0.03/0.18 WORST_CASE(?,O(1)) 0.03/0.18 0.03/0.18 Preprocessing Cost Relations 0.03/0.18 ===================================== 0.03/0.18 0.03/0.18 #### Computed strongly connected components 0.03/0.18 0. recursive : [f19/5] 0.03/0.18 1. non_recursive : [exit_location/1] 0.03/0.18 2. recursive : [f28/3] 0.03/0.18 3. non_recursive : [f36/5] 0.03/0.18 4. non_recursive : [f28_loop_cont/6] 0.03/0.18 5. non_recursive : [f19_loop_cont/6] 0.03/0.18 6. non_recursive : [f0/5] 0.03/0.18 0.03/0.18 #### Obtained direct recursion through partial evaluation 0.03/0.18 0. SCC is partially evaluated into f19/5 0.03/0.18 1. SCC is completely evaluated into other SCCs 0.03/0.18 2. SCC is partially evaluated into f28/3 0.03/0.18 3. SCC is completely evaluated into other SCCs 0.03/0.18 4. SCC is partially evaluated into f28_loop_cont/6 0.03/0.18 5. SCC is partially evaluated into f19_loop_cont/6 0.03/0.18 6. SCC is partially evaluated into f0/5 0.03/0.18 0.03/0.18 Control-Flow Refinement of Cost Relations 0.03/0.18 ===================================== 0.03/0.18 0.03/0.18 ### Specialization of cost equations f19/5 0.03/0.18 * CE 3 is refined into CE [12] 0.03/0.18 * CE 4 is refined into CE [13] 0.03/0.18 * CE 2 is refined into CE [14] 0.03/0.18 0.03/0.18 0.03/0.18 ### Cost equations --> "Loop" of f19/5 0.03/0.18 * CEs [14] --> Loop 12 0.03/0.18 * CEs [12] --> Loop 13 0.03/0.18 * CEs [13] --> Loop 14 0.03/0.18 0.03/0.18 ### Ranking functions of CR f19(B,C,E,F,G) 0.03/0.18 * RF of phase [12]: [B+1] 0.03/0.18 0.03/0.18 #### Partial ranking functions of CR f19(B,C,E,F,G) 0.03/0.18 * Partial RF of phase [12]: 0.03/0.18 - RF of loop [12:1]: 0.03/0.18 B+1 0.03/0.18 0.03/0.18 0.03/0.18 ### Specialization of cost equations f28/3 0.03/0.18 * CE 9 is refined into CE [15] 0.03/0.18 * CE 8 is refined into CE [16] 0.03/0.18 * CE 7 is refined into CE [17] 0.03/0.18 0.03/0.18 0.03/0.18 ### Cost equations --> "Loop" of f28/3 0.03/0.18 * CEs [17] --> Loop 15 0.03/0.18 * CEs [15] --> Loop 16 0.03/0.18 * CEs [16] --> Loop 17 0.03/0.18 0.03/0.18 ### Ranking functions of CR f28(C,E,F) 0.03/0.18 * RF of phase [15]: [C+1] 0.03/0.18 0.03/0.18 #### Partial ranking functions of CR f28(C,E,F) 0.03/0.18 * Partial RF of phase [15]: 0.03/0.18 - RF of loop [15:1]: 0.03/0.18 C+1 0.03/0.18 0.03/0.18 0.03/0.18 ### Specialization of cost equations f28_loop_cont/6 0.03/0.18 * CE 11 is refined into CE [18] 0.03/0.18 * CE 10 is refined into CE [19] 0.03/0.18 0.03/0.18 0.03/0.18 ### Cost equations --> "Loop" of f28_loop_cont/6 0.03/0.18 * CEs [18] --> Loop 18 0.03/0.18 * CEs [19] --> Loop 19 0.03/0.18 0.03/0.18 ### Ranking functions of CR f28_loop_cont(A,B,C,D,E,F) 0.03/0.18 0.03/0.18 #### Partial ranking functions of CR f28_loop_cont(A,B,C,D,E,F) 0.03/0.18 0.03/0.18 0.03/0.18 ### Specialization of cost equations f19_loop_cont/6 0.03/0.18 * CE 6 is refined into CE [20,21,22,23] 0.03/0.18 * CE 5 is refined into CE [24] 0.03/0.18 