/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_speedpldi2_bb1_in/6,eval_speedpldi2_bb2_in/6,eval_speedpldi2_bb3_in/6] 1. non_recursive : [eval_speedpldi2_stop/5] 2. non_recursive : [eval_speedpldi2_bb4_in/5] 3. non_recursive : [exit_location/1] 4. non_recursive : [eval_speedpldi2_bb1_in_loop_cont/6] 5. non_recursive : [eval_speedpldi2_2/5] 6. non_recursive : [eval_speedpldi2_1/5] 7. non_recursive : [eval_speedpldi2_0/5] 8. non_recursive : [eval_speedpldi2_bb0_in/5] 9. non_recursive : [eval_speedpldi2_start/5] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into eval_speedpldi2_bb1_in/6 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_speedpldi2_bb1_in_loop_cont/6 5. SCC is partially evaluated into eval_speedpldi2_2/5 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 partially evaluated into eval_speedpldi2_start/5 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations eval_speedpldi2_bb1_in/6 * CE 8 is refined into CE [11] * CE 7 is refined into CE [12] * CE 6 is refined into CE [13] * CE 5 is refined into CE [14] ### Cost equations --> "Loop" of eval_speedpldi2_bb1_in/6 * CEs [13] --> Loop 11 * CEs [14] --> Loop 12 * CEs [11] --> Loop 13 * CEs [12] --> Loop 14 ### Ranking functions of CR eval_speedpldi2_bb1_in(V_m,V_v1_0,V_v2_0,B,C,D) * RF of phase [11,12]: [2*V_v1_0+V_v2_0-1] #### Partial ranking functions of CR eval_speedpldi2_bb1_in(V_m,V_v1_0,V_v2_0,B,C,D) * Partial RF of phase [11,12]: - RF of loop [11:1]: V_m-V_v2_0 depends on loops [12:1] V_v1_0 - RF of loop [12:1]: -V_m+V_v2_0+1 depends on loops [11:1] V_v2_0 depends on loops [11:1] ### Specialization of cost equations eval_speedpldi2_bb1_in_loop_cont/6 * CE 10 is refined into CE [15] * CE 9 is refined into CE [16] ### Cost equations --> "Loop" of eval_speedpldi2_bb1_in_loop_cont/6 * CEs [15] --> Loop 15 * CEs [16] --> Loop 16 ### Ranking functions of CR eval_speedpldi2_bb1_in_loop_cont(A,B,C,D,E,F) #### Partial ranking functions of CR eval_speedpldi2_bb1_in_loop_cont(A,B,C,D,E,F) ### Specialization of cost equations eval_speedpldi2_2/5 * CE 4 is refined into CE [17,18,19,20] * CE 2 is refined into CE [21] * CE 3 is refined into CE [22] ### Cost equations --> "Loop" of eval_speedpldi2_2/5 * CEs [18,20] --> Loop 17 * CEs [19] --> Loop 18 * CEs [21] --> Loop 19 * CEs [22] --> Loop 20 * CEs [17] --> Loop 21 ### Ranking functions of CR eval_speedpldi2_2(V_m,V_n,V_v1_0,V_v2_0,B) #### Partial ranking functions of CR eval_speedpldi2_2(V_m,V_n,V_v1_0,V_v2_0,B) ### Specialization of cost equations eval_speedpldi2_start/5 * CE 1 is refined into CE [23,24,25,26,27] ### Cost equations --> "Loop" of eval_speedpldi2_start/5 * CEs [27] --> Loop 22 * CEs [26] --> Loop 23 * CEs [25] --> Loop 24 * CEs [24] --> Loop 25 * CEs [23] --> Loop 26 ### Ranking functions of CR eval_speedpldi2_start(V_m,V_n,V_v1_0,V_v2_0,B) #### Partial ranking functions of CR eval_speedpldi2_start(V_m,V_n,V_v1_0,V_v2_0,B) Computing Bounds ===================================== #### Cost of chains of eval_speedpldi2_bb1_in(V_m,V_v1_0,V_v2_0,B,C,D): * Chain [[11,12],14]: 1*it(11)+1*it(12)+0 Such that:it(11) =< V_v1_0 aux(16) =< 2*V_v1_0+V_v2_0 aux(17) =< 2*V_v1_0+V_v2_0-D it(11) =< aux(16) it(12) =< aux(16) it(11) =< aux(17) it(12) =< aux(17) with precondition: [B=2,C=0,V_m>=1,V_v1_0>=1,V_v2_0>=0,V_m>=D,V_v1_0+V_v2_0>=D] * Chain [[11,12],13]: 1*it(11)+1*it(12)+0 Such that:it(11) =< V_v1_0 aux(20) =< 2*V_v1_0+V_v2_0 it(11) =< aux(20) it(12) =< aux(20) with precondition: [B=3,V_m>=1,V_v1_0>=1,V_v2_0>=0] * Chain [14]: 0 with precondition: [V_v1_0=0,B=2,C=0,V_v2_0=D,V_m>=1,V_v2_0>=0] * Chain [13]: 0 with precondition: [B=3,V_m>=1,V_v1_0>=0,V_v2_0>=0] #### Cost of chains of eval_speedpldi2_bb1_in_loop_cont(A,B,C,D,E,F): * Chain [16]: 0 with precondition: [A=2,B>=1,C>=0] * Chain [15]: 0 with precondition: [A=3,B>=1,C>=0] #### Cost of chains of eval_speedpldi2_2(V_m,V_n,V_v1_0,V_v2_0,B): * Chain [21]: 0 with precondition: [V_n=0,V_m>=1] * Chain [20]: 0 with precondition: [0>=V_m] * Chain [19]: 0 with precondition: [0>=V_n+1] * Chain [18]: 0 with precondition: [V_m>=1,V_n>=0] * Chain [17]: 2*s(1)+2*s(4)+0 Such that:aux(21) =< V_n aux(22) =< 2*V_n s(1) =< aux(21) s(1) =< aux(22) s(4) =< aux(22) with precondition: [V_m>=1,V_n>=1] #### Cost of chains of eval_speedpldi2_start(V_m,V_n,V_v1_0,V_v2_0,B): * Chain [26]: 0 with precondition: [V_n=0,V_m>=1] * Chain [25]: 0 with precondition: [0>=V_m] * Chain [24]: 0 with precondition: [0>=V_n+1] * Chain [23]: 0 with precondition: [V_m>=1,V_n>=0] * Chain [22]: 2*s(10)+2*s(11)+0 Such that:s(8) =< V_n s(9) =< 2*V_n s(10) =< s(8) s(10) =< s(9) s(11) =< s(9) with precondition: [V_m>=1,V_n>=1] Closed-form bounds of eval_speedpldi2_start(V_m,V_n,V_v1_0,V_v2_0,B): ------------------------------------- * Chain [26] with precondition: [V_n=0,V_m>=1] - Upper bound: 0 - Complexity: constant * Chain [25] with precondition: [0>=V_m] - Upper bound: 0 - Complexity: constant * Chain [24] with precondition: [0>=V_n+1] - Upper bound: 0 - Complexity: constant * Chain [23] with precondition: [V_m>=1,V_n>=0] - Upper bound: 0 - Complexity: constant * Chain [22] with precondition: [V_m>=1,V_n>=1] - Upper bound: 6*V_n - Complexity: n ### Maximum cost of eval_speedpldi2_start(V_m,V_n,V_v1_0,V_v2_0,B): nat(2*V_n)*2+nat(V_n)*2 Asymptotic class: n * Total analysis performed in 204 ms.