0.59/0.61 WORST_CASE(?,O(n^1)) 0.59/0.61 0.59/0.61 Preprocessing Cost Relations 0.59/0.61 ===================================== 0.59/0.61 0.59/0.61 #### Computed strongly connected components 0.59/0.61 0. recursive : [f8/8] 0.59/0.61 1. recursive : [f16/8,f4/8,f8_loop_cont/9] 0.59/0.61 2. non_recursive : [exit_location/1] 0.59/0.61 3. non_recursive : [f20/5] 0.59/0.61 4. non_recursive : [f4_loop_cont/6] 0.59/0.61 5. non_recursive : [f0/5] 0.59/0.61 0.59/0.61 #### Obtained direct recursion through partial evaluation 0.59/0.61 0. SCC is partially evaluated into f8/8 0.59/0.61 1. SCC is partially evaluated into f4/8 0.59/0.61 2. SCC is completely evaluated into other SCCs 0.59/0.61 3. SCC is completely evaluated into other SCCs 0.59/0.61 4. SCC is partially evaluated into f4_loop_cont/6 0.59/0.61 5. SCC is partially evaluated into f0/5 0.59/0.61 0.59/0.61 Control-Flow Refinement of Cost Relations 0.59/0.61 ===================================== 0.59/0.61 0.59/0.61 ### Specialization of cost equations f8/8 0.59/0.61 * CE 13 is refined into CE [14] 0.59/0.61 * CE 10 is refined into CE [15] 0.59/0.61 * CE 9 is refined into CE [16] 0.59/0.61 * CE 12 is refined into CE [17] 0.59/0.61 * CE 11 is refined into CE [18] 0.59/0.61 0.59/0.61 0.59/0.61 ### Cost equations --> "Loop" of f8/8 0.59/0.61 * CEs [17] --> Loop 14 0.59/0.61 * CEs [18] --> Loop 15 0.59/0.61 * CEs [14] --> Loop 16 0.59/0.61 * CEs [15] --> Loop 17 0.59/0.61 * CEs [16] --> Loop 18 0.59/0.61 0.59/0.61 ### Ranking functions of CR f8(A,B,C,D,F,G,H,I) 0.59/0.61 * RF of phase [14,15]: [-A+B] 0.59/0.61 0.59/0.61 #### Partial ranking functions of CR f8(A,B,C,D,F,G,H,I) 0.59/0.61 * Partial RF of phase [14,15]: 0.59/0.61 - RF of loop [14:1,15:1]: 0.59/0.61 -A+B 0.59/0.61 0.59/0.61 0.59/0.61 ### Specialization of cost equations f4/8 0.59/0.61 * CE 5 is refined into CE [19] 0.59/0.61 * CE 4 is refined into CE [20,21] 0.59/0.61 * CE 6 is refined into CE [22] 0.59/0.61 * CE 2 is refined into CE [23,24] 0.59/0.61 * CE 3 is refined into CE [25,26] 0.59/0.61 0.59/0.61 0.59/0.61 ### Cost equations --> "Loop" of f4/8 0.59/0.61 * CEs [24] --> Loop 19 0.59/0.61 * CEs [23] --> Loop 20 0.59/0.61 * CEs [26] --> Loop 21 0.59/0.61 * CEs [25] --> Loop 22 0.59/0.61 * CEs [19] --> Loop 23 0.59/0.61 * CEs [21] --> Loop 24 0.59/0.61 * CEs [20] --> Loop 25 0.59/0.61 * CEs [22] --> Loop 26 0.59/0.61 0.59/0.61 ### Ranking functions of CR f4(A,B,C,D,F,G,H,I) 0.59/0.61 * RF of phase [20,22]: [-A+B-1] 0.59/0.61 0.59/0.61 #### Partial ranking functions of CR f4(A,B,C,D,F,G,H,I) 0.59/0.61 * Partial RF of phase [20,22]: 0.59/0.61 - RF of loop [20:1]: 0.59/0.61 -A+B-2 0.59/0.61 - RF of loop [22:1]: 0.59/0.61 -A+B-1 0.59/0.61 0.59/0.61 0.59/0.61 ### Specialization of cost equations f4_loop_cont/6 0.59/0.61 * CE 7 is refined into CE [27] 0.59/0.61 * CE 8 is refined into CE [28] 0.59/0.61 0.59/0.61 0.59/0.61 ### Cost equations --> "Loop" of f4_loop_cont/6 0.59/0.61 * CEs [27] --> Loop 27 0.59/0.61 * CEs [28] --> Loop 28 0.59/0.61 0.59/0.61 ### Ranking functions of CR f4_loop_cont(A,B,C,D,E,F) 0.59/0.61 0.59/0.61 #### Partial ranking functions of CR f4_loop_cont(A,B,C,D,E,F) 0.59/0.61 0.59/0.61 0.59/0.61 ### Specialization of cost equations f0/5 0.59/0.61 * CE 1 is refined into CE [29,30,31,32,33,34,35,36,37,38] 0.59/0.61 0.59/0.61 0.59/0.61 ### Cost equations --> "Loop" of f0/5 0.59/0.61 * CEs [33,37] --> Loop 29 0.59/0.61 * CEs [32,34,36] --> Loop 30 0.59/0.61 * CEs [31] --> Loop 31 0.59/0.61 * CEs [38] --> Loop 32 0.59/0.61 * CEs [29,35] --> Loop 33 0.59/0.61 * CEs [30] --> Loop 34 0.59/0.61 0.59/0.61 ### Ranking functions of CR f0(A,B,C,D,F) 0.59/0.61 0.59/0.61 #### Partial ranking functions of CR f0(A,B,C,D,F) 0.59/0.61 0.59/0.61 0.59/0.61 Computing Bounds 0.59/0.61 ===================================== 0.59/0.61 0.59/0.61 #### Cost of chains of f8(A,B,C,D,F,G,H,I): 0.59/0.61 * Chain [[14,15],18]: 2*it(14)+0 0.59/0.61 Such that:aux(1) =< -A+B 0.59/0.61 aux(2) =< -A+G 0.59/0.61 it(14) =< aux(1) 0.59/0.61 it(14) =< aux(2) 0.59/0.61 0.59/0.61 with precondition: [F=2,I=0,A+H=C+G,C>=0,G>=A+1,B>=G+1] 0.59/0.61 0.59/0.61 * Chain [[14,15],17]: 2*it(14)+0 0.59/0.61 Such that:aux(3) =< -A+B 0.59/0.61 it(14) =< aux(3) 0.59/0.61 0.59/0.61 with precondition: [F=2,B=G,A+H=B+C,C>=0,B>=A+1] 0.59/0.61 0.59/0.61 * Chain [[14,15],16]: 2*it(14)+0 0.59/0.61 Such that:aux(4) =< -A+B 0.59/0.61 it(14) =< aux(4) 0.59/0.61 0.59/0.61 with precondition: [F=3,C>=0,B>=A+1] 0.59/0.61 0.59/0.61 * Chain [18]: 0 0.59/0.61 with precondition: [F=2,I=0,A=G,C=H,C>=0,B>=A+1] 0.59/0.61 0.59/0.61 * Chain [17]: 0 0.59/0.61 with precondition: [F=2,B=A,I=D,B=G,C=H,C>=0] 0.59/0.61 0.59/0.61 * Chain [16]: 0 0.59/0.61 with precondition: [F=3,C>=0,B>=A] 0.59/0.61 0.59/0.61 0.59/0.61 #### Cost of chains of f4(A,B,C,D,F,G,H,I): 0.59/0.61 * Chain [[20,22],26]: 2*it(20)+2*s(7)+0 0.59/0.61 Such that:aux(5) =< B 0.59/0.61 aux(8) =< -A+B 0.59/0.61 aux(5) =< aux(8) 0.59/0.61 it(20) =< aux(8) 0.59/0.61 s(9) =< it(20)*aux(5) 0.59/0.61 s(7) =< s(9) 0.59/0.61 s(7) =< aux(8) 0.59/0.61 0.59/0.61 with precondition: [F=3,A>=0,B>=A+2] 0.59/0.61 0.59/0.61 * Chain [[20,22],25]: 2*it(20)+2*s(7)+0 0.59/0.61 Such that:aux(5) =< B 0.59/0.61 aux(9) =< -A+B 0.59/0.61 aux(5) =< aux(9) 0.59/0.61 it(20) =< aux(9) 0.59/0.61 s(9) =< it(20)*aux(5) 0.59/0.61 s(7) =< s(9) 0.59/0.61 s(7) =< aux(9) 0.59/0.61 0.59/0.61 with precondition: [F=3,A>=0,B>=A+2] 0.59/0.61 0.59/0.61 * Chain [[20,22],24]: 4*it(20)+2*s(7)+0 0.59/0.61 Such that:aux(5) =< B 0.59/0.61 aux(10) =< -A+B 0.59/0.61 it(20) =< aux(10) 0.59/0.61 aux(5) =< aux(10) 0.59/0.61 s(9) =< it(20)*aux(5) 0.59/0.61 s(7) =< s(9) 0.59/0.61 s(7) =< aux(10) 0.59/0.61 0.59/0.61 with precondition: [F=3,A>=0,B>=A+3] 0.59/0.61 0.59/0.61 * Chain [[20,22],21,26]: 2*it(20)+2*s(7)+1 0.59/0.61 Such that:aux(5) =< B 0.59/0.61 aux(11) =< -A+B 0.59/0.61 aux(5) =< aux(11) 0.59/0.61 it(20) =< aux(11) 0.59/0.61 s(9) =< it(20)*aux(5) 0.59/0.61 s(7) =< s(9) 0.59/0.61 s(7) =< aux(11) 0.59/0.61 0.59/0.61 with precondition: [F=3,A>=0,B>=A+2] 0.59/0.61 0.59/0.61 * Chain [[20,22],21,23]: 2*it(20)+2*s(7)+1 0.59/0.61 Such that:aux(5) =< G 0.59/0.61 aux(12) =< -A+G 0.59/0.61 aux(5) =< aux(12) 0.59/0.61 it(20) =< aux(12) 0.59/0.61 s(9) =< it(20)*aux(5) 0.59/0.61 s(7) =< s(9) 0.59/0.61 s(7) =< aux(12) 0.59/0.61 0.59/0.61 with precondition: [F=4,H=0,I=0,B=G,A>=0,B>=A+2] 0.59/0.61 0.59/0.61 * Chain [[20,22],19,26]: 4*it(20)+2*s(7)+1 0.59/0.61 Such that:aux(5) =< B 0.59/0.61 aux(13) =< -A+B 0.59/0.61 it(20) =< aux(13) 0.59/0.61 aux(5) =< aux(13) 0.59/0.61 s(9) =< it(20)*aux(5) 0.59/0.61 s(7) =< s(9) 0.59/0.61 s(7) =< aux(13) 0.59/0.61 0.59/0.61 with precondition: [F=3,A>=0,B>=A+3] 0.59/0.61 0.59/0.61 * Chain [[20,22],19,25]: 4*it(20)+2*s(7)+1 0.59/0.61 Such that:aux(5) =< B 0.59/0.61 aux(14) =< -A+B 0.59/0.61 it(20) =< aux(14) 0.59/0.61 aux(5) =< aux(14) 0.59/0.61 s(9) =< it(20)*aux(5) 0.59/0.61 s(7) =< s(9) 0.59/0.61 s(7) =< aux(14) 0.59/0.61 0.59/0.61 with precondition: [F=3,A>=0,B>=A+3] 0.59/0.61 0.59/0.61 * Chain [[20,22],19,21,26]: 4*it(20)+2*s(7)+2 0.59/0.61 Such that:aux(5) =< B 0.59/0.61 aux(15) =< -A+B 0.59/0.61 it(20) =< aux(15) 0.59/0.61 aux(5) =< aux(15) 0.59/0.61 s(9) =< it(20)*aux(5) 0.59/0.61 s(7) =< s(9) 0.59/0.61 s(7) =< aux(15) 0.59/0.61 0.59/0.61 with precondition: [F=3,A>=0,B>=A+3] 0.59/0.61 0.59/0.61 * Chain [[20,22],19,21,23]: 4*it(20)+2*s(7)+2 0.59/0.61 Such that:aux(5) =< G 0.59/0.61 aux(16) =< -A+G 0.59/0.61 it(20) =< aux(16) 0.59/0.61 aux(5) =< aux(16) 0.59/0.61 s(9) =< it(20)*aux(5) 0.59/0.61 s(7) =< s(9) 0.59/0.61 s(7) =< aux(16) 0.59/0.61 0.59/0.61 with precondition: [F=4,H=0,B=G,A>=0,B>=A+3] 0.59/0.61 0.59/0.61 * Chain [26]: 0 0.59/0.61 with precondition: [F=3,A>=0] 0.59/0.61 0.59/0.61 * Chain [25]: 0 0.59/0.61 with precondition: [F=3,A>=0,B>=A+1] 0.59/0.61 0.59/0.61 * Chain [24]: 2*s(11)+0 0.59/0.61 Such that:s(10) =< -A+B 0.59/0.61 s(11) =< s(10) 0.59/0.61 0.59/0.61 with precondition: [F=3,A>=0,B>=A+2] 0.59/0.61 0.59/0.61 * Chain [23]: 0 0.59/0.61 with precondition: [F=4,H=C,I=D,A=G,A>=0,A>=B] 0.59/0.61 0.59/0.61 * Chain [21,26]: 1 0.59/0.61 with precondition: [F=3,B=A+1,B>=1] 0.59/0.61 0.59/0.61 * Chain [21,23]: 1 0.59/0.61 with precondition: [F=4,H=0,B=A+1,B=G,D=I,B>=1] 0.59/0.61 0.59/0.61 * Chain [19,26]: 2*s(13)+1 0.59/0.61 Such that:s(12) =< -A+B 0.59/0.61 s(13) =< s(12) 0.59/0.61 0.59/0.61 with precondition: [F=3,A>=0,B>=A+2] 0.59/0.61 0.59/0.62 * Chain [19,25]: 2*s(13)+1 0.59/0.62 Such that:s(12) =< -A+B 0.59/0.62 s(13) =< s(12) 0.59/0.62 0.59/0.62 with precondition: [F=3,A>=0,B>=A+2] 0.59/0.62 0.59/0.62 * Chain [19,21,26]: 2*s(13)+2 0.59/0.62 Such that:s(12) =< -A+B 0.59/0.62 s(13) =< s(12) 0.59/0.62 0.59/0.62 with precondition: [F=3,A>=0,B>=A+2] 0.59/0.62 0.59/0.62 * Chain [19,21,23]: 2*s(13)+2 0.59/0.62 Such that:s(12) =< -A+B 0.59/0.62 s(13) =< s(12) 0.59/0.62 0.59/0.62 with precondition: [F=4,H=0,B=G,A>=0,B>=A+2] 0.59/0.62 0.59/0.62 0.59/0.62 #### Cost of chains of f4_loop_cont(A,B,C,D,E,F): 0.59/0.62 * Chain [28]: 0 0.59/0.62 with precondition: [A=3] 0.59/0.62 0.59/0.62 * Chain [27]: 0 0.59/0.62 with precondition: [A=4] 0.59/0.62 0.59/0.62 0.59/0.62 #### Cost of chains of f0(A,B,C,D,F): 0.59/0.62 * Chain [34]: 0 0.59/0.62 with precondition: [] 0.59/0.62 0.59/0.62 * Chain [33]: 1 0.59/0.62 with precondition: [B=1] 0.59/0.62 0.59/0.62 * Chain [32]: 0 0.59/0.62 with precondition: [0>=B] 0.59/0.62 0.59/0.62 * Chain [31]: 0 0.59/0.62 with precondition: [B>=1] 0.59/0.62 0.59/0.62 * Chain [30]: 18*s(60)+8*s(62)+2 0.59/0.62 Such that:aux(23) =< B 0.59/0.62 s(60) =< aux(23) 0.59/0.62 s(61) =< s(60)*aux(23) 0.59/0.62 s(62) =< s(61) 0.59/0.62 s(62) =< aux(23) 0.59/0.62 0.59/0.62 with precondition: [B>=2] 0.59/0.62 0.59/0.62 * Chain [29]: 20*s(73)+10*s(75)+2 0.59/0.62 Such that:aux(26) =< B 0.59/0.62 s(73) =< aux(26) 0.59/0.62 s(74) =< s(73)*aux(26) 0.59/0.62 s(75) =< s(74) 0.59/0.62 s(75) =< aux(26) 0.59/0.62 0.59/0.62 with precondition: [B>=3] 0.59/0.62 0.59/0.62 0.59/0.62 Closed-form bounds of f0(A,B,C,D,F): 0.59/0.62 ------------------------------------- 0.59/0.62 * Chain [34] with precondition: [] 0.59/0.62 - Upper bound: 0 0.59/0.62 - Complexity: constant 0.59/0.62 * Chain [33] with precondition: [B=1] 0.59/0.62 - Upper bound: 1 0.59/0.62 - Complexity: constant 0.59/0.62 * Chain [32] with precondition: [0>=B] 0.59/0.62 - Upper bound: 0 0.59/0.62 - Complexity: constant 0.59/0.62 * Chain [31] with precondition: [B>=1] 0.59/0.62 - Upper bound: 0 0.59/0.62 - Complexity: constant 0.59/0.62 * Chain [30] with precondition: [B>=2] 0.59/0.62 - Upper bound: 26*B+2 0.59/0.62 - Complexity: n 0.59/0.62 * Chain [29] with precondition: [B>=3] 0.59/0.62 - Upper bound: 30*B+2 0.59/0.62 - Complexity: n 0.59/0.62 0.59/0.62 ### Maximum cost of f0(A,B,C,D,F): nat(B)*30+1+1 0.59/0.62 Asymptotic class: n 0.59/0.62 * Total analysis performed in 530 ms. 0.59/0.62 0.62/0.72 EOF