0.77/0.84 WORST_CASE(?,O(n^1)) 0.77/0.84 0.77/0.84 Preprocessing Cost Relations 0.77/0.84 ===================================== 0.77/0.84 0.77/0.84 #### Computed strongly connected components 0.77/0.84 0. recursive : [f4/7,f6/7,f7/7] 0.77/0.84 1. non_recursive : [exit_location/1] 0.77/0.84 2. non_recursive : [f14/5] 0.77/0.84 3. non_recursive : [f4_loop_cont/6] 0.77/0.84 4. non_recursive : [f0/5] 0.77/0.84 0.77/0.84 #### Obtained direct recursion through partial evaluation 0.77/0.84 0. SCC is partially evaluated into f4/7 0.77/0.84 1. SCC is completely evaluated into other SCCs 0.77/0.84 2. SCC is completely evaluated into other SCCs 0.77/0.84 3. SCC is partially evaluated into f4_loop_cont/6 0.77/0.84 4. SCC is partially evaluated into f0/5 0.77/0.84 0.77/0.84 Control-Flow Refinement of Cost Relations 0.77/0.84 ===================================== 0.77/0.84 0.77/0.84 ### Specialization of cost equations f4/7 0.77/0.84 * CE 13 is refined into CE [16] 0.77/0.84 * CE 12 is refined into CE [17] 0.77/0.84 * CE 3 is refined into CE [18] 0.77/0.84 * CE 2 is refined into CE [19] 0.77/0.84 * CE 7 is refined into CE [20] 0.77/0.84 * CE 6 is refined into CE [21] 0.77/0.84 * CE 5 is refined into CE [22] 0.77/0.84 * CE 4 is refined into CE [23] 0.77/0.84 * CE 11 is discarded (unfeasible) 0.77/0.84 * CE 10 is refined into CE [24] 0.77/0.84 * CE 9 is discarded (unfeasible) 0.77/0.84 * CE 8 is refined into CE [25] 0.77/0.84 0.77/0.84 0.77/0.84 ### Cost equations --> "Loop" of f4/7 0.77/0.84 * CEs [20] --> Loop 16 0.77/0.84 * CEs [21] --> Loop 17 0.77/0.84 * CEs [22] --> Loop 18 0.77/0.84 * CEs [23] --> Loop 19 0.77/0.84 * CEs [24] --> Loop 20 0.77/0.84 * CEs [25] --> Loop 21 0.77/0.84 * CEs [16] --> Loop 22 0.77/0.84 * CEs [17] --> Loop 23 0.77/0.84 * CEs [18] --> Loop 24 0.77/0.84 * CEs [19] --> Loop 25 0.77/0.84 0.77/0.84 ### Ranking functions of CR f4(A,B,C,D,F,G,H) 0.77/0.84 * RF of phase [16,18]: [B-D,C-D] 0.77/0.84 * RF of phase [17,19]: [C-D+1] 0.77/0.84 0.77/0.84 #### Partial ranking functions of CR f4(A,B,C,D,F,G,H) 0.77/0.84 * Partial RF of phase [16,18]: 0.77/0.84 - RF of loop [16:1,18:1]: 0.77/0.84 B-D 0.77/0.84 C-D 0.77/0.84 * Partial RF of phase [17,19]: 0.77/0.84 - RF of loop [17:1,19:1]: 0.77/0.84 C-D+1 0.77/0.84 0.77/0.84 0.77/0.84 ### Specialization of cost equations f4_loop_cont/6 0.77/0.84 * CE 15 is refined into CE [26] 0.77/0.84 * CE 14 is refined into CE [27] 0.77/0.84 0.77/0.84 0.77/0.84 ### Cost equations --> "Loop" of