0.07/0.45 WORST_CASE(?,O(n^2)) 0.07/0.45 0.07/0.45 Preprocessing Cost Relations 0.07/0.45 ===================================== 0.07/0.45 0.07/0.45 #### Computed strongly connected components 0.07/0.45 0. recursive : [eval_realheapsort_step1_bb2_in/3,eval_realheapsort_step1_bb3_in/3,eval_realheapsort_step1_bb4_in/3] 0.07/0.45 1. recursive : [eval_realheapsort_step1_28/8,eval_realheapsort_step1_29/8,eval_realheapsort_step1__critedge_in/8,eval_realheapsort_step1_bb1_in/8,eval_realheapsort_step1_bb2_in_loop_cont/9] 0.07/0.45 2. non_recursive : [eval_realheapsort_step1_stop/5] 0.07/0.45 3. non_recursive : [eval_realheapsort_step1_bb5_in/5] 0.07/0.45 4. non_recursive : [exit_location/1] 0.07/0.45 5. non_recursive : [eval_realheapsort_step1_bb1_in_loop_cont/6] 0.07/0.45 6. non_recursive : [eval_realheapsort_step1_2/5] 0.07/0.45 7. non_recursive : [eval_realheapsort_step1_1/5] 0.07/0.45 8. non_recursive : [eval_realheapsort_step1_0/5] 0.07/0.45 9. non_recursive : [eval_realheapsort_step1_bb0_in/5] 0.07/0.45 10. non_recursive : [eval_realheapsort_step1_start/5] 0.07/0.45 0.07/0.45 #### Obtained direct recursion through partial evaluation 0.07/0.45 0. SCC is partially evaluated into eval_realheapsort_step1_bb2_in/3 0.07/0.45 1. SCC is partially evaluated into eval_realheapsort_step1_bb1_in/8 0.07/0.45 2. SCC is completely evaluated into other SCCs 0.07/0.45 3. SCC is completely evaluated into other SCCs 0.07/0.45 4. SCC is completely evaluated into other SCCs 0.07/0.45 5. SCC is partially evaluated into eval_realheapsort_step1_bb1_in_loop_cont/6 0.07/0.45 6. SCC is partially evaluated into eval_realheapsort_step1_2/5 0.07/0.45 7. SCC is completely evaluated into other SCCs 0.07/0.45 8. SCC is completely evaluated into other SCCs 0.07/0.45 9. SCC is completely evaluated into other SCCs 0.07/0.45 10. SCC is partially evaluated into eval_realheapsort_step1_start/5 0.07/0.45 0.07/0.45 Control-Flow Refinement of Cost Relations 0.07/0.45 ===================================== 0.07/0.45 0.07/0.45 ### Specialization of cost equations eval_realheapsort_step1_bb2_in/3 0.07/0.45 * CE 13 is refined into CE [14] 0.07/0.45 * CE 10 is refined into CE [15] 0.07/0.45 * CE 12 is refined into CE [16] 0.07/0.45 * CE 11 is refined into CE [17] 0.07/0.45 0.07/0.45 0.07/0.45 ### Cost equations --> "Loop" of eval_realheapsort_step1_bb2_in/3 0.07/0.45 * CEs [17] --> Loop 14 0.07/0.45 * CEs [14] --> Loop 15 0.07/0.45 * CEs [15] --> Loop 16 0.07/0.45 * CEs [16] --> Loop 17 0.07/0.45 0.07/0.45 ### Ranking functions of CR eval_realheapsort_step1_bb2_in(V_j_0,B,C) 0.07/0.45 * RF of phase [14]: [V_j_0] 0.07/0.45 0.07/0.45 #### Partial ranking functions of CR eval_realheapsort_step1_bb2_in(V_j_0,B,C) 0.07/0.45 * Partial RF of phase [14]: 0.07/0.45 - RF of loop [14:1]: 0.07/0.45 V_j_0 0.07/0.45 0.07/0.45 0.07/0.45 ### Specialization of cost equations eval_realheapsort_step1_bb1_in/8 0.07/0.45 * CE 6 is refined into CE [18] 0.07/0.45 * CE 4 is refined into CE [19,20] 0.07/0.45 * CE 7 is refined into CE [21] 0.07/0.45 * CE 5 is refined into CE [22,23,24] 0.07/0.45 0.07/0.45 0.07/0.45 ### Cost equations --> "Loop" of eval_realheapsort_step1_bb1_in/8 0.07/0.45 * CEs [24] --> Loop 18 0.07/0.45 * CEs [23] --> Loop 19 0.07/0.45 * CEs [22] --> Loop 20 0.07/0.45 * CEs [18] --> Loop 21 0.07/0.45 * CEs [19,20] --> Loop 22 0.07/0.45 * CEs [21] --> Loop 23 0.07/0.45 0.07/0.45 ### Ranking functions of CR eval_realheapsort_step1_bb1_in(V_33,V_N,V_j_0,V_k_0,B,C,D,E) 0.07/0.45 * RF of phase [18,19,20]: [V_N-V_k_0] 0.07/0.45 0.07/0.45 #### Partial ranking functions of CR eval_realheapsort_step1_bb1_in(V_33,V_N,V_j_0,V_k_0,B,C,D,E) 0.07/0.45 * Partial RF of phase [18,19,20]: 0.07/0.45 - RF of loop [18:1,19:1,20:1]: 0.07/0.45 V_N-V_k_0 0.07/0.45 0.07/0.45 0.07/0.45 ### Specialization of cost equations eval_realheapsort_step1_bb1_in_loop_cont/6 0.07/0.45 * CE 8 is refined into CE [25] 0.07/0.45 * CE 9 is refined into CE [26] 0.07/0.45 0.07/0.45 0.07/0.45 ### Cost equations --> "Loop" of eval_realheapsort_step1_bb1_in_loop_cont/6 0.07/0.45 * CEs [25] --> Loop 24 0.07/0.45 * CEs [26] --> Loop 25 0.07/0.45 0.07/0.45 ### Ranking functions of CR eval_realheapsort_step1_bb1_in_loop_cont(A,B,C,D,E,F) 0.07/0.45 0.07/0.45 #### Partial ranking functions of CR eval_realheapsort_step1_bb1_in_loop_cont(A,B,C,D,E,F) 0.07/0.45 0.07/0.45 0.07/0.45 ### Specialization of cost equations eval_realheapsort_step1_2/5 0.07/0.45 * CE 3 is refined into CE [27,28,29,30] 0.07/0.45 * CE 2 is refined into CE [31] 0.07/0.45 0.07/0.45 0.07/0.45 ### Cost equations --> "Loop" of eval_realheapsort_step1_2/5 0.07/0.45 * CEs [27,28,29,30] --> Loop 26 0.07/0.45 * CEs [31] --> Loop 27 0.07/0.45 0.07/0.45 ### Ranking functions of CR eval_realheapsort_step1_2(V_33,V_N,V_j_0,V_k_0,B) 0.07/0.45 0.07/0.45 #### Partial ranking functions of CR eval_realheapsort_step1_2(V_33,V_N,V_j_0,V_k_0,B) 0.07/0.45 0.07/0.45 0.07/0.45 ### Specialization of cost equations eval_realheapsort_step1_start/5 0.07/0.45 * CE 1 is refined into CE [32,33] 0.07/0.45 0.07/0.45 0.07/0.45 ### Cost equations --> "Loop" of eval_realheapsort_step1_start/5 0.07/0.45 * CEs [33] --> Loop 28 0.07/0.45 * CEs [32] --> Loop 29 0.07/0.45 0.07/0.45 ### Ranking functions of CR eval_realheapsort_step1_start(V_33,V_N,V_j_0,V_k_0,B) 0.07/0.45 0.07/0.45 #### Partial ranking functions of CR eval_realheapsort_step1_start(V_33,V_N,V_j_0,V_k_0,B) 0.07/0.45 0.07/0.45 0.07/0.45 Computing Bounds 0.07/0.45 ===================================== 0.07/0.45 0.07/0.45 #### Cost of chains of eval_realheapsort_step1_bb2_in(V_j_0,B,C): 0.07/0.45 * Chain [[14],17]: 1*it(14)+0 0.07/0.45 Such that:it(14) =< V_j_0 0.07/0.45 0.07/0.45 with precondition: [B=2,0>=C,V_j_0>=1,2*C+1>=0] 0.07/0.45 0.07/0.45 * Chain [[14],16]: 1*it(14)+0 0.07/0.45 Such that:it(14) =< V_j_0-C 0.07/0.45 0.07/0.45 with precondition: [B=2,C>=1,V_j_0>=2*C+1] 0.07/0.45 0.07/0.45 * Chain [[14],15]: 1*it(14)+0 0.07/0.45 Such that:it(14) =< V_j_0 0.07/0.45 0.07/0.45 with precondition: [B=3,V_j_0>=1] 0.07/0.45 0.07/0.45 * Chain [16]: 0 0.07/0.45 with precondition: [B=2,V_j_0=C,V_j_0>=1] 0.07/0.45 0.07/0.45 * Chain [15]: 0 0.07/0.45 with precondition: [B=3,2*V_j_0+1>=0] 0.07/0.45 0.07/0.45 0.07/0.45 #### Cost of chains