0.03/0.17 WORST_CASE(?,O(1)) 0.03/0.17 0.03/0.17 Preprocessing Cost Relations 0.03/0.17 ===================================== 0.03/0.17 0.03/0.17 #### Computed strongly connected components 0.03/0.17 0. recursive : [f9/5] 0.03/0.17 1. non_recursive : [exit_location/1] 0.03/0.17 2. recursive : [f17/3] 0.03/0.17 3. non_recursive : [f24/4] 0.03/0.17 4. non_recursive : [f17_loop_cont/5] 0.03/0.17 5. non_recursive : [f9_loop_cont/5] 0.03/0.17 6. non_recursive : [f0/4] 0.03/0.17 0.03/0.17 #### Obtained direct recursion through partial evaluation 0.03/0.17 0. SCC is partially evaluated into f9/5 0.03/0.17 1. SCC is completely evaluated into other SCCs 0.03/0.17 2. SCC is partially evaluated into f17/3 0.03/0.17 3. SCC is completely evaluated into other SCCs 0.03/0.17 4. SCC is partially evaluated into f17_loop_cont/5 0.03/0.17 5. SCC is partially evaluated into f9_loop_cont/5 0.03/0.17 6. SCC is partially evaluated into f0/4 0.03/0.17 0.03/0.17 Control-Flow Refinement of Cost Relations 0.03/0.17 ===================================== 0.03/0.17 0.03/0.17 ### Specialization of cost equations f9/5 0.03/0.17 * CE 3 is refined into CE [12] 0.03/0.17 * CE 4 is refined into CE [13] 0.03/0.17 * CE 2 is refined into CE [14] 0.03/0.17 0.03/0.17 0.03/0.17 ### Cost equations --> "Loop" of f9/5 0.03/0.17 * CEs [14] --> Loop 12 0.03/0.17 * CEs [12] --> Loop 13 0.03/0.17 * CEs [13] --> Loop 14 0.03/0.17 0.03/0.17 ### Ranking functions of CR f9(A,C,E,F,G) 0.03/0.17 * RF of phase [12]: [-C+50] 0.03/0.17 0.03/0.17 #### Partial ranking functions of CR f9(A,C,E,F,G) 0.03/0.17 * Partial RF of phase [12]: 0.03/0.17 - RF of loop [12:1]: 0.03/0.17 -C+50 0.03/0.17 0.03/0.17 0.03/0.17 ### Specialization of cost equations f17/3 0.03/0.17 * CE 9 is refined into CE [15] 0.03/0.17 * CE 8 is refined into CE [16] 0.03/0.17 * CE 7 is refined into CE [17] 0.03/0.17 0.03/0.17 0.03/0.17 ### Cost equations --> "Loop" of f17/3 0.03/0.17 * CEs [17] --> Loop 15 0.03/0.17 * CEs [15] --> Loop 16 0.03/0.17 * CEs [16] --> Loop 17 0.03/0.17 0.03/0.17 ### Ranking functions of CR f17(A,E,F) 0.03/0.17 * RF of phase [15]: [-A+50] 0.03/0.17 0.03/0.17 #### Partial ranking functions of CR f17(A,E,F) 0.03/0.17 * Partial RF of phase [15]: 0.03/0.17 - RF of loop [15:1]: 0.03/0.17 -A+50 0.03/0.17 0.03/0.17 0.03/0.17 ### Specialization of cost equations f17_loop_cont/5 0.03/0.17 * CE 11 is refined into CE [18] 0.03/0.17 * CE 10 is refined into CE [19] 0.03/0.17 0.03/0.17 0.03/0.17 ### Cost equations --> "Loop" of f17_loop_cont/5 0.03/0.17 * CEs [18] --> Loop 18 0.03/0.17 * CEs [19] --> Loop 19 0.03/0.17 0.03/0.17 ### Ranking functions of CR f17_loop_cont(A,B,C,D,E) 0.03/0.17 0.03/0.17 #### Partial ranking functions of CR f17_loop_cont(A,B,C,D,E) 0.03/0.17 0.03/0.17 0.03/0.17 ### Specialization of cost equations f9_loop_cont/5 0.03/0.17 * CE 6 is refined into CE [20,21,22,23] 0.03/0.17 * CE 5 is refined into CE [24] 