0.72/0.74 MAYBE 0.72/0.74 0.72/0.74 Preprocessing Cost Relations 0.72/0.74 ===================================== 0.72/0.74 0.72/0.74 #### Computed strongly connected components 0.72/0.74 0. recursive : [f25/9] 0.72/0.74 1. recursive : [f15/11,f25_loop_cont/12,f41/11] 0.72/0.74 2. non_recursive : [exit_location/1] 0.72/0.74 3. non_recursive : [f48/9] 0.72/0.74 4. non_recursive : [f15_loop_cont/10] 0.72/0.74 5. non_recursive : [f0/9] 0.72/0.74 0.72/0.74 #### Obtained direct recursion through partial evaluation 0.72/0.74 0. SCC is partially evaluated into f25/9 0.72/0.74 1. SCC is partially evaluated into f15/11 0.72/0.74 2. SCC is completely evaluated into other SCCs 0.72/0.74 3. SCC is completely evaluated into other SCCs 0.72/0.74 4. SCC is partially evaluated into f15_loop_cont/10 0.72/0.74 5. SCC is partially evaluated into f0/9 0.72/0.74 0.72/0.74 Control-Flow Refinement of Cost Relations 0.72/0.74 ===================================== 0.72/0.74 0.72/0.74 ### Specialization of cost equations f25/9 0.72/0.74 * CE 13 is refined into CE [14] 0.72/0.74 * CE 12 is refined into CE [15] 0.72/0.74 * CE 11 is refined into CE [16] 0.72/0.74 * CE 10 is refined into CE [17] 0.72/0.74 0.72/0.74 0.72/0.74 ### Cost equations --> "Loop" of f25/9 0.72/0.74 * CEs [17] --> Loop 14 0.72/0.74 * CEs [14] --> Loop 15 0.72/0.74 * CEs [15] --> Loop 16 0.72/0.74 * CEs [16] --> Loop 17 0.72/0.74 0.72/0.74 ### Ranking functions of CR f25(E,F,G,H,K,L,M,N,O) 0.72/0.74 * RF of phase [14]: [E-H] 0.72/0.74 0.72/0.74 #### Partial ranking functions of CR f25(E,F,G,H,K,L,M,N,O) 0.72/0.74 * Partial RF of phase [14]: 0.72/0.74 - RF of loop [14:1]: 0.72/0.74 E-H 0.72/0.74 0.72/0.74 0.72/0.74 ### Specialization of cost equations f15/11 0.72/0.74 * CE 6 is refined into CE [18] 0.72/0.74 * CE 2 is refined into CE [19,20] 0.72/0.74 * CE 7 is refined into CE [21] 0.72/0.74 * CE 5 is refined into CE [22,23] 0.72/0.74 * CE 3 is refined into CE [24,25] 0.72/0.74 * CE 4 is refined into CE [26] 0.72/0.74 0.72/0.74 0.72/0.74 ### Cost equations --> "Loop" of f15/11 0.72/0.74 * CEs [25] --> Loop 18 0.72/0.74 * CEs [26] --> Loop 19 0.72/0.74 * CEs [23] --> Loop 20 0.72/0.74 * CEs [24] --> Loop 21 0.72/0.74 * CEs [22] --> Loop 22 0.72/0.74 * CEs [18] --> Loop 23 0.72/0.74 * CEs [20] --> Loop 24 0.72/0.74 * CEs [19] --> Loop 25 0.72/0.74 * CEs [21] --> Loop 26 0.72/0.74 0.72/0.74 ### Ranking functions of CR f15(A,B,E,F,G,H,K,L,M,N,O) 0.72/0.74 * RF of phase [18,19,20,21,22]: [-F+10] 0.72/0.74 0.72/0.74 #### Partial ranking functions of CR f15(A,B,E,F,G,H,K,L,M,N,O) 0.72/0.74 * Partial RF of phase [18,19,20,21,22]: 0.72/0.74 - RF of loop [18:1]: 0.72/0.74 E-1 depends on loops [20:1,22:1] 0.72/0.74 - RF of loop [18:1,19:1,20:1,21:1,22:1]: 0.72/0.74 -F+10 0.72/0.74 - RF of loop [20:1]: 0.72/0.74 -E+35 depends on loops [18:1,21:1] 0.72/0.74 - RF of loop [22:1]: 0.72/0.74 -E+2 depends on loops [18:1,21:1] 0.72/0.74 0.72/0.74 0.72/0.74 ### Specialization of cost equations f15_loop_cont/10 0.72/0.74 * CE 8 is refined into CE [27] 0.72/0.74 * CE 9 is refined into CE [28] 0.72/0.74 0.72/0.74 0.72/0.74 ### Cost equations --> "Loop" of f15_loop_cont/10 0.72/0.74 * CEs [27] --> Loop 27 0.72/0.74 * CEs [28] --> Loop 28 0.72/0.74 0.72/0.74 ### Ranking functions of CR f15_loop_cont(A,B,C,D,E,F,G,H,I,J) 0.72/0.74 0.72/0.74 #### Partial ranking functions of CR f15_loop_cont(A,B,C,D,E,F,G,H,I,J) 0.72/0.74 0.72/0.74 0.72/0.74 ### Specialization of cost equations f0/9 0.72/0.74 * CE 1 is refined into CE [29,30,31,32,33,34] 0.72/0.74 0.72/0.74 0.72/0.74 ### Cost equations --> "Loop" of f0/9 0.72/0.74 * CEs [29,30,31,32,33,34] --> Loop 29 0.72/0.74 0.72/0.74 ### Ranking functions of CR f0(A,B,C,D,E,F,G,H,K) 0.72/0.74 0.72/0.74 #### Partial ranking functions of CR f0(A,B,C,D,E,F,G,H,K) 0.72/0.74 0.72/0.74 0.72/0.74 Computing Bounds 0.72/0.74 ===================================== 0.72/0.74 0.72/0.74 #### Cost of chains of f25(E,F,G,H,K,L,M,N,O): 0.72/0.74 * Chain [[14],17]: 1*it(14)+0 0.72/0.74 Such that:it(14) =< -H+L 0.72/0.74 0.72/0.74 with precondition: [K=2,E=L,F=M,E=O,9>=F,H>=1,E>=H+1] 0.72/0.74 0.72/0.74 * Chain [[14],16]: 1*it(14)+0 0.72/0.74 Such that:it(14) =< -H+L+1 0.72/0.74 0.72/0.74 with precondition: [K=3,E=L+1,F+1=M,E=O,9>=F,H>=1,E>=H+1] 0.72/0.74 0.72/0.74 * Chain [[14],15]: 1*it(14)+0 0.72/0.74 Such that:it(14) =< E-H 0.72/0.74 0.72/0.74 with precondition: [K=4,9>=F,H>=1,E>=H+1] 0.72/0.74 0.72/0.74 * Chain [17]: 0 0.72/0.74 with precondition: [K=2,N=G,E=L,F=M,H=O,9>=F,H>=1,H>=E] 0.72/0.74 0.72/0.74 * Chain [16]: 0 0.72/0.74 with precondition: [K=3,N=G,E=L+1,F+1=M,H=O,9>=F,H>=1,H>=E] 0.72/0.74 0.72/0.74 * Chain [15]: 0 0.72/0.74 with precondition: [K=4,9>=F,H>=1] 0.72/0.74 0.72/0.74 0.72/0.74 #### Cost of chains of f15(A,B,E,F,G,H,K,L,M,N,O): 0.72/0.74 * Chain [[18,19,20,21,22],26]: 3*it(18)+2*it(21)+1*s(7)+1*s(8)+1*s(9)+0 0.72/0.74 Such that:aux(3) =< E-F+8 0.72/0.74 aux(17) =< -35*F+350 0.72/0.74 aux(18) =< -F+10 0.72/0.74 it(21) =< aux(17) 0.72/0.74 s(9) =< aux(17) 0.72/0.74 it(18) =< aux(18) 0.72/0.74 it(21) =< aux(18) 0.72/0.74 aux(4) =< aux(3)+1 0.72/0.74 s(8) =< it(18)*aux(4) 0.72/0.74 s(7) =< it(18)*aux(3) 0.72/0.74 0.72/0.74 with precondition: [A=10,B=35,K=4,9>=F,F>=0] 0.72/0.74 0.72/0.74 * Chain [[18,19,20,21,22],25]: 3*it(18)+2*it(21)+1*s(7)+1*s(8)+1*s(9)+0 0.72/0.74 Such that:aux(3) =< E-F+8 0.72/0.74 aux(14) =< -35*F+315 0.72/0.74 aux(13) =< -35*F+350 