0.04/0.25 WORST_CASE(?,O(n^2)) 0.04/0.25 0.04/0.25 Preprocessing Cost Relations 0.04/0.25 ===================================== 0.04/0.25 0.04/0.25 #### Computed strongly connected components 0.04/0.25 0. recursive : [evalfbb1in/4,evalfbb2in/4] 0.04/0.25 1. recursive : [evalfbb2in_loop_cont/7,evalfbb3in/6,evalfbb4in/6] 0.04/0.25 2. non_recursive : [evalfstop/4] 0.04/0.25 3. non_recursive : [evalfreturnin/4] 0.04/0.25 4. non_recursive : [exit_location/1] 0.04/0.25 5. non_recursive : [evalfbb4in_loop_cont/5] 0.04/0.25 6. non_recursive : [evalfentryin/4] 0.04/0.25 7. non_recursive : [evalfstart/4] 0.04/0.25 0.04/0.25 #### Obtained direct recursion through partial evaluation 0.04/0.25 0. SCC is partially evaluated into evalfbb2in/4 0.04/0.25 1. SCC is partially evaluated into evalfbb4in/6 0.04/0.25 2. SCC is completely evaluated into other SCCs 0.04/0.25 3. SCC is completely evaluated into other SCCs 0.04/0.25 4. SCC is completely evaluated into other SCCs 0.04/0.25 5. SCC is partially evaluated into evalfbb4in_loop_cont/5 0.04/0.25 6. SCC is partially evaluated into evalfentryin/4 0.04/0.25 7. SCC is partially evaluated into evalfstart/4 0.04/0.25 0.04/0.25 Control-Flow Refinement of Cost Relations 0.04/0.25 ===================================== 0.04/0.25 0.04/0.25 ### Specialization of cost equations evalfbb2in/4 0.04/0.25 * CE 11 is refined into CE [12] 0.04/0.25 * CE 10 is refined into CE [13] 0.04/0.25 * CE 9 is refined into CE [14] 0.04/0.25 0.04/0.25 0.04/0.25 ### Cost equations --> "Loop" of evalfbb2in/4 0.04/0.25 * CEs [14] --> Loop 12 0.04/0.25 * CEs [12] --> Loop 13 0.04/0.25 * CEs [13] --> Loop 14 0.04/0.25 0.04/0.25 ### Ranking functions of CR evalfbb2in(A,C,D,E) 0.04/0.25 * RF of phase [12]: [A-C+1] 0.04/0.25 0.04/0.25 #### Partial ranking functions of CR evalfbb2in(A,C,D,E) 0.04/0.25 * Partial RF of phase [12]: 0.04/0.25 - RF of loop [12:1]: 0.04/0.25 A-C+1 0.04/0.25 0.04/0.25 0.04/0.25 ### Specialization of cost equations evalfbb4in/6 0.04/0.25 * CE 5 is refined into CE [15] 0.04/0.25 * CE 3 is refined into CE [16,17] 0.04/0.25 * CE 6 is refined into CE [18] 0.04/0.25 * CE 4 is refined into CE [19] 0.04/0.25 0.04/0.25 0.04/0.25 ### Cost equations --> "Loop" of evalfbb4in/6 0.04/0.25 * CEs [19] --> Loop 15 0.04/0.25 * CEs [15] --> Loop 16 0.04/0.25 * CEs [16,17] --> Loop 17 0.04/0.25 * CEs [18] --> Loop 18 0.04/0.25 0.04/0.25 ### Ranking functions of CR evalfbb4in(A,B,C,D,E,F) 0.04/0.25 * RF of phase [15]: [-A+B] 0.04/0.25 0.04/0.25 #### Partial ranking functions of CR evalfbb4in(A,B,C,D,E,F) 0.04/0.25 * Partial RF of phase [15]: 0.04/0.25 - RF of loop [15:1]: 0.04/0.25 -A+B 0.04/0.25 0.04/0.25 0.04/0.25 ### Specialization of cost equations evalfbb4in_loop_cont/5 0.04/0.25 * CE 7 is refined into CE [20] 0.04/0.25 * CE 8 is refined into CE [21] 0.04/0.25 0.04/0.25 0.04/0.25 ### Cost equations --> "Loop" of evalfbb4in_loop_cont/5 0.04/0.25 * CEs [20] --> Loop 19 0.04/0.25 * CEs [21] --> Loop 20 0.04/0.25 0.04/0.25 ### Ranking functions of CR evalfbb4in_loop_cont(A,B,C,D,E) 0.04/0.25 0.04/0.25 #### Partial ranking functions of CR evalfbb4in_loop_cont(A,B,C,D,E) 0.04/0.25 0.04/0.25 0.04/0.25 ### Specialization of cost equations evalfentryin/4 0.04/0.25 * CE 2 is refined into CE [22,23,24,25,26] 0.04/0.25 0.04/0.25 0.04/0.25 ### Cost equations --> "Loop" of evalfentryin/4 0.04/0.25 * CEs [24] --> Loop 21 0.04/0.25 * CEs [23,26] --> Loop 22 0.04/0.25 * CEs [25] --> Loop 23 0.04/0.25 * CEs [22] --> Loop 24 0.04/0.25 0.04/0.25 ### Ranking functions of CR evalfentryin(A,B,C,D) 0.04/0.25 0.04/0.25 #### Partial ranking functions of CR evalfentryin(A,B,C,D) 0.04/0.25 0.04/0.25 0.04/0.25 ### Specialization of cost equations evalfstart/4 0.04/0.25 * CE 1 is refined into CE [27,28,29,30] 0.04/0.25 0.04/0.25 0.04/0.25 ### Cost equations --> "Loop" of evalfstart/4 0.04/0.25 * CEs [30] --> Loop 25 0.04/0.25 * CEs [29] --> Loop 26 0.04/0.25 * CEs [28] --> Loop 27 0.04/0.25 * CEs [27] --> Loop 28 0.04/0.25 0.04/0.25 ### Ranking functions of CR evalfstart(A,B,C,D) 0.04/0.25 0.04/0.25 #### Partial ranking functions of CR evalfstart(A,B,C,D) 0.04/0.25 0.04/0.25 0.04/0.25 Computing Bounds 0.04/0.25 ===================================== 0.04/0.25 0.04/0.25 #### Cost of chains of evalfbb2in(A,C,D,E): 0.04/0.25 * Chain [[12],14]: 1*it(12)+0 0.04/0.25 Such that:it(12) =< -C+E 0.04/0.25 0.04/0.25 with precondition: [D=2,A+1=E,C>=0,A>=C] 0.04/0.25 0.04/0.25 * Chain [[12],13]: 1*it(12)+0 0.04/0.25 Such that:it(12) =< A-C+1 0.04/0.25 0.04/0.25 with precondition: [D=3,C>=0,A>=C] 0.04/0.25 0.04/0.25 * Chain [13]: 0 0.04/0.25 with precondition: [D=3,A>=0,C>=0] 0.04/0.25 0.04/0.25 0.04/0.25 #### Cost of chains of evalfbb4in(A,B,C,D,E,F): 0.04/0.25 * Chain [[15],18]: 1*it(15)+1*s(3)+0 0.04/0.25 Such that:it(15) =< -A+B 0.04/0.25 aux(1) =< B 0.04/0.25 s(3) =< it(15)*aux(1) 0.04/0.25 0.04/0.25 with precondition: [D=3,A>=0,B>=A+1] 0.04/0.25 0.04/0.25 * Chain [[15],17]: 1*it(15)+1*s(3)+1*s(4)+0 0.04/0.25 Such that:it(15) =< -A+B 0.04/0.25 aux(2) =< B 0.04/0.25 s(4) =< aux(2) 0.04/0.25 s(3) =< it(15)*aux(2) 0.04/0.25 0.04/0.25 with precondition: [D=3,A>=0,B>=A+2] 0.04/0.25 0.04/0.25 * Chain [[15],16]: 1*it(15)+1*s(3)+0 0.04/0.25 Such that:it(15) =< -A+E 