0.03/0.46 WORST_CASE(?,O(n^2)) 0.03/0.46 0.03/0.46 Preprocessing Cost Relations 0.03/0.46 ===================================== 0.03/0.46 0.03/0.46 #### Computed strongly connected components 0.03/0.46 0. recursive : [evalEx1bb1in/5,evalEx1bb4in/5] 0.03/0.46 1. recursive : [evalEx1bb4in_loop_cont/10,evalEx1bb5in/9,evalEx1bb6in/9,evalEx1bbin/9] 0.03/0.46 2. non_recursive : [evalEx1stop/5] 0.03/0.46 3. non_recursive : [evalEx1returnin/5] 0.03/0.46 4. non_recursive : [exit_location/1] 0.03/0.46 5. non_recursive : [evalEx1bb6in_loop_cont/6] 0.03/0.46 6. non_recursive : [evalEx1entryin/5] 0.03/0.46 7. non_recursive : [evalEx1start/5] 0.03/0.46 0.03/0.46 #### Obtained direct recursion through partial evaluation 0.03/0.46 0. SCC is partially evaluated into evalEx1bb4in/5 0.03/0.46 1. SCC is partially evaluated into evalEx1bb6in/9 0.03/0.46 2. SCC is completely evaluated into other SCCs 0.03/0.46 3. SCC is completely evaluated into other SCCs 0.03/0.46 4. SCC is completely evaluated into other SCCs 0.03/0.46 5. SCC is partially evaluated into evalEx1bb6in_loop_cont/6 0.03/0.46 6. SCC is partially evaluated into evalEx1entryin/5 0.03/0.46 7. SCC is partially evaluated into evalEx1start/5 0.03/0.46 0.03/0.46 Control-Flow Refinement of Cost Relations 0.03/0.46 ===================================== 0.03/0.46 0.03/0.46 ### Specialization of cost equations evalEx1bb4in/5 0.03/0.46 * CE 12 is refined into CE [13] 0.03/0.46 * CE 11 is refined into CE [14] 0.03/0.46 * CE 10 is refined into CE [15] 0.03/0.46 * CE 9 is refined into CE [16] 0.03/0.46 0.03/0.46 0.03/0.46 ### Cost equations --> "Loop" of evalEx1bb4in/5 0.03/0.46 * CEs [15] --> Loop 13 0.03/0.46 * CEs [16] --> Loop 14 0.03/0.46 * CEs [13] --> Loop 15 0.03/0.46 * CEs [14] --> Loop 16 0.03/0.46 0.03/0.46 ### Ranking functions of CR evalEx1bb4in(C,D,F,G,H) 0.03/0.46 * RF of phase [13,14]: [-C+D] 0.03/0.46 0.03/0.46 #### Partial ranking functions of CR evalEx1bb4in(C,D,F,G,H) 0.03/0.46 * Partial RF of phase [13,14]: 0.03/0.46 - RF of loop [13:1]: 0.03/0.46 D-1 0.03/0.46 - RF of loop [13:1,14:1]: 0.03/0.46 -C+D 0.03/0.46 0.03/0.46 0.03/0.46 ### Specialization of cost equations evalEx1bb6in/9 0.03/0.46 * CE 5 is refined into CE [17] 0.03/0.46 * CE 3 is refined into CE [18,19] 0.03/0.46 * CE 6 is refined into CE [20] 0.03/0.46 * CE 4 is refined into CE [21,22] 0.03/0.46 0.03/0.46 0.03/0.46 ### Cost equations --> "Loop" of evalEx1bb6in/9 0.03/0.46 * CEs [22] --> Loop 17 0.03/0.46 * CEs [21] --> Loop 18 0.03/0.46 * CEs [17] --> Loop 19 0.03/0.46 * CEs [19] --> Loop 20 0.03/0.46 * CEs [18] --> Loop 21 0.03/0.46 * CEs [20] --> Loop 22 0.03/0.46 0.03/0.46 ### Ranking functions of CR evalEx1bb6in(A,B,C,D,F,G,H,I,J) 0.03/0.46 * RF of phase [17]: [-A+B-1] 0.03/0.46 0.03/0.46 #### Partial