0.53/0.53 WORST_CASE(?,O(n^2)) 0.53/0.53 0.53/0.53 Preprocessing Cost Relations 0.53/0.53 ===================================== 0.53/0.53 0.53/0.53 #### Computed strongly connected components 0.53/0.53 0. recursive : [f7/9] 0.53/0.53 1. recursive : [f4/9,f7_loop_cont/10] 0.53/0.53 2. non_recursive : [exit_location/1] 0.53/0.53 3. non_recursive : [f19/5] 0.53/0.53 4. non_recursive : [f4_loop_cont/6] 0.53/0.53 5. non_recursive : [f0/5] 0.53/0.53 0.53/0.53 #### Obtained direct recursion through partial evaluation 0.53/0.53 0. SCC is partially evaluated into f7/9 0.53/0.53 1. SCC is partially evaluated into f4/9 0.53/0.53 2. SCC is completely evaluated into other SCCs 0.53/0.53 3. SCC is completely evaluated into other SCCs 0.53/0.53 4. SCC is partially evaluated into f4_loop_cont/6 0.53/0.53 5. SCC is partially evaluated into f0/5 0.53/0.53 0.53/0.53 Control-Flow Refinement of Cost Relations 0.53/0.53 ===================================== 0.53/0.53 0.53/0.53 ### Specialization of cost equations f7/9 0.53/0.53 * CE 12 is refined into CE [13] 0.53/0.53 * CE 11 is refined into CE [14] 0.53/0.53 * CE 10 is refined into CE [15] 0.53/0.53 * CE 9 is refined into CE [16] 0.53/0.53 * CE 8 is refined into CE [17] 0.53/0.53 0.53/0.53 0.53/0.53 ### Cost equations --> "Loop" of f7/9 0.53/0.53 * CEs [15] --> Loop 13 0.53/0.53 * CEs [16] --> Loop 14 0.53/0.53 * CEs [17] --> Loop 15 0.53/0.53 * CEs [13] --> Loop 16 0.53/0.53 * CEs [14] --> Loop 17 0.53/0.53 0.53/0.53 ### Ranking functions of CR f7(A,B,C,D,F,G,H,I,J) 0.53/0.53 * RF of phase [13,14,15]: [B-C] 0.53/0.53 0.53/0.53 #### Partial ranking functions of CR f7(A,B,C,D,F,G,H,I,J) 0.53/0.53 * Partial RF of phase [13,14,15]: 0.53/0.53 - RF of loop [13:1,14:1]: 0.53/0.53 -A+B-1 0.53/0.53 - RF of loop [13:1,14:1,15:1]: 0.53/0.53 B-C 0.53/0.53 0.53/0.53 0.53/0.53 ### Specialization of cost equations f4/9 0.53/0.53 * CE 4 is refined into CE [18] 0.53/0.53 * CE 2 is refined into CE [19,20] 0.53/0.53 * CE 5 is refined into CE [21] 0.53/0.53 * CE 3 is refined into CE [22,23] 0.53/0.53 0.53/0.53 0.53/0.53 ### Cost equations --> "Loop" of f4/9 0.53/0.53 * CEs [23] --> Loop 18 0.53/0.53 * CEs [22] --> Loop 19 0.53/0.53 * CEs [18] --> Loop 20 0.53/0.53 * CEs [20] --> Loop 21 0.53/0.53 * CEs [19] --> Loop 22 0.53/0.53 * CEs [21] --> Loop 23 0.53/0.53 0.53/0.53 ### Ranking functions of CR f4(A,B,C,D,F,G,H,I,J) 0.53/0.53 * RF of phase [18]: [-A+B-1] 0.53/0.53 0.53/0.53 #### Partial ranking functions of CR f4(A,B,C,D,F,G,H,I,J) 0.53/0.53 * Partial RF of phase [18]: 0.53/0.53 - RF of loop [18:1]: 0.53/0.53 -A+B-1 0.53/0.53 0.53/0.53 0.53/0.53 ### Specialization of cost equations f4_loop_cont/6 0.53/0.53 * CE 6 is refined into CE [24] 0.53/0.53 * CE 7 is refined into CE [25] 0.53/0.53 0.53/0.53 0.53/0.53 ### Cost equations --> "Loop" of f4_loop_cont/6 0.53/0.53 * CEs [24] --> Loop 24 0.53/0.53 * CEs [25] --> Loop 25 0.53/0.53 0.53/0.53 ### Ranking functions of CR f4_loop_cont(A,B,C,D,E,F) 0.53/0.53 0.53/0.53 #### Partial ranking functions of CR f4_loop_cont(A,B,C,D,E,F) 0.53/0.53 0.53/0.53 0.53/0.53 ### Specialization of cost equations f0/5 0.53/0.53 * CE 1 is refined into CE [26,27,28,29,30,31,32,33,34] 0.53/0.53 0.53/0.53 0.53/0.53 ### Cost equations --> "Loop" of f0/5 0.53/0.53 * CEs [30] --> Loop 26 0.53/0.53 * CEs [29,33,34] --> Loop 27 0.53/0.53 * CEs [28] --> Loop 28 0.53/0.53 * CEs [32] --> Loop 29 0.53/0.53 * CEs [26,31] --> Loop 30 0.53/0.53 * CEs [27] --> Loop 31 0.53/0.53 0.53/0.53 ### Ranking functions of CR f0(A,B,C,D,F) 0.53/0.53 0.53/0.53 #### Partial ranking functions of CR f0(A,B,C,D,F) 0.53/0.53 0.53/0.53 0.53/0.53 Computing Bounds 0.53/0.53 ===================================== 0.53/0.53 0.53/0.53 #### Cost of chains of f7(A,B,C,D,F,G,H,I,J): 0.53/0.53 * Chain [[13,14,15],17]: 2*it(13)+1*it(15)+0 0.53/0.53 Such that:aux(1) =< -A+B 0.53/0.53 aux(2) =< B-I 0.53/0.53 aux(5) =< B-C 0.53/0.53 it(13) =< aux(1) 0.53/0.53 it(13) =< aux(2) 0.53/0.53 it(13) =< aux(5) 0.53/0.53 it(15) =< aux(5) 0.53/0.53 0.53/0.53 with precondition: [F=2,A+1=G,H=I,C>=A+1,B>=C+1,H>=C,B>=H] 0.53/0.53 0.53/0.53 * Chain [[13,14,15],16]: 2*it(13)+1*it(15)+0 0.53/0.53 Such that:aux(1) =< -A+B 0.53/0.53 aux(6) =< B-C 0.53/0.53 it(13) =< aux(1) 0.53/0.53 it(13) =< aux(6) 0.53/0.53 it(15) =< aux(6) 0.53/0.53 0.53/0.53 with precondition: [F=3,C>=A+1,B>=C+1] 0.53/0.53 0.53/0.53 * Chain [17]: 0 0.53/0.53 with precondition: [F=2,C=B,J=D,A+1=G,C=H,C=I,C>=A+1] 0.53/0.53 0.53/0.53 * Chain [16]: 0 0.53/0.53 with precondition: [F=3,C>=A+1,B>=C] 0.53/0.53 0.53/0.53 0.53/0.53 #### Cost of chains of f4(A,B,C,D,F,G,H,I,J): 0.53/0.53 * Chain [[18],23]: 1*it(18)+2*s(11)+1*s(12)+0 0.53/0.53 Such that:aux(7) =< B 0.53/0.53 aux(11) =< -A+B 0.53/0.53 aux(7) =< aux(11) 0.53/0.53 it(18) =< aux(11) 0.53/0.53 aux(8) =< aux(7)+1 0.53/0.53 s(13) =< it(18)*aux(7) 0.53/0.53 s(15) =< it(18)*aux(8) 0.53/0.53 s(11) =< s(15) 0.53/0.53 s(11) =< aux(11) 0.53/0.53 s(11) =< s(13) 0.53/0.53 s(12) =< s(13) 0.53/0.53 0.53/0.53 with precondition: [F=3,A>=0,B>=A+2] 0.53/0.53 0.53/0.53 * Chain [[18],22]: 1*it(18)+2*s(11)+1*s(12)+0 0.53/0.53 Such that:aux(7) =< B 0.53/0.53 aux(12) =< -A+B 0.53/0.53 aux(7) =< aux(12) 0.53/0.53 it(18) =< aux(12) 0.53/0.53 aux(8) =< aux(7)+1 0.53/0.53 s(13) =< it(18)*aux(7) 0.53/0.53 s(15) =< it(18)*aux(8) 0.53/0.53 s(11) =< s(15) 0.53/0.53 s(11) =< aux(12) 0.53/0.53 s(11) =< s(13) 0.53/0.53 s(12) =< s(13) 0.53/0.53 0.53/0.53 with precondition: [F=3,A>=0,B>=A+2] 0.53/0.53 0.53/0.53 * Chain [[18],21]: 4*it(18)+2*s(11)+1*s(12)+0 0.53/0.53 Such that:aux(7) =< B 0.53/0.53 aux(14) =< -A+B 0.53/0.53 it(18) =< aux(14) 0.53/0.53 aux(7) =< aux(14) 0.53/0.53 aux(8) =< aux(7)+1 0.53/0.53 s(13) =< it(18)*aux(7) 0.53/0.53 s(15) =< it(18)*aux(8) 0.53/0.53 s(11) =< s(15) 0.53/0.53 s(11) =< aux(14) 0.53/0.53 s(11) =< s(13) 0.53/0.53 s(12) =< s(13) 0.53/0.53 0.53/0.53 with precondition: [F=3,A>=0,B>=A+3] 0.53/0.53 0.53/0.53 * Chain [[18],20]: 1*it(18)+2*s(11)+1*s(12)+0 0.53/0.53 Such that:aux(7) =< B 0.53/0.53 aux(15) =< -A+B 0.53/0.53 aux(7) =< aux(15) 0.53/0.53 it(18) =< aux(15) 0.53/0.53 aux(8) =< aux(7)+1 0.53/0.53 s(13) =< it(18)*aux(7) 0.53/0.53 s(15) =< it(18)*aux(8) 0.53/0.53 s(11) =< s(15) 0.53/0.53 s(11) =< aux(15) 0.53/0.53 s(11) =< s(13) 0.53/0.53 s(12) =< s(13) 0.53/0.53 0.53/0.53 with precondition: [F=4,G=H,G=I,A>=0,G>=A+1,B>=G+1] 0.53/0.53 0.53/0.53 * Chain [[18],19,23]: 1*it(18)+2*s(11)+1*s(12)+1 0.53/0.53 Such that:aux(7) =< B 0.53/0.53 aux(16) =< -A+B 0.53/0.53 aux(7) =< aux(16) 0.53/0.53 it(18) =< aux(16) 0.53/0.53 aux(8) =< aux(7)+1 0.53/0.53 s(13) =< it(18)*aux(7) 0.53/0.53 s(15) =< it(18)*aux(8) 0.53/0.53 s(11) =< s(15) 0.53/0.53 s(11) =< aux(16) 0.53/0.53 s(11) =< s(13) 0.53/0.53 s(12) =< s(13) 0.53/0.53 0.53/0.53 with precondition: [F=3,A>=0,B>=A+2] 0.53/0.53 0.53/0.53 * Chain [[18],19,20]: 1*it(18)+2*s(11)+1*s(12)+1 0.53/0.53 Such that:aux(7) =< B 0.53/0.53 aux(17) =< -A+B 0.53/0.53 aux(7) =< aux(17) 0.53/0.53 it(18) =< aux(17) 0.53/0.53 aux(8) =< aux(7)+1 0.53/0.53 s(13) =< it(18)*aux(7) 0.53/0.53 s(15) =< it(18)*aux(8) 0.53/0.53 s(11) =< s(15) 0.53/0.53 s(11) =< aux(17) 0.53/0.53 s(11) =< s(13) 0.53/0.53 s(12) =< s(13) 0.53/0.53 0.53/0.53 with precondition: [F=4,G=H,G=I,A>=0,G>=A+2,B>=G] 0.53/0.53 0.53/0.53 * Chain [23]: 0 0.53/0.53 with precondition: [F=3,A>=0] 0.53/0.53 0.53/0.53 * Chain [22]: 0 0.53/0.53 with precondition: [F=3,A>=0,B>=A+1] 0.53/0.53 0.53/0.53 * Chain [21]: 3*s(18)+0 0.53/0.53 Such that:aux(13) =< -A+B 0.53/0.53 s(18) =< aux(13) 0.53/0.53 0.53/0.53 with precondition: [F=3,A>=0,B>=A+2] 0.53/0.53 0.53/0.53 * Chain [20]: 0 0.53/0.53 with precondition: [F=4,I=C,J=D,A=G,B=H,A>=0,A>=B] 0.53/0.53 0.53/0.53 * Chain [19,23]: 1 0.53/0.53 with precondition: [F=3,B=A+1,B>=1] 0.53/0.53 0.53/0.53 * Chain [19,20]: 1 0.53/0.53 with precondition: [F=4,B=A+1,B=G,B=H,B=I,D=J,B>=1] 0.53/0.53 0.53/0.53 0.53/0.53 #### Cost of chains of f4_loop_cont(A,B,C,D,E,F): 0.53/0.53 * Chain [25]: 0 0.53/0.53 with precondition: [A=3] 0.53/0.53 0.53/0.53 * Chain [24]: 0 0.53/0.53 with precondition: [A=4] 0.53/0.53 0.53/0.53 0.53/0.53 #### Cost of chains of f0(A,B,C,D,F): 0.53/0.53 * Chain [31]: 0 0.53/0.53 with precondition: [] 0.53/0.53 0.53/0.53 * Chain [30]: 1 0.53/0.53 with precondition: [B=1] 0.53/0.53 0.53/0.53 * Chain [29]: 0 0.53/0.53 with precondition: [0>=B] 0.53/0.53 0.53/0.53 * Chain [28]: 0 0.53/0.53 with precondition: [B>=1] 0.53/0.53 0.53/0.53 * Chain [27]: 8*s(49)+10*s(53)+5*s(54)+1 0.53/0.53 Such that:aux(23) =< B 0.53/0.53 s(49) =< aux(23) 0.53/0.53 s(50) =< aux(23)+1 0.53/0.53 s(51) =< s(49)*aux(23) 0.53/0.53 s(52) =< s(49)*s(50) 0.53/0.53 s(53) =< s(52) 0.53/0.53 s(53) =< aux(23) 0.53/0.53 s(53) =< s(51) 0.53/0.53 s(54) =< s(51) 0.53/0.53 0.53/0.53 with precondition: [B>=2] 0.53/0.53 0.53/0.53 * Chain [26]: 4*s(73)+2*s(77)+1*s(78)+0 0.53/0.53 Such that:aux(24) =< B 0.53/0.53 s(73) =< aux(24) 0.53/0.53 s(74) =< aux(24)+1 0.53/0.53 s(75) =< s(73)*aux(24) 0.53/0.53 s(76) =< s(73)*s(74) 0.53/0.53 s(77) =< s(76) 0.53/0.53 s(77) =< aux(24) 0.53/0.53 s(77) =< s(75) 0.53/0.53 s(78) =< s(75) 0.53/0.53 0.53/0.53 with precondition: [B>=3] 0.53/0.53 0.53/0.53 0.53/0.53 Closed-form bounds of f0(A,B,C,D,F): 0.53/0.53 ------------------------------------- 0.53/0.53 * Chain [31] with precondition: [] 0.53/0.53 - Upper bound: 0 0.53/0.53 - Complexity: constant 0.53/0.53 * Chain [30] with precondition: [B=1] 0.53/0.53 - Upper bound: 1 0.53/0.53 - Complexity: constant 0.53/0.53 * Chain [29] with precondition: [0>=B] 0.53/0.53 - Upper bound: 0 0.53/0.53 - Complexity: constant 0.53/0.53 * Chain [28] with precondition: [B>=1] 0.53/0.53 - Upper bound: 0 0.53/0.53 - Complexity: constant 0.53/0.53 * Chain [27] with precondition: [B>=2] 0.53/0.53 - Upper bound: 18*B+1+5*B*B 0.53/0.53 - Complexity: n^2 0.53/0.53 * Chain [26] with precondition: [B>=3] 0.53/0.53 - Upper bound: 6*B+B*B 0.53/0.53 - Complexity: n^2 0.53/0.53 0.53/0.53 ### Maximum cost of f0(A,B,C,D,F): max([1,nat(B)*12+1+nat(B)*4*nat(B)+(nat(B)*nat(B)+nat(B)*6)]) 0.53/0.53 Asymptotic class: n^2 0.53/0.53 * Total analysis performed in 450 ms. 0.53/0.53 0.53/0.64 EOF