0.03/0.26 WORST_CASE(?,O(n^2)) 0.03/0.26 0.03/0.26 Preprocessing Cost Relations 0.03/0.26 ===================================== 0.03/0.26 0.03/0.26 #### Computed strongly connected components 0.03/0.26 0. recursive : [evalsipmabubblebb1in/4,evalsipmabubblebb2in/4,evalsipmabubblebb3in/4,evalsipmabubblebb4in/4] 0.03/0.26 1. recursive : [evalsipmabubblebb4in_loop_cont/6,evalsipmabubblebb5in/5,evalsipmabubblebb6in/5] 0.03/0.26 2. non_recursive : [evalsipmabubblestop/3] 0.03/0.26 3. non_recursive : [evalsipmabubblereturnin/3] 0.03/0.26 4. non_recursive : [exit_location/1] 0.03/0.26 5. non_recursive : [evalsipmabubblebb6in_loop_cont/4] 0.03/0.26 6. non_recursive : [evalsipmabubbleentryin/3] 0.03/0.26 7. non_recursive : [evalsipmabubblestart/3] 0.03/0.26 0.03/0.26 #### Obtained direct recursion through partial evaluation 0.03/0.26 0. SCC is partially evaluated into evalsipmabubblebb4in/4 0.03/0.26 1. SCC is partially evaluated into evalsipmabubblebb6in/5 0.03/0.26 2. SCC is completely evaluated into other SCCs 0.03/0.26 3. SCC is completely evaluated into other SCCs 0.03/0.26 4. SCC is completely evaluated into other SCCs 0.03/0.26 5. SCC is partially evaluated into evalsipmabubblebb6in_loop_cont/4 0.03/0.26 6. SCC is partially evaluated into evalsipmabubbleentryin/3 0.03/0.26 7. SCC is partially evaluated into evalsipmabubblestart/3 0.03/0.26 0.03/0.26 Control-Flow Refinement of Cost Relations 0.03/0.26 ===================================== 0.03/0.26 0.03/0.26 ### Specialization of cost equations evalsipmabubblebb4in/4 0.03/0.26 * CE 11 is refined into CE [12] 0.03/0.26 * CE 10 is refined into CE [13] 0.03/0.26 * CE 9 is refined into CE [14] 0.03/0.26 0.03/0.26 0.03/0.26 ### Cost equations --> "Loop" of evalsipmabubblebb4in/4 0.03/0.26 * CEs [14] --> Loop 12 0.03/0.26 * CEs [12] --> Loop 13 0.03/0.26 * CEs [13] --> Loop 14 0.03/0.26 0.03/0.26 ### Ranking functions of CR evalsipmabubblebb4in(A,B,E,F) 0.03/0.26 * RF of phase [12]: [A-B] 0.03/0.26 0.03/0.26 #### Partial ranking functions of CR evalsipmabubblebb4in(A,B,E,F) 0.03/0.26 * Partial RF of phase [12]: 0.03/0.26 - RF of loop [12:1]: 0.03/0.26 A-B 0.03/0.26 0.03/0.26 0.03/0.26 ### Specialization of cost equations evalsipmabubblebb6in/5 0.03/0.26 * CE 5 is refined into CE [15] 0.03/0.26 * CE 3 is refined into CE [16,17] 0.03/0.26 * CE 6 is refined into CE [18] 0.03/0.26 * CE 4 is refined into CE [19,20] 0.03/0.26 0.03/0.26 0.03/0.26 ### Cost equations --> "Loop" of evalsipmabubblebb6in/5 0.03/0.26 * CEs [20] --> Loop 15 0.03/0.26 * CEs [19] --> Loop 16 0.03/0.26 * CEs [15] --> Loop 17 0.03/0.26 * CEs [17] --> Loop 18 0.03/0.26 * CEs [16] --> Loop 19 0.03/0.26 * CEs [18] --> Loop 20 0.03/0.26 0.03/0.26 ### Ranking functions of CR evalsipmabubblebb6in(A,B,E,F,G) 0.03/0.26 * RF of phase [15]: [A] 0.03/0.26 0.03/0.26 #### Partial ranking functions of CR evalsipmabubblebb6in(A,B,E,F,G) 0.03/0.26 * Partial RF of phase [15]: 0.03/0.26 - RF of loop [15:1]: 0.03/0.26 A 0.03/0.26 0.03/0.26 0.03/0.26 ### Specialization of cost equations evalsipmabubblebb6in_loop_cont/4 0.03/0.26 * CE 7 is refined into CE [21] 0.03/0.26 * CE 8 is refined into CE [22] 0.03/0.26 0.03/0.26 0.03/0.26 ### Cost equations --> "Loop" of