/export/starexec/sandbox2/solver/bin/starexec_run_C /export/starexec/sandbox2/benchmark/theBenchmark.c /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(n^2)) Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. non_recursive : [eval_realheapsort_step2_stop/1] 1. non_recursive : [eval_realheapsort_step2_bb11_in/1] 2. recursive : [eval_realheapsort_step2_14/5,eval_realheapsort_step2_15/6,eval_realheapsort_step2_16/7,eval_realheapsort_step2_23/6,eval_realheapsort_step2_24/7,eval_realheapsort_step2_25/8,eval_realheapsort_step2_26/8,eval_realheapsort_step2_27/8,eval_realheapsort_step2_bb3_in/5,eval_realheapsort_step2_bb4_in/5,eval_realheapsort_step2_bb5_in/5,eval_realheapsort_step2_bb6_in/5,eval_realheapsort_step2_bb7_in/7,eval_realheapsort_step2_bb8_in/6,eval_realheapsort_step2_bb9_in/8] 3. recursive : [eval_realheapsort_step2_2/3,eval_realheapsort_step2_3/3,eval_realheapsort_step2_bb10_in/4,eval_realheapsort_step2_bb1_in/3,eval_realheapsort_step2_bb2_in/3,eval_realheapsort_step2_bb3_in_loop_cont/5] 4. non_recursive : [eval_realheapsort_step2_bb1_in_loop_cont/2] 5. non_recursive : [eval_realheapsort_step2_bb0_in/2] 6. non_recursive : [eval_realheapsort_step2_start/2] #### Obtained direct recursion through partial evaluation 0. SCC is completely evaluated into other SCCs 1. SCC is completely evaluated into other SCCs 2. SCC is partially evaluated into eval_realheapsort_step2_bb3_in/5 3. SCC is partially evaluated into eval_realheapsort_step2_bb1_in/3 4. SCC is completely evaluated into other SCCs 5. SCC is partially evaluated into eval_realheapsort_step2_bb0_in/2 6. SCC is partially evaluated into eval_realheapsort_step2_start/2 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations eval_realheapsort_step2_bb3_in/5 * CE 11 is refined into CE [12] * CE 9 is refined into CE [13] * CE 6 is refined into CE [14] * CE 7 is refined into CE [15] * CE 8 is refined into CE [16] * CE 10 is refined into CE [17] ### Cost equations --> "Loop" of eval_realheapsort_step2_bb3_in/5 * CEs [13] --> Loop 12 * CEs [14] --> Loop 13 * CEs [15] --> Loop 14 * CEs [16] --> Loop 15 * CEs [17] --> Loop 16 * CEs [12] --> Loop 17 ### Ranking functions of CR eval_realheapsort_step2_bb3_in(V_N,V_k_0,V_j_0,B,C) * RF of phase [13,14]: [V_N/2-V_j_0-3/2,V_N/2-V_k_0/2-V_j_0-3/2] #### Partial ranking functions of CR eval_realheapsort_step2_bb3_in(V_N,V_k_0,V_j_0,B,C) * Partial RF of phase [13,14]: - RF of loop [13:1,14:1]: V_N/2-V_j_0-3/2 V_N/2-V_k_0/2-V_j_0-3/2 ### Specialization of cost equations eval_realheapsort_step2_bb1_in/3 * CE 5 is refined into CE [18] * CE 4 is