0.03/0.23 MAYBE 0.03/0.23 0.03/0.23 Preprocessing Cost Relations 0.03/0.23 ===================================== 0.03/0.23 0.03/0.23 #### Computed strongly connected components 0.03/0.23 0. recursive : [g/5] 0.03/0.23 1. non_recursive : [exit_location/1] 0.03/0.23 2. recursive : [h/5] 0.03/0.23 3. recursive : [i/2] 0.03/0.23 4. non_recursive : [i_loop_cont/2] 0.03/0.23 5. non_recursive : [h_loop_cont/5] 0.03/0.23 6. non_recursive : [g_loop_cont/5] 0.03/0.23 7. non_recursive : [f/4] 0.03/0.23 0.03/0.23 #### Obtained direct recursion through partial evaluation 0.03/0.23 0. SCC is partially evaluated into g/5 0.03/0.23 1. SCC is completely evaluated into other SCCs 0.03/0.23 2. SCC is partially evaluated into h/5 0.03/0.23 3. SCC is partially evaluated into i/2 0.03/0.23 4. SCC is completely evaluated into other SCCs 0.03/0.23 5. SCC is partially evaluated into h_loop_cont/5 0.03/0.23 6. SCC is partially evaluated into g_loop_cont/5 0.03/0.23 7. SCC is partially evaluated into f/4 0.03/0.23 0.03/0.23 Control-Flow Refinement of Cost Relations 0.03/0.23 ===================================== 0.03/0.23 0.03/0.23 ### Specialization of cost equations g/5 0.03/0.23 * CE 3 is refined into CE [14] 0.03/0.23 * CE 4 is refined into CE [15] 0.03/0.23 * CE 2 is refined into CE [16] 0.03/0.23 0.03/0.23 0.03/0.23 ### Cost equations --> "Loop" of g/5 0.03/0.23 * CEs [16] --> Loop 14 0.03/0.23 * CEs [14] --> Loop 15 0.03/0.23 * CEs [15] --> Loop 16 0.03/0.23 0.03/0.23 ### Ranking functions of CR g(A,B,D,E,F) 0.03/0.23 * RF of phase [14]: [A] 0.03/0.23 0.03/0.23 #### Partial ranking functions of CR g(A,B,D,E,F) 0.03/0.23 * Partial RF of phase [14]: 0.03/0.23 - RF of loop [14:1]: 0.03/0.23 A 0.03/0.23 0.03/0.23 0.03/0.23 ### Specialization of cost equations h/5 0.03/0.23 * CE 8 is refined into CE [17] 0.03/0.23 * CE 9 is refined into CE [18] 0.03/0.23 * CE 7 is refined into CE [19] 0.03/0.23 0.03/0.23 0.03/0.23 ### Cost equations --> "Loop" of h/5 0.03/0.23 * CEs [19] --> Loop 17 0.03/0.23 * CEs [17] --> Loop 18 0.03/0.23 * CEs [18] --> Loop 19 0.03/0.23 0.03/0.23 ### Ranking functions of CR h(B,C,D,E,F) 0.03/0.23 * RF of phase [17]: [B] 0.03/0.23 0.03/0.23 #### Partial ranking functions of CR h(B,C,D,E,F) 0.03/0.23 * Partial RF of phase [17]: 0.03/0.23 - RF of loop [17:1]: 0.03/0.23 B 0.03/0.23 0.03/0.23 0.03/0.23 ### Specialization of cost equations i/2 0.03/0.23 * CE 13 is refined into CE [20] 0.03/0.23 * CE 12 is refined into CE [21] 0.03/0.23 