0.03/0.33 MAYBE 0.03/0.33 0.03/0.33 Preprocessing Cost Relations 0.03/0.33 ===================================== 0.03/0.33 0.03/0.33 #### Computed strongly connected components 0.03/0.33 0. recursive : [f11/9] 0.03/0.33 1. non_recursive : [exit_location/1] 0.03/0.33 2. recursive : [f21/1] 0.03/0.33 3. non_recursive : [f21_loop_cont/2] 0.03/0.33 4. non_recursive : [f11_loop_cont/8] 0.03/0.33 5. non_recursive : [f0/7] 0.03/0.33 0.03/0.33 #### Obtained direct recursion through partial evaluation 0.03/0.33 0. SCC is partially evaluated into f11/9 0.03/0.33 1. SCC is completely evaluated into other SCCs 0.03/0.33 2. SCC is partially evaluated into f21/1 0.03/0.33 3. SCC is completely evaluated into other SCCs 0.03/0.33 4. SCC is partially evaluated into f11_loop_cont/8 0.03/0.33 5. SCC is partially evaluated into f0/7 0.03/0.33 0.03/0.33 Control-Flow Refinement of Cost Relations 0.03/0.33 ===================================== 0.03/0.33 0.03/0.33 ### Specialization of cost equations f11/9 0.03/0.33 * CE 4 is refined into CE [10] 0.03/0.33 * CE 5 is refined into CE [11] 0.03/0.33 * CE 2 is refined into CE [12] 0.03/0.33 * CE 3 is refined into CE [13] 0.03/0.33 0.03/0.33 0.03/0.33 ### Cost equations --> "Loop" of f11/9 0.03/0.33 * CEs [12] --> Loop 10 0.03/0.33 * CEs [13] --> Loop 11 0.03/0.33 * CEs [10] --> Loop 12 0.03/0.33 * CEs [11] --> Loop 13 0.03/0.33 0.03/0.33 ### Ranking functions of CR f11(A,B,C,D,H,I,J,K,L) 0.03/0.33 * RF of phase [10,11]: [A+C,A/2] 0.03/0.33 0.03/0.33 #### Partial ranking functions of CR f11(A,B,C,D,H,I,J,K,L) 0.03/0.33 * Partial RF of phase [10,11]: 0.03/0.33 - RF of loop [10:1]: 0.03/0.33 B+2 0.03/0.33 -C+3 0.03/0.33 - RF of loop [10:1,11:1]: 0.03/0.33 A/2 0.03/0.33 - RF of loop [11:1]: 0.03/0.33 A/2-B/2 0.03/0.33 A/2+C/2-1/2 0.03/0.33 0.03/0.33 0.03/0.33 ### Specialization of cost equations f21/1 0.03/0.33 * CE 9 is refined into CE [14] 0.03/0.33 * CE 8 is refined into CE [15] 0.03/0.33 0.03/0.33 0.03/0.33 ### Cost equations --> "Loop" of f21/1 0.03/0.33 * CEs [15] --> Loop 14 0.03/0.33 * CEs [14] --> Loop 15 0.03/0.33 0.03/0.33 ### Ranking functions of CR f21(H) 0.03/0.33 0.03/0.33 #### Partial ranking functions of CR f21(H) 0.03/0.33 0.03/0.33 0.03/0.33 ### Specialization of cost equations f11_loop_cont/8 0.03/0.33 * CE 7 is refined into CE [16,17] 0.03/0.33 * CE 6 is refined into CE [18] 0.03/0.33 0.03/0.33 0.03/0.33 ### Cost equations --> "Loop" of f11_loop_cont/8 0.03/0.33 * CEs [16] --> Loop 16 0.03/0.33 * CEs [18] --> Loop 17 0.03/0.33 * CEs [17] --> Loop 18 0.03/0.33 0.03/0.33 ### Ranking functions of CR f11_loop_cont(A,B,C,D,E,F,G,H) 0.03/0.33 0.03/0.33 #### Partial ranking functions of CR f11_loop_cont(A,B,C,D,E,F,G,H) 0.03/0.33 0.03/0.33 0.03/0.33 ### Specialization of cost equations f0/7 0.03/0.33 * CE 1 is refined into CE [19,20,21,22] 0.03/0.33 0.03/0.33 0.03/0.33 ### Cost equations --> "Loop" of f0/7 0.03/0.33 * CEs [22] --> Loop 19 0.03/0.33 * CEs [19,20,21] --> Loop 20 0.03/0.33 0.03/0.33 ### Ranking functions of CR f0(A,B,C,D,E,F,H) 0.03/0.33 0.03/0.33 #### Partial ranking functions of CR f0(A,B,C,D,E,F,H) 0.03/0.33 0.03/0.33 0.03/0.33 Computing Bounds 0.03/0.33 ===================================== 0.03/0.33 