f4_loop_cont/6 0.77/0.84 * CEs [26] --> Loop 26 0.77/0.84 * CEs [27] --> Loop 27 0.77/0.84 0.77/0.84 ### Ranking functions of CR f4_loop_cont(A,B,C,D,E,F) 0.77/0.84 0.77/0.84 #### Partial ranking functions of CR f4_loop_cont(A,B,C,D,E,F) 0.77/0.84 0.77/0.84 0.77/0.84 ### Specialization of cost equations f0/5 0.77/0.84 * CE 1 is refined into CE [28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44] 0.77/0.84 0.77/0.84 0.77/0.84 ### Cost equations --> "Loop" of f0/5 0.77/0.84 * CEs [37] --> Loop 28 0.77/0.84 * CEs [33,39,44] --> Loop 29 0.77/0.84 * CEs [36,43] --> Loop 30 0.77/0.84 * CEs [35,42] --> Loop 31 0.77/0.84 * CEs [34] --> Loop 32 0.77/0.84 * CEs [32,38,41] --> Loop 33 0.77/0.84 * CEs [40] --> Loop 34 0.77/0.84 * CEs [30,31] --> Loop 35 0.77/0.84 * CEs [28,29] --> Loop 36 0.77/0.84 0.77/0.84 ### Ranking functions of CR f0(A,B,C,D,F) 0.77/0.84 0.77/0.84 #### Partial ranking functions of CR f0(A,B,C,D,F) 0.77/0.84 0.77/0.84 0.77/0.84 Computing Bounds 0.77/0.84 ===================================== 0.77/0.84 0.77/0.84 #### Cost of chains of f4(A,B,C,D,F,G,H): 0.77/0.84 * Chain [[17,19],25]: 2*it(17)+0 0.77/0.84 Such that:aux(1) =< C-D+1 0.77/0.84 aux(2) =< -D+H 0.77/0.84 it(17) =< aux(1) 0.77/0.84 it(17) =< aux(2) 0.77/0.84 0.77/0.84 with precondition: [F=2,G=0,B>=0,D>=B+1,H>=D+1,C+1>=H] 0.77/0.84 0.77/0.84 * Chain [[17,19],22]: 2*it(17)+0 0.77/0.84 Such that:aux(3) =< C-D+1 0.77/0.84 it(17) =< aux(3) 0.77/0.84 0.77/0.84 with precondition: [F=3,B>=0,D>=B+1,C>=D] 0.77/0.84 0.77/0.84 * Chain [[17,19],21,[16,18],24]: 2*it(16)+2*it(17)+1 0.77/0.84 Such that:aux(4) =< B 0.77/0.84 aux(6) =< C+1 0.77/0.84 aux(8) =< H 0.77/0.84 aux(9) =< C-D+1 0.77/0.84 it(16) =< aux(4) 0.77/0.84 it(16) =< aux(8) 0.77/0.84 it(16) =< aux(6) 0.77/0.84 it(17) =< aux(9) 0.77/0.84 0.77/0.84 with precondition: [F=2,G=0,H>=1,D>=B+1,C>=D,B>=H+1] 0.77/0.84 0.77/0.84 * Chain [[17,19],21,[16,18],23]: 2*it(16)+2*it(17)+1 0.77/0.84 Such that:aux(6) =< C+1 0.77/0.84 aux(10) =< H 0.77/0.84 aux(11) =< C-D+1 0.77/0.84 it(16) =< aux(10) 0.77/0.84 it(16) =< aux(6) 0.77/0.84 it(17) =< aux(11) 0.77/0.84 0.77/0.84 with precondition: [F=2,B=H,B>=1,D>=B+1,C>=D] 0.77/0.84 0.77/0.84 * Chain [[17,19],21,[16,18],22]: 2*it(16)+2*it(17)+1 0.77/0.84 Such that:aux(12) =< B 0.77/0.84 aux(6) =< C+1 0.77/0.84 aux(13) =< C-D+1 0.77/0.84 it(16) =< aux(12) 0.77/0.84 it(16) =< aux(6) 0.77/0.84 it(17) =< aux(13) 0.77/0.84 0.77/0.84 with precondition: [F=3,B>=1,D>=B+1,C>=D] 0.77/0.84 0.77/0.84 * Chain [[17,19],21,24]: 2*it(17)+1 0.77/0.84 Such that:aux(14) =< C-D+1 0.77/0.84 it(17) =< aux(14) 0.77/0.84 0.77/0.84 with precondition: [F=2,G=0,H=0,B>=1,D>=B+1,C>=D] 0.77/0.84 0.77/0.84 * Chain [[17,19],21,23]: 2*it(17)+1 0.77/0.84 Such that:aux(15) =< C-D+1 0.77/0.84 it(17) =< aux(15) 0.77/0.84 0.77/0.84 with precondition: [B=0,F=2,H=0,0>=G+1,D>=1,C>=D] 0.77/0.84 0.77/0.84 * Chain [[17,19],21,22]: 2*it(17)+1 0.77/0.84 Such that:aux(16) =< C-D+1 0.77/0.84 it(17) =< aux(16) 0.77/0.84 0.77/0.84 with precondition: [F=3,B>=0,D>=B+1,C>=D] 0.77/0.84 0.77/0.84 * Chain [[17,19],20,[16,18],24]: 2*it(16)+2*it(17)+1 0.77/0.84 Such that:aux(4) =< B 0.77/0.84 aux(6) =< C+1 0.77/0.84 aux(8) =< H 0.77/0.84 aux(17) =< C-D+1 0.77/0.84 it(16) =< aux(4) 0.77/0.84 it(16) =< aux(8) 0.77/0.84 it(16) =< aux(6) 0.77/0.84 it(17) =< aux(17) 0.77/0.84 0.77/0.84 with precondition: [F=2,G=0,H>=1,D>=B+1,C>=D,B>=H+1] 0.77/0.84 0.77/0.84 * Chain [[17,19],20,[16,18],23]: 2*it(16)+2*it(17)+1 0.77/0.84 Such that:aux(6) =< C+1 0.77/0.84 aux(10) =< H 0.77/0.84 aux(18) =< C-D+1 0.77/0.84 it(16) =< aux(10) 0.77/0.84 it(16) =< aux(6) 0.77/0.84 it(17) =< aux(18) 0.77/0.84 0.77/0.84 with precondition: [F=2,B=H,B>=1,D>=B+1,C>=D] 0.77/0.84 0.77/0.84 * Chain [[17,19],20,[16,18],22]: 2*it(16)+2*it(17)+1 0.77/0.84 Such that:aux(12) =< B 0.77/0.84 aux(6) =< C+1 0.77/0.84 aux(19) =< C-D+1 0.77/0.84 it(16) =< aux(12) 0.77/0.84 it(16) =< aux(6) 0.77/0.84 it(17) =< aux(19) 0.77/0.84 0.77/0.84 with precondition: [F=3,B>=1,D>=B+1,C>=D] 0.77/0.84 0.77/0.84 * Chain [[17,19],20,24]: 2*it(17)+1 0.77/0.84 Such that:aux(20) =< C-D+1 0.77/0.84 it(17) =< aux(20) 0.77/0.84 0.77/0.84 with precondition: [F=2,G=0,H=0,B>=1,D>=B+1,C>=D] 0.77/0.84 0.77/0.84 * Chain [[17,19],20,23]: 2*it(17)+1 0.77/0.84 Such that:aux(21) =< C-D+1 0.77/0.84 it(17) =< aux(21) 0.77/0.84 0.77/0.84 with precondition: [B=0,F=2,H=0,D>=1,G>=1,C>=D] 0.77/0.84 0.77/0.84 * Chain [[17,19],20,22]: 2*it(17)+1 0.77/0.84 Such that:aux(22) =< C-D+1 0.77/0.84 it(17) =< aux(22) 0.77/0.84 0.77/0.84 with precondition: [F=3,B>=0,D>=B+1,C>=D] 0.77/0.84 0.77/0.84 * Chain [25]: 0 0.77/0.84 with precondition: [F=2,G=0,D=H,B>=0,D>=B+1,C+1>=D] 0.77/0.84 0.77/0.84 * Chain [22]: 0 0.77/0.84 with precondition: [F=3,B>=0,D>=0,C>=B,C+1>=D] 0.77/0.84 0.77/0.84 * Chain [21,[16,18],24]: 2*it(16)+1 0.77/0.84 Such that:aux(4) =< B 0.77/0.84 aux(6) =< D 0.77/0.84 aux(8) =< H 0.77/0.84 it(16) =< aux(4) 0.77/0.84 it(16) =< aux(8) 0.77/0.84 it(16) =< aux(6) 