0.03/0.23 0.03/0.23 ### Cost equations --> "Loop" of i/2 0.03/0.23 * CEs [21] --> Loop 20 0.03/0.23 * CEs [20] --> Loop 21 0.03/0.23 0.03/0.23 ### Ranking functions of CR i(C,D) 0.03/0.23 * RF of phase [20]: [C] 0.03/0.23 0.03/0.23 #### Partial ranking functions of CR i(C,D) 0.03/0.23 * Partial RF of phase [20]: 0.03/0.23 - RF of loop [20:1]: 0.03/0.23 C 0.03/0.23 0.03/0.23 0.03/0.23 ### Specialization of cost equations h_loop_cont/5 0.03/0.23 * CE 11 is refined into CE [22,23] 0.03/0.23 * CE 10 is refined into CE [24] 0.03/0.23 0.03/0.23 0.03/0.23 ### Cost equations --> "Loop" of h_loop_cont/5 0.03/0.23 * CEs [23] --> Loop 22 0.03/0.23 * CEs [22] --> Loop 23 0.03/0.23 * CEs [24] --> Loop 24 0.03/0.23 0.03/0.23 ### Ranking functions of CR h_loop_cont(A,B,C,D,E) 0.03/0.23 0.03/0.23 #### Partial ranking functions of CR h_loop_cont(A,B,C,D,E) 0.03/0.23 0.03/0.23 0.03/0.23 ### Specialization of cost equations g_loop_cont/5 0.03/0.23 * CE 6 is refined into CE [25,26,27,28,29,30] 0.03/0.23 * CE 5 is refined into CE [31] 0.03/0.23 0.03/0.23 0.03/0.23 ### Cost equations --> "Loop" of g_loop_cont/5 0.03/0.23 * CEs [25,27,28] --> Loop 25 0.03/0.23 * CEs [29,30] --> Loop 26 0.03/0.23 * CEs [26] --> Loop 27 0.03/0.23 * CEs [31] --> Loop 28 0.03/0.23 0.03/0.23 ### Ranking functions of CR g_loop_cont(A,B,C,D,E) 0.03/0.23 0.03/0.23 #### Partial ranking functions of CR g_loop_cont(A,B,C,D,E) 0.03/0.23 0.03/0.23 0.03/0.23 ### Specialization of cost equations f/4 0.03/0.23 * CE 1 is refined into CE [32,33,34,35,36,37] 0.03/0.23 0.03/0.23 0.03/0.23 ### Cost equations --> "Loop" of f/4 0.03/0.23 * CEs [32,34,35] --> Loop 29 0.03/0.23 * CEs [36,37] --> Loop 30 0.03/0.23 * CEs [33] --> Loop 31 0.03/0.23 0.03/0.23 ### Ranking functions of CR f(A,B,C,D) 0.03/0.23 0.03/0.23 #### Partial ranking functions of CR f(A,B,C,D) 0.03/0.23 0.03/0.23 0.03/0.23 Computing Bounds 0.03/0.23 ===================================== 0.03/0.23 0.03/0.23 #### Cost of chains of g(A,B,D,E,F): 0.03/0.23 * Chain [[14],16]: 1*it(14)+0 0.03/0.23 Such that:it(14) =< A 0.03/0.23 0.03/0.23 with precondition: [D=2,A>=1,B>=1] 0.03/0.23 0.03/0.23 * Chain [[14],15]: 1*it(14)+0 0.03/0.23 Such that:it(14) =< A 0.03/0.23 0.03/0.23 with precondition: [D=4,E=0,A>=1,B>=1,F+2>=2*A+2*B] 0.03/0.23 0.03/0.23 * Chain [16]: 0 0.03/0.23 with precondition: [D=2,B>=1] 0.03/0.23 0.03/0.23 * Chain [15]: 0 0.03/0.23 with precondition: [D=4,A=E,B=F,0>=A,B>=1] 0.03/0.23 0.03/0.23 0.03/0.23 #### Cost of chains