0.03/0.26 WORST_CASE(?,O(n^2)) 0.03/0.26 0.03/0.26 Preprocessing Cost Relations 0.03/0.26 ===================================== 0.03/0.26 0.03/0.26 #### Computed strongly connected components 0.03/0.26 0. recursive : [evalSimpleMultipleDepbb1in/7,evalSimpleMultipleDepbb2in/7,evalSimpleMultipleDepbb3in/7,evalSimpleMultipleDepbbin/7] 0.03/0.26 1. non_recursive : [evalSimpleMultipleDepstop/5] 0.03/0.26 2. non_recursive : [evalSimpleMultipleDepreturnin/5] 0.03/0.26 3. non_recursive : [exit_location/1] 0.03/0.26 4. non_recursive : [evalSimpleMultipleDepbb3in_loop_cont/6] 0.03/0.26 5. non_recursive : [evalSimpleMultipleDepentryin/5] 0.03/0.26 6. non_recursive : [evalSimpleMultipleDepstart/5] 0.03/0.26 0.03/0.26 #### Obtained direct recursion through partial evaluation 0.03/0.26 0. SCC is partially evaluated into evalSimpleMultipleDepbb3in/7 0.03/0.26 1. SCC is completely evaluated into other SCCs 0.03/0.26 2. SCC is completely evaluated into other SCCs 0.03/0.26 3. SCC is completely evaluated into other SCCs 0.03/0.26 4. SCC is partially evaluated into evalSimpleMultipleDepbb3in_loop_cont/6 0.03/0.26 5. SCC is partially evaluated into evalSimpleMultipleDepentryin/5 0.03/0.26 6. SCC is partially evaluated into evalSimpleMultipleDepstart/5 0.03/0.26 0.03/0.26 Control-Flow Refinement of Cost Relations 0.03/0.26 ===================================== 0.03/0.26 0.03/0.26 ### Specialization of cost equations evalSimpleMultipleDepbb3in/7 0.03/0.26 * CE 6 is refined into CE [9] 0.03/0.26 * CE 5 is refined into CE [10] 0.03/0.26 * CE 3 is refined into CE [11] 0.03/0.26 * CE 4 is refined into CE [12] 0.03/0.26 0.03/0.26 0.03/0.26 ### Cost equations --> "Loop" of evalSimpleMultipleDepbb3in/7 0.03/0.26 * CEs [11] --> Loop 9 0.03/0.26 * CEs [12] --> Loop 10 0.03/0.26 * CEs [9] --> Loop 11 0.03/0.26 * CEs [10] --> Loop 12 0.03/0.26 0.03/0.26 ### Ranking functions of CR evalSimpleMultipleDepbb3in(A,B,C,D,E,F,G) 0.03/0.26 0.03/0.26 #### Partial ranking functions of CR evalSimpleMultipleDepbb3in(A,B,C,D,E,F,G) 0.03/0.26 * Partial RF of phase [9,10]: 0.03/0.26 - RF of loop [9:1]: 0.03/0.26 -A+D depends on loops [10:1] 0.03/0.26 - RF of loop [10:1]: 0.03/0.26 -B+C 0.03/0.26 0.03/0.26 0.03/0.26 ### Specialization of cost equations evalSimpleMultipleDepbb3in_loop_cont/6 0.03/0.26 * CE 8 is refined into CE [13] 0.03/0.26 * CE 7 is refined into CE [14] 0.03/0.26 0.03/0.26 0.03/0.26 ### Cost equations --> "Loop" of evalSimpleMultipleDepbb3in_loop_cont/6 0.03/0.26 * CEs [13] --> Loop 13 0.03/0.26 * CEs [14] --> Loop 14 0.03/0.26 0.03/0.26 ### Ranking functions of CR evalSimpleMultipleDepbb3in_loop_cont(A,B,C,D,E,F) 0.03/0.26 0.03/0.26 #### Partial ranking functions of CR evalSimpleMultipleDepbb3in_loop_cont(A,B,C,D,E,F) 0.03/0.26 0.03/0.26 0.03/0.26 ### Specialization of cost equations evalSimpleMultipleDepentryin/5 0.03/0.26 * CE 2 is refined into CE [15,16,17,18] 0.03/0.26 0.03/0.26 0.03/0.26 ### Cost equations --> "Loop" of evalSimpleMultipleDepentryin/5 0.03/0.26 * CEs [15,18] --> Loop 15 0.03/0.26 * CEs [16] --> Loop 16 0.03/0.26 * CEs [17] --> Loop 17 0.03/0.26 0.03/0.26 ### Ranking functions of CR evalSimpleMultipleDepentryin(A,B,C,D,E) 0.03/0.26 0.03/0.26 #### Partial ranking functions of CR evalSimpleMultipleDepentryin(A,B,C,D,E) 