0.04/0.57 MAYBE 0.04/0.57 0.04/0.57 Preprocessing Cost Relations 0.04/0.57 ===================================== 0.04/0.57 0.04/0.57 #### Computed strongly connected components 0.04/0.57 0. recursive : [f1/9] 0.04/0.57 1. non_recursive : [exit_location/1] 0.04/0.57 2. non_recursive : [f300/5] 0.04/0.57 3. non_recursive : [f1_loop_cont/6] 0.04/0.57 4. non_recursive : [f2/5] 0.04/0.57 0.04/0.57 #### Obtained direct recursion through partial evaluation 0.04/0.57 0. SCC is partially evaluated into f1/9 0.04/0.57 1. SCC is completely evaluated into other SCCs 0.04/0.57 2. SCC is completely evaluated into other SCCs 0.04/0.57 3. SCC is partially evaluated into f1_loop_cont/6 0.04/0.57 4. SCC is partially evaluated into f2/5 0.04/0.57 0.04/0.57 Control-Flow Refinement of Cost Relations 0.04/0.57 ===================================== 0.04/0.57 0.04/0.57 ### Specialization of cost equations f1/9 0.04/0.57 * CE 9 is refined into CE [12] 0.04/0.57 * CE 8 is refined into CE [13] 0.04/0.57 * CE 2 is refined into CE [14] 0.04/0.57 * CE 3 is refined into CE [15] 0.04/0.57 * CE 5 is refined into CE [16] 0.04/0.57 * CE 6 is refined into CE [17] 0.04/0.57 * CE 4 is refined into CE [18] 0.04/0.57 * CE 7 is refined into CE [19] 0.04/0.57 0.04/0.57 0.04/0.57 ### Cost equations --> "Loop" of f1/9 0.04/0.57 * CEs [14] --> Loop 12 0.04/0.57 * CEs [15] --> Loop 13 0.04/0.57 * CEs [16] --> Loop 14 0.04/0.57 * CEs [17] --> Loop 15 0.04/0.57 * CEs [18] --> Loop 16 0.04/0.57 * CEs [19] --> Loop 17 0.04/0.57 * CEs [12] --> Loop 18 0.04/0.57 * CEs [13] --> Loop 19 0.04/0.57 0.04/0.57 ### Ranking functions of CR f1(A,B,C,D,G,H,I,J,K) 0.04/0.57 0.04/0.57 #### Partial ranking functions of CR f1(A,B,C,D,G,H,I,J,K) 0.04/0.57 * Partial RF of phase [12,13,16]: 0.04/0.57 - RF of loop [12:1,13:1]: 0.04/0.57 -A+B 0.04/0.57 0.04/0.57 0.04/0.57 ### Specialization of cost equations f1_loop_cont/6 0.04/0.57 * CE 11 is refined into CE [20] 0.04/0.57 * CE 10 is refined into CE [21] 0.04/0.57 0.04/0.57 0.04/0.57 ### Cost equations --> "Loop" of f1_loop_cont/6 0.04/0.57 * CEs [20] --> Loop 20 0.04/0.57 * CEs [21] --> Loop 21 0.04/0.57 0.04/0.57 ### Ranking functions of CR f1_loop_cont(A,B,C,D,E,F) 0.04/0.57 0.04/0.57 #### Partial ranking functions of CR f1_loop_cont(A,B,C,D,E,F) 0.04/0.57 0.04/0.57 0.04/0.57 ### Specialization of cost equations f2/5 0.04/0.57 * CE 1 is refined into CE [22,23,24,25,26,27,28,29,30,31,32,33] 0.04/0.57 0.04/0.57 0.04/0.57 ### Cost equations --> "Loop" of f2/5 0.04/0.57 * CEs [32,33] --> Loop 22 0.04/0.57 * CEs [30,31] --> Loop 23 0.04/0.57 * CEs [24] --> Loop 24 0.04/0.57 * CEs [25,26,29] --> Loop 25 0.04/0.57 * CEs [22,23,28] --> Loop 26 0.04/0.57 * CEs [27] --> Loop 27 0.04/0.57 0.04/0.57 ### Ranking