/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_xnu_bb3_in/8,eval_xnu_bb4_in/8] 1. recursive : [eval_xnu_1/6,eval_xnu_2/7,eval_xnu_3/8,eval_xnu_4/9,eval_xnu_7/9,eval_xnu_8/10,eval_xnu_bb1_in/5,eval_xnu_bb2_in/5,eval_xnu_bb3_in_loop_cont/6,eval_xnu_bb5_in/9] 2. non_recursive : [eval_xnu_stop/1] 3. non_recursive : [eval_xnu_bb6_in/1] 4. non_recursive : [eval_xnu_bb1_in_loop_cont/2] 5. non_recursive : [eval_xnu_bb0_in/2] 6. non_recursive : [eval_xnu_start/2] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into eval_xnu_bb3_in/8 1. SCC is partially evaluated into eval_xnu_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_xnu_bb0_in/2 6. SCC is partially evaluated into eval_xnu_start/2 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations eval_xnu_bb3_in/8 * CE 14 is refined into CE [15] * CE 13 is refined into CE [16] ### Cost equations --> "Loop" of eval_xnu_bb3_in/8 * CEs [16] --> Loop 9 * CEs [15] --> Loop 10 ### Ranking functions of CR eval_xnu_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_xnu_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_xnu_bb1_in/5 * CE 12 is refined into CE [17] * CE 4 is refined into CE [18] * CE 5 is refined into CE [19] * CE 6 is refined into CE [20] * CE 7 is refined into CE [21] * CE 8 is refined into CE [22,23] * CE 9 is refined into CE [24] * CE 10 is refined into CE [25] * CE 11 is refined into CE [26,27] * CE 3 is refined into CE [28] ### Cost equations --> "Loop" of eval_xnu_bb1_in/5 * CEs [18] --> Loop 11 * CEs [23,27] --> Loop 12 * CEs [22,26] --> Loop 13 * CEs [20,21,24,25] --> Loop 14 * CEs [19] --> Loop 15 * CEs [28] --> Loop 16 * CEs [17] --> Loop 17 ### Ranking functions of CR eval_xnu_bb1_in(V_len,V_i_0,V_end_0,V_beg_0,B) * RF of phase [11,12,13,14,15,16]: [V_len-V_i_0] #### Partial ranking functions of CR eval_xnu_bb1_in(V_len,V_i_0,V_end_0,V_beg_0,B) * Partial RF of phase [11,12,13,14,15,16]: - RF of loop [11:1,12:1,13:1,14:1,15:1,16:1]: V_len-V_i_0 - RF of loop [12:1]: V_end_0-V_beg_0 depends on loops [16:1] V_i_0-V_beg_0 depends on loops [11:1,16:1] V_len/2-V_beg_0/2-1/2 - RF of loop [12:1,13:1,14:1,15:1,16:1]: V_len-V_end_0 - RF of loop [13:1,14:1,15:1]: V_len-V_beg_0 ### Specialization of cost equations eval_xnu_bb0_in/2 * CE 2 is refined into CE [29,30] ### Cost equations --> "Loop" of eval_xnu_bb0_in/2 * CEs [30] --> Loop 18 * CEs [29] --> Loop 19 ### Ranking functions of CR eval_xnu_bb0_in(V_len,B) #### Partial ranking functions of CR eval_xnu_bb0_in(V_len,B) ### Specialization of cost equations eval_xnu_start/2 * CE 1 is refined into CE [31,32] ### Cost equations --> "Loop" of eval_xnu_start/2 * CEs [32] --> Loop 20 * CEs [31] --> Loop 21 ### Ranking functions of CR eval_xnu_start(V_len,B) #### Partial ranking functions of CR eval_xnu_start(V_len,B) Computing Bounds ===================================== #### Cost of chains of eval_xnu_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_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_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_xnu_bb1_in(V_len,V_i_0,V_end_0,V_beg_0,B): * Chain [[11,12,13,14,15,16],17]: 1*it(11)+1*it(12)+3*it(13)+1*it(16)+2*s(11)+4*s(13)+0 Such that:aux(16) =< V_len it(12) =< V_len/2-V_beg_0/2 aux(25) =< V_len-V_i_0 aux(26) =< V_len-V_end_0 aux(27) =< V_len-V_beg_0 aux(28) =< V_i_0-V_beg_0 aux(29) =< V_end_0-V_beg_0 aux(24) =< aux(27) aux(8) =< aux(28) aux(24) =< aux(28) aux(8) =< aux(29) aux(14) =< aux(16) it(11) =< aux(25) it(12) =< aux(25) it(13) =< aux(25) it(16) =< aux(25) it(12) =< aux(26) it(13) =< aux(26) it(16) =< aux(26) it(13) =< aux(27) s(12) =< aux(27) aux(14) =< aux(16) aux(13) =< it(16)*aux(16) aux(4) =< it(16)*aux(16) s(12) =< it(16)+it(11)+aux(24) s(12) =< it(16)+it(11)+aux(28) it(12) =< it(16)+it(11)+aux(24) it(12) =< it(16)+it(11)+aux(28) aux(15) =< it(16)*aux(14) aux(4) =< it(16)*aux(14) aux(7) =< aux(13) aux(7) =< aux(15) it(12) =< aux(4)+aux(29) it(12) =< aux(7)+aux(8) s(12) =< it(12)*aux(27) s(13) =< aux(27) s(11) =< s(12) 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 [17]: 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_xnu_bb0_in(V_len,B): * Chain [19]: 0 with precondition: [0>=V_len] * Chain [18]: 1*s(16)+9*s(25)+2*s(34)+0 Such that:s(16) =< V_len/2 aux(31) =< V_len s(24) =< aux(31) s(25) =< aux(31) s(16) =< aux(31) s(28) =< aux(31) s(24) =< aux(31) s(29) =< s(25)*aux(31) s(30) =< s(25)*aux(31) s(28) =< s(25)+s(25) s(28) =< s(25)+s(25) s(16) =< s(25)+s(25) s(16) =< s(25)+s(25) s(31) =< s(25)*s(24) s(30) =< s(25)*s(24) s(32) =< s(29) s(32) =< s(31) s(16) =< s(30) s(16) =< s(32) s(28) =< s(16)*aux(31) s(34) =< s(28) with precondition: [V_len>=1] #### Cost of chains of eval_xnu_start(V_len,B): * Chain [21]: 0 with precondition: [0>=V_len] * Chain [20]: 1*s(35)+9*s(38)+2*s(44)+0 Such that:s(36) =< V_len s(35) =< V_len/2 s(37) =< s(36) s(38) =< s(36) s(35) =< s(36) s(39) =< s(36) s(37) =< s(36) s(40) =< s(38)*s(36) s(41) =< s(38)*s(36) s(39) =< s(38)+s(38) s(39) =< s(38)+s(38) s(35) =< s(38)+s(38) s(35) =< s(38)+s(38) s(42) =< s(38)*s(37) s(41) =< s(38)*s(37) s(43) =< s(40) s(43) =< s(42) s(35) =< s(41) s(35) =< s(43) s(39) =< s(35)*s(36) s(44) =< s(39) with precondition: [V_len>=1] Closed-form bounds of eval_xnu_start(V_len,B): ------------------------------------- * Chain [21] with precondition: [0>=V_len] - Upper bound: 0 - Complexity: constant * Chain [20] with precondition: [V_len>=1] - Upper bound: 23/2*V_len - Complexity: n ### Maximum cost of eval_xnu_start(V_len,B): nat(V_len)*11+nat(V_len/2) Asymptotic class: n * Total analysis performed in 565 ms.