0.03/0.28 WORST_CASE(?,O(n^2)) 0.03/0.28 0.03/0.28 Preprocessing Cost Relations 0.03/0.28 ===================================== 0.03/0.28 0.03/0.28 #### Computed strongly connected components 0.03/0.28 0. recursive : [evalfbb1in/3,evalfbb2in/3] 0.03/0.28 1. recursive : [evalfbb2in_loop_cont/7,evalfbb3in/6,evalfbb4in/6] 0.03/0.28 2. non_recursive : [evalfstop/4] 0.03/0.28 3. non_recursive : [evalfreturnin/4] 0.03/0.28 4. non_recursive : [exit_location/1] 0.03/0.28 5. non_recursive : [evalfbb4in_loop_cont/5] 0.03/0.28 6. non_recursive : [evalfentryin/4] 0.03/0.28 7. non_recursive : [evalfstart/4] 0.03/0.28 0.03/0.28 #### Obtained direct recursion through partial evaluation 0.03/0.28 0. SCC is partially evaluated into evalfbb2in/3 0.03/0.28 1. SCC is partially evaluated into evalfbb4in/6 0.03/0.28 2. SCC is completely evaluated into other SCCs 0.03/0.28 3. SCC is completely evaluated into other SCCs 0.03/0.28 4. SCC is completely evaluated into other SCCs 0.03/0.28 5. SCC is partially evaluated into evalfbb4in_loop_cont/5 0.03/0.28 6. SCC is partially evaluated into evalfentryin/4 0.03/0.28 7. SCC is partially evaluated into evalfstart/4 0.03/0.28 0.03/0.28 Control-Flow Refinement of Cost Relations 0.03/0.28 ===================================== 0.03/0.28 0.03/0.28 ### Specialization of cost equations evalfbb2in/3 0.03/0.28 * CE 11 is refined into CE [12] 0.03/0.28 * CE 10 is refined into CE [13] 0.03/0.28 * CE 9 is refined into CE [14] 0.03/0.28 0.03/0.28 0.03/0.28 ### Cost equations --> "Loop" of evalfbb2in/3 0.03/0.28 * CEs [14] --> Loop 12 0.03/0.28 * CEs [12] --> Loop 13 0.03/0.28 * CEs [13] --> Loop 14 0.03/0.28 0.03/0.28 ### Ranking functions of CR evalfbb2in(C,D,E) 0.03/0.28 * RF of phase [12]: [C] 0.03/0.28 0.03/0.28 #### Partial ranking functions of CR evalfbb2in(C,D,E) 0.03/0.28 * Partial RF of phase [12]: 0.03/0.28 - RF of loop [12:1]: 0.03/0.28 C 0.03/0.28 0.03/0.28 0.03/0.28 ### Specialization of cost equations evalfbb4in/6 0.03/0.28 * CE 5 is refined into CE [15] 0.03/0.28 * CE 3 is refined into CE [16,17] 0.03/0.28 * CE 6 is refined into CE [18] 0.03/0.28 * CE 4 is refined into CE [19,20] 0.03/0.28 0.03/0.28 0.03/0.28 ### Cost equations --> "Loop" of evalfbb4in/6 0.03/0.28 * CEs [20] --> Loop 15 0.03/0.28 * CEs [19] --> Loop 16 0.03/0.28 * CEs [15] --> Loop 17 0.03/0.28 * CEs [16] --> Loop 18 0.03/0.28 * CEs [17] --> Loop 19 0.03/0.28 * CEs [18] --> Loop 20 0.03/0.28 0.03/0.28 ### Ranking functions of CR evalfbb4in(A,B,C,D,E,F) 0.03/0.28 * RF of phase [15]: [B] 0.03/0.28 * RF of