functions of CR f2(A,B,C,D,G) 0.04/0.57 0.04/0.57 #### Partial ranking functions of CR f2(A,B,C,D,G) 0.04/0.57 0.04/0.57 0.04/0.57 Computing Bounds 0.04/0.57 ===================================== 0.04/0.57 0.04/0.57 #### Cost of chains of f1(A,B,C,D,G,H,I,J,K): 0.04/0.57 * Chain [[17]]...: 1*it(17)+0 0.04/0.57 with precondition: [A=B] 0.04/0.57 0.04/0.57 * Chain [[17],18]: 1*it(17)+0 0.04/0.57 with precondition: [G=3,A=B] 0.04/0.57 0.04/0.57 * Chain [[17],15,19]: 1*it(17)+1 0.04/0.57 with precondition: [G=2,A=B,A+1=H,A=I,0>=J+1] 0.04/0.57 0.04/0.57 * Chain [[17],15,18]: 1*it(17)+1 0.04/0.57 with precondition: [G=3,A=B] 0.04/0.57 0.04/0.57 * Chain [[17],14,19]: 1*it(17)+1 0.04/0.57 with precondition: [G=2,A=B,A+1=H,A=I,J>=1] 0.04/0.57 0.04/0.57 * Chain [[17],14,18]: 1*it(17)+1 0.04/0.57 with precondition: [G=3,A=B] 0.04/0.57 0.04/0.57 * Chain [[12,13,16]]...: 2*it(12)+1*it(16)+0 0.04/0.57 Such that:aux(3) =< -A+B 0.04/0.57 it(12) =< aux(3) 0.04/0.57 0.04/0.57 with precondition: [B>=A+1] 0.04/0.57 0.04/0.57 * Chain [[12,13,16],[17]]...: 2*it(12)+2*it(16)+0 0.04/0.57 Such that:aux(4) =< -A+B 0.04/0.57 it(12) =< aux(4) 0.04/0.57 0.04/0.57 with precondition: [B>=A+1] 0.04/0.57 0.04/0.57 * Chain [[12,13,16],[17],18]: 2*it(12)+2*it(16)+0 0.04/0.57 Such that:aux(5) =< -A+B 0.04/0.57 it(12) =< aux(5) 0.04/0.57 0.04/0.57 with precondition: [G=3,B>=A+1] 0.04/0.57 0.04/0.57 * Chain [[12,13,16],[17],15,19]: 2*it(12)+2*it(16)+1 0.04/0.57 Such that:aux(6) =< -A+I 0.04/0.57 it(12) =< aux(6) 0.04/0.57 0.04/0.57 with precondition: [G=2,B+1=H,B=I,0>=J+1,B>=A+1] 0.04/0.57 0.04/0.57 * Chain [[12,13,16],[17],15,18]: 2*it(12)+2*it(16)+1 0.04/0.57 Such that:aux(7) =< -A+B 0.04/0.57 it(12) =< aux(7) 0.04/0.57 0.04/0.57 with precondition: [G=3,B>=A+1] 0.04/0.57 0.04/0.57 * Chain [[12,13,16],[17],14,19]: 2*it(12)+2*it(16)+1 0.04/0.57 Such that:aux(8) =< -A+I 0.04/0.57 it(12) =< aux(8) 0.04/0.57 0.04/0.57 with precondition: [G=2,B+1=H,B=I,J>=1,B>=A+1] 0.04/0.57 0.04/0.57 * Chain [[12,13,16],[17],14,18]: 2*it(12)+2*it(16)+1 0.04/0.57 Such that:aux(9) =< -A+B 0.04/0.57 it(12) =< aux(9) 0.04/0.57 0.04/0.57 with precondition: [G=3,B>=A+1] 0.04/0.57 0.04/0.57 * Chain [[12,13,16],18]: 2*it(12)+1*it(16)+0 0.04/0.57 Such that:aux(10) =< -A+B 0.04/0.57 it(12) =< aux(10) 0.04/0.57 0.04/0.57 with precondition: [G=3,B>=A+1] 0.04/0.57 0.04/0.57 * Chain [[12,13,16],15,19]: 2*it(12)+1*it(16)+1 0.04/0.57 Such that:aux(11) =< -A+I 0.04/0.57 it(12) =< aux(11) 0.04/0.57 0.04/0.57 with precondition: [G=2,B+1=H,B=I,0>=J+1,B>=A+1] 0.04/0.57 0.04/0.57 * Chain [[12,13,16],15,18]: 2*it(12)+1*it(16)+1 0.04/0.57 Such that:aux(12) =< -A+B 0.04/0.57 it(12) =< aux(12) 0.04/0.57 0.04/0.57 with precondition: [G=3,B>=A+1] 0.04/0.57 0.04/0.57 * Chain [[12,13,16],14,19]: 2*it(12)+1*it(16)+1 0.04/0.57 Such that:aux(13) =< -A+I 0.04/0.57 it(12) =< aux(13) 0.04/0.57 0.04/0.57 with precondition: [G=2,B+1=H,B=I,J>=1,B>=A+1] 0.04/0.57 0.04/0.57 * Chain [[12,13,16],14,18]: 2*it(12)+1*it(16)+1 0.04/0.57 Such that:aux(14) =< -A+B 0.04/0.57 it(12) =< aux(14) 0.04/0.57 0.04/0.57 with precondition: [G=3,B>=A+1] 0.04/0.57 0.04/0.57 * Chain [19]: 0 0.04/0.57 with precondition: [G=2,J=C,A=H,B=I,A>=B+1] 0.04/0.57 0.04/0.57 * Chain [18]: 0 0.04/0.57 with precondition: [G=3] 0.04/0.57 0.04/0.57 * Chain [15,19]: 1 0.04/0.57 with precondition: [G=2,A=B,A+1=H,A=I,0>=J+1] 0.04/0.57 0.04/0.57 * Chain [15,18]: 1 0.04/0.57 with precondition: [G=3,A=B] 0.04/0.57 0.04/0.57 * Chain [14,19]: 1 0.04/0.57 with precondition: [G=2,A=B,A+1=H,A=I,J>=1] 0.04/0.57 0.04/0.57 * Chain [14,18]: 1 0.04/0.57 with precondition: [G=3,A=B] 0.04/0.57 0.04/0.57 0.04/0.57 #### Cost of chains of f1_loop_cont(A,B,C,D,E,F): 0.04/0.57 * Chain [21]: 0 0.04/0.57 with precondition: [A=2] 0.04/0.57 0.04/0.57 * Chain [20]: 0 0.04/0.57 with precondition: [A=3] 0.04/0.57 0.04/0.57 0.04/0.57 #### Cost of chains of f2(A,B,C,D,G): 0.04/0.57 * Chain [27]: 0 0.04/0.57 with precondition: [] 0.04/0.57 0.04/0.57 * Chain [26]: 1*aux(22)+0 0.04/0.57 with precondition: [B=A] 0.04/0.57 0.04/0.57 * Chain [25]: 20*s(46)+15*s(47)+1 0.04/0.57 Such that:aux(23) =< -A+B 0.04/0.57 s(46) =< aux(23) 0.04/0.57 0.04/0.57 with precondition: [B>=A+1] 0.04/0.57 0.04/0.57 * Chain [24]: 0 0.04/0.57 with precondition: [A>=B+1] 0.04/0.57 0.04/0.57 * Chain [23]...: 1*aux(24)+0 0.04/0.57 with precondition: [B=A] 0.04/0.57 0.04/0.57 * Chain [22]...: 8*s(57)+6*s(58)+0 0.04/0.57 Such that:aux(25) =< -A+B 0.04/0.57 s(57) =< aux(25) 0.04/0.57 0.04/0.57 with precondition: [B>=A+1] 0.04/0.57 0.04/0.57 0.04/0.57 Closed-form bounds of f2(A,B,C,D,G): 0.04/0.57 ------------------------------------- 0.04/0.57 * Chain [27] with precondition: [] 0.04/0.57 - Upper bound: 0 0.04/0.57 - Complexity: constant 0.04/0.57 * Chain [26] with precondition: [B=A] 0.04/0.57 - Upper bound: inf 0.04/0.57 - Complexity: infinity 0.04/0.57 * Chain [25] with precondition: [B>=A+1] 0.04/0.57 - Upper bound: inf 0.04/0.57 - Complexity: infinity 0.04/0.57 * Chain [24] with precondition: [A>=B+1] 0.04/0.57 - Upper bound: 0 0.04/0.57 - Complexity: constant 0.04/0.57 * Chain [23]... with precondition: [B=A] 0.04/0.57 - Upper bound: inf 0.04/0.57 - Complexity: infinity 0.04/0.57 * Chain [22]... with precondition: [B>=A+1] 0.04/0.57 - Upper bound: inf 0.04/0.57 - Complexity: infinity 0.04/0.57 0.04/0.57 ### Maximum cost of f2(A,B,C,D,G): inf 0.04/0.57 Asymptotic class: infinity 0.04/0.57 * Total analysis performed in 494 ms. 0.04/0.57 0.57/0.67 EOF