0.04/0.26 WORST_CASE(?,O(n^1)) 0.04/0.26 0.04/0.26 Preprocessing Cost Relations 0.04/0.26 ===================================== 0.04/0.26 0.04/0.26 #### Computed strongly connected components 0.04/0.26 0. recursive : [evalspeedpldi2bb2in/6,evalspeedpldi2bb3in/6,evalspeedpldi2bb5in/6] 0.04/0.26 1. non_recursive : [evalspeedpldi2stop/4] 0.04/0.26 2. non_recursive : [evalspeedpldi2returnin/4] 0.04/0.26 3. non_recursive : [exit_location/1] 0.04/0.26 4. non_recursive : [evalspeedpldi2bb5in_loop_cont/5] 0.04/0.26 5. non_recursive : [evalspeedpldi2entryin/4] 0.04/0.26 6. non_recursive : [evalspeedpldi2start/4] 0.04/0.26 0.04/0.26 #### Obtained direct recursion through partial evaluation 0.04/0.26 0. SCC is partially evaluated into evalspeedpldi2bb5in/6 0.04/0.26 1. SCC is completely evaluated into other SCCs 0.04/0.26 2. SCC is completely evaluated into other SCCs 0.04/0.26 3. SCC is completely evaluated into other SCCs 0.04/0.26 4. SCC is partially evaluated into evalspeedpldi2bb5in_loop_cont/5 0.04/0.26 5. SCC is partially evaluated into evalspeedpldi2entryin/4 0.04/0.26 6. SCC is partially evaluated into evalspeedpldi2start/4 0.04/0.26 0.04/0.26 Control-Flow Refinement of Cost Relations 0.04/0.26 ===================================== 0.04/0.26 0.04/0.26 ### Specialization of cost equations evalspeedpldi2bb5in/6 0.04/0.26 * CE 8 is refined into CE [11] 0.04/0.26 * CE 7 is refined into CE [12] 0.04/0.26 * CE 6 is refined into CE [13] 0.04/0.26 * CE 5 is refined into CE [14] 0.04/0.26 0.04/0.26 0.04/0.26 ### Cost equations --> "Loop" of evalspeedpldi2bb5in/6 0.04/0.26 * CEs [13] --> Loop 11 0.04/0.26 * CEs [14] --> Loop 12 0.04/0.26 * CEs [11] --> Loop 13 0.04/0.26 * CEs [12] --> Loop 14 0.04/0.26 0.04/0.26 ### Ranking functions of CR evalspeedpldi2bb5in(A,B,C,D,E,F) 0.04/0.26 * RF of phase [11,12]: [B+2*C-1] 0.04/0.26 0.04/0.26 #### Partial ranking functions of CR evalspeedpldi2bb5in(A,B,C,D,E,F) 0.04/0.26 * Partial RF of phase [11,12]: 0.04/0.26 - RF of loop [11:1]: 0.04/0.26 A-B depends on loops [12:1] 0.04/0.26 C 0.04/0.26 - RF of loop [12:1]: 0.04/0.26 -A+B+1 depends on loops [11:1] 0.04/0.26 B depends on loops [11:1] 0.04/0.26 0.04/0.26 0.04/0.26 ### Specialization of cost equations evalspeedpldi2bb5in_loop_cont/5 0.04/0.26 * CE 10 is refined into CE [15] 0.04/0.26 * CE 9 is refined into CE [16] 0.04/0.26 0.04/0.26 0.04/0.26 ### Cost equations --> "Loop" of evalspeedpldi2bb5in_loop_cont/5 0.04/0.26 * CEs [15] --> Loop 15 0.04/0.26 * CEs [16] --> Loop 16 0.04/0.26 0.04/0.26 ### Ranking functions of CR evalspeedpldi2bb5in_loop_cont(A,B,C,D,E) 0.04/0.26 0.04/0.26 #### Partial ranking functions of CR evalspeedpldi2bb5in_loop_cont(A,B,C,D,E) 0.04/0.26 0.04/0.26 0.04/0.26 ### Specialization of cost equations evalspeedpldi2entryin/4 0.04/0.26 * CE 4 is refined into CE [17,18,19,20] 0.04/0.26 * CE 3 is refined into CE [21] 0.04/0.26 * CE 2 is refined into CE [22] 0.04/0.26 0.04/0.26 0.04/0.26 ### Cost equations --> "Loop" of evalspeedpldi2entryin/4 0.04/0.26 * CEs [18,20] --> Loop 17 0.04/0.26 * CEs [19] --> Loop 18 0.04/0.26 * CEs [21] --> Loop 19 0.04/0.26 * CEs [22] --> Loop 20 0.04/0.26 * CEs [17] --> Loop 21 0.04/0.26 0.04/0.26 ### Ranking functions of CR evalspeedpldi2entryin(A,B,C,D) 0.04/0.26 0.04/0.26 #### Partial ranking functions of CR evalspeedpldi2entryin(A,B,C,D) 0.04/0.26 0.04/0.26 0.04/0.26 ### Specialization of cost equations evalspeedpldi2start/4 0.04/0.26 * CE 1 is refined into CE [23,24,25,26,27] 0.04/0.26 0.04/0.26 0.04/0.26 ### Cost equations --> "Loop" of evalspeedpldi2start/4 0.04/0.26 * CEs [27] --> Loop 22 0.04/0.26 * CEs [26] --> Loop 23 0.04/0.26 * CEs [25] --> Loop 24 0.04/0.26 * CEs [24] --> Loop 25 0.04/0.26 * CEs [23] --> Loop 26 0.04/0.26 0.04/0.26 ### Ranking functions of CR evalspeedpldi2start(A,B,C,D) 0.04/0.26 0.04/0.26 #### Partial ranking functions of CR evalspeedpldi2start(A,B,C,D) 0.04/0.26 0.04/0.26 0.04/0.26 Computing Bounds 0.04/0.26 ===================================== 0.04/0.26 0.04/0.26 #### Cost of chains of evalspeedpldi2bb5in(A,B,C,D,E,F): 0.04/0.26 * Chain [[11,12],14]: 1*it(11)+1*it(12)+0 0.04/0.26 Such that:aux(17) =< B+2*C 0.04/0.26 aux(18) =< B+2*C-E 0.04/0.26 it(11) =< C 0.04/0.26 it(11) =< aux(17) 0.04/0.26 it(12) =< aux(17) 0.04/0.26 it(11) =< aux(18) 0.04/0.26 it(12) =< aux(18) 0.04/0.26 0.04/0.26 with precondition: [D=2,F=0,A>=1,B>=0,C>=1,A>=E,B+C>=E] 0.04/0.26 0.04/0.26 * Chain [[11,12],13]: 1*it(11)+1*it(12)+0 0.04/0.26 Such that:it(11) =< C 0.04/0.26 aux(20) =< B+2*C 0.04/0.26 it(11) =< aux(20) 0.04/0.26 it(12) =< aux(20) 0.04/0.26 0.04/0.26 with precondition: [D=3,A>=1,B>=0,C>=1] 0.04/0.26 0.04/0.26 * Chain [14]: 0 0.04/0.26 with precondition: [C=0,D=2,F=0,B=E,A>=1,B>=0] 0.04/0.26 0.04/0.26 * Chain [13]: 0 0.04/0.26 with precondition: [D=3,A>=1,B>=0,C>=0] 0.04/0.26 0.04/0.26 0.04/0.26 #### Cost of chains of evalspeedpldi2bb5in_loop_cont(A,B,C,D,E): 0.04/0.26 * Chain [16]: 0 0.04/0.26 with precondition: [A=2,B>=1] 0.04/0.26 0.04/0.26 * Chain [15]: 0 0.04/0.26 with precondition: [A=3,B>=1] 0.04/0.26 0.04/0.26 0.04/0.26 #### Cost of chains of evalspeedpldi2entryin(A,B,C,D): 0.04/0.26 * Chain [21]: 0 0.04/0.26 with precondition: [A=0,B>=1] 0.04/0.26 0.04/0.26 * Chain [20]: 0 0.04/0.26 with precondition: [0>=A+1] 0.04/0.26 0.04/0.26 * Chain [19]: 0 0.04/0.26 with precondition: [0>=B] 0.04/0.26 0.04/0.26 * Chain [18]: 0 0.04/0.26 with precondition: [A>=0,B>=1] 0.04/0.26 0.04/0.26 * Chain [17]: 2*s(3)+2*s(4)+0 0.04/0.26 Such that:aux(21) =< A 0.04/0.26 aux(22) =< 2*A 0.04/0.26 s(3) =< aux(21) 0.04/0.26 s(3) =< aux(22) 0.04/0.26 s(4) =< aux(22) 0.04/0.26 0.04/0.26 with precondition: [A>=1,B>=1] 0.04/0.26 0.04/0.26 0.04/0.26 #### Cost of chains of evalspeedpldi2start(A,B,C,D): 0.04/0.26 * Chain [26]: 0 0.04/0.26 with precondition: [A=0,B>=1] 0.04/0.26 0.04/0.26 * Chain [25]: 0 0.04/0.26 with precondition: [0>=A+1] 0.04/0.26 0.04/0.26 * Chain [24]: 0 0.04/0.26 with precondition: [0>=B] 0.04/0.26 0.04/0.26 * Chain [23]: 0 0.04/0.26 with precondition: [A>=0,B>=1] 0.04/0.26 0.04/0.26 * Chain [22]: 2*s(10)+2*s(11)+0 0.04/0.26 Such that:s(8) =< A 0.04/0.26 s(9) =< 2*A 0.04/0.26 s(10) =< s(8) 0.04/0.26 s(10) =< s(9) 0.04/0.26 s(11) =< s(9) 0.04/0.26 0.04/0.26 with precondition: [A>=1,B>=1] 0.04/0.26 0.04/0.26 0.04/0.26 Closed-form bounds of evalspeedpldi2start(A,B,C,D): 0.04/0.26 ------------------------------------- 0.04/0.26 * Chain [26] with precondition: [A=0,B>=1] 0.04/0.26 - Upper bound: 0 0.04/0.26 - Complexity: constant 0.04/0.26 * Chain [25] with precondition: [0>=A+1] 0.04/0.26 - Upper bound: 0 0.04/0.26 - Complexity: constant 0.04/0.26 * Chain [24] with precondition: [0>=B] 0.04/0.26 - Upper bound: 0 0.04/0.26 - Complexity: constant 0.04/0.26 * Chain [23] with precondition: [A>=0,B>=1] 0.04/0.26 - Upper bound: 0 0.04/0.26 - Complexity: constant 0.04/0.26 * Chain [22] with precondition: [A>=1,B>=1] 0.04/0.26 - Upper bound: 6*A 0.04/0.26 - Complexity: n 0.04/0.26 0.04/0.26 ### Maximum cost of evalspeedpldi2start(A,B,C,D): nat(2*A)*2+nat(A)*2 0.04/0.26 Asymptotic class: n 0.04/0.26 * Total analysis performed in 192 ms. 0.04/0.26 0.04/0.36 EOF