0.04/0.36 WORST_CASE(?,O(n^2)) 0.04/0.36 0.04/0.36 Preprocessing Cost Relations 0.04/0.36 ===================================== 0.04/0.36 0.04/0.36 #### Computed strongly connected components 0.04/0.36 0. recursive : [evalfbb1in/4,evalfbb2in/4] 0.04/0.36 1. recursive : [evalfbb2in_loop_cont/8,evalfbb3in/7,evalfbb4in/7] 0.04/0.36 2. non_recursive : [evalfstop/5] 0.04/0.36 3. non_recursive : [evalfreturnin/5] 0.04/0.36 4. non_recursive : [exit_location/1] 0.04/0.36 5. non_recursive : [evalfbb4in_loop_cont/6] 0.04/0.36 6. non_recursive : [evalfentryin/5] 0.04/0.36 7. non_recursive : [evalfstart/5] 0.04/0.36 0.04/0.36 #### Obtained direct recursion through partial evaluation 0.04/0.36 0. SCC is partially evaluated into evalfbb2in/4 0.04/0.36 1. SCC is partially evaluated into evalfbb4in/7 0.04/0.36 2. SCC is completely evaluated into other SCCs 0.04/0.36 3. SCC is completely evaluated into other SCCs 0.04/0.36 4. SCC is completely evaluated into other SCCs 0.04/0.36 5. SCC is partially evaluated into evalfbb4in_loop_cont/6 0.04/0.36 6. SCC is partially evaluated into evalfentryin/5 0.04/0.36 7. SCC is partially evaluated into evalfstart/5 0.04/0.36 0.04/0.36 Control-Flow Refinement of Cost Relations 0.04/0.36 ===================================== 0.04/0.36 0.04/0.36 ### Specialization of cost equations evalfbb2in/4 0.04/0.36 * CE 11 is refined into CE [12] 0.04/0.36 * CE 10 is refined into CE [13] 0.04/0.36 * CE 9 is refined into CE [14] 0.04/0.36 0.04/0.36 0.04/0.36 ### Cost equations --> "Loop" of evalfbb2in/4 0.04/0.36 * CEs [14] --> Loop 12 0.04/0.36 * CEs [12] --> Loop 13 0.04/0.36 * CEs [13] --> Loop 14 0.04/0.36 0.04/0.36 ### Ranking functions of CR evalfbb2in(C,D,E,F) 0.04/0.36 * RF of phase [12]: [-C+D+1] 0.04/0.36 0.04/0.36 #### Partial ranking functions of CR evalfbb2in(C,D,E,F) 0.04/0.36 * Partial RF of phase [12]: 0.04/0.36 - RF of loop [12:1]: 0.04/0.36 -C+D+1 0.04/0.36 0.04/0.36 0.04/0.36 ### Specialization of cost equations evalfbb4in/7 0.04/0.36 * CE 5 is refined into CE [15] 0.04/0.36 * CE 3 is refined into CE [16,17] 0.04/0.36 * CE 6 is refined into CE [18] 0.04/0.36 * CE 4 is refined into CE [19,20] 0.04/0.36 0.04/0.36 0.04/0.36 ### Cost equations --> "Loop" of evalfbb4in/7 0.04/0.36 * CEs [20] --> Loop 15 0.04/0.36 * CEs [19] --> Loop 16 0.04/0.36 * CEs [15] --> Loop 17 0.04/0.36 * CEs [16] --> Loop 18 0.04/0.36 * CEs [17] --> Loop 19 0.04/0.36 * CEs [18] --> Loop 20 0.04/0.36 0.04/0.36 ### Ranking functions of CR evalfbb4in(A,B,C,D,E,F,G) 0.04/0.36 * RF of phase [15]: [-A+B+1] 0.04/0.36 * RF of phase [16]: [-A+B+1] 0.04/0.36 