0.03/0.21 WORST_CASE(?,O(n^1)) 0.03/0.21 0.03/0.21 Preprocessing Cost Relations 0.03/0.21 ===================================== 0.03/0.21 0.03/0.21 #### Computed strongly connected components 0.03/0.21 0. recursive : [evalspeedpldi4bb2in/4,evalspeedpldi4bb3in/4,evalspeedpldi4bb4in/4,evalspeedpldi4bb5in/4] 0.03/0.21 1. non_recursive : [evalspeedpldi4stop/3] 0.03/0.21 2. non_recursive : [evalspeedpldi4returnin/3] 0.03/0.21 3. non_recursive : [exit_location/1] 0.03/0.21 4. non_recursive : [evalspeedpldi4bb5in_loop_cont/4] 0.03/0.21 5. non_recursive : [evalspeedpldi4entryin/3] 0.03/0.21 6. non_recursive : [evalspeedpldi4start/3] 0.03/0.21 0.03/0.21 #### Obtained direct recursion through partial evaluation 0.03/0.21 0. SCC is partially evaluated into evalspeedpldi4bb5in/4 0.03/0.21 1. SCC is completely evaluated into other SCCs 0.03/0.21 2. SCC is completely evaluated into other SCCs 0.03/0.21 3. SCC is completely evaluated into other SCCs 0.03/0.21 4. SCC is partially evaluated into evalspeedpldi4bb5in_loop_cont/4 0.03/0.21 5. SCC is partially evaluated into evalspeedpldi4entryin/3 0.03/0.21 6. SCC is partially evaluated into evalspeedpldi4start/3 0.03/0.21 0.03/0.21 Control-Flow Refinement of Cost Relations 0.03/0.21 ===================================== 0.03/0.21 0.03/0.21 ### Specialization of cost equations evalspeedpldi4bb5in/4 0.03/0.21 * CE 8 is refined into CE [11] 0.03/0.21 * CE 7 is refined into CE [12] 0.03/0.21 * CE 6 is refined into CE [13] 0.03/0.21 * CE 5 is refined into CE [14] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of evalspeedpldi4bb5in/4 0.03/0.21 * CEs [13] --> Loop 11 0.03/0.21 * CEs [14] --> Loop 12 0.03/0.21 * CEs [11] --> Loop 13 0.03/0.21 * CEs [12] --> Loop 14 0.03/0.21 0.03/0.21 ### Ranking functions of CR evalspeedpldi4bb5in(A,B,C,D) 0.03/0.21 * RF of phase [11]: [-A+B+1,B] 0.03/0.21 * RF of phase [12]: [B] 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR evalspeedpldi4bb5in(A,B,C,D) 0.03/0.21 * Partial RF of phase [11]: 0.03/0.21 - RF of loop [11:1]: 0.03/0.21 -A+B+1 0.03/0.21 B 0.03/0.21 * Partial RF of phase [12]: 0.03/0.21 - RF of loop [12:1]: 0.03/0.21 B 0.03/0.21 0.03/0.21 0.03/0.21 ### Specialization of cost equations evalspeedpldi4bb5in_loop_cont/4 0.03/0.21 * CE 10 is refined into CE [15] 0.03/0.21 * CE 9 is refined into CE [16] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of evalspeedpldi4bb5in_loop_cont/4 0.03/0.21 * CEs [15] --> Loop 15 0.03/0.21 * CEs [16] --> Loop 16 0.03/0.21 0.03/0.21 ### Ranking functions of CR evalspeedpldi4bb5in_loop_cont(A,B,C,D) 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR evalspeedpldi4bb5in_loop_cont(A,B,C,D) 0.03/0.21 0.03/0.21 0.03/0.21 ### Specialization of cost equations evalspeedpldi4entryin/3 0.03/0.21 * CE 3 is refined into CE [17] 0.03/0.21 * CE 4 is refined into CE [18,19,20,21,22] 0.03/0.21 * CE 2 is refined into CE [23] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of evalspeedpldi4entryin/3 0.03/0.21 * CEs [17] --> Loop 17 0.03/0.21 * CEs [19,22] --> Loop 18 0.03/0.21 * CEs [18,20,21] --> Loop 19 0.03/0.21 * CEs [23] --> Loop 20 0.03/0.21 0.03/0.21 ### Ranking functions of CR evalspeedpldi4entryin(A,B,C) 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR evalspeedpldi4entryin(A,B,C) 0.03/0.21 0.03/0.21 0.03/0.21 ### Specialization of cost equations evalspeedpldi4start/3 0.03/0.21 * CE 1 is refined into CE [24,25,26,27] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of evalspeedpldi4start/3 0.03/0.21 * CEs [27] --> Loop 21 0.03/0.21 * CEs [26] --> Loop 22 0.03/0.21 * CEs [25] --> Loop 23 0.03/0.21 * CEs [24] --> Loop 24 0.03/0.21 0.03/0.21 ### Ranking functions of CR evalspeedpldi4start(A,B,C) 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR evalspeedpldi4start(A,B,C) 0.03/0.21 0.03/0.21 0.03/0.21 Computing Bounds 0.03/0.21 ===================================== 0.03/0.21 0.03/0.21 #### Cost of chains of evalspeedpldi4bb5in(A,B,C,D): 0.03/0.21 * Chain [[11],[12],14]: 1*it(11)+1*it(12)+0 0.03/0.21 Such that:it(12) =< -A+B 0.03/0.21 it(11) =< -A+B+1 0.03/0.21 it(12) =< A 0.03/0.21 0.03/0.21 with precondition: [C=2,D=0,A>=2,B>=A+1] 0.03/0.21 0.03/0.21 * Chain [[11],[12],13]: 1*it(11)+1*it(12)+0 0.03/0.21 Such that:it(12) =< -A+B 0.03/0.21 it(11) =< -A+B+1 0.03/0.21 it(12) =< A 0.03/0.21 0.03/0.21 with precondition: [C=3,A>=2,B>=A+1] 0.03/0.21 0.03/0.21 * Chain [[11],14]: 1*it(11)+0 0.03/0.21 Such that:it(11) =< -A+B+1 0.03/0.21 0.03/0.21 with precondition: [C=2,D=0,A>=1,B>=A] 0.03/0.21 0.03/0.21 * Chain [[11],13]: 1*it(11)+0 0.03/0.21 Such that:it(11) =< -A+B+1 0.03/0.21 0.03/0.21 with precondition: [C=3,A>=1,B>=A] 0.03/0.21 0.03/0.21 * Chain [13]: 0 0.03/0.21 with precondition: [C=3,A>=1] 0.03/0.21 0.03/0.21 0.03/0.21 #### Cost of chains of evalspeedpldi4bb5in_loop_cont(A,B,C,D): 0.03/0.21 * Chain [16]: 0 0.03/0.21 with precondition: [A=2,B>=1] 0.03/0.21 0.03/0.21 * Chain [15]: 0 0.03/0.21 with precondition: [A=3,B>=1] 0.03/0.21 0.03/0.21 0.03/0.21 #### Cost of chains of evalspeedpldi4entryin(A,B,C): 0.03/0.21 * Chain [20]: 0 0.03/0.21 with precondition: [0>=A] 0.03/0.21 0.03/0.21 * Chain [19]: 2*s(1)+0 0.03/0.21 Such that:aux(1) =< -A+B+1 0.03/0.21 s(1) =< aux(1) 0.03/0.21 0.03/0.21 with precondition: [A>=1,B>=A+1] 0.03/0.21 0.03/0.21 * Chain [18]: 2*s(3)+2*s(4)+0 0.03/0.21 Such that:aux(2) =< -A+B 0.03/0.21 aux(3) =< -A+B+1 0.03/0.21 aux(4) =< A 0.03/0.21 s(3) =< aux(2) 0.03/0.21 s(4) =< aux(3) 0.03/0.21 s(3) =< aux(4) 0.03/0.21 0.03/0.21 with precondition: [A>=2,B>=A+1] 0.03/0.21 0.03/0.21 * Chain [17]: 0 0.03/0.21 with precondition: [A>=B] 0.03/0.21 0.03/0.21 0.03/0.21 #### Cost of chains of evalspeedpldi4start(A,B,C): 0.03/0.21 * Chain [24]: 0 0.03/0.21 with precondition: [0>=A] 0.03/0.21 0.03/0.21 * Chain [23]: 2*s(8)+0 0.03/0.21 Such that:s(7) =< -A+B+1 0.03/0.21 s(8) =< s(7) 0.03/0.21 0.03/0.21 with precondition: [A>=1,B>=A+1] 0.03/0.21 0.03/0.21 * Chain [22]: 2*s(12)+2*s(13)+0 0.03/0.21 Such that:s(9) =< -A+B 0.03/0.21 s(10) =< -A+B+1 0.03/0.21 s(11) =< A 0.03/0.21 s(12) =< s(9) 0.03/0.21 s(13) =< s(10) 0.03/0.21 s(12) =< s(11) 0.03/0.21 0.03/0.21 with precondition: [A>=2,B>=A+1] 0.03/0.21 0.03/0.21 * Chain [21]: 0 0.03/0.21 with precondition: [A>=B] 0.03/0.21 0.03/0.21 0.03/0.21 Closed-form bounds of evalspeedpldi4start(A,B,C): 0.03/0.21 ------------------------------------- 0.03/0.21 * Chain [24] with precondition: [0>=A] 0.03/0.21 - Upper bound: 0 0.03/0.21 - Complexity: constant 0.03/0.21 * Chain [23] with precondition: [A>=1,B>=A+1] 0.03/0.21 - Upper bound: -2*A+2*B+2 0.03/0.21 - Complexity: n 0.03/0.21 * Chain [22] with precondition: [A>=2,B>=A+1] 0.03/0.21 - Upper bound: -4*A+4*B+2 0.03/0.21 - Complexity: n 0.03/0.21 * Chain [21] with precondition: [A>=B] 0.03/0.21 - Upper bound: 0 0.03/0.21 - Complexity: constant 0.03/0.21 0.03/0.21 ### Maximum cost of evalspeedpldi4start(A,B,C): nat(-A+B+1)*2+nat(-A+B)*2 0.03/0.21 Asymptotic class: n 0.03/0.21 * Total analysis performed in 153 ms. 0.03/0.21 0.03/0.32 EOF