0.03/0.26 0.03/0.26 0.03/0.26 ### Specialization of cost equations evalSimpleMultipleDepstart/5 0.03/0.26 * CE 1 is refined into CE [19,20,21] 0.03/0.26 0.03/0.26 0.03/0.26 ### Cost equations --> "Loop" of evalSimpleMultipleDepstart/5 0.03/0.26 * CEs [21] --> Loop 18 0.03/0.26 * CEs [20] --> Loop 19 0.03/0.26 * CEs [19] --> Loop 20 0.03/0.26 0.03/0.26 ### Ranking functions of CR evalSimpleMultipleDepstart(A,B,C,D,E) 0.03/0.26 0.03/0.26 #### Partial ranking functions of CR evalSimpleMultipleDepstart(A,B,C,D,E) 0.03/0.26 0.03/0.26 0.03/0.26 Computing Bounds 0.03/0.26 ===================================== 0.03/0.26 0.03/0.26 #### Cost of chains of evalSimpleMultipleDepbb3in(A,B,C,D,E,F,G): 0.03/0.26 * Chain [[9,10],12]: 1*it(9)+1*it(10)+0 0.03/0.26 Such that:aux(2) =< -A+D 0.03/0.26 it(10) =< -B+C 0.03/0.26 aux(11) =< D 0.03/0.26 aux(1) =< it(10)*aux(11) 0.03/0.26 it(9) =< aux(1)+aux(2) 0.03/0.26 0.03/0.26 with precondition: [E=2,F=0,C=G,A>=0,B>=0,C>=B+1] 0.03/0.26 0.03/0.26 * Chain [[9,10],11]: 1*it(9)+1*it(10)+0 0.03/0.26 Such that:aux(2) =< -A+D 0.03/0.26 it(10) =< -B+C 0.03/0.26 aux(11) =< D 0.03/0.26 aux(1) =< it(10)*aux(11) 0.03/0.26 it(9) =< aux(1)+aux(2) 0.03/0.26 0.03/0.26 with precondition: [E=3,A>=0,B>=0,C>=B+1] 0.03/0.26 0.03/0.26 * Chain [12]: 0 0.03/0.26 with precondition: [E=2,A=F,B=G,A>=0,B>=0,B>=C] 0.03/0.26 0.03/0.26 * Chain [11]: 0 0.03/0.26 with precondition: [E=3,A>=0,B>=0] 0.03/0.26 0.03/0.26 0.03/0.26 #### Cost of chains of evalSimpleMultipleDepbb3in_loop_cont(A,B,C,D,E,F): 0.03/0.26 * Chain [14]: 0 0.03/0.26 with precondition: [A=2] 0.03/0.26 0.03/0.26 * Chain [13]: 0 0.03/0.26 with precondition: [A=3] 0.03/0.26 0.03/0.26 0.03/0.26 #### Cost of chains of evalSimpleMultipleDepentryin(A,B,C,D,E): 0.03/0.26 * Chain [17]: 0 0.03/0.26 with precondition: [] 0.03/0.26 0.03/0.26 * Chain [16]: 0 0.03/0.26 with precondition: [0>=C] 0.03/0.26 0.03/0.26 * Chain [15]: 2*s(2)+2*s(5)+0 0.03/0.26 Such that:aux(16) =< C 0.03/0.26 aux(17) =< D 0.03/0.26 s(2) =< aux(16) 0.03/0.26 s(4) =< s(2)*aux(17) 0.03/0.26 s(5) =< s(4)+aux(17) 0.03/0.26 0.03/0.26 with precondition: [C>=1] 0.03/0.26 0.03/0.26 0.03/0.26 #### Cost of chains of evalSimpleMultipleDepstart(A,B,C,D,E): 0.03/0.26 * Chain [20]: 0 0.03/0.26 with precondition: [] 0.03/0.26 0.03/0.26 * Chain [19]: 0 0.03/0.26 with precondition: [0>=C] 0.03/0.26 0.03/0.26 * Chain [18]: 2*s(13)+2*s(15)+0 0.03/0.26 Such that:s(11) =< C 0.03/0.26 s(12) =< D 0.03/0.26 s(13) =< s(11) 0.03/0.26 s(14) =< s(13)*s(12) 0.03/0.26 s(15) =< s(14)+s(12) 0.03/0.26 0.03/0.26 with precondition: [C>=1] 0.03/0.26 0.03/0.26 0.03/0.26 Closed-form bounds of evalSimpleMultipleDepstart(A,B,C,D,E): 0.03/0.26 ------------------------------------- 0.03/0.26 * Chain [20] with precondition: [] 0.03/0.26 - Upper bound: 0 0.03/0.26 - Complexity: constant 0.03/0.26 * Chain [19] with precondition: [0>=C] 0.03/0.26 - Upper bound: 0 0.03/0.26 - Complexity: constant 0.03/0.26 * Chain [18] with precondition: [C>=1] 0.03/0.26 - Upper bound: 2*C*nat(D)+2*C+nat(D)*2 0.03/0.26 - Complexity: n^2 0.03/0.26 0.03/0.26 ### Maximum cost of evalSimpleMultipleDepstart(A,B,C,D,E): nat(C)*2*nat(D)+nat(C)*2+nat(D)*2 0.03/0.26 Asymptotic class: n^2 0.03/0.26 * Total analysis performed in 189 ms. 0.03/0.26 0.03/0.36 EOF