refined into CE [19,20,21,22,23,24,25,26] ### Cost equations --> "Loop" of eval_realheapsort_step2_bb1_in/3 * CEs [21] --> Loop 18 * CEs [20] --> Loop 19 * CEs [22] --> Loop 20 * CEs [25] --> Loop 21 * CEs [26] --> Loop 22 * CEs [19,24] --> Loop 23 * CEs [23] --> Loop 24 * CEs [18] --> Loop 25 ### Ranking functions of CR eval_realheapsort_step2_bb1_in(V_N,V_k_0,B) * RF of phase [18,19,20,21,22]: [V_N-V_k_0-3] #### Partial ranking functions of CR eval_realheapsort_step2_bb1_in(V_N,V_k_0,B) * Partial RF of phase [18,19,20,21,22]: - RF of loop [18:1]: V_N-V_k_0-5 - RF of loop [19:1,21:1]: V_N-V_k_0-4 - RF of loop [20:1,22:1]: V_N-V_k_0-3 ### Specialization of cost equations eval_realheapsort_step2_bb0_in/2 * CE 3 is refined into CE [27,28] * CE 2 is refined into CE [29] ### Cost equations --> "Loop" of eval_realheapsort_step2_bb0_in/2 * CEs [28] --> Loop 26 * CEs [29] --> Loop 27 * CEs [27] --> Loop 28 ### Ranking functions of CR eval_realheapsort_step2_bb0_in(V_N,B) #### Partial ranking functions of CR eval_realheapsort_step2_bb0_in(V_N,B) ### Specialization of cost equations eval_realheapsort_step2_start/2 * CE 1 is refined into CE [30,31,32] ### Cost equations --> "Loop" of eval_realheapsort_step2_start/2 * CEs [32] --> Loop 29 * CEs [31] --> Loop 30 * CEs [30] --> Loop 31 ### Ranking functions of CR eval_realheapsort_step2_start(V_N,B) #### Partial ranking functions of CR eval_realheapsort_step2_start(V_N,B) Computing Bounds ===================================== #### Cost of chains of eval_realheapsort_step2_bb3_in(V_N,V_k_0,V_j_0,B,C): * Chain [[13,14],17]: 2*it(13)+0 Such that:aux(1) =< V_N/2-V_k_0/2-V_j_0 aux(3) =< V_N/2-V_j_0 aux(5) =< -V_j_0+C it(13) =< aux(1) it(13) =< aux(5) it(13) =< aux(3) with precondition: [B=2,V_k_0>=0,V_j_0>=0,C>=2*V_j_0+1,V_N>=2*V_j_0+V_k_0+4,V_k_0+2*C+2>=V_N,V_N>=V_k_0+C+2] * Chain [[13,14],16,17]: 2*it(13)+1 Such that:aux(3) =< -V_j_0+C/2 aux(6) =< -V_k_0/2-V_j_0+C/2 it(13) =< aux(6) it(13) =< aux(3) with precondition: [B=2,V_N=C,V_k_0>=0,V_j_0>=0,V_N>=4*V_j_0+V_k_0+5] * Chain [[13,14],15,17]: 2*it(13)+1 Such that:aux(3) =< -V_j_0+C/2 aux(7) =< -V_k_0/2-V_j_0+C/2 it(13) =< aux(7) it(13) =< aux(3) with precondition: [B=2,V_N=C,V_k_0>=0,V_j_0>=0,V_N>=4*V_j_0+V_k_0+6] * Chain [[13,14],12,17]: 2*it(13)+1 Such that:aux(3) =< V_k_0/2-V_j_0+C/2+1 aux(1) =< -V_j_0+C/2+1 aux(8) =< -V_j_0+C/2 it(13) =< aux(1) it(13) =< aux(8) it(13) =< aux(3) with precondition: [B=2,V_N=V_k_0+C+2,V_k_0>=0,V_j_0>=0,V_N>=4*V_j_0+V_k_0+5] * Chain [17]: 0 with precondition: [B=2,V_j_0=C,V_N>=3,V_k_0>=0,V_N>=V_k_0+2,V_N>=V_j_0,4*V_N>=3*V_k_0+V_j_0+9,V_k_0+2*V_j_0+2>=V_N] * Chain [16,17]: 1 with precondition: [B=2,V_N=C,V_N=2*V_j_0+V_k_0+3,V_k_0>=0,V_N>=V_k_0+3] * Chain [15,17]: 1 with precondition: [B=2,V_N=C,V_k_0>=0,V_j_0>=0,V_N>=2*V_j_0+V_k_0+4] * Chain [12,17]: 1 with precondition: [B=2,V_N=2*V_j_0+V_k_0+3,V_N=V_k_0+C+2,V_k_0>=0,V_N>=V_k_0+3] #### Cost of chains of eval_realheapsort_step2_bb1_in(V_N,V_k_0,B): * Chain [[18,19,20,21,22],23,24,25]: 9*it(18)+2*s(29)+2*s(32)+2*s(35)+2*s(39)+3 Such that:aux(9) =< V_N/2 aux(10) =< V_N/2-V_k_0/2 aux(21) =< V_N-V_k_0 it(18) =< aux(21) aux(12) =< aux(10) aux(11) =< aux(9) aux(16) =< aux(10)*2-1 aux(14) =< aux(10)-1/2 s(31) =< it(18)*aux(10) s(30) =< it(18)*aux(9) s(34) =< it(18)*aux(12) s(33) =< it(18)*aux(11) s(41) =< it(18)*aux(16) s(37) =< it(18)*aux(14) s(39) =< s(34) s(39) =< s(41) s(39) =< s(33) s(35) =< s(34) s(35) =< s(37) s(35) =< s(33) s(32) =< s(34) s(32) =< s(33) s(29) =< s(31) s(29) =< s(30) with precondition: [B=3,V_k_0>=0,V_N>=V_k_0+4] * Chain [23,24,25]: 3 with precondition: [B=3,V_N=V_k_0+3,V_N>=3] #### Cost of chains of eval_realheapsort_step2_bb0_in(V_N,B): * Chain [28]: 3 with precondition: [V_N=3] * Chain [27]: 0 with precondition: [2>=V_N] * Chain [26]: 9*s(46)+2*s(57)+2*s(58)+2*s(59)+2*s(60)+3 Such that:s(45) =< V_N aux(22) =< V_N/2 s(46) =< s(45) s(47) =< aux(22) s(49) =< aux(22)*2-1 s(50) =< aux(22)-1/2 s(51) =< s(46)*aux(22) s(53) =< s(46)*s(47) s(55) =< s(46)*s(49) s(56) =< s(46)*s(50) s(57) =< s(53) s(57) =< s(55) s(58) =< s(53) s(58) =< s(56) s(59) =< s(53) s(60) =< s(51) with precondition: [V_N>=4] #### Cost of chains of eval_realheapsort_step2_start(V_N,B): * Chain [31]: 3 with precondition: [V_N=3] * Chain [30]: 0 with precondition: [2>=V_N] * Chain [29]: 9*s(63)+2*s(71)+2*s(72)+2*s(73)+2*s(74)+3 Such that:s(61) =< V_N s(62) =< V_N/2 s(63) =< s(61) s(64) =< s(62) s(65) =< s(62)*2-1 s(66) =< s(62)-1/2 s(67) =< s(63)*s(62) s(68) =< s(63)*s(64) s(69) =< s(63)*s(65) s(70) =< s(63)*s(66) s(71) =< s(68) s(71) =< s(69) s(72) =< s(68) s(72) =< s(70) s(73) =< s(68) s(74) =< s(67) with precondition: [V_N>=4] Closed-form bounds of eval_realheapsort_step2_start(V_N,B): ------------------------------------- * Chain [31] with precondition: [V_N=3] - Upper bound: 3 - Complexity: constant * Chain [30] with precondition: [2>=V_N] - Upper bound: 0 - Complexity: constant * Chain [29] with precondition: [V_N>=4] - Upper bound: 9*V_N+3+V_N/2*(8*V_N) - Complexity: n^2 ### Maximum cost of eval_realheapsort_step2_start(V_N,B): max([3,nat(V_N)*9+3+nat(V_N)*8*nat(V_N/2)]) Asymptotic class: n^2 * Total analysis performed in 510 ms.