of h(B,C,D,E,F): 0.03/0.23 * Chain [[17],19]: 1*it(17)+0 0.03/0.23 Such that:it(17) =< B 0.03/0.23 0.03/0.23 with precondition: [D=2,B>=1,C>=1] 0.03/0.23 0.03/0.23 * Chain [[17],18]: 1*it(17)+0 0.03/0.23 Such that:it(17) =< B 0.03/0.23 0.03/0.23 with precondition: [D=3,E=0,B>=1,C>=1,F+2>=2*B+2*C] 0.03/0.23 0.03/0.23 * Chain [19]: 0 0.03/0.23 with precondition: [D=2,C>=1] 0.03/0.23 0.03/0.23 * Chain [18]: 0 0.03/0.23 with precondition: [D=3,B=E,C=F,0>=B,C>=1] 0.03/0.23 0.03/0.23 0.03/0.23 #### Cost of chains of i(C,D): 0.03/0.23 * Chain [[20],21]: 1*it(20)+0 0.03/0.23 Such that:it(20) =< C 0.03/0.23 0.03/0.23 with precondition: [D=2,C>=1] 0.03/0.23 0.03/0.23 * Chain [21]: 0 0.03/0.23 with precondition: [D=2] 0.03/0.23 0.03/0.23 0.03/0.23 #### Cost of chains of h_loop_cont(A,B,C,D,E): 0.03/0.23 * Chain [24]: 0 0.03/0.23 with precondition: [A=2] 0.03/0.23 0.03/0.23 * Chain [23]: 0 0.03/0.23 with precondition: [A=3] 0.03/0.23 0.03/0.23 * Chain [22]: 1*s(1)+0 0.03/0.23 Such that:s(1) =< D 0.03/0.23 0.03/0.23 with precondition: [A=3,D>=1] 0.03/0.23 0.03/0.23 0.03/0.23 #### Cost of chains of g_loop_cont(A,B,C,D,E): 0.03/0.23 * Chain [28]: 0 0.03/0.23 with precondition: [A=2,D=1] 0.03/0.23 0.03/0.23 * Chain [27]: 0 0.03/0.23 with precondition: [A=4,D=1] 0.03/0.23 0.03/0.23 * Chain [26]: 1 0.03/0.23 with precondition: [A=4,D=1,0>=C] 0.03/0.23 0.03/0.23 * Chain [25]: 3*s(3)+1*s(6)+0 0.03/0.23 Such that:aux(1) =< C 0.03/0.23 s(3) =< aux(1) 0.03/0.23 0.03/0.23 with precondition: [A=4,D=1,C>=1] 0.03/0.23 0.03/0.23 0.03/0.23 #### Cost of chains of f(A,B,C,D): 0.03/0.23 * Chain [31]: 0 0.03/0.23 with precondition: [] 0.03/0.23 0.03/0.23 * Chain [30]: 1*aux(2)+0 0.03/0.23 with precondition: [0>=A] 0.03/0.23 0.03/0.23 * Chain [29]: 3*s(10)+4*s(14)+0 0.03/0.23 Such that:aux(3) =< A 0.03/0.23 s(10) =< aux(3) 0.03/0.23 0.03/0.23 with precondition: [A>=1] 0.03/0.23 0.03/0.23 0.03/0.23 Closed-form bounds of f(A,B,C,D): 0.03/0.23 ------------------------------------- 0.03/0.23 * Chain [31] with precondition: [] 0.03/0.23 - Upper bound: 0 0.03/0.23 - Complexity: constant 0.03/0.23 * Chain [30] with precondition: [0>=A] 0.03/0.23 - Upper bound: inf 0.03/0.23 - Complexity: infinity 0.03/0.23 * Chain [29] with precondition: [A>=1] 0.03/0.23 - Upper bound: inf 0.03/0.23 - Complexity: infinity 0.03/0.23 0.03/0.23 ### Maximum cost of f(A,B,C,D): inf 0.03/0.23 Asymptotic class: infinity 0.03/0.23 * Total analysis performed in 172 ms. 0.03/0.23 0.03/0.34 EOF