V_beg_0 aux(27) =< V_end_0-V_beg_0 aux(22) =< aux(25) aux(6) =< aux(26) aux(22) =< aux(26) aux(6) =< aux(27) aux(12) =< aux(14) it(11) =< aux(23) it(12) =< aux(23) it(13) =< aux(23) it(15) =< aux(23) it(12) =< aux(24) it(13) =< aux(24) it(15) =< aux(24) it(13) =< aux(25) s(5) =< aux(25) s(6) =< aux(25) aux(12) =< aux(14) aux(11) =< it(15)*aux(14) aux(2) =< it(15)*aux(14) s(5) =< it(15)+it(11)+aux(22) s(5) =< it(15)+it(11)+aux(26) it(12) =< it(15)+it(11)+aux(22) it(12) =< it(15)+it(11)+aux(26) aux(13) =< it(15)*aux(12) aux(2) =< it(15)*aux(12) aux(5) =< aux(11) aux(5) =< aux(13) it(12) =< aux(2)+aux(27) it(12) =< aux(5)+aux(6) s(5) =< it(12)*aux(25) with precondition: [B=3,V_beg_0>=0,V_len>=V_i_0+1,V_i_0>=V_end_0,V_end_0>=V_beg_0] * Chain [16]: 0 with precondition: [B=3,V_beg_0>=0,V_i_0>=V_len,V_i_0>=V_end_0,V_end_0>=V_beg_0] #### Cost of chains of eval_Loopus2015_original_bb0_in(V_len,B): * Chain [18]: 0 with precondition: [0>=V_len] * Chain [17]: 1*s(8)+5*s(17)+1*s(20)+0 Such that:s(8) =< V_len/2 aux(29) =< V_len s(16) =< aux(29) s(17) =< aux(29) s(8) =< aux(29) s(20) =< aux(29) s(16) =< aux(29) s(22) =< s(17)*aux(29) s(23) =< s(17)*aux(29) s(20) =< s(17)+s(17) s(20) =< s(17)+s(17) s(8) =< s(17)+s(17) s(8) =< s(17)+s(17) s(24) =< s(17)*s(16) s(23) =< s(17)*s(16) s(25) =< s(22) s(25) =< s(24) s(8) =< s(23) s(8) =< s(25) s(20) =< s(8)*aux(29) with precondition: [V_len>=1] #### Cost of chains of eval_Loopus2015_original_start(V_len,B): * Chain [20]: 0 with precondition: [0>=V_len] * Chain [19]: 1*s(26)+5*s(29)+1*s(30)+0 Such that:s(27) =< V_len s(26) =< V_len/2 s(28) =< s(27) s(29) =< s(27) s(26) =< s(27) s(30) =< s(27) s(28) =< s(27) s(31) =< s(29)*s(27) s(32) =< s(29)*s(27) s(30) =< s(29)+s(29) s(30) =< s(29)+s(29) s(26) =< s(29)+s(29) s(26) =< s(29)+s(29) s(33) =< s(29)*s(28) s(32) =< s(29)*s(28) s(34) =< s(31) s(34) =< s(33) s(26) =< s(32) s(26) =< s(34) s(30) =< s(26)*s(27) with precondition: [V_len>=1] Closed-form bounds of eval_Loopus2015_original_start(V_len,B): ------------------------------------- * Chain [20] with precondition: [0>=V_len] - Upper bound: 0 - Complexity: constant * Chain [19] with precondition: [V_len>=1] - Upper bound: 13/2*V_len - Complexity: n ### Maximum cost of eval_Loopus2015_original_start(V_len,B): nat(V_len)*6+nat(V_len/2) Asymptotic class: n * Total analysis performed in 416 ms.