0.77/0.84 0.77/0.84 with precondition: [F=2,G=0,C+1=D,H>=1,C>=B,B>=H+1] 0.77/0.84 0.77/0.84 * Chain [21,[16,18],23]: 2*it(16)+1 0.77/0.84 Such that:aux(6) =< D 0.77/0.84 aux(10) =< H 0.77/0.84 it(16) =< aux(10) 0.77/0.84 it(16) =< aux(6) 0.77/0.84 0.77/0.84 with precondition: [F=2,C+1=D,B=H,B>=1,C>=B] 0.77/0.84 0.77/0.84 * Chain [21,[16,18],22]: 2*it(16)+1 0.77/0.84 Such that:aux(12) =< B 0.77/0.84 aux(6) =< D 0.77/0.84 it(16) =< aux(12) 0.77/0.84 it(16) =< aux(6) 0.77/0.84 0.77/0.84 with precondition: [F=3,C+1=D,B>=1,C>=B] 0.77/0.84 0.77/0.84 * Chain [21,24]: 1 0.77/0.84 with precondition: [F=2,G=0,H=0,C+1=D,B>=1,C>=B] 0.77/0.84 0.77/0.84 * Chain [21,23]: 1 0.77/0.84 with precondition: [B=0,F=2,H=0,D=C+1,0>=G+1,D>=1] 0.77/0.84 0.77/0.84 * Chain [21,22]: 1 0.77/0.84 with precondition: [F=3,D=C+1,B>=0,D>=B+1] 0.77/0.84 0.77/0.84 * Chain [20,[16,18],24]: 2*it(16)+1 0.77/0.84 Such that:aux(4) =< B 0.77/0.84 aux(6) =< D 0.77/0.84 aux(8) =< H 0.77/0.84 it(16) =< aux(4) 0.77/0.84 it(16) =< aux(8) 0.77/0.84 it(16) =< aux(6) 0.77/0.84 0.77/0.84 with precondition: [F=2,G=0,C+1=D,H>=1,C>=B,B>=H+1] 0.77/0.84 0.77/0.84 * Chain [20,[16,18],23]: 2*it(16)+1 0.77/0.84 Such that:aux(6) =< D 0.77/0.84 aux(10) =< H 0.77/0.84 it(16) =< aux(10) 0.77/0.84 it(16) =< aux(6) 0.77/0.84 0.77/0.84 with precondition: [F=2,C+1=D,B=H,B>=1,C>=B] 0.77/0.84 0.77/0.84 * Chain [20,[16,18],22]: 2*it(16)+1 0.77/0.84 Such that:aux(12) =< B 0.77/0.84 aux(6) =< D 0.77/0.84 it(16) =< aux(12) 0.77/0.84 it(16) =< aux(6) 0.77/0.84 0.77/0.84 with precondition: [F=3,C+1=D,B>=1,C>=B] 0.77/0.84 0.77/0.84 * Chain [20,24]: 1 0.77/0.84 with precondition: [F=2,G=0,H=0,C+1=D,B>=1,C>=B] 0.77/0.84 0.77/0.84 * Chain [20,23]: 1 0.77/0.84 with precondition: [B=0,F=2,H=0,D=C+1,D>=1,G>=1] 0.77/0.84 0.77/0.84 * Chain [20,22]: 1 0.77/0.84 with precondition: [F=3,D=C+1,B>=0,D>=B+1] 0.77/0.84 0.77/0.84 0.77/0.84 #### Cost of chains of f4_loop_cont(A,B,C,D,E,F): 0.77/0.84 * Chain [27]: 0 0.77/0.84 with precondition: [A=2,C>=0,D>=C] 0.77/0.84 0.77/0.84 * Chain [26]: 0 0.77/0.84 with precondition: [A=3,C>=0,D>=C] 0.77/0.84 0.77/0.84 0.77/0.84 #### Cost of chains of f0(A,B,C,D,F): 0.77/0.84 * Chain [36]: 1 0.77/0.84 with precondition: [B=0,C=0] 0.77/0.84 0.77/0.84 * Chain [35]: 4*s(64)+1 0.77/0.84 Such that:aux(42) =< C 0.77/0.84 s(64) =< aux(42) 0.77/0.84 0.77/0.84 with precondition: [B=0,C>=1] 0.77/0.84 0.77/0.84 * Chain [34]: 1 0.77/0.84 with precondition: [B=C,B>=0] 0.77/0.84 0.77/0.84 * Chain [33]: 