ranking functions of CR evalEx1bb6in(A,B,C,D,F,G,H,I,J) 0.03/0.46 * Partial RF of phase [17]: 0.03/0.46 - RF of loop [17:1]: 0.03/0.46 -A+B-1 0.03/0.46 0.03/0.46 0.03/0.46 ### Specialization of cost equations evalEx1bb6in_loop_cont/6 0.03/0.46 * CE 7 is refined into CE [23] 0.03/0.46 * CE 8 is refined into CE [24] 0.03/0.46 0.03/0.46 0.03/0.46 ### Cost equations --> "Loop" of evalEx1bb6in_loop_cont/6 0.03/0.46 * CEs [23] --> Loop 23 0.03/0.46 * CEs [24] --> Loop 24 0.03/0.46 0.03/0.46 ### Ranking functions of CR evalEx1bb6in_loop_cont(A,B,C,D,E,F) 0.03/0.46 0.03/0.46 #### Partial ranking functions of CR evalEx1bb6in_loop_cont(A,B,C,D,E,F) 0.03/0.46 0.03/0.46 0.03/0.46 ### Specialization of cost equations evalEx1entryin/5 0.03/0.46 * CE 2 is refined into CE [25,26,27,28,29,30,31,32,33] 0.03/0.46 0.03/0.46 0.03/0.46 ### Cost equations --> "Loop" of evalEx1entryin/5 0.03/0.46 * CEs [29] --> Loop 25 0.03/0.46 * CEs [28,32,33] --> Loop 26 0.03/0.46 * CEs [27] --> Loop 27 0.03/0.46 * CEs [31] --> Loop 28 0.03/0.46 * CEs [25,30] --> Loop 29 0.03/0.46 * CEs [26] --> Loop 30 0.03/0.46 0.03/0.46 ### Ranking functions of CR evalEx1entryin(A,B,C,D,F) 0.03/0.46 0.03/0.46 #### Partial ranking functions of CR evalEx1entryin(A,B,C,D,F) 0.03/0.46 0.03/0.46 0.03/0.46 ### Specialization of cost equations evalEx1start/5 0.03/0.46 * CE 1 is refined into CE [34,35,36,37,38,39] 0.03/0.46 0.03/0.46 0.03/0.46 ### Cost equations --> "Loop" of evalEx1start/5 0.03/0.46 * CEs [39] --> Loop 31 0.03/0.46 * CEs [38] --> Loop 32 0.03/0.46 * CEs [37] --> Loop 33 0.03/0.46 * CEs [36] --> Loop 34 0.03/0.46 * CEs [35] --> Loop 35 0.03/0.46 * CEs [34] --> Loop 36 0.03/0.46 0.03/0.46 ### Ranking functions of CR evalEx1start(A,B,C,D,F) 0.03/0.46 0.03/0.46 #### Partial ranking functions of CR evalEx1start(A,B,C,D,F) 0.03/0.46 0.03/0.46 0.03/0.47 Computing Bounds 0.03/0.47 ===================================== 0.03/0.47 0.03/0.47 #### Cost of chains of evalEx1bb4in(C,D,F,G,H): 0.03/0.47 * Chain [[13,14],16]: 1*it(13)+1*it(14)+0 0.03/0.47 Such that:it(13) =< D-H 0.03/0.47 aux(3) =< -C+D 0.03/0.47 it(13) =< aux(3) 0.03/0.47 it(14) =< aux(3) 0.03/0.47 0.03/0.47 with precondition: [F=2,G=H,C>=1,D>=C+1,G>=C,D>=G] 0.03/0.47 0.03/0.47 * Chain [[13,14],15]: 2*it(13)+0 0.03/0.47 Such that:aux(4) =< -C+D 0.03/0.47 it(13) =< aux(4) 0.03/0.47 0.03/0.47 with precondition: [F=3,C>=1,D>=C+1] 0.03/0.47 0.03/0.47 * Chain [16]: 0 0.03/0.47 with precondition: [F=2,D=C,D=G,D=H,D>=1] 0.03/0.47 0.03/0.47 * Chain [15]: 0 0.03/0.47 with precondition: [F=3,C>=1,D>=C] 0.03/0.47 0.03/0.47 0.03/0.47 #### Cost of chains of evalEx1bb6in(A,B,C,D,F,G,H,I,J): 0.03/0.47 * Chain [[17],22]: 1*it(17)+1*s(7)+1*s(8)+0 0.03/0.47 Such that:aux(5) =< B 0.03/0.47 aux(8) =< -A+B 0.03/0.47 aux(5) =< aux(8) 