phase [16]: [B] 0.03/0.28 0.03/0.28 #### Partial ranking functions of CR evalfbb4in(A,B,C,D,E,F) 0.03/0.28 * Partial RF of phase [15]: 0.03/0.28 - RF of loop [15:1]: 0.03/0.28 B 0.03/0.28 * Partial RF of phase [16]: 0.03/0.28 - RF of loop [16:1]: 0.03/0.28 B 0.03/0.28 0.03/0.28 0.03/0.28 ### Specialization of cost equations evalfbb4in_loop_cont/5 0.03/0.28 * CE 7 is refined into CE [21] 0.03/0.28 * CE 8 is refined into CE [22] 0.03/0.28 0.03/0.28 0.03/0.28 ### Cost equations --> "Loop" of evalfbb4in_loop_cont/5 0.03/0.28 * CEs [21] --> Loop 21 0.03/0.28 * CEs [22] --> Loop 22 0.03/0.29 0.03/0.29 ### Ranking functions of CR evalfbb4in_loop_cont(A,B,C,D,E) 0.03/0.29 0.03/0.29 #### Partial ranking functions of CR evalfbb4in_loop_cont(A,B,C,D,E) 0.03/0.29 0.03/0.29 0.03/0.29 ### Specialization of cost equations evalfentryin/4 0.03/0.29 * CE 2 is refined into CE [23,24,25,26,27,28,29,30,31] 0.03/0.29 0.03/0.29 0.03/0.29 ### Cost equations --> "Loop" of evalfentryin/4 0.03/0.29 * CEs [27] --> Loop 23 0.03/0.29 * CEs [26,29] --> Loop 24 0.03/0.29 * CEs [28] --> Loop 25 0.03/0.29 * CEs [25] --> Loop 26 0.03/0.29 * CEs [24,30] --> Loop 27 0.03/0.29 * CEs [31] --> Loop 28 0.03/0.29 * CEs [23] --> Loop 29 0.03/0.29 0.03/0.29 ### Ranking functions of CR evalfentryin(A,B,C,D) 0.03/0.29 0.03/0.29 #### Partial ranking functions of CR evalfentryin(A,B,C,D) 0.03/0.29 0.03/0.29 0.03/0.29 ### Specialization of cost equations evalfstart/4 0.03/0.29 * CE 1 is refined into CE [32,33,34,35,36,37,38] 0.03/0.29 0.03/0.29 0.03/0.29 ### Cost equations --> "Loop" of evalfstart/4 0.03/0.29 * CEs [38] --> Loop 30 0.03/0.29 * CEs [37] --> Loop 31 0.03/0.29 * CEs [36] --> Loop 32 0.03/0.29 * CEs [35] --> Loop 33 0.03/0.29 * CEs [34] --> Loop 34 0.03/0.29 * CEs [33] --> Loop 35 0.03/0.29 * CEs [32] --> Loop 36 0.03/0.29 0.03/0.29 ### Ranking functions of CR evalfstart(A,B,C,D) 0.03/0.29 0.03/0.29 #### Partial ranking functions of CR evalfstart(A,B,C,D) 0.03/0.29 0.03/0.29 0.03/0.29 Computing Bounds 0.03/0.29 ===================================== 0.03/0.29 0.03/0.29 #### Cost of chains of evalfbb2in(C,D,E): 0.03/0.29 * Chain [[12],14]: 1*it(12)+0 0.03/0.29 Such that:it(12) =< C 0.03/0.29 0.03/0.29 with precondition: [D=2,E=0,C>=1] 0.03/0.29 0.03/0.29 * Chain [[12],13]: 1*it(12)+0 0.03/0.29 Such that:it(12) =< C 0.03/0.29 0.03/0.29 with precondition: [D=3,C>=1] 0.03/0.29 0.03/0.29 * Chain [14]: 0 0.03/0.29 with precondition: [D=2,C=E,0>=C] 0.03/0.29 0.03/0.29 * Chain [13]: 0 0.03/0.29 with precondition: [D=3] 0.03/0.29 