0.03/0.18 0.03/0.18 ### Cost equations --> "Loop" of f19_loop_cont/6 0.03/0.18 * CEs [20,23] --> Loop 20 0.03/0.18 * CEs [21] --> Loop 21 0.03/0.18 * CEs [22] --> Loop 22 0.03/0.18 * CEs [24] --> Loop 23 0.03/0.18 0.03/0.18 ### Ranking functions of CR f19_loop_cont(A,B,C,D,E,F) 0.03/0.18 0.03/0.18 #### Partial ranking functions of CR f19_loop_cont(A,B,C,D,E,F) 0.03/0.18 0.03/0.18 0.03/0.18 ### Specialization of cost equations f0/5 0.03/0.18 * CE 1 is refined into CE [25,26,27,28] 0.03/0.18 0.03/0.18 0.03/0.18 ### Cost equations --> "Loop" of f0/5 0.03/0.18 * CEs [25,26,27,28] --> Loop 24 0.03/0.18 0.03/0.18 ### Ranking functions of CR f0(A,B,C,D,E) 0.03/0.18 0.03/0.18 #### Partial ranking functions of CR f0(A,B,C,D,E) 0.03/0.18 0.03/0.18 0.03/0.18 Computing Bounds 0.03/0.18 ===================================== 0.03/0.18 0.03/0.18 #### Cost of chains of f19(B,C,E,F,G): 0.03/0.18 * Chain [[12],14]: 1*it(12)+0 0.03/0.18 Such that:it(12) =< B+1 0.03/0.18 0.03/0.18 with precondition: [E=3,999>=B,B>=0] 0.03/0.18 0.03/0.18 * Chain [[12],13]: 1*it(12)+0 0.03/0.18 Such that:it(12) =< B+1 0.03/0.18 0.03/0.18 with precondition: [E=4,F+1=0,G=999,999>=B,B>=0] 0.03/0.18 0.03/0.18 * Chain [14]: 0 0.03/0.18 with precondition: [E=3,999>=B] 0.03/0.18 0.03/0.18 0.03/0.18 #### Cost of chains of f28(C,E,F): 0.03/0.18 * Chain [[15],17]: 1*it(15)+0 0.03/0.18 Such that:it(15) =< C+1 0.03/0.18 0.03/0.18 with precondition: [E=2,F+1=0,C>=0] 0.03/0.18 0.03/0.18 * Chain [[15],16]: 1*it(15)+0 0.03/0.18 Such that:it(15) =< C+1 0.03/0.18 0.03/0.18 with precondition: [E=3,C>=0] 0.03/0.18 0.03/0.18 * Chain [17]: 0 0.03/0.18 with precondition: [E=2,C=F,0>=C+1] 0.03/0.18 0.03/0.18 * Chain [16]: 0 0.03/0.18 with precondition: [E=3] 0.03/0.18 0.03/0.18 0.03/0.18 #### Cost of chains of f28_loop_cont(A,B,C,D,E,F): 0.03/0.18 * Chain [19]: 0 0.03/0.18 with precondition: [A=2,E=1] 0.03/0.18 0.03/0.18 * Chain [18]: 0 0.03/0.18 with precondition: [A=3,E=1] 0.03/0.18 0.03/0.18 0.03/0.18 #### Cost of chains of f19_loop_cont(A,B,C,D,E,F): 0.03/0.18 * Chain [23]: 0 0.03/0.18 with precondition: [A=3,E=1] 0.03/0.18 0.03/0.18 * Chain [22]: 0 0.03/0.18 with precondition: [A=4,E=1] 0.03/0.18 0.03/0.18 * Chain [21]: 0 0.03/0.18 with precondition: [A=4,E=1,0>=D+1] 0.03/0.18 0.03/0.18 * Chain [20]: 2*s(1)+0 0.03/0.18 Such that:aux(1) =< D+1 0.03/0.18 s(1) =< aux(1) 0.03/0.18 0.03/0.18 with precondition: [A=4,E=1,D>=0] 0.03/0.18 0.03/0.18 0.03/0.18 #### Cost of chains of f0(A,B,C,D,E): 0.03/0.18 * Chain [24]: 5000 0.03/0.18 with precondition: [] 0.03/0.18 0.03/0.18 0.03/0.18 Closed-form bounds of f0(A,B,C,D,E): 0.03/0.18 ------------------------------------- 0.03/0.18 * Chain [24] with precondition: [] 0.03/0.18 - Upper bound: 5000 0.03/0.18 - Complexity: constant 0.03/0.18 0.03/0.18 ### Maximum cost of f0(A,B,C,D,E): 5000 0.03/0.18 Asymptotic class: constant 0.03/0.18 * Total analysis performed in 118 ms. 0.03/0.18 0.03/0.28 EOF