/export/starexec/sandbox/solver/bin/starexec_run_its /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(n^1)) Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. recursive : [eval_random2d_12/8,eval_random2d_13/8,eval_random2d_LeafBlock1_in/8,eval_random2d_LeafBlock3_in/8,eval_random2d_LeafBlock5_in/8,eval_random2d_LeafBlock_in/8,eval_random2d_NewDefault_in/8,eval_random2d_NodeBlock7_in/8,eval_random2d_NodeBlock9_in/8,eval_random2d_NodeBlock_in/8,eval_random2d_bb1_in/8,eval_random2d_bb2_in/8,eval_random2d_bb3_in/8,eval_random2d_bb4_in/8,eval_random2d_bb5_in/8,eval_random2d_bb6_in/8,eval_random2d_bb7_in/8] 1. non_recursive : [eval_random2d_stop/5] 2. non_recursive : [eval_random2d_bb8_in/5] 3. non_recursive : [exit_location/1] 4. non_recursive : [eval_random2d_bb1_in_loop_cont/6] 5. non_recursive : [eval_random2d_10/5] 6. non_recursive : [eval_random2d_9/5] 7. non_recursive : [eval_random2d_8/5] 8. non_recursive : [eval_random2d_7/5] 9. non_recursive : [eval_random2d_6/5] 10. non_recursive : [eval_random2d_5/5] 11. non_recursive : [eval_random2d_4/5] 12. non_recursive : [eval_random2d_3/5] 13. non_recursive : [eval_random2d_2/5] 14. non_recursive : [eval_random2d_1/5] 15. non_recursive : [eval_random2d_0/5] 16. non_recursive : [eval_random2d_bb0_in/5] 17. non_recursive : [eval_random2d_start/5] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into eval_random2d_bb1_in/8 1. SCC is completely evaluated into other SCCs 2. SCC is completely evaluated into other SCCs 3. SCC is completely evaluated into other SCCs 4. SCC is partially evaluated into eval_random2d_bb1_in_loop_cont/6 5. SCC is partially evaluated into eval_random2d_10/5 6. SCC is completely evaluated into other SCCs 7. SCC is completely evaluated into other SCCs 8. SCC is completely evaluated into other SCCs 9. SCC is completely evaluated into other SCCs 10. SCC is completely evaluated into other SCCs 11. SCC is completely evaluated into other SCCs 12. SCC is completely evaluated into other SCCs 13. SCC is completely evaluated into other SCCs 14. SCC is completely evaluated into other SCCs 15. SCC is completely evaluated into other SCCs 16. SCC is completely evaluated into other SCCs 17. SCC is partially evaluated into eval_random2d_start/5 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations eval_random2d_bb1_in/8 * CE 10 is refined into CE [13] * CE 9 is refined into CE [14] * CE 7 is refined into CE [15] * CE 8 is refined into CE [16] * CE 5 is refined into CE [17] * CE 4 is refined into CE [18] * CE 3 is refined into CE [19] * CE 6 is refined into CE [20] ### Cost equations --> "Loop" of eval_random2d_bb1_in/8 * CEs [15] --> Loop 13 * CEs [16] --> Loop 14 * CEs [17] --> Loop 15 * CEs [18] --> Loop 16 * CEs [19] --> Loop 17 * CEs [20] --> Loop 18 * CEs [13] --> Loop 19 * CEs [14] --> Loop 20 ### Ranking functions of CR eval_random2d_bb1_in(V_1,V_2,V_N,V_i_0,B,C,D,E) * RF of phase [13,14,15,16,17,18]: [V_N-V_i_0] #### Partial