0.03/0.47 it(17) =< aux(8) 0.03/0.47 s(7) =< aux(8) 0.03/0.47 s(9) =< it(17)*aux(5) 0.03/0.47 s(7) =< s(9) 0.03/0.47 s(8) =< s(9) 0.03/0.47 0.03/0.47 with precondition: [F=3,A>=0,B>=A+2] 0.03/0.47 0.03/0.47 * Chain [[17],21]: 1*it(17)+1*s(7)+1*s(8)+0 0.03/0.47 Such that:aux(5) =< B 0.03/0.47 aux(9) =< -A+B 0.03/0.47 aux(5) =< aux(9) 0.03/0.47 it(17) =< aux(9) 0.03/0.47 s(7) =< aux(9) 0.03/0.47 s(9) =< it(17)*aux(5) 0.03/0.47 s(7) =< s(9) 0.03/0.47 s(8) =< s(9) 0.03/0.47 0.03/0.47 with precondition: [F=3,A>=0,B>=A+2] 0.03/0.47 0.03/0.47 * Chain [[17],20]: 3*it(17)+1*s(7)+1*s(8)+0 0.03/0.47 Such that:aux(5) =< B 0.03/0.47 aux(10) =< -A+B 0.03/0.47 it(17) =< aux(10) 0.03/0.47 aux(5) =< aux(10) 0.03/0.47 s(7) =< aux(10) 0.03/0.47 s(9) =< it(17)*aux(5) 0.03/0.47 s(7) =< s(9) 0.03/0.47 s(8) =< s(9) 0.03/0.47 0.03/0.47 with precondition: [F=3,A>=0,B>=A+3] 0.03/0.47 0.03/0.47 * Chain [[17],19]: 1*it(17)+1*s(7)+1*s(8)+0 0.03/0.47 Such that:aux(5) =< B 0.03/0.47 aux(11) =< -A+B 0.03/0.47 aux(5) =< aux(11) 0.03/0.47 it(17) =< aux(11) 0.03/0.47 s(7) =< aux(11) 0.03/0.47 s(9) =< it(17)*aux(5) 0.03/0.47 s(7) =< s(9) 0.03/0.47 s(8) =< s(9) 0.03/0.47 0.03/0.47 with precondition: [F=4,G=H,G=I,G=J,A>=0,G>=A+1,B>=G+1] 0.03/0.47 0.03/0.47 * Chain [[17],18,22]: 1*it(17)+1*s(7)+1*s(8)+1 0.03/0.47 Such that:aux(5) =< B 0.03/0.47 aux(12) =< -A+B 0.03/0.47 aux(5) =< aux(12) 0.03/0.47 it(17) =< aux(12) 0.03/0.47 s(7) =< aux(12) 0.03/0.47 s(9) =< it(17)*aux(5) 0.03/0.47 s(7) =< s(9) 0.03/0.47 s(8) =< s(9) 0.03/0.47 0.03/0.47 with precondition: [F=3,A>=0,B>=A+2] 0.03/0.47 0.03/0.47 * Chain [[17],18,19]: 1*it(17)+1*s(7)+1*s(8)+1 0.03/0.47 Such that:aux(5) =< B 0.03/0.47 aux(13) =< -A+B 0.03/0.47 aux(5) =< aux(13) 0.03/0.47 it(17) =< aux(13) 0.03/0.47 s(7) =< aux(13) 0.03/0.47 s(9) =< it(17)*aux(5) 0.03/0.47 s(7) =< s(9) 0.03/0.47 s(8) =< s(9) 0.03/0.47 0.03/0.47 with precondition: [F=4,G=H,G=I,G=J,A>=0,G>=A+2,B>=G] 0.03/0.47 0.03/0.47 * Chain [22]: 0 0.03/0.47 with precondition: [F=3,A>=0] 0.03/0.47 0.03/0.47 * Chain [21]: 0 0.03/0.47 with precondition: [F=3,A>=0,B>=A+1] 0.03/0.47 0.03/0.47 * Chain [20]: 2*s(11)+0 0.03/0.47 Such that:s(10) =< -A+B 0.03/0.47 s(11) =< s(10) 0.03/0.47 0.03/0.47 with precondition: [F=3,A>=0,B>=A+2] 0.03/0.47 0.03/0.47 * Chain [19]: 0 0.03/0.47 with precondition: [F=4,I=C,J=D,A=G,B=H,A>=0,A>=B] 0.03/0.47 0.03/0.47 * Chain [18,22]: 1 0.03/0.47 with precondition: [F=3,B=A+1,B>=1] 0.03/0.47 0.03/0.47 * Chain [18,19]: 1 0.03/0.47 with precondition: [F=4,B=A+1,B=G,B=H,B=I,B=J,B>=1] 0.03/0.47 0.03/0.47 0.03/0.47 #### Cost of chains of evalEx1bb6in_loop_cont(A,B,C,D,E,F): 0.03/0.47 * Chain [24]: 0 0.03/0.47 with precondition: [A=3] 0.03/0.47 0.03/0.47 * Chain [23]: 0 0.03/0.47 with precondition: [A=4] 0.03/0.47 0.03/0.47 0.03/0.47 #### Cost of chains of evalEx1entryin(A,B,C,D,F): 0.03/0.47 * Chain [30]: 0 0.03/0.47 with precondition: [] 0.03/0.47 0.03/0.47 * Chain [29]: 1 0.03/0.47 with precondition: [A=1] 0.03/0.47 0.03/0.47 * Chain [28]: 0 0.03/0.47 with precondition: [0>=A] 0.03/0.47 0.03/0.47 * Chain [27]: 0 0.03/0.47 with precondition: [A>=1] 0.03/0.47 0.03/0.47 * Chain [26]: 7*s(35)+5*s(36)+5*s(38)+1 0.03/0.47 Such that:aux(19) =< A 0.03/0.47 s(35) =< aux(19) 0.03/0.47 s(36) =< aux(19) 0.03/0.47 s(37) =< s(35)*aux(19) 0.03/0.47 s(36) =< s(37) 0.03/0.47 s(38) =< s(37) 0.03/0.47 0.03/0.47 with precondition: [A>=2] 0.03/0.47 0.03/0.47 * Chain [25]: 3*s(53)+1*s(54)+1*s(56)+0 0.03/0.47 Such that:aux(20) =< A 0.03/0.47 s(53) =< aux(20) 0.03/0.47 s(54) =< aux(20) 0.03/0.47 s(55) =< s(53)*aux(20) 0.03/0.47 s(54) =< s(55) 0.03/0.47 s(56) =< s(55) 0.03/0.47 0.03/0.47 with precondition: [A>=3] 0.03/0.47 0.03/0.47 0.03/0.47 #### Cost of chains of evalEx1start(A,B,C,D,F): 0.03/0.47 * Chain [36]: 0 0.03/0.47 with precondition: [] 0.03/0.47 0.03/0.47 * Chain [35]: 1 0.03/0.47 with precondition: [A=1] 0.03/0.47 0.03/0.47 * Chain [34]: 0 0.03/0.47 with precondition: [0>=A] 0.03/0.47 0.03/0.47 * Chain [33]: 0 0.03/0.47 with precondition: [A>=1] 0.03/0.47 0.03/0.47 * Chain [32]: 7*s(58)+5*s(59)+5*s(61)+1 0.03/0.47 Such that:s(57) =< A 0.03/0.47 s(58) =< s(57) 0.03/0.47 s(59) =< s(57) 0.03/0.47 s(60) =< s(58)*s(57) 0.03/0.47 s(59) =< s(60) 0.03/0.47 s(61) =< s(60) 0.03/0.47 0.03/0.47 with precondition: [A>=2] 0.03/0.47 0.03/0.47 * Chain [31]: 3*s(63)+1*s(64)+1*s(66)+0 0.03/0.47 Such that:s(62) =< A 0.03/0.47 s(63) =< s(62) 0.03/0.47 s(64) =< s(62) 0.03/0.47 s(65) =< s(63)*s(62) 0.03/0.47 s(64) =< s(65) 0.03/0.47 s(66) =< s(65) 0.03/0.47 0.03/0.47 with precondition: [A>=3] 0.03/0.47 0.03/0.47 0.03/0.47 Closed-form bounds of evalEx1start(A,B,C,D,F): 0.03/0.47 ------------------------------------- 0.03/0.47 * Chain [36] with precondition: [] 0.03/0.47 - Upper bound: 0 0.03/0.47 - Complexity: constant 0.03/0.47 * Chain [35] with precondition: [A=1] 0.03/0.47 - Upper bound: 1 0.03/0.47 - Complexity: constant 0.03/0.47 * Chain [34] with precondition: [0>=A] 0.03/0.47 - Upper bound: 0 0.03/0.47 - Complexity: constant 0.03/0.47 * Chain [33] with precondition: [A>=1] 0.03/0.47 - Upper bound: 0 0.03/0.47 - Complexity: constant 0.03/0.47 * Chain [32] with precondition: [A>=2] 0.03/0.47 - Upper bound: 12*A+1+5*A*A 0.03/0.47 - Complexity: n^2 0.03/0.47 * Chain [31] with precondition: [A>=3] 0.03/0.47 - Upper bound: 4*A+A*A 0.03/0.47 - Complexity: n^2 0.03/0.47 0.03/0.47 ### Maximum cost of evalEx1start(A,B,C,D,F): max([1,nat(A)*8+1+nat(A)*4*nat(A)+(nat(A)*nat(A)+nat(A)*4)]) 0.03/0.47 Asymptotic class: n^2 0.03/0.47 * Total analysis performed in 384 ms. 0.03/0.47 0.47/0.57 EOF