0.03/0.17 0.03/0.17 0.03/0.17 ### Cost equations --> "Loop" of f9_loop_cont/5 0.03/0.17 * CEs [21] --> Loop 20 0.03/0.17 * CEs [20,23] --> Loop 21 0.03/0.17 * CEs [22] --> Loop 22 0.03/0.17 * CEs [24] --> Loop 23 0.03/0.17 0.03/0.17 ### Ranking functions of CR f9_loop_cont(A,B,C,D,E) 0.03/0.17 0.03/0.17 #### Partial ranking functions of CR f9_loop_cont(A,B,C,D,E) 0.03/0.17 0.03/0.17 0.03/0.17 ### Specialization of cost equations f0/4 0.03/0.17 * CE 1 is refined into CE [25,26,27,28] 0.03/0.17 0.03/0.17 0.03/0.17 ### Cost equations --> "Loop" of f0/4 0.03/0.17 * CEs [25,26,27,28] --> Loop 24 0.03/0.17 0.03/0.17 ### Ranking functions of CR f0(A,B,C,E) 0.03/0.17 0.03/0.17 #### Partial ranking functions of CR f0(A,B,C,E) 0.03/0.17 0.03/0.17 0.03/0.17 Computing Bounds 0.03/0.17 ===================================== 0.03/0.17 0.03/0.17 #### Cost of chains of f9(A,C,E,F,G): 0.03/0.17 * Chain [[12],14]: 1*it(12)+0 0.03/0.17 Such that:it(12) =< -C+50 0.03/0.17 0.03/0.17 with precondition: [A=0,E=3,49>=C,C>=0] 0.03/0.17 0.03/0.17 * Chain [[12],13]: 1*it(12)+0 0.03/0.17 Such that:it(12) =< -C+50 0.03/0.17 0.03/0.17 with precondition: [A=0,E=4,F=0,G=50,49>=C,C>=0] 0.03/0.17 0.03/0.17 * Chain [14]: 0 0.03/0.17 with precondition: [A=0,E=3,C>=0] 0.03/0.17 0.03/0.17 0.03/0.17 #### Cost of chains of f17(A,E,F): 0.03/0.17 * Chain [[15],17]: 1*it(15)+0 0.03/0.17 Such that:it(15) =< -A+50 0.03/0.17 0.03/0.17 with precondition: [E=2,F=50,49>=A] 0.03/0.17 0.03/0.17 * Chain [[15],16]: 1*it(15)+0 0.03/0.17 Such that:it(15) =< -A+50 0.03/0.17 0.03/0.17 with precondition: [E=3,49>=A] 0.03/0.17 0.03/0.17 * Chain [17]: 0 0.03/0.17 with precondition: [E=2,A=F,A>=50] 0.03/0.17 0.03/0.17 * Chain [16]: 0 0.03/0.17 with precondition: [E=3] 0.03/0.17 0.03/0.17 0.03/0.17 #### Cost of chains of f17_loop_cont(A,B,C,D,E): 0.03/0.17 * Chain [19]: 0 0.03/0.17 with precondition: [A=2] 0.03/0.17 0.03/0.17 * Chain [18]: 0 0.03/0.17 with precondition: [A=3] 0.03/0.17 0.03/0.17 0.03/0.17 #### Cost of chains of f9_loop_cont(A,B,C,D,E): 0.03/0.17 * Chain [23]: 0 0.03/0.17 with precondition: [A=3] 0.03/0.17 0.03/0.17 * Chain [22]: 0 0.03/0.17 with precondition: [A=4] 0.03/0.17 0.03/0.17 * Chain [21]: 2*s(1)+0 0.03/0.17 Such that:aux(1) =< -B+50 0.03/0.17 s(1) =< aux(1) 0.03/0.17 0.03/0.17 with precondition: [A=4,49>=B] 0.03/0.17 0.03/0.17 * Chain [20]: 0 0.03/0.17 with precondition: [A=4,B>=50] 0.03/0.17 0.03/0.17 0.03/0.17 #### Cost of chains of f0(A,B,C,E): 0.03/0.17 * Chain [24]: 250 0.03/0.17 with precondition: [] 0.03/0.17 0.03/0.17 0.03/0.17 Closed-form bounds of f0(A,B,C,E): 0.03/0.17 ------------------------------------- 0.03/0.17 * Chain [24] with precondition: [] 0.03/0.17 - Upper bound: 250 0.03/0.17 - Complexity: constant 0.03/0.17 0.03/0.17 ### Maximum cost of f0(A,B,C,E): 250 0.03/0.17 Asymptotic class: constant 0.03/0.17 * Total analysis performed in 111 ms. 0.03/0.17 0.03/0.27 EOF