0.03/0.29 0.03/0.29 #### Cost of chains of evalfbb4in(A,B,C,D,E,F): 0.03/0.29 * Chain [[16],20]: 1*it(16)+1*s(3)+0 0.03/0.29 Such that:aux(1) =< A 0.03/0.29 it(16) =< B 0.03/0.29 s(3) =< it(16)*aux(1) 0.03/0.29 0.03/0.29 with precondition: [D=3,A>=1,B>=1] 0.03/0.29 0.03/0.29 * Chain [[16],19]: 1*it(16)+1*s(3)+1*s(4)+0 0.03/0.29 Such that:it(16) =< B 0.03/0.29 aux(2) =< A 0.03/0.29 s(4) =< aux(2) 0.03/0.29 s(3) =< it(16)*aux(2) 0.03/0.29 0.03/0.29 with precondition: [D=3,A>=1,B>=2] 0.03/0.29 0.03/0.29 * Chain [[16],18]: 1*it(16)+1*s(3)+0 0.03/0.29 Such that:aux(1) =< A 0.03/0.29 it(16) =< B 0.03/0.29 s(3) =< it(16)*aux(1) 0.03/0.29 0.03/0.29 with precondition: [D=3,A>=1,B>=2] 0.03/0.29 0.03/0.29 * Chain [[16],17]: 1*it(16)+1*s(3)+0 0.03/0.29 Such that:aux(1) =< A 0.03/0.29 it(16) =< B 0.03/0.29 s(3) =< it(16)*aux(1) 0.03/0.29 0.03/0.29 with precondition: [D=4,E=0,F=0,A>=1,B>=1] 0.03/0.29 0.03/0.29 * Chain [[15],20]: 1*it(15)+0 0.03/0.29 Such that:it(15) =< B 0.03/0.29 0.03/0.29 with precondition: [D=3,0>=A,B>=1] 0.03/0.29 0.03/0.29 * Chain [[15],18]: 1*it(15)+0 0.03/0.29 Such that:it(15) =< B 0.03/0.29 0.03/0.29 with precondition: [D=3,0>=A,B>=2] 0.03/0.29 0.03/0.29 * Chain [[15],17]: 1*it(15)+0 0.03/0.29 Such that:it(15) =< B 0.03/0.29 0.03/0.29 with precondition: [D=4,E=0,A=F,0>=A,B>=1] 0.03/0.29 0.03/0.29 * Chain [20]: 0 0.03/0.29 with precondition: [D=3] 0.03/0.29 0.03/0.29 * Chain [19]: 1*s(4)+0 0.03/0.29 Such that:s(4) =< A 0.03/0.29 0.03/0.29 with precondition: [D=3,A>=1,B>=1] 0.03/0.29 0.03/0.29 * Chain [18]: 0 0.03/0.29 with precondition: [D=3,B>=1] 0.03/0.29 0.03/0.29 * Chain [17]: 0 0.03/0.29 with precondition: [D=4,F=C,B=E,0>=B] 0.03/0.29 0.03/0.29 0.03/0.29 #### Cost of chains of evalfbb4in_loop_cont(A,B,C,D,E): 0.03/0.29 * Chain [22]: 0 0.03/0.29 with precondition: [A=3] 0.03/0.29 0.03/0.29 * Chain [21]: 0 0.03/0.29 with precondition: [A=4] 0.03/0.29 0.03/0.29 0.03/0.29 #### Cost of chains of evalfentryin(A,B,C,D): 0.03/0.29 * Chain [29]: 0 0.03/0.29 with precondition: [] 0.03/0.29 0.03/0.29 * Chain [28]: 0 0.03/0.29 with precondition: [0>=A] 0.03/0.29 0.03/0.29 * Chain [27]: 2*s(16)+0 0.03/0.29 Such that:aux(6) =< A 0.03/0.29 s(16) =< aux(6) 0.03/0.29 0.03/0.29 with precondition: [0>=B,A>=1] 0.03/0.29 0.03/0.29 * Chain [26]: 1*s(18)+0 0.03/0.29 Such that:s(18) =< A 0.03/0.29 0.03/0.29 with precondition: [0>=B,A>=2] 0.03/0.29 0.03/0.29 * Chain [25]: 0 0.03/0.29 with precondition: [A>=1] 0.03/0.29 0.03/0.29 * Chain [24]: 2*s(19)+1*s(21)+2*s(22)+0 0.03/0.29 Such that:aux(7) =< A 0.03/0.29 