0.03/0.18 WORST_CASE(?,O(n^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 : [lbl32/6] 0.03/0.18 1. non_recursive : [exit_location/1] 0.03/0.18 2. non_recursive : [stop/5] 0.03/0.18 3. non_recursive : [lbl32_loop_cont/6] 0.03/0.18 4. non_recursive : [start/5] 0.03/0.18 5. non_recursive : [start0/5] 0.03/0.18 0.03/0.18 #### Obtained direct recursion through partial evaluation 0.03/0.18 0. SCC is partially evaluated into lbl32/6 0.03/0.18 1. SCC is completely evaluated into other SCCs 0.03/0.18 2. SCC is completely evaluated into other SCCs 0.03/0.18 3. SCC is partially evaluated into lbl32_loop_cont/6 0.03/0.18 4. SCC is partially evaluated into start/5 0.03/0.18 5. SCC is partially evaluated into start0/5 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 lbl32/6 0.03/0.18 * CE 6 is refined into CE [9] 0.03/0.18 * CE 4 is refined into CE [10] 0.03/0.18 * CE 5 is refined into CE [11] 0.03/0.18 0.03/0.18 0.03/0.18 ### Cost equations --> "Loop" of lbl32/6 0.03/0.18 * CEs [11] --> Loop 9 0.03/0.18 * CEs [9] --> Loop 10 0.03/0.18 * CEs [10] --> Loop 11 0.03/0.18 0.03/0.18 ### Ranking functions of CR lbl32(A,B,C,D,E,F) 0.03/0.18 * RF of phase [9]: [D-1] 0.03/0.18 0.03/0.18 #### Partial ranking functions of CR lbl32(A,B,C,D,E,F) 0.03/0.18 * Partial RF of phase [9]: 0.03/0.18 - RF of loop [9:1]: 0.03/0.18 D-1 0.03/0.18 0.03/0.18 0.03/0.18 ### Specialization of cost equations lbl32_loop_cont/6 0.03/0.18 * CE 8 is refined into CE [12] 0.03/0.18 * CE 7 is refined into CE [13] 0.03/0.18 0.03/0.18 0.03/0.18 ### Cost equations --> "Loop" of lbl32_loop_cont/6 0.03/0.18 * CEs [12] --> Loop 12 0.03/0.18 * CEs [13] --> Loop 13 0.03/0.18 0.03/0.18 ### Ranking functions of CR lbl32_loop_cont(A,B,C,D,E,F) 0.03/0.18 0.03/0.18 #### Partial ranking functions of CR lbl32_loop_cont(A,B,C,D,E,F) 0.03/0.18 0.03/0.18 0.03/0.18 ### Specialization of cost equations start/5 0.03/0.18 * CE 3 is refined into CE [14,15,16,17] 0.03/0.18 * CE 2 is refined into CE [18] 0.03/0.18 0.03/0.18 0.03/0.18 ### Cost equations --> "Loop" of start/5 0.03/0.18 * CEs [15,17] --> Loop 14 0.03/0.18 * CEs [16] --> Loop 15 0.03/0.18 * CEs [18] --> Loop 16 0.03/0.18 * CEs [14] --> Loop 17 0.03/0.18 0.03/0.18 ### Ranking functions of CR start(A,B,C,D,E) 0.03/0.18 0.03/0.18 #### Partial ranking functions of CR start(A,B,C,D,E) 0.03/0.18 0.03/0.18 0.03/0.18 ### Specialization of cost equations start0/5 0.03/0.18 * CE 1 is refined into CE [19,20,21,22] 0.03/0.18 0.03/0.18 0.03/0.18 ### Cost equations --> "Loop" of start0/5 0.03/0.18 * CEs [22] --> Loop 18 0.03/0.18 * CEs [21] --> Loop 19 0.03/0.18 * CEs [20] --> Loop 20 0.03/0.18 * CEs [19] --> Loop 21 0.03/0.18 0.03/0.18 ### Ranking functions of CR start0(A,B,C,D,E) 0.03/0.18 0.03/0.18 #### Partial ranking functions of CR start0(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 lbl32(A,B,C,D,E,F): 0.03/0.18 * Chain [[9],11]: 1*it(9)+0 0.03/0.18 Such that:it(9) =< D 0.03/0.18 0.03/0.18 with precondition: [E=2,F=1,B=C,D>=2,A>=D+1] 0.03/0.18 0.03/0.18 * Chain [[9],10]: 1*it(9)+0 0.03/0.18 Such that:it(9) =< D 0.03/0.18 0.03/0.18 with precondition: [E=3,B=C,D>=2,A>=D+1] 0.03/0.18 0.03/0.18 * Chain [11]: 0 0.03/0.18 with precondition: [D=1,E=2,F=1,C=B,A>=2] 0.03/0.18 0.03/0.18 * Chain [10]: 0 0.03/0.18 with precondition: [E=3,C=B,D>=1,A>=D+1] 0.03/0.18 0.03/0.18 0.03/0.18 #### Cost of chains of lbl32_loop_cont(A,B,C,D,E,F): 0.03/0.18 * Chain [13]: 0 0.03/0.18 with precondition: [A=2,D=C,B>=2] 0.03/0.18 0.03/0.18 * Chain [12]: 0 0.03/0.18 with precondition: [A=3,D=C,B>=2] 0.03/0.18 0.03/0.18 0.03/0.18 #### Cost of chains of start(A,B,C,D,E): 0.03/0.18 * Chain [17]: 0 0.03/0.18 with precondition: [A=2,D=2,C=B] 0.03/0.18 0.03/0.18 * Chain [16]: 0 0.03/0.18 with precondition: [D=A,C=B,1>=D] 0.03/0.18 0.03/0.18 * Chain [15]: 0 0.03/0.18 with precondition: [D=A,C=B,D>=2] 0.03/0.18 0.03/0.18 * Chain [14]: 2*s(1)+0 0.03/0.18 Such that:aux(1) =< A 0.03/0.18 s(1) =< aux(1) 0.03/0.18 0.03/0.18 with precondition: [D=A,C=B,D>=3] 0.03/0.18 0.03/0.18 0.03/0.18 #### Cost of chains of start0(A,B,C,D,E): 0.03/0.18 * Chain [21]: 0 0.03/0.18 with precondition: [A=2] 0.03/0.18 0.03/0.18 * Chain [20]: 0 0.03/0.18 with precondition: [1>=A] 0.03/0.18 0.03/0.18 * Chain [19]: 0 0.03/0.18 with precondition: [A>=2] 0.03/0.18 0.03/0.18 * Chain [18]: 2*s(4)+0 0.03/0.18 Such that:s(3) =< A 0.03/0.18 s(4) =< s(3) 0.03/0.18 0.03/0.18 with precondition: [A>=3] 0.03/0.18 0.03/0.18 0.03/0.18 Closed-form bounds of start0(A,B,C,D,E): 0.03/0.18 ------------------------------------- 0.03/0.18 * Chain [21] with precondition: [A=2] 0.03/0.18 - Upper bound: 0 0.03/0.18 - Complexity: constant 0.03/0.18 * Chain [20] with precondition: [1>=A] 0.03/0.18 - Upper bound: 0 0.03/0.18 - Complexity: constant 0.03/0.18 * Chain [19] with precondition: [A>=2] 0.03/0.18 - Upper bound: 0 0.03/0.18 - Complexity: constant 0.03/0.18 * Chain [18] with precondition: [A>=3] 0.03/0.18 - Upper bound: 2*A 0.03/0.18 - Complexity: n 0.03/0.18 0.03/0.18 ### Maximum cost of start0(A,B,C,D,E): nat(A)*2 0.03/0.18 Asymptotic class: n 0.03/0.18 * Total analysis performed in 124 ms. 0.03/0.18 0.03/0.29 EOF