ranking functions of CR eval_random2d_bb1_in(V_1,V_2,V_N,V_i_0,B,C,D,E) * Partial RF of phase [13,14,15,16,17,18]: - RF of loop [13:1,14:1,15:1,16:1,17:1,18:1]: V_N-V_i_0 ### Specialization of cost equations eval_random2d_bb1_in_loop_cont/6 * CE 12 is refined into CE [21] * CE 11 is refined into CE [22] ### Cost equations --> "Loop" of eval_random2d_bb1_in_loop_cont/6 * CEs [21] --> Loop 21 * CEs [22] --> Loop 22 ### Ranking functions of CR eval_random2d_bb1_in_loop_cont(A,B,C,D,E,F) #### Partial ranking functions of CR eval_random2d_bb1_in_loop_cont(A,B,C,D,E,F) ### Specialization of cost equations eval_random2d_10/5 * CE 2 is refined into CE [23,24,25,26] ### Cost equations --> "Loop" of eval_random2d_10/5 * CEs [24,26] --> Loop 23 * CEs [23] --> Loop 24 * CEs [25] --> Loop 25 ### Ranking functions of CR eval_random2d_10(V_1,V_2,V_N,V_i_0,B) #### Partial ranking functions of CR eval_random2d_10(V_1,V_2,V_N,V_i_0,B) ### Specialization of cost equations eval_random2d_start/5 * CE 1 is refined into CE [27,28,29] ### Cost equations --> "Loop" of eval_random2d_start/5 * CEs [29] --> Loop 26 * CEs [28] --> Loop 27 * CEs [27] --> Loop 28 ### Ranking functions of CR eval_random2d_start(V_1,V_2,V_N,V_i_0,B) #### Partial ranking functions of CR eval_random2d_start(V_1,V_2,V_N,V_i_0,B) Computing Bounds ===================================== #### Cost of chains of eval_random2d_bb1_in(V_1,V_2,V_N,V_i_0,B,C,D,E): * Chain [[13,14,15,16,17,18],20]: 6*it(13)+0 Such that:aux(3) =< V_N-V_i_0 it(13) =< aux(3) with precondition: [B=2,V_N=C,V_N=E,V_i_0>=0,V_N>=V_i_0+1] * Chain [[13,14,15,16,17,18],19]: 6*it(13)+0 Such that:aux(4) =< V_N-V_i_0 it(13) =< aux(4) with precondition: [B=3,V_i_0>=0,V_N>=V_i_0+1] * Chain [20]: 0 with precondition: [B=2,C=V_1,D=V_2,V_i_0=E,V_i_0>=0,V_i_0>=V_N] * Chain [19]: 0 with precondition: [B=3,V_i_0>=0] #### Cost of chains of eval_random2d_bb1_in_loop_cont(A,B,C,D,E,F): * Chain [22]: 0 with precondition: [A=2] * Chain [21]: 0 with precondition: [A=3] #### Cost of chains of eval_random2d_10(V_1,V_2,V_N,V_i_0,B): * Chain [25]: 0 with precondition: [] * Chain [24]: 0 with precondition: [0>=V_N] * Chain [23]: 12*s(2)+0 Such that:aux(5) =< V_N s(2) =< aux(5) with precondition: [V_N>=1] #### Cost of chains of eval_random2d_start(V_1,V_2,V_N,V_i_0,B): * Chain [28]: 0 with precondition: [] * Chain [27]: 0 with precondition: [0>=V_N] * Chain [26]: 12*s(6)+0 Such that:s(5) =< V_N s(6) =< s(5) with precondition: [V_N>=1] Closed-form bounds of eval_random2d_start(V_1,V_2,V_N,V_i_0,B): ------------------------------------- * Chain [28] with precondition: [] - Upper bound: 0 - Complexity: constant * Chain [27] with precondition: [0>=V_N] - Upper bound: 0 - Complexity: constant * Chain [26] with precondition: [V_N>=1] - Upper bound: 12*V_N - Complexity: n ### Maximum cost of eval_random2d_start(V_1,V_2,V_N,V_i_0,B): nat(V_N)*12 Asymptotic class: n * Total analysis performed in 359 ms.