aux(8) =< B 0.03/0.29 s(19) =< aux(7) 0.03/0.29 s(21) =< aux(8) 0.03/0.29 s(22) =< s(19)*aux(8) 0.03/0.29 0.03/0.29 with precondition: [A>=1,B>=1] 0.03/0.29 0.03/0.29 * Chain [23]: 2*s(28)+2*s(29)+1*s(30)+0 0.03/0.29 Such that:s(27) =< A 0.03/0.29 s(26) =< B 0.03/0.29 s(28) =< s(27) 0.03/0.29 s(29) =< s(28)*s(26) 0.03/0.29 s(30) =< s(26) 0.03/0.29 0.03/0.29 with precondition: [A>=2,B>=1] 0.03/0.29 0.03/0.29 0.03/0.29 #### Cost of chains of evalfstart(A,B,C,D): 0.03/0.29 * Chain [36]: 0 0.03/0.29 with precondition: [] 0.03/0.29 0.03/0.29 * Chain [35]: 0 0.03/0.29 with precondition: [0>=A] 0.03/0.29 0.03/0.29 * Chain [34]: 2*s(32)+0 0.03/0.29 Such that:s(31) =< A 0.03/0.29 s(32) =< s(31) 0.03/0.29 0.03/0.29 with precondition: [0>=B,A>=1] 0.03/0.29 0.03/0.29 * Chain [33]: 1*s(33)+0 0.03/0.29 Such that:s(33) =< A 0.03/0.29 0.03/0.29 with precondition: [0>=B,A>=2] 0.03/0.29 0.03/0.29 * Chain [32]: 0 0.03/0.29 with precondition: [A>=1] 0.03/0.29 0.03/0.29 * Chain [31]: 2*s(36)+1*s(37)+2*s(38)+0 0.03/0.29 Such that:s(34) =< A 0.03/0.29 s(35) =< B 0.03/0.29 s(36) =< s(34) 0.03/0.29 s(37) =< s(35) 0.03/0.29 s(38) =< s(36)*s(35) 0.03/0.29 0.03/0.29 with precondition: [A>=1,B>=1] 0.03/0.29 0.03/0.29 * Chain [30]: 2*s(41)+2*s(42)+1*s(43)+0 0.03/0.29 Such that:s(39) =< A 0.03/0.29 s(40) =< B 0.03/0.29 s(41) =< s(39) 0.03/0.29 s(42) =< s(41)*s(40) 0.03/0.29 s(43) =< s(40) 0.03/0.29 0.03/0.29 with precondition: [A>=2,B>=1] 0.03/0.29 0.03/0.29 0.03/0.29 Closed-form bounds of evalfstart(A,B,C,D): 0.03/0.29 ------------------------------------- 0.03/0.29 * Chain [36] with precondition: [] 0.03/0.29 - Upper bound: 0 0.03/0.29 - Complexity: constant 0.03/0.29 * Chain [35] with precondition: [0>=A] 0.03/0.29 - Upper bound: 0 0.03/0.29 - Complexity: constant 0.03/0.29 * Chain [34] with precondition: [0>=B,A>=1] 0.03/0.29 - Upper bound: 2*A 0.03/0.29 - Complexity: n 0.03/0.29 * Chain [33] with precondition: [0>=B,A>=2] 0.03/0.29 - Upper bound: A 0.03/0.29 - Complexity: n 0.03/0.29 * Chain [32] with precondition: [A>=1] 0.03/0.29 - Upper bound: 0 0.03/0.29 - Complexity: constant 0.03/0.29 * Chain [31] with precondition: [A>=1,B>=1] 0.03/0.29 - Upper bound: 2*A*B+2*A+B 0.03/0.29 - Complexity: n^2 0.03/0.29 * Chain [30] with precondition: [A>=2,B>=1] 0.03/0.29 - Upper bound: 2*A*B+2*A+B 0.03/0.29 - Complexity: n^2 0.03/0.29 0.03/0.29 ### Maximum cost of evalfstart(A,B,C,D): nat(A)*2*nat(B)+nat(B)+nat(A)+nat(A) 0.03/0.29 Asymptotic class: n^2 0.03/0.29 * Total analysis performed in 219 ms. 0.03/0.29 0.03/0.39 EOF