0.03/0.21 MAYBE 0.03/0.21 0.03/0.21 Preprocessing Cost Relations 0.03/0.21 ===================================== 0.03/0.21 0.03/0.21 #### Computed strongly connected components 0.03/0.21 0. recursive : [f3/7] 0.03/0.21 1. non_recursive : [exit_location/1] 0.03/0.21 2. recursive : [f6/3] 0.03/0.21 3. non_recursive : [f6_loop_cont/2] 0.03/0.21 4. non_recursive : [f3_loop_cont/7] 0.03/0.21 5. non_recursive : [f0/6] 0.03/0.21 0.03/0.21 #### Obtained direct recursion through partial evaluation 0.03/0.21 0. SCC is partially evaluated into f3/7 0.03/0.21 1. SCC is completely evaluated into other SCCs 0.03/0.21 2. SCC is partially evaluated into f6/3 0.03/0.21 3. SCC is completely evaluated into other SCCs 0.03/0.21 4. SCC is partially evaluated into f3_loop_cont/7 0.03/0.21 5. SCC is partially evaluated into f0/6 0.03/0.21 0.03/0.21 Control-Flow Refinement of Cost Relations 0.03/0.21 ===================================== 0.03/0.21 0.03/0.21 ### Specialization of cost equations f3/7 0.03/0.21 * CE 4 is refined into CE [11] 0.03/0.21 * CE 5 is refined into CE [12] 0.03/0.21 * CE 3 is refined into CE [13] 0.03/0.21 * CE 2 is refined into CE [14] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of f3/7 0.03/0.21 * CEs [13] --> Loop 11 0.03/0.21 * CEs [14] --> Loop 12 0.03/0.21 * CEs [11] --> Loop 13 0.03/0.21 * CEs [12] --> Loop 14 0.03/0.21 0.03/0.21 ### Ranking functions of CR f3(C,D,E,G,H,I,J) 0.03/0.21 * RF of phase [11,12]: [C] 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR f3(C,D,E,G,H,I,J) 0.03/0.21 * Partial RF of phase [11,12]: 0.03/0.21 - RF of loop [11:1]: 0.03/0.21 C/2 0.03/0.21 - RF of loop [12:1]: 0.03/0.21 C 0.03/0.21 0.03/0.21 0.03/0.21 ### Specialization of cost equations f6/3 0.03/0.21 * CE 10 is refined into CE [15] 0.03/0.21 * CE 8 is refined into CE [16] 0.03/0.21 * CE 9 is refined into CE [17] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of f6/3 0.03/0.21 * CEs [16] --> Loop 15 0.03/0.21 * CEs [17] --> Loop 16 0.03/0.21 * CEs [15] --> Loop 17 0.03/0.21 0.03/0.21 ### Ranking functions of CR f6(A,E,G) 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR f6(A,E,G) 0.03/0.21 0.03/0.21 0.03/0.21 ### Specialization of cost equations f3_loop_cont/7 0.03/0.21 * CE 7 is refined into CE [18,19] 0.03/0.21 * CE 6 is refined into CE [20] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of f3_loop_cont/7 0.03/0.21 * CEs [18] --> Loop 18 0.03/0.21 * CEs [20] --> Loop 19 0.03/0.21 * CEs [19] --> Loop 20 0.03/0.21 0.03/0.21 ### Ranking functions of CR f3_loop_cont(A,B,C,D,E,F,G) 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR f3_loop_cont(A,B,C,D,E,F,G) 0.03/0.21 0.03/0.21 0.03/0.21 ### Specialization of cost equations f0/6 0.03/0.21 * CE 1 is refined into CE [21,22,23,24,25,26] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of f0/6 0.03/0.21 * CEs [26] --> Loop 21 0.03/0.21 * CEs [24] --> Loop 22 0.03/0.21 * CEs [22,25] --> Loop 23 0.03/0.21 * CEs [23] --> Loop 24 0.03/0.21 * CEs [21] --> Loop 25 0.03/0.21 0.03/0.21 ### Ranking functions of CR f0(A,B,C,D,E,G) 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR f0(A,B,C,D,E,G) 0.03/0.21 0.03/0.21 0.03/0.21 Computing Bounds 0.03/0.21 ===================================== 