0.03/0.35 WORST_CASE(?,O(n^2)) 0.03/0.35 0.03/0.35 Preprocessing Cost Relations 0.03/0.35 ===================================== 0.03/0.35 0.03/0.35 #### Computed strongly connected components 0.03/0.35 0. recursive : [evalinsertsortbb1in/4,evalinsertsortbb2in/4,evalinsertsortbb3in/4] 0.03/0.35 1. recursive : [evalinsertsortbb2in_loop_cont/9,evalinsertsortbb4in/8,evalinsertsortbb5in/8,evalinsertsortbbin/8] 0.03/0.35 2. non_recursive : [evalinsertsortstop/5] 0.03/0.35 3. non_recursive : [evalinsertsortreturnin/5] 0.03/0.35 4. non_recursive : [exit_location/1] 0.03/0.35 5. non_recursive : [evalinsertsortbb5in_loop_cont/6] 0.03/0.35 6. non_recursive : [evalinsertsortentryin/5] 0.03/0.35 7. non_recursive : [evalinsertsortstart/5] 0.03/0.35 0.03/0.35 #### Obtained direct recursion through partial evaluation 0.03/0.35 0. SCC is partially evaluated into evalinsertsortbb2in/4 0.03/0.35 1. SCC is partially evaluated into evalinsertsortbb5in/8 0.03/0.35 2. SCC is completely evaluated into other SCCs 0.03/0.35 3. SCC is completely evaluated into other SCCs 0.03/0.35 4. SCC is completely evaluated into other SCCs 0.03/0.35 5. SCC is partially evaluated into evalinsertsortbb5in_loop_cont/6 0.03/0.35 6. SCC is partially evaluated into evalinsertsortentryin/5 0.03/0.35 7. SCC is partially evaluated into evalinsertsortstart/5 0.03/0.35 0.03/0.35 Control-Flow Refinement of Cost Relations 0.03/0.35 ===================================== 0.03/0.35 0.03/0.35 ### Specialization of cost equations evalinsertsortbb2in/4 0.03/0.35 * CE 12 is refined into CE [13] 0.03/0.35 * CE 9 is refined into CE [14] 0.03/0.35 * CE 11 is refined into CE [15] 0.03/0.35 * CE 10 is refined into CE [16] 0.03/0.35 0.03/0.35 0.03/0.35 ### Cost equations --> "Loop" of evalinsertsortbb2in/4 0.03/0.35 * CEs [16] --> Loop 13 0.03/0.35 * CEs [13] --> Loop 14 0.03/0.35 * CEs [14] --> Loop 15 0.03/0.35 * CEs [15] --> Loop 16 0.03/0.35 0.03/0.35 ### Ranking functions of CR evalinsertsortbb2in(C,D,F,G) 0.03/0.35 * RF of phase [13]: [D+1] 0.03/0.35 0.03/0.35 #### Partial ranking functions of CR evalinsertsortbb2in(C,D,F,G) 0.03/0.35 * Partial RF of phase [13]: 0.03/0.35 - RF of loop [13:1]: 0.03/0.35 D+1 0.03/0.35 0.03/0.35 0.03/0.35 ### Specialization of cost equations evalinsertsortbb5in/8 0.03/0.35 * CE 5 is refined into CE [17] 0.03/0.35 * CE 3 is refined into CE [18,19] 0.03/0.35 * CE 6 is refined into CE [20] 0.03/0.35 * CE 4 is refined into CE [21,22,23] 0.03/0.35 0.03/0.35 0.03/0.35 ### Cost equations --> "Loop" of evalinsertsortbb5in/8 0.03/0.35 * CEs [23] --> Loop 17 0.03/0.35 * CEs [22] --> Loop 18 0.03/0.35 * CEs [21] --> Loop 19 0.03/0.35 * CEs [17] --> Loop 20 0.03/0.35 * CEs [18,19] --> Loop 21 0.03/0.35 * CEs [20] --> Loop 22 0.03/0.35 0.03/0.35 ### Ranking functions of CR evalinsertsortbb5in(A,B,C,D,F,G,H,I) 0.03/0.35 * RF of phase [17,18,19]: [-A+B] 0.03/0.35 0.03/0.35 #### Partial ranking functions of CR evalinsertsortbb5in(A,B,C,D,F,G,H,I) 0.03/0.35 * Partial RF of phase [17,18,19]: 0.03/0.35 - RF of loop [17:1,18:1,19:1]: 0.03/0.35 -A+B 0.03/0.35 0.03/0.35 0.03/0.35 ### Specialization of cost equations evalinsertsortbb5in_loop_cont/6 0.03/0.35 * CE 7 is refined into CE [24] 0.03/0.35 * CE 8 is refined into CE [25] 0.03/0.35 0.03/0.35 0.03/0.35 ### Cost equations --> "Loop" of evalinsertsortbb5in_loop_cont/6 0.03/0.35 * CEs [24] --> Loop 23 0.03/0.35 * CEs [25] --> Loop 24 0.03/0.35 0.03/0.35 ### Ranking functions of CR evalinsertsortbb5in_loop_cont(A,B,C,D,E,F) 0.03/0.35 0.03/0.35 #### Partial ranking functions of CR evalinsertsortbb5in_loop_cont(A,B,C,D,E,F) 0.03/0.35 0.03/0.35 0.03/0.35 ### Specialization of cost equations evalinsertsortentryin/5 0.03/0.35 * CE 2 is refined into CE [26,27,28,29,30] 0.03/0.35 0.03/0.35 0.03/0.35 ### Cost equations --> "Loop" of evalinsertsortentryin/5 0.03/0.35 * CEs [28] --> Loop 25 0.03/0.35 * CEs [27,30] --> Loop 26 0.03/0.35 * CEs [29] --> Loop 27 0.03/0.35 * CEs [26] --> Loop 28 0.03/0.35 0.03/0.35 ### Ranking functions of CR evalinsertsortentryin(A,B,C,D,F) 0.03/0.35 0.03/0.35 #### Partial ranking functions of CR evalinsertsortentryin(A,B,C,D,F) 0.03/0.35 0.03/0.35 0.03/0.35 ### Specialization of cost equations evalinsertsortstart/5 0.03/0.35 * CE 1 is refined into CE [31,32,33,34] 0.03/0.35 0.03/0.35 0.03/0.35 ### Cost equations --> "Loop" of evalinsertsortstart/5 0.03/0.35 * CEs [34] --> Loop 29 0.03/0.35 * CEs [33] --> Loop 30 0.03/0.35 * CEs [32] --> Loop 31 0.03/0.35 * CEs [31] --> Loop 32 0.03/0.35 0.03/0.35 ### Ranking functions of CR evalinsertsortstart(A,B,C,D,F) 0.03/0.35 0.03/0.35 #### Partial ranking functions of CR evalinsertsortstart(A,B,C,D,F) 0.03/0.35 0.03/0.35 0.03/0.35 Computing Bounds 0.03/0.35 ===================================== 0.03/0.35 0.03/0.35 #### Cost of chains of evalinsertsortbb2in(C,D,F,G): 0.03/0.35 * Chain [[13],16]: 1*it(13)+0 0.03/0.35 Such that:it(13) =< D+1 0.03/0.35 0.03/0.35 with precondition: [F=2,G+1=0,D>=0] 0.03/0.35 0.03/0.35 * Chain [[13],15]: 1*it(13)+0 0.03/0.35 Such that:it(13) =< D-G 0.03/0.35 0.03/0.35 with precondition: [F=2,G>=0,D>=G+1] 0.03/0.35 0.03/0.35 * Chain [[13],14]: 1*it(13)+0 0.03/0.35 Such that:it(13) =< D+1 0.03/0.35 0.03/0.35 with precondition: [F=3,D>=0] 0.03/0.35 0.03/0.35 * Chain [15]: 0 0.03/0.35 with precondition: [F=2,D=G,D>=0] 0.03/0.35 0.03/0.35 * Chain [14]: 0 0.03/0.35 with precondition: [F=3,D+1>=0] 0.03/0.35 0.03/0.35 0.03/0.35 #### Cost of chains of evalinsertsortbb5in(A,B,C,D,F,G,H,I): 0.03/0.35 * Chain [[17,18,19],22]: 3*it(17)+1*s(5)+1*s(6)+0 0.03/0.35 Such that:aux(1) =< B 0.03/0.35 aux(5) =< -A+B 0.03/0.35 it(17) =< aux(5) 0.03/0.35 aux(2) =< aux(1) 0.03/0.35 s(5) =< it(17)*aux(1) 0.03/0.35 s(6) =< it(17)*aux(2) 0.03/0.35 0.03/0.35 with precondition: [F=3,A>=1,B>=A+1] 0.03/0.35 0.03/0.35 * Chain [[17,18,19],21]: 3*it(17)+1*s(5)+1*s(6)+1*s(7)+0 0.03/0.35 Such that:aux(6) =< -A+B 0.03/0.35 aux(7) =< B 0.03/0.35 s(7) =< aux(7) 0.03/0.35 it(17) =< aux(6) 0.03/0.35 aux(2) =< aux(7) 0.03/0.35 s(5) =< it(17)*aux(7) 0.03/0.35 s(6) =< it(17)*aux(2) 0.03/0.35 0.03/0.35 with precondition: [F=3,A>=1,B>=A+2] 0.03/0.35 0.03/0.35 * Chain [[17,18,19],20]: 3*it(17)+1*s(5)+1*s(6)+0 