of eval_realheapsort_step1_bb1_in(V_33,V_N,V_j_0,V_k_0,B,C,D,E): 0.07/0.45 * Chain [[18,19,20],23]: 3*it(18)+1*s(5)+1*s(6)+0 0.07/0.45 Such that:aux(1) =< V_N 0.07/0.45 aux(5) =< V_N-V_k_0 0.07/0.45 it(18) =< aux(5) 0.07/0.45 aux(2) =< aux(1)+1 0.07/0.45 s(5) =< it(18)*aux(1) 0.07/0.45 s(6) =< it(18)*aux(2) 0.07/0.45 0.07/0.45 with precondition: [B=3,V_N>=3,V_k_0>=1,V_N>=V_k_0+1] 0.07/0.45 0.07/0.45 * Chain [[18,19,20],22]: 3*it(18)+1*s(5)+1*s(6)+1*s(7)+0 0.07/0.45 Such that:aux(6) =< V_N 0.07/0.45 aux(7) =< V_N-V_k_0 0.07/0.45 s(7) =< aux(6) 0.07/0.45 it(18) =< aux(7) 0.07/0.45 aux(2) =< aux(6)+1 0.07/0.45 s(5) =< it(18)*aux(6) 0.07/0.45 s(6) =< it(18)*aux(2) 0.07/0.45 0.07/0.45 with precondition: [B=3,V_k_0>=1,V_N>=V_k_0+2] 0.07/0.45 0.07/0.45 * Chain [[18,19,20],21]: 3*it(18)+1*s(5)+1*s(6)+0 0.07/0.45 Such that:aux(1) =< C 0.07/0.45 aux(8) =< -V_k_0+C 0.07/0.45 it(18) =< aux(8) 0.07/0.45 aux(2) =< aux(1)+1 0.07/0.45 s(5) =< it(18)*aux(1) 0.07/0.45 s(6) =< it(18)*aux(2) 0.07/0.45 0.07/0.45 with precondition: [B=4,V_N=C,V_N=E,V_N>=3,V_k_0>=1,2*D+1>=0,V_N>=V_k_0+1,V_N>=D+1] 0.07/0.45 0.07/0.45 * Chain [23]: 0 0.07/0.45 with precondition: [B=3,V_N>=3,V_k_0>=1] 0.07/0.45 0.07/0.45 * Chain [22]: 1*s(7)+0 0.07/0.45 Such that:s(7) =< V_k_0 0.07/0.45 0.07/0.45 with precondition: [B=3,V_N>=3,V_k_0>=1,V_N>=V_k_0+1] 0.07/0.45 0.07/0.45 0.07/0.45 #### Cost of chains of eval_realheapsort_step1_bb1_in_loop_cont(A,B,C,D,E,F): 0.07/0.45 * Chain [25]: 0 0.07/0.45 with precondition: [A=3,C>=3] 0.07/0.45 0.07/0.45 * Chain [24]: 0 0.07/0.45 with precondition: [A=4,C>=3] 0.07/0.45 0.07/0.45 0.07/0.45 #### Cost of chains of eval_realheapsort_step1_2(V_33,V_N,V_j_0,V_k_0,B): 0.07/0.45 * Chain [27]: 0 0.07/0.45 with precondition: [2>=V_N] 0.07/0.45 0.07/0.45 * Chain [26]: 1*s(17)+10*s(18)+3*s(20)+3*s(21)+0 0.07/0.45 Such that:s(17) =< 1 0.07/0.45 aux(12) =< V_N 0.07/0.45 s(18) =< aux(12) 0.07/0.45 s(19) =< aux(12)+1 0.07/0.45 s(20) =< s(18)*aux(12) 0.07/0.45 s(21) =< s(18)*s(19) 0.07/0.45 0.07/0.45 with precondition: [V_N>=3] 0.07/0.45 0.07/0.45 0.07/0.45 #### Cost of chains of eval_realheapsort_step1_start(V_33,V_N,V_j_0,V_k_0,B): 0.07/0.45 * Chain [29]: 0 0.07/0.45 with precondition: [2>=V_N] 0.07/0.45 0.07/0.45 * Chain [28]: 1*s(35)+10*s(37)+3*s(39)+3*s(40)+0 0.07/0.45 Such that:s(35) =< 1 0.07/0.45 s(36) =< V_N 0.07/0.45 s(37) =< s(36) 0.07/0.45 s(38) =< s(36)+1 0.07/0.45 s(39) =< s(37)*s(36) 0.07/0.45 s(40) =< s(37)*s(38) 0.07/0.45 0.07/0.45 with precondition: [V_N>=3] 0.07/0.45 0.07/0.45 0.07/0.45 Closed-form bounds of eval_realheapsort_step1_start(V_33,V_N,V_j_0,V_k_0,B): 0.07/0.45 ------------------------------------- 0.07/0.45 * Chain [29] with precondition: [2>=V_N] 0.07/0.45 - Upper bound: 0 0.07/0.45 - Complexity: constant 0.07/0.45 * Chain [28] with precondition: [V_N>=3] 0.07/0.45 - Upper bound: 13*V_N+1+6*V_N*V_N 0.07/0.45 - Complexity: n^2 0.07/0.45 0.07/0.45 ### Maximum cost of eval_realheapsort_step1_start(V_33,V_N,V_j_0,V_k_0,B): nat(V_N)*13+1+nat(V_N)*6*nat(V_N) 0.07/0.45 Asymptotic class: n^2 0.07/0.45 * Total analysis performed in 339 ms. 0.07/0.45 0.45/0.55 EOF