evalsipmabubblebb6in_loop_cont/4 0.03/0.26 * CEs [21] --> Loop 21 0.03/0.26 * CEs [22] --> Loop 22 0.03/0.26 0.03/0.26 ### Ranking functions of CR evalsipmabubblebb6in_loop_cont(A,B,C,D) 0.03/0.26 0.03/0.26 #### Partial ranking functions of CR evalsipmabubblebb6in_loop_cont(A,B,C,D) 0.03/0.26 0.03/0.26 0.03/0.26 ### Specialization of cost equations evalsipmabubbleentryin/3 0.03/0.26 * CE 2 is refined into CE [23,24,25,26,27,28,29,30] 0.03/0.26 0.03/0.26 0.03/0.26 ### Cost equations --> "Loop" of evalsipmabubbleentryin/3 0.03/0.26 * CEs [28] --> Loop 23 0.03/0.26 * CEs [27,29] --> Loop 24 0.03/0.26 * CEs [26] --> Loop 25 0.03/0.26 * CEs [30] --> Loop 26 0.03/0.26 * CEs [23,24] --> Loop 27 0.03/0.26 * CEs [25] --> Loop 28 0.03/0.26 0.03/0.26 ### Ranking functions of CR evalsipmabubbleentryin(A,B,E) 0.03/0.26 0.03/0.26 #### Partial ranking functions of CR evalsipmabubbleentryin(A,B,E) 0.03/0.26 0.03/0.26 0.03/0.26 ### Specialization of cost equations evalsipmabubblestart/3 0.03/0.26 * CE 1 is refined into CE [31,32,33,34,35,36] 0.03/0.26 0.03/0.26 0.03/0.26 ### Cost equations --> "Loop" of evalsipmabubblestart/3 0.03/0.26 * CEs [36] --> Loop 29 0.03/0.26 * CEs [35] --> Loop 30 0.03/0.26 * CEs [34] --> Loop 31 0.03/0.26 * CEs [33] --> Loop 32 0.03/0.26 * CEs [32] --> Loop 33 0.03/0.26 * CEs [31] --> Loop 34 0.03/0.26 0.03/0.26 ### Ranking functions of CR evalsipmabubblestart(A,B,E) 0.03/0.26 0.03/0.26 #### Partial ranking functions of CR evalsipmabubblestart(A,B,E) 0.03/0.26 0.03/0.26 0.03/0.26 Computing Bounds 0.03/0.26 ===================================== 0.03/0.26 0.03/0.26 #### Cost of chains of evalsipmabubblebb4in(A,B,E,F): 0.03/0.26 * Chain [[12],14]: 1*it(12)+0 0.03/0.26 Such that:it(12) =< -B+F 0.03/0.26 0.03/0.26 with precondition: [E=2,A=F,B>=0,A>=B+1] 0.03/0.26 0.03/0.26 * Chain [[12],13]: 1*it(12)+0 0.03/0.26 Such that:it(12) =< A-B 0.03/0.26 0.03/0.26 with precondition: [E=3,B>=0,A>=B+1] 0.03/0.26 0.03/0.26 * Chain [14]: 0 0.03/0.26 with precondition: [E=2,B=A,B=F,B>=0] 0.03/0.26 0.03/0.26 * Chain [13]: 0 0.03/0.26 with precondition: [E=3,B>=0,A>=B] 0.03/0.26 0.03/0.26 0.03/0.26 #### Cost of chains of evalsipmabubblebb6in(A,B,E,F,G): 0.03/0.26 * Chain [[15],20]: 1*it(15)+1*s(3)+0 0.03/0.26 Such that:aux(3) =< A 0.03/0.26 it(15) =< aux(3) 0.03/0.26 s(3) =< it(15)*aux(3) 0.03/0.26 0.03/0.26 with precondition: [E=3,A>=1] 0.03/0.26 0.03/0.26 * Chain [[15],19]: 1*it(15)+1*s(3)+0 0.03/0.26 Such that:aux(4) =< A 0.03/0.26 it(15) =< aux(4) 0.03/0.26 s(3) =< it(15)*aux(4) 0.03/0.26 0.03/0.26 with precondition: [E=3,A>=1] 0.03/0.26 0.03/0.26 * Chain [[15],18]: 2*it(15)+1*s(3)+0 0.03/0.26 Such that:aux(5) =< A 0.03/0.26 it(15) =< aux(5) 0.03/0.26 s(3) =< it(15)*aux(5) 0.03/0.26 0.03/0.26 with precondition: [E=3,A>=2] 0.03/0.26 0.03/0.26 * Chain [[15],16,20]: 1*it(15)+1*s(3)+1 0.03/0.26 Such that:aux(6) =< A 0.03/0.26 it(15) =< aux(6) 0.03/0.26 s(3) =< it(15)*aux(6) 0.03/0.26 0.03/0.26 with precondition: [E=3,A>=1] 0.03/0.26 0.03/0.26 * Chain [[15],16,17]: 1*it(15)+1*s(3)+1 0.03/0.26 Such that:aux(7) =< A 0.03/0.26 it(15) =< aux(7) 0.03/0.26 s(3) =< it(15)*aux(7) 0.03/0.26 0.03/0.26 with precondition: [E=4,F+1=0,G=0,A>=1] 0.03/0.26 0.03/0.26 * Chain [20]: 0 0.03/0.26 with precondition: [E=3] 0.03/0.26 0.03/0.26 * Chain [19]: 0 0.03/0.26 with precondition: [E=3,A>=0] 0.03/0.26 0.03/0.26 * Chain [18]: 1*s(4)+0 0.03/0.26 Such that:s(4) =< A 0.03/0.26 0.03/0.26 with precondition: [E=3,A>=1] 0.03/0.26 0.03/0.26 * Chain [17]: 0 0.03/0.26 with precondition: [E=4,G=B,A=F,0>=A+1] 0.03/0.26 0.03/0.26 * Chain [16,20]: 1 0.03/0.26 with precondition: [A=0,E=3] 0.03/0.26 0.03/0.26 * Chain [16,17]: 1 0.03/0.26 with precondition: [A=0,E=4,F+1=0,G=0] 0.03/0.26 0.03/0.26 0.03/0.26 #### Cost of chains of evalsipmabubblebb6in_loop_cont(A,B,C,D): 0.03/0.26 * Chain [22]: 0 0.03/0.26 with precondition: [A=3] 0.03/0.26 0.03/0.26 * Chain [21]: 0 0.03/0.26 with precondition: [A=4] 0.03/0.26 0.03/0.26 0.03/0.26 #### Cost of chains of evalsipmabubbleentryin(A,B,E): 0.03/0.26 * Chain [28]: 0 0.03/0.26 with precondition: [] 0.03/0.26 0.03/0.26 * Chain [27]: 1 0.03/0.26 with precondition: [A=0] 0.03/0.26 0.03/0.26 * Chain [26]: 0 0.03/0.26 with precondition: [0>=A+1] 0.03/0.26 0.03/0.26 * Chain [25]: 0 0.03/0.26 with precondition: [A>=0] 0.03/0.26 0.03/0.26 * Chain [24]: 5*s(16)+4*s(17)+1 0.03/0.26 Such that:aux(9) =< A 0.03/0.26 s(16) =< aux(9) 0.03/0.26 s(17) =< s(16)*aux(9) 0.03/0.26 0.03/0.26 with precondition: [A>=1] 0.03/0.26 0.03/0.26 * Chain [23]: 2*s(22)+1*s(23)+0 0.03/0.26 Such that:s(21) =< A 0.03/0.26 s(22) =< s(21) 0.03/0.26 s(23) =< s(22)*s(21) 0.03/0.26 0.03/0.26 with precondition: [A>=2] 0.03/0.26 0.03/0.26 0.03/0.26 #### Cost of chains of evalsipmabubblestart(A,B,E): 0.03/0.26 * Chain [34]: 0 0.03/0.26 with precondition: [] 0.03/0.26 0.03/0.26 * Chain [33]: 1 0.03/0.26 with precondition: [A=0] 0.03/0.26 0.03/0.26 * Chain [32]: 0 0.03/0.26 with precondition: [0>=A+1] 0.03/0.26 0.03/0.26 * Chain [31]: 0 0.03/0.26 with precondition: [A>=0] 0.03/0.26 0.03/0.26 * Chain [30]: 5*s(25)+4*s(26)+1 0.03/0.26 Such that:s(24) =< A 0.03/0.26 s(25) =< s(24) 0.03/0.26 s(26) =< s(25)*s(24) 0.03/0.26 0.03/0.26 with precondition: [A>=1] 0.03/0.26 0.03/0.26 * Chain [29]: 2*s(28)+1*s(29)+0 0.03/0.26 Such that:s(27) =< A 0.03/0.26 s(28) =< s(27) 0.03/0.26 s(29) =< s(28)*s(27) 0.03/0.26 0.03/0.26 with precondition: [A>=2] 0.03/0.26 0.03/0.26 0.03/0.26 Closed-form bounds of evalsipmabubblestart(A,B,E): 0.03/0.26 ------------------------------------- 0.03/0.26 * Chain [34] with precondition: [] 0.03/0.26 - Upper bound: 0 0.03/0.26 - Complexity: constant 0.03/0.26 * Chain [33] with precondition: [A=0] 0.03/0.26 - Upper bound: 1 0.03/0.26 - Complexity: constant 0.03/0.26 * Chain [32] with precondition: [0>=A+1] 0.03/0.26 - Upper bound: 0 0.03/0.26 - Complexity: constant 0.03/0.26 * Chain [31] with precondition: [A>=0] 0.03/0.26 - Upper bound: 0 0.03/0.26 - Complexity: constant 0.03/0.26 * Chain [30] with precondition: [A>=1] 0.03/0.26 - Upper bound: 5*A+1+4*A*A 0.03/0.26 - Complexity: n^2 0.03/0.26 * Chain [29] with precondition: [A>=2] 0.03/0.26 - Upper bound: 2*A+A*A 0.03/0.26 - Complexity: n^2 0.03/0.26 0.03/0.26 ### Maximum cost of evalsipmabubblestart(A,B,E): max([1,nat(A)*3+1+nat(A)*3*nat(A)+(nat(A)*nat(A)+nat(A)*2)]) 0.03/0.26 Asymptotic class: n^2 0.03/0.26 * Total analysis performed in 198 ms. 0.03/0.26 0.03/0.37 EOF