8*s(69)+1 0.77/0.84 Such that:aux(43) =< B 0.77/0.84 aux(44) =< B+1 0.77/0.84 s(69) =< aux(43) 0.77/0.84 s(69) =< aux(44) 0.77/0.84 0.77/0.84 with precondition: [B=C,B>=1] 0.77/0.84 0.77/0.84 * Chain [32]: 4*s(76)+1 0.77/0.84 Such that:s(74) =< B+1 0.77/0.84 aux(45) =< B 0.77/0.84 s(76) =< aux(45) 0.77/0.84 s(76) =< s(74) 0.77/0.84 0.77/0.84 with precondition: [B=C,B>=2] 0.77/0.84 0.77/0.84 * Chain [31]: 0 0.77/0.84 with precondition: [B>=0,C>=B] 0.77/0.84 0.77/0.84 * Chain [30]: 8*s(79)+1 0.77/0.84 Such that:aux(47) =< -B+C 0.77/0.84 s(79) =< aux(47) 0.77/0.84 0.77/0.84 with precondition: [B>=0,C>=B+1] 0.77/0.84 0.77/0.84 * Chain [29]: 12*s(83)+8*s(87)+1 0.77/0.84 Such that:aux(48) =< -B+C 0.77/0.84 aux(49) =< B 0.77/0.84 aux(50) =< C+1 0.77/0.84 s(83) =< aux(48) 0.77/0.84 s(87) =< aux(49) 0.77/0.84 s(87) =< aux(50) 0.77/0.84 0.77/0.84 with precondition: [B>=1,C>=B+1] 0.77/0.84 0.77/0.84 * Chain [28]: 4*s(98)+4*s(99)+1 0.77/0.84 Such that:s(96) =< -B+C 0.77/0.84 s(95) =< C+1 0.77/0.84 aux(51) =< B 0.77/0.84 s(98) =< aux(51) 0.77/0.84 s(98) =< s(95) 0.77/0.84 s(99) =< s(96) 0.77/0.84 0.77/0.84 with precondition: [B>=2,C>=B+1] 0.77/0.84 0.77/0.84 0.77/0.84 Closed-form bounds of f0(A,B,C,D,F): 0.77/0.84 ------------------------------------- 0.77/0.84 * Chain [36] with precondition: [B=0,C=0] 0.77/0.84 - Upper bound: 1 0.77/0.84 - Complexity: constant 0.77/0.84 * Chain [35] with precondition: [B=0,C>=1] 0.77/0.84 - Upper bound: 4*C+1 0.77/0.84 - Complexity: n 0.77/0.84 * Chain [34] with precondition: [B=C,B>=0] 0.77/0.84 - Upper bound: 1 0.77/0.84 - Complexity: constant 0.77/0.84 * Chain [33] with precondition: [B=C,B>=1] 0.77/0.84 - Upper bound: 8*B+1 0.77/0.84 - Complexity: n 0.77/0.84 * Chain [32] with precondition: [B=C,B>=2] 0.77/0.84 - Upper bound: 4*B+1 0.77/0.84 - Complexity: n 0.77/0.84 * Chain [31] with precondition: [B>=0,C>=B] 0.77/0.84 - Upper bound: 0 0.77/0.84 - Complexity: constant 0.77/0.84 * Chain [30] with precondition: [B>=0,C>=B+1] 0.77/0.84 - Upper bound: -8*B+8*C+1 0.77/0.84 - Complexity: n 0.77/0.84 * Chain [29] with precondition: [B>=1,C>=B+1] 0.77/0.84 - Upper bound: -4*B+12*C+1 0.77/0.84 - Complexity: n 0.77/0.84 * Chain [28] with precondition: [B>=2,C>=B+1] 0.77/0.84 - Upper bound: 4*C+1 0.77/0.84 - Complexity: n 0.77/0.84 0.77/0.84 ### Maximum cost of f0(A,B,C,D,F): max([-4*B+12*C+1,max([-8*B+8*C+1,4*C+1])]) 0.77/0.84 Asymptotic class: n 0.77/0.84 * Total analysis performed in 749 ms. 0.77/0.84 0.85/0.94 EOF