0.72/0.74 aux(16) =< -F+9 0.72/0.74 aux(15) =< -F+10 0.72/0.74 it(21) =< aux(13) 0.72/0.74 s(9) =< aux(13) 0.72/0.74 it(21) =< aux(14) 0.72/0.74 s(9) =< aux(14) 0.72/0.74 it(18) =< aux(15) 0.72/0.74 it(21) =< aux(15) 0.72/0.74 it(18) =< aux(16) 0.72/0.74 it(21) =< aux(16) 0.72/0.74 aux(4) =< aux(3)+1 0.72/0.74 s(8) =< it(18)*aux(4) 0.72/0.74 s(7) =< it(18)*aux(3) 0.72/0.74 0.72/0.74 with precondition: [A=10,B=35,K=4,8>=F,F>=0] 0.72/0.74 0.72/0.74 * Chain [[18,19,20,21,22],24]: 3*it(18)+2*it(21)+1*s(7)+1*s(8)+1*s(9)+1*s(10)+0 0.72/0.74 Such that:aux(3) =< E-F+8 0.72/0.74 s(10) =< E-F+9 0.72/0.74 aux(14) =< -35*F+315 0.72/0.74 aux(13) =< -35*F+350 0.72/0.74 aux(16) =< -F+9 0.72/0.74 aux(15) =< -F+10 0.72/0.74 it(21) =< aux(13) 0.72/0.74 s(9) =< aux(13) 0.72/0.74 it(21) =< aux(14) 0.72/0.74 s(9) =< aux(14) 0.72/0.74 it(18) =< aux(15) 0.72/0.74 it(21) =< aux(15) 0.72/0.74 it(18) =< aux(16) 0.72/0.74 it(21) =< aux(16) 0.72/0.74 aux(4) =< aux(3)+1 0.72/0.74 s(8) =< it(18)*aux(4) 0.72/0.74 s(7) =< it(18)*aux(3) 0.72/0.74 0.72/0.74 with precondition: [A=10,B=35,K=4,8>=F,F>=0,E+7>=F] 0.72/0.74 0.72/0.74 * Chain [[18,19,20,21,22],23]: 3*it(18)+2*it(21)+1*s(7)+1*s(8)+1*s(9)+0 0.72/0.74 Such that:aux(3) =< E-F+8 0.72/0.74 aux(19) =< -35*F+350 0.72/0.74 aux(20) =< -F+10 0.72/0.74 it(21) =< aux(19) 0.72/0.74 s(9) =< aux(19) 0.72/0.74 it(18) =< aux(20) 0.72/0.74 it(21) =< aux(20) 0.72/0.74 aux(4) =< aux(3)+1 0.72/0.74 s(8) =< it(18)*aux(4) 0.72/0.74 s(7) =< it(18)*aux(3) 0.72/0.74 0.72/0.74 with precondition: [A=10,B=35,K=5,M=10,9>=F,O>=1,O+1>=L,L+10>=E+F,O+9>=E+F,E+10>=F+L] 0.72/0.74 0.72/0.74 * Chain [26]: 0 0.72/0.74 with precondition: [A=10,B=35,K=4,F>=0] 0.72/0.74 0.72/0.74 * Chain [25]: 0 0.72/0.74 with precondition: [A=10,B=35,K=4,9>=F,F>=0] 0.72/0.74 0.72/0.74 * Chain [24]: 1*s(10)+0 0.72/0.74 Such that:s(10) =< E 0.72/0.74 0.72/0.74 with precondition: [A=10,B=35,K=4,9>=F,E>=2,F>=0] 0.72/0.74 0.72/0.74 0.72/0.74 #### Cost of chains of f15_loop_cont(A,B,C,D,E,F,G,H,I,J): 0.72/0.74 * Chain [28]: 0 0.72/0.74 with precondition: [A=4,B=10,C=35,D=285] 0.72/0.74 0.72/0.74 * Chain [27]: 0 0.72/0.74 with precondition: [A=5,B=10,C=35,D=285] 0.72/0.74 0.72/0.74 0.72/0.74 #### Cost of chains of f0(A,B,C,D,E,F,G,H,K): 0.72/0.74 * Chain [29]: 1*aux(25)+0 0.72/0.74 with precondition: [] 0.72/0.74 0.72/0.74 0.72/0.74 Closed-form bounds of f0(A,B,C,D,E,F,G,H,K): 0.72/0.74 ------------------------------------- 0.72/0.74 * Chain [29] with precondition: [] 0.72/0.74 - Upper bound: inf 0.72/0.74 - Complexity: infinity 0.72/0.74 0.72/0.74 ### Maximum cost of f0(A,B,C,D,E,F,G,H,K): inf 0.72/0.74 Asymptotic class: infinity 0.72/0.74 * Total analysis performed in 636 ms. 0.72/0.74 0.74/0.84 EOF