0.03/0.21 0.03/0.21 #### Cost of chains of f3(C,D,E,G,H,I,J): 0.03/0.21 * Chain [[11,12],14]: 1*it(11)+1*it(12)+0 0.03/0.21 Such that:aux(1) =< C 0.03/0.21 aux(2) =< C+1 0.03/0.21 it(11) =< C/2 0.03/0.21 it(11) =< aux(1) 0.03/0.21 it(12) =< aux(1) 0.03/0.21 it(11) =< aux(2) 0.03/0.21 it(12) =< aux(2) 0.03/0.21 0.03/0.21 with precondition: [G=2,C>=1] 0.03/0.21 0.03/0.21 * Chain [[11,12],13]: 1*it(11)+1*it(12)+0 0.03/0.21 Such that:aux(1) =< C 0.03/0.21 aux(2) =< C-H 0.03/0.21 it(11) =< C/2 0.03/0.21 it(11) =< aux(1) 0.03/0.21 it(12) =< aux(1) 0.03/0.21 it(11) =< aux(2) 0.03/0.21 it(12) =< aux(2) 0.03/0.21 0.03/0.21 with precondition: [G=3,0>=H,C>=1,H+1>=0] 0.03/0.21 0.03/0.21 * Chain [14]: 0 0.03/0.21 with precondition: [G=2] 0.03/0.21 0.03/0.21 * Chain [13]: 0 0.03/0.21 with precondition: [G=3,I=D,C=H,0>=C] 0.03/0.21 0.03/0.21 0.03/0.21 #### Cost of chains of f6(A,E,G): 0.03/0.21 * Chain [[15,16]]...: 2*it(15)+0 0.03/0.21 with precondition: [A>=0,1>=A,G=2] 0.03/0.21 0.03/0.21 * Chain [[15,16],17]: 2*it(15)+0 0.03/0.21 with precondition: [G=2,1>=A,A>=0] 0.03/0.21 0.03/0.21 * Chain [17]: 0 0.03/0.21 with precondition: [G=2,1>=A,A>=0] 0.03/0.21 0.03/0.21 0.03/0.21 #### Cost of chains of f3_loop_cont(A,B,C,D,E,F,G): 0.03/0.21 * Chain [20]...: 2*s(2)+0 0.03/0.21 with precondition: [A=3,B=0,C=0] 0.03/0.21 0.03/0.21 * Chain [19]: 0 0.03/0.21 with precondition: [A=2,B=0,C=0] 0.03/0.21 0.03/0.21 * Chain [18]: 1*s(3)+0 0.03/0.21 with precondition: [A=3,B=0,C=0] 0.03/0.21 0.03/0.21 0.03/0.21 #### Cost of chains of f0(A,B,C,D,E,G): 0.03/0.21 * Chain [25]: 0 0.03/0.21 with precondition: [] 0.03/0.21 0.03/0.21 * Chain [24]: 1*s(4)+0 0.03/0.21 with precondition: [0>=C] 0.03/0.21 0.03/0.21 * Chain [23]: 2*s(7)+2*s(8)+1*s(13)+0 0.03/0.21 Such that:aux(4) =< C 0.03/0.21 aux(5) =< C+1 0.03/0.21 aux(6) =< C/2 0.03/0.21 s(7) =< aux(6) 0.03/0.21 s(7) =< aux(4) 0.03/0.21 s(8) =< aux(4) 0.03/0.21 s(7) =< aux(5) 0.03/0.21 s(8) =< aux(5) 0.03/0.21 0.03/0.21 with precondition: [C>=1] 0.03/0.21 0.03/0.21 * Chain [22]...: 2*s(14)+0 0.03/0.21 with precondition: [0>=C] 0.03/0.21 0.03/0.21 * Chain [21]...: 1*s(17)+1*s(18)+2*s(19)+0 0.03/0.21 Such that:s(15) =< C 0.03/0.21 s(16) =< C+1 0.03/0.21 s(17) =< C/2 0.03/0.21 s(17) =< s(15) 0.03/0.21 s(18) =< s(15) 0.03/0.21 s(17) =< s(16) 0.03/0.21 s(18) =< s(16) 0.03/0.21 0.03/0.21 with precondition: [C>=1] 0.03/0.21 0.03/0.21 0.03/0.21 Closed-form bounds of f0(A,B,C,D,E,G): 0.03/0.21 ------------------------------------- 0.03/0.21 * Chain [25] with precondition: [] 0.03/0.21 - Upper bound: 0 0.03/0.21 - Complexity: constant 0.03/0.21 * Chain [24] with precondition: [0>=C] 0.03/0.21 - Upper bound: inf 0.03/0.21 - Complexity: infinity 0.03/0.21 * Chain [23] with precondition: [C>=1] 0.03/0.21 - Upper bound: inf 0.03/0.21 - Complexity: infinity 0.03/0.21 * Chain [22]... with precondition: [0>=C] 0.03/0.21 - Upper bound: inf 0.03/0.21 - Complexity: infinity 0.03/0.21 * Chain [21]... with precondition: [C>=1] 0.03/0.21 - Upper bound: inf 0.03/0.21 - Complexity: infinity 0.03/0.21 0.03/0.21 ### Maximum cost of f0(A,B,C,D,E,G): inf 0.03/0.21 Asymptotic class: infinity 0.03/0.21 * Total analysis performed in 151 ms. 0.03/0.21 0.03/0.32 EOF