0.04/0.36 #### Partial ranking functions of CR evalfbb4in(A,B,C,D,E,F,G) 0.04/0.36 * Partial RF of phase [15]: 0.04/0.36 - RF of loop [15:1]: 0.04/0.36 -A+B+1 0.04/0.36 * Partial RF of phase [16]: 0.04/0.36 - RF of loop [16:1]: 0.04/0.36 -A+B+1 0.04/0.36 0.04/0.36 0.04/0.36 ### Specialization of cost equations evalfbb4in_loop_cont/6 0.04/0.36 * CE 7 is refined into CE [21] 0.04/0.36 * CE 8 is refined into CE [22] 0.04/0.36 0.04/0.36 0.04/0.36 ### Cost equations --> "Loop" of evalfbb4in_loop_cont/6 0.04/0.36 * CEs [21] --> Loop 21 0.04/0.36 * CEs [22] --> Loop 22 0.04/0.36 0.04/0.36 ### Ranking functions of CR evalfbb4in_loop_cont(A,B,C,D,E,F) 0.04/0.36 0.04/0.36 #### Partial ranking functions of CR evalfbb4in_loop_cont(A,B,C,D,E,F) 0.04/0.36 0.04/0.36 0.04/0.36 ### Specialization of cost equations evalfentryin/5 0.04/0.36 * CE 2 is refined into CE [23,24,25,26,27,28,29,30,31] 0.04/0.36 0.04/0.36 0.04/0.36 ### Cost equations --> "Loop" of evalfentryin/5 0.04/0.36 * CEs [27] --> Loop 23 0.04/0.36 * CEs [26,31] --> Loop 24 0.04/0.36 * CEs [28] --> Loop 25 0.04/0.36 * CEs [24] --> Loop 26 0.04/0.36 * CEs [23,29] --> Loop 27 0.04/0.36 * CEs [30] --> Loop 28 0.04/0.36 * CEs [25] --> Loop 29 0.04/0.36 0.04/0.36 ### Ranking functions of CR evalfentryin(A,B,C,D,E) 0.04/0.36 0.04/0.36 #### Partial ranking functions of CR evalfentryin(A,B,C,D,E) 0.04/0.36 0.04/0.36 0.04/0.36 ### Specialization of cost equations evalfstart/5 0.04/0.36 * CE 1 is refined into CE [32,33,34,35,36,37,38] 0.04/0.36 0.04/0.36 0.04/0.36 ### Cost equations --> "Loop" of evalfstart/5 0.04/0.36 * CEs [38] --> Loop 30 0.04/0.36 * CEs [37] --> Loop 31 0.04/0.36 * CEs [36] --> Loop 32 0.04/0.36 * CEs [35] --> Loop 33 0.04/0.36 * CEs [34] --> Loop 34 0.04/0.36 * CEs [33] --> Loop 35 0.04/0.36 * CEs [32] --> Loop 36 0.04/0.36 0.04/0.36 ### Ranking functions of CR evalfstart(A,B,C,D,E) 0.04/0.36 0.04/0.36 #### Partial ranking functions of CR evalfstart(A,B,C,D,E) 0.04/0.36 0.04/0.36 0.04/0.36 Computing Bounds 0.04/0.36 ===================================== 0.04/0.36 0.04/0.36 #### Cost of chains of evalfbb2in(C,D,E,F): 0.04/0.36 * Chain [[12],14]: 1*it(12)+0 0.04/0.36 Such that:it(12) =< -C+F 0.04/0.36 0.04/0.36 with precondition: [E=2,D+1=F,C>=1,D>=C] 0.04/0.36 0.04/0.36 * Chain [[12],13]: 1*it(12)+0 0.04/0.36 Such that:it(12) =< -C+D+1 0.04/0.36 0.04/0.36 with precondition: [E=3,C>=1,D>=C] 0.04/0.36 0.04/0.36 * Chain [14]: 0 0.04/0.36 with precondition: [E=2,C=F,C>=1,C>=D+1] 0.04/0.36 0.04/0.36 * Chain [13]: 0 0.04/0.36 with precondition: [E=3,C>=1] 0.04/0.36 0.04/0.36 0.04/0.36 #### Cost of chains of evalfbb4in(A,B,C,D,E,F,G): 0.04/0.36 * Chain [[16],20]: 1*it(16)+0 0.04/0.36 Such that:it(16) =< -A+B+1 0.04/0.36 0.04/0.36 with precondition: [E=3,0>=D,A>=1,B>=A] 0.04/0.36 0.04/0.36 * Chain [[16],18]: 1*it(16)+0 0.04/0.36 Such that:it(16) =< -A+B 0.04/0.36 0.04/0.36 with precondition: [E=3,0>=D,A>=1,B>=A+1] 0.04/0.36 0.04/0.36 * Chain [[16],17]: 1*it(16)+0 0.04/0.36 Such that:it(16) =< -A+F 0.04/0.36 0.04/0.36 with precondition: [E=4,G=1,B+1=F,0>=D,A>=1,B>=A] 0.04/0.36 0.04/0.36 * Chain [[15],20]: 1*it(15)+1*s(3)+0 0.04/0.36 Such that:it(15) =< -A+B+1 0.04/0.36 aux(1) =< D+1 0.04/0.36 s(3) =< it(15)*aux(1) 0.04/0.36 0.04/0.36 with precondition: [E=3,A>=1,D>=1,B>=A] 0.04/0.36 0.04/0.36 * Chain [[15],19]: 1*it(15)+1*s(3)+1*s(4)+0 0.04/0.36 Such that:it(15) =< -A+B 0.04/0.36 s(4) =< D 0.04/0.36 aux(1) =< D+1 0.04/0.36 s(3) =< it(15)*aux(1) 0.04/0.36 0.04/0.36 with precondition: [E=3,A>=1,D>=1,B>=A+1] 0.04/0.36 0.04/0.36 * Chain [[15],18]: 1*it(15)+1*s(3)+0 0.04/0.36 Such that:it(15) =< -A+B 0.04/0.36 aux(1) =< D+1 0.04/0.36 s(3) =< it(15)*aux(1) 0.04/0.36 0.04/0.36 with precondition: [E=3,A>=1,D>=1,B>=A+1] 0.04/0.36 0.04/0.36 * Chain [[15],17]: 1*it(15)+1*s(3)+0 0.04/0.36 Such that:it(15) =< -A+F 0.04/0.36 aux(1) =< D+1 0.04/0.36 s(3) =< it(15)*aux(1) 0.04/0.36 0.04/0.36 with precondition: [E=4,B+1=F,D+1=G,A>=1,D>=1,B>=A] 0.04/0.36 0.04/0.36 * Chain [20]: 0 0.04/0.36 with precondition: [E=3,A>=1] 0.04/0.36 0.04/0.36 * Chain [19]: 1*s(4)+0 0.04/0.36 Such that:s(4) =< D 0.04/0.36 0.04/0.36 with precondition: [E=3,A>=1,D>=1,B>=A] 0.04/0.36 0.04/0.36 * Chain [18]: 0 0.04/0.36 with precondition: [E=3,A>=1,B>=A] 0.04/0.36 0.04/0.36 * Chain [17]: 0 0.04/0.36 with precondition: [E=4,G=C,A=F,A>=1,A>=B+1] 0.04/0.36 0.04/0.36 0.04/0.36 #### Cost of chains of evalfbb4in_loop_cont(A,B,C,D,E,F): 0.04/0.36 * Chain [22]: 0 0.04/0.36 with precondition: [A=3] 0.04/0.36 0.04/0.36 * Chain [21]: 0 0.04/0.36 with precondition: [A=4] 0.04/0.36 0.04/0.36 0.04/0.36 #### Cost of chains of evalfentryin(A,B,C,D,E): 0.04/0.36 * Chain [29]: 0 0.04/0.36 with precondition: [] 0.04/0.36 0.04/0.36 * Chain [28]: 0 0.04/0.36 with precondition: [0>=B] 0.04/0.36 0.04/0.36 * Chain [27]: 2*s(16)+0 0.04/0.36 Such that:aux(4) =< B 0.04/0.36 s(16) =< aux(4) 0.04/0.36 0.04/0.36 with precondition: [0>=D,B>=1] 0.04/0.36 0.04/0.36 * Chain [26]: 1*s(18)+0 0.04/0.36 Such that:s(18) =< B 0.04/0.36 0.04/0.36 with precondition: [0>=D,B>=2] 0.04/0.36 0.04/0.36 * Chain [25]: 0 0.04/0.36 with precondition: [B>=1] 0.04/0.36 0.04/0.36 * Chain [24]: 2*s(19)+1*s(20)+2*s(22)+0 