0.03/0.35 Such that:aux(1) =< G 0.03/0.35 aux(8) =< -A+G 0.03/0.35 it(17) =< aux(8) 0.03/0.35 aux(2) =< aux(1) 0.03/0.35 s(5) =< it(17)*aux(1) 0.03/0.35 s(6) =< it(17)*aux(2) 0.03/0.35 0.03/0.35 with precondition: [F=4,B=G,A>=1,I+1>=0,B>=A+1,B>=I+2] 0.03/0.35 0.03/0.35 * Chain [22]: 0 0.03/0.35 with precondition: [F=3,A>=1] 0.03/0.35 0.03/0.35 * Chain [21]: 1*s(7)+0 0.03/0.35 Such that:s(7) =< A 0.03/0.35 0.03/0.35 with precondition: [F=3,A>=1,B>=A+1] 0.03/0.35 0.03/0.35 * Chain [20]: 0 0.03/0.35 with precondition: [F=4,H=C,I=D,A=G,A>=1,A>=B] 0.03/0.35 0.03/0.35 0.03/0.35 #### Cost of chains of evalinsertsortbb5in_loop_cont(A,B,C,D,E,F): 0.03/0.35 * Chain [24]: 0 0.03/0.35 with precondition: [A=3] 0.03/0.35 0.03/0.35 * Chain [23]: 0 0.03/0.35 with precondition: [A=4] 0.03/0.35 0.03/0.35 0.03/0.35 #### Cost of chains of evalinsertsortentryin(A,B,C,D,F): 0.03/0.35 * Chain [28]: 0 0.03/0.35 with precondition: [] 0.03/0.35 0.03/0.35 * Chain [27]: 0 0.03/0.35 with precondition: [1>=B] 0.03/0.35 0.03/0.35 * Chain [26]: 1*s(16)+6*s(18)+2*s(20)+2*s(21)+0 0.03/0.35 Such that:s(16) =< 1 0.03/0.35 aux(11) =< B 0.03/0.35 s(18) =< aux(11) 0.03/0.35 s(19) =< aux(11) 0.03/0.35 s(20) =< s(18)*aux(11) 0.03/0.35 s(21) =< s(18)*s(19) 0.03/0.35 0.03/0.35 with precondition: [B>=2] 0.03/0.35 0.03/0.35 * Chain [25]: 4*s(30)+1*s(33)+1*s(34)+0 0.03/0.35 Such that:aux(12) =< B 0.03/0.35 s(30) =< aux(12) 0.03/0.35 s(32) =< aux(12) 0.03/0.35 s(33) =< s(30)*aux(12) 0.03/0.35 s(34) =< s(30)*s(32) 0.03/0.35 0.03/0.35 with precondition: [B>=3] 0.03/0.35 0.03/0.35 0.03/0.35 #### Cost of chains of evalinsertsortstart(A,B,C,D,F): 0.03/0.35 * Chain [32]: 0 0.03/0.35 with precondition: [] 0.03/0.35 0.03/0.35 * Chain [31]: 0 0.03/0.35 with precondition: [1>=B] 0.03/0.35 0.03/0.35 * Chain [30]: 1*s(35)+6*s(37)+2*s(39)+2*s(40)+0 0.03/0.35 Such that:s(35) =< 1 0.03/0.35 s(36) =< B 0.03/0.35 s(37) =< s(36) 0.03/0.35 s(38) =< s(36) 0.03/0.35 s(39) =< s(37)*s(36) 0.03/0.35 s(40) =< s(37)*s(38) 0.03/0.35 0.03/0.35 with precondition: [B>=2] 0.03/0.35 0.03/0.35 * Chain [29]: 4*s(42)+1*s(44)+1*s(45)+0 0.03/0.35 Such that:s(41) =< B 0.03/0.35 s(42) =< s(41) 0.03/0.35 s(43) =< s(41) 0.03/0.35 s(44) =< s(42)*s(41) 0.03/0.35 s(45) =< s(42)*s(43) 0.03/0.35 0.03/0.35 with precondition: [B>=3] 0.03/0.35 0.03/0.35 0.03/0.35 Closed-form bounds of evalinsertsortstart(A,B,C,D,F): 0.03/0.35 ------------------------------------- 0.03/0.35 * Chain [32] with precondition: [] 0.03/0.35 - Upper bound: 0 0.03/0.35 - Complexity: constant 0.03/0.35 * Chain [31] with precondition: [1>=B] 0.03/0.35 - Upper bound: 0 0.03/0.35 - Complexity: constant 0.03/0.35 * Chain [30] with precondition: [B>=2] 0.03/0.35 - Upper bound: 6*B+1+4*B*B 0.03/0.35 - Complexity: n^2 0.03/0.35 * Chain [29] with precondition: [B>=3] 0.03/0.35 - Upper bound: 2*B*B+4*B 0.03/0.35 - Complexity: n^2 0.03/0.35 0.03/0.35 ### Maximum cost of evalinsertsortstart(A,B,C,D,F): nat(B)*2+1+nat(B)*2*nat(B)+(nat(B)*2*nat(B)+nat(B)*4) 0.03/0.35 Asymptotic class: n^2 0.03/0.35 * Total analysis performed in 274 ms. 0.03/0.35 0.03/0.45 EOF