1.18/1.19 MAYBE 1.18/1.19 1.18/1.19 Preprocessing Cost Relations 1.18/1.19 ===================================== 1.18/1.19 1.18/1.19 #### Computed strongly connected components 1.18/1.19 0. recursive : [f10/12,f21/12] 1.18/1.19 1. non_recursive : [exit_location/1] 1.18/1.19 2. non_recursive : [f32/8] 1.18/1.19 3. non_recursive : [f10_loop_cont/9] 1.18/1.19 4. non_recursive : [f0/8] 1.18/1.19 1.18/1.19 #### Obtained direct recursion through partial evaluation 1.18/1.19 0. SCC is partially evaluated into f10/12 1.18/1.19 1. SCC is completely evaluated into other SCCs 1.18/1.19 2. SCC is completely evaluated into other SCCs 1.18/1.19 3. SCC is partially evaluated into f10_loop_cont/9 1.18/1.19 4. SCC is partially evaluated into f0/8 1.18/1.19 1.18/1.19 Control-Flow Refinement of Cost Relations 1.18/1.19 ===================================== 1.18/1.19 1.18/1.19 ### Specialization of cost equations f10/12 1.18/1.19 * CE 9 is refined into CE [12] 1.18/1.19 * CE 8 is refined into CE [13] 1.18/1.19 * CE 7 is refined into CE [14] 1.18/1.19 * CE 2 is refined into CE [15] 1.18/1.19 * CE 3 is refined into CE [16] 1.18/1.19 * CE 6 is refined into CE [17] 1.18/1.19 * CE 4 is refined into CE [18] 1.18/1.19 * CE 5 is refined into CE [19] 1.18/1.19 1.18/1.19 1.18/1.19 ### Cost equations --> "Loop" of f10/12 1.18/1.19 * CEs [15] --> Loop 12 1.18/1.19 * CEs [18] --> Loop 13 1.18/1.19 * CEs [16] --> Loop 14 1.18/1.19 * CEs [19] --> Loop 15 1.18/1.19 * CEs [17] --> Loop 16 1.18/1.19 * CEs [12] --> Loop 17 1.18/1.19 * CEs [13] --> Loop 18 1.18/1.19 * CEs [14] --> Loop 19 1.18/1.19 1.18/1.19 ### Ranking functions of CR f10(A,B,C,E,F,G,J,K,L,M,N,O) 1.18/1.19 1.18/1.19 #### Partial ranking functions of CR f10(A,B,C,E,F,G,J,K,L,M,N,O) 1.18/1.19 * Partial RF of phase [12,13,14,15,16]: 1.18/1.19 - RF of loop [12:1,13:1]: 1.18/1.19 C depends on loops [14:1,15:1] 1.18/1.19 - RF of loop [12:1,14:1]: 1.18/1.19 -F+3 depends on loops [13:1,15:1,16:1] 1.18/1.19 - RF of loop [13:1,15:1,16:1]: 1.18/1.19 F depends on loops [12:1,14:1] 1.18/1.19 - RF of loop [14:1,15:1]: 1.18/1.19 -A+3 1.18/1.19 -B/2+1/2 depends on loops [16:1] 1.18/1.19 - RF of loop [16:1]: 1.18/1.19 B depends on loops [14:1,15:1] 1.18/1.19 1.18/1.19 1.18/1.19 ### Specialization of cost equations f10_loop_cont/9 1.18/1.19 * CE 11 is refined into CE [20] 1.18/1.19 * CE 10 is refined into CE [21] 1.18/1.19 1.18/1.19 1.18/1.19 ### Cost equations --> "Loop" of f10_loop_cont/9 1.18/1.19 * CEs [20] --> Loop 20 1.18/1.19 * CEs [21] --> Loop 21 1.18/1.19 1.18/1.19 ### Ranking functions of CR f10_loop_cont(A,B,C,D,E,F,G,H,I) 1.18/1.19 1.18/1.19 #### Partial ranking functions of CR f10_loop_cont(A,B,C,D,E,F,G,H,I) 1.18/1.19 1.18/1.19 1.18/1.19 ### Specialization of cost equations f0/8 1.18/1.19 * CE 1 is refined into CE [22,23,24,25] 1.18/1.19 1.18/1.19 1.18/1.19 ### Cost equations --> "Loop" of f0/8 1.18/1.19 * CEs [22,23,24,25] --> Loop 22 1.18/1.19 1.18/1.19 ### Ranking functions of CR f0(A,B,C,D,E,F,G,J) 1.18/1.19 1.18/1.19 #### Partial ranking functions of CR f0(A,B,C,D,E,F,G,J) 1.18/1.19 1.18/1.19 1.18/1.19 Computing Bounds 1.18/1.19 ===================================== 1.18/1.19 1.18/1.19 #### Cost of chains of f10(A,B,C,E,F,G,J,K,L,M,N,O): 1.18/1.19 * Chain [[12,13,14,15,16],19]: 2*it(12)+2*it(14)+1*it(16)+0 1.18/1.19 Such that:aux(26) =< -3*A+9 1.18/1.19 aux(27) =< -3*A+3*K 1.18/1.19 aux(28) =< -A+3 1.18/1.19 aux(29) =< -A+K 1.18/1.19 aux(15) =< B 1.18/1.19 aux(13) =< aux(26) 1.18/1.19 aux(13) =< aux(27) 1.18/1.19 it(14) =< aux(28) 1.18/1.19 it(14) =< aux(29) 1.18/1.19 it(16) =< aux(13)+aux(13)+aux(15) 1.18/1.19 1.18/1.19 with precondition: [E=2,J=2,N=0,O=0,2>=F,3>=K,A>=1,C>=0,F>=1,M>=0,K>=A,A>=B,K>=L,C+2*K>=A+L+1,C+4*K>=2*A+2*L+F] 1.18/1.19 1.18/1.19 * Chain [[12,13,14,15,16],18]: 2*it(12)+2*it(14)+1*it(16)+0 1.18/1.19 Such that:aux(26) =< -3*A+9 1.18/1.19 aux(27) =< -3*A+3*K 1.18/1.19 aux(28) =< -A+3 1.18/1.19 aux(29) =< -A+K 1.18/1.19 aux(15) =< B 1.18/1.19 aux(13) =< aux(26) 1.18/1.19 aux(13) =< aux(27) 1.18/1.19 it(14) =< aux(28) 1.18/1.19 it(14) =< aux(29) 1.18/1.19 it(16) =< aux(13)+aux(13)+aux(15) 1.18/1.19 1.18/1.19 with precondition: [E=2,J=2,N=3,O=1,2>=F,3>=K,A>=1,C>=0,F>=1,M>=0,K>=A,A>=B,K>=L,C+K>=A+1,C+F+2*K>=2*A+3] 1.18/1.19 1.18/1.19 * Chain [[12,13,14,15,16],17]: 2*it(12)+2*it(14)+1*it(16)+0 1.18/1.19 Such that:aux(15) =< B 1.18/1.19 aux(38) =< -3*A+9 1.18/1.19 aux(39) =< -A+3 1.18/1.19 it(14) =< aux(39) 1.18/1.19 it(16) =< aux(38)+aux(38)+aux(15) 1.18/1.19 1.18/1.19 with precondition: [E=2,J=3,3>=A,2>=F,A>=1,C>=0,F>=1,A>=B] 1.18/1.19 1.18/1.19 * Chain [17]: 0 1.18/1.19 with precondition: [E=2,J=3,A>=1,C>=0,F>=0,A>=B] 1.18/1.19 1.18/1.19 1.18/1.19 #### Cost of chains of f10_loop_cont(A,B,C,D,E,F,G,H,I): 1.18/1.19 * Chain [21]: 0 1.18/1.19 with precondition: [A=2,E=0,F=2] 1.18/1.19 1.18/1.19 * Chain [20]: 0 1.18/1.19 with precondition: [A=3,E=0,F=2] 1.18/1.19 1.18/1.19 1.18/1.19 #### Cost of chains of f0(A,B,C,D,E,F,G,J): 1.18/1.19 * Chain [22]: 1*aux(47)+0 1.18/1.19 with precondition: [] 1.18/1.19 1.18/1.19 1.18/1.19 Closed-form bounds of f0(A,B,C,D,E,F,G,J): 1.18/1.19 ------------------------------------- 1.18/1.19 * Chain [22] with precondition: [] 1.18/1.19 - Upper bound: inf 1.18/1.19 - Complexity: infinity 1.18/1.19 1.18/1.19 ### Maximum cost of f0(A,B,C,D,E,F,G,J): inf 1.18/1.19 Asymptotic class: infinity 1.18/1.19 * Total analysis performed in 1071 ms. 1.18/1.19 1.18/1.29 EOF