0.04/0.36 Such that:s(20) =< D 0.04/0.36 aux(5) =< B 0.04/0.36 aux(6) =< D+1 0.04/0.36 s(19) =< aux(5) 0.04/0.36 s(22) =< s(19)*aux(6) 0.04/0.36 0.04/0.36 with precondition: [B>=1,D>=1] 0.04/0.36 0.04/0.36 * Chain [23]: 1*s(26)+2*s(29)+2*s(30)+0 0.04/0.36 Such that:s(27) =< B 0.04/0.36 s(26) =< D 0.04/0.36 s(28) =< D+1 0.04/0.36 s(29) =< s(27) 0.04/0.36 s(30) =< s(29)*s(28) 0.04/0.36 0.04/0.36 with precondition: [B>=2,D>=1] 0.04/0.36 0.04/0.36 0.04/0.36 #### Cost of chains of evalfstart(A,B,C,D,E): 0.04/0.36 * Chain [36]: 0 0.04/0.36 with precondition: [] 0.04/0.36 0.04/0.36 * Chain [35]: 0 0.04/0.36 with precondition: [0>=B] 0.04/0.36 0.04/0.36 * Chain [34]: 2*s(32)+0 0.04/0.36 Such that:s(31) =< B 0.04/0.36 s(32) =< s(31) 0.04/0.36 0.04/0.36 with precondition: [0>=D,B>=1] 0.04/0.36 0.04/0.36 * Chain [33]: 1*s(33)+0 0.04/0.36 Such that:s(33) =< B 0.04/0.36 0.04/0.36 with precondition: [0>=D,B>=2] 0.04/0.36 0.04/0.36 * Chain [32]: 0 0.04/0.36 with precondition: [B>=1] 0.04/0.36 0.04/0.36 * Chain [31]: 1*s(34)+2*s(37)+2*s(38)+0 0.04/0.36 Such that:s(35) =< B 0.04/0.36 s(34) =< D 0.04/0.36 s(36) =< D+1 0.04/0.36 s(37) =< s(35) 0.04/0.36 s(38) =< s(37)*s(36) 0.04/0.36 0.04/0.36 with precondition: [B>=1,D>=1] 0.04/0.36 0.04/0.36 * Chain [30]: 1*s(40)+2*s(42)+2*s(43)+0 0.04/0.36 Such that:s(39) =< B 0.04/0.36 s(40) =< D 0.04/0.36 s(41) =< D+1 0.04/0.36 s(42) =< s(39) 0.04/0.36 s(43) =< s(42)*s(41) 0.04/0.36 0.04/0.36 with precondition: [B>=2,D>=1] 0.04/0.36 0.04/0.36 0.04/0.36 Closed-form bounds of evalfstart(A,B,C,D,E): 0.04/0.36 ------------------------------------- 0.04/0.36 * Chain [36] with precondition: [] 0.04/0.36 - Upper bound: 0 0.04/0.36 - Complexity: constant 0.04/0.36 * Chain [35] with precondition: [0>=B] 0.04/0.36 - Upper bound: 0 0.04/0.36 - Complexity: constant 0.04/0.36 * Chain [34] with precondition: [0>=D,B>=1] 0.04/0.36 - Upper bound: 2*B 0.04/0.36 - Complexity: n 0.04/0.36 * Chain [33] with precondition: [0>=D,B>=2] 0.04/0.36 - Upper bound: B 0.04/0.36 - Complexity: n 0.04/0.36 * Chain [32] with precondition: [B>=1] 0.04/0.36 - Upper bound: 0 0.04/0.36 - Complexity: constant 0.04/0.36 * Chain [31] with precondition: [B>=1,D>=1] 0.04/0.36 - Upper bound: (D+1)*(2*B)+2*B+D 0.04/0.36 - Complexity: n^2 0.04/0.36 * Chain [30] with precondition: [B>=2,D>=1] 0.04/0.36 - Upper bound: (D+1)*(2*B)+2*B+D 0.04/0.36 - Complexity: n^2 0.04/0.36 0.04/0.36 ### Maximum cost of evalfstart(A,B,C,D,E): nat(B)*2*nat(D+1)+nat(D)+nat(B)+nat(B) 0.04/0.36 Asymptotic class: n^2 0.04/0.36 * Total analysis performed in 287 ms. 0.04/0.36 0.04/0.46 EOF