0.03/0.33 #### Cost of chains of f11(A,B,C,D,H,I,J,K,L): 0.03/0.33 * Chain [[10,11],13]: 1*it(10)+1*it(11)+0 0.03/0.33 Such that:aux(3) =< A/2 0.03/0.33 aux(4) =< A/2+1/2 0.03/0.33 it(11) =< A/2-B/2 0.03/0.33 it(11) =< 3/8*A+5/8 0.03/0.33 aux(5) =< A+1 0.03/0.33 aux(6) =< A+C 0.03/0.33 aux(2) =< aux(5) 0.03/0.33 it(10) =< aux(5) 0.03/0.33 it(11) =< aux(5) 0.03/0.33 aux(2) =< aux(6) 0.03/0.33 it(10) =< aux(6) 0.03/0.33 it(11) =< aux(6) 0.03/0.33 it(10) =< aux(2) 0.03/0.33 it(11) =< aux(2) 0.03/0.33 it(10) =< aux(3) 0.03/0.33 it(11) =< aux(3) 0.03/0.33 it(10) =< aux(4) 0.03/0.33 it(11) =< aux(4) 0.03/0.33 0.03/0.33 with precondition: [H=2,A>=1,C>=0,4>=2*C+A,B+C>=1] 0.03/0.33 0.03/0.33 * Chain [[10,11],12]: 1*it(10)+1*it(11)+0 0.03/0.33 Such that:aux(2) =< A-B-I+J 0.03/0.33 aux(1) =< A+C 0.03/0.33 aux(3) =< A/2 0.03/0.33 it(11) =< A/2-B/2 0.03/0.33 it(11) =< A/2-B/2-I/2+J/2 0.03/0.33 aux(4) =< A/2-I/2 0.03/0.33 it(10) =< B-J 0.03/0.33 it(10) =< aux(1) 0.03/0.33 it(11) =< aux(1) 0.03/0.33 it(10) =< aux(2) 0.03/0.33 it(11) =< aux(2) 0.03/0.33 it(10) =< aux(3) 0.03/0.33 it(11) =< aux(3) 0.03/0.33 it(10) =< aux(4) 0.03/0.33 it(11) =< aux(4) 0.03/0.33 0.03/0.33 with precondition: [H=3,B+C=J+K,0>=I,C>=0,I+1>=0,4>=2*C+A,A>=I+2,B>=J,B+C>=1,3*I+4*B+4>=4*J+A,A+2*J>=2*B+I,B+C+I>=J] 0.03/0.33 0.03/0.33 * Chain [13]: 0 0.03/0.33 with precondition: [H=2,C>=0,4>=2*C+A,B+C>=1] 0.03/0.33 0.03/0.33 0.03/0.33 #### Cost of chains of f21(H): 0.03/0.33 * Chain [[14]]...: 1*it(14)+0 0.03/0.33 with precondition: [H=2] 0.03/0.33 0.03/0.33 * Chain [[14],15]: 1*it(14)+0 0.03/0.33 with precondition: [H=2] 0.03/0.33 0.03/0.33 * Chain [15]: 0 0.03/0.33 with precondition: [H=2] 0.03/0.33 0.03/0.33 0.03/0.33 #### Cost of chains of f11_loop_cont(A,B,C,D,E,F,G,H): 0.03/0.33 * Chain [18]...: 1*s(2)+0 0.03/0.33 with precondition: [A=3,G=4,F>=1] 0.03/0.33 0.03/0.33 * Chain [17]: 0 0.03/0.33 with precondition: [A=2,G=4,F>=1] 0.03/0.33 0.03/0.33 * Chain [16]: 1*s(3)+0 0.03/0.33 with precondition: [A=3,G=4,F>=1] 0.03/0.33 0.03/0.33 0.03/0.33 #### Cost of chains of f0(A,B,C,D,E,F,H): 0.03/0.33 * Chain [20]: 1*aux(17)+0 0.03/0.33 with precondition: [] 0.03/0.33 0.03/0.33 * Chain [19]...: 1*s(21)+1*s(23)+1*s(24)+0 0.03/0.33 Such that:s(21) =< 3/2 0.03/0.33 aux(18) =< 2 0.03/0.33 aux(19) =< 4 0.03/0.33 aux(20) =< 5 0.03/0.33 aux(21) =< 5/2 0.03/0.33 s(21) =< aux(18) 0.03/0.33 s(18) =< aux(19) 0.03/0.33 s(18) =< aux(20) 0.03/0.33 s(21) =< aux(20) 0.03/0.33 s(23) =< aux(20) 0.03/0.33 s(23) =< aux(21) 0.03/0.33 s(23) =< aux(19) 0.03/0.33 s(21) =< aux(19) 0.03/0.33 s(23) =< s(18) 0.03/0.33 s(21) =< s(18) 0.03/0.33 s(23) =< aux(18) 0.03/0.33 s(21) =< aux(21) 0.03/0.33 0.03/0.33 with precondition: [] 0.03/0.33 0.03/0.33 0.03/0.33 Closed-form bounds of f0(A,B,C,D,E,F,H): 0.03/0.33 ------------------------------------- 0.03/0.33 * Chain [20] with precondition: [] 0.03/0.33 - Upper bound: inf 0.03/0.33 - Complexity: infinity 0.03/0.33 * Chain [19]... with precondition: [] 0.03/0.33 - Upper bound: inf 0.03/0.33 - Complexity: infinity 0.03/0.33 0.03/0.33 ### Maximum cost of f0(A,B,C,D,E,F,H): inf 0.03/0.33 Asymptotic class: infinity 0.03/0.33 * Total analysis performed in 258 ms. 0.03/0.33 0.03/0.43 EOF