0.04/0.25 aux(1) =< E 0.04/0.25 s(3) =< it(15)*aux(1) 0.04/0.25 0.04/0.25 with precondition: [D=4,B=E,B=F,A>=0,B>=A+1] 0.04/0.25 0.04/0.25 * Chain [18]: 0 0.04/0.25 with precondition: [D=3,A>=0] 0.04/0.25 0.04/0.25 * Chain [17]: 1*s(4)+0 0.04/0.25 Such that:s(4) =< A+1 0.04/0.25 0.04/0.25 with precondition: [D=3,A>=0,B>=A+1] 0.04/0.25 0.04/0.25 * Chain [16]: 0 0.04/0.25 with precondition: [D=4,F=C,A=E,A>=0,A>=B] 0.04/0.25 0.04/0.25 0.04/0.25 #### Cost of chains of evalfbb4in_loop_cont(A,B,C,D,E): 0.04/0.25 * Chain [20]: 0 0.04/0.25 with precondition: [A=3] 0.04/0.25 0.04/0.25 * Chain [19]: 0 0.04/0.25 with precondition: [A=4] 0.04/0.25 0.04/0.25 0.04/0.25 #### Cost of chains of evalfentryin(A,B,C,D): 0.04/0.25 * Chain [24]: 0 0.04/0.25 with precondition: [] 0.04/0.25 0.04/0.25 * Chain [23]: 0 0.04/0.25 with precondition: [0>=B] 0.04/0.25 0.04/0.25 * Chain [22]: 2*s(9)+1*s(10)+2*s(12)+0 0.04/0.25 Such that:s(10) =< 1 0.04/0.25 aux(5) =< B 0.04/0.25 s(9) =< aux(5) 0.04/0.25 s(12) =< s(9)*aux(5) 0.04/0.25 0.04/0.25 with precondition: [B>=1] 0.04/0.25 0.04/0.25 * Chain [21]: 2*s(16)+1*s(19)+0 0.04/0.25 Such that:aux(6) =< B 0.04/0.25 s(16) =< aux(6) 0.04/0.25 s(19) =< s(16)*aux(6) 0.04/0.25 0.04/0.25 with precondition: [B>=2] 0.04/0.25 0.04/0.25 0.04/0.25 #### Cost of chains of evalfstart(A,B,C,D): 0.04/0.25 * Chain [28]: 0 0.04/0.25 with precondition: [] 0.04/0.25 0.04/0.25 * Chain [27]: 0 0.04/0.25 with precondition: [0>=B] 0.04/0.25 0.04/0.25 * Chain [26]: 1*s(20)+2*s(22)+2*s(23)+0 0.04/0.25 Such that:s(20) =< 1 0.04/0.25 s(21) =< B 0.04/0.25 s(22) =< s(21) 0.04/0.25 s(23) =< s(22)*s(21) 0.04/0.25 0.04/0.25 with precondition: [B>=1] 0.04/0.25 0.04/0.25 * Chain [25]: 2*s(25)+1*s(26)+0 0.04/0.25 Such that:s(24) =< B 0.04/0.25 s(25) =< s(24) 0.04/0.25 s(26) =< s(25)*s(24) 0.04/0.25 0.04/0.25 with precondition: [B>=2] 0.04/0.25 0.04/0.25 0.04/0.25 Closed-form bounds of evalfstart(A,B,C,D): 0.04/0.25 ------------------------------------- 0.04/0.25 * Chain [28] with precondition: [] 0.04/0.25 - Upper bound: 0 0.04/0.25 - Complexity: constant 0.04/0.25 * Chain [27] with precondition: [0>=B] 0.04/0.25 - Upper bound: 0 0.04/0.25 - Complexity: constant 0.04/0.25 * Chain [26] with precondition: [B>=1] 0.04/0.25 - Upper bound: 2*B+1+2*B*B 0.04/0.25 - Complexity: n^2 0.04/0.25 * Chain [25] with precondition: [B>=2] 0.04/0.25 - Upper bound: 2*B+B*B 0.04/0.25 - Complexity: n^2 0.04/0.25 0.04/0.25 ### Maximum cost of evalfstart(A,B,C,D): nat(B)*nat(B)+nat(B)*2+(nat(B)*nat(B)+1) 0.04/0.25 Asymptotic class: n^2 0.04/0.25 * Total analysis performed in 183 ms. 0.04/0.25 0.04/0.35 EOF