0.03/0.28 WORST_CASE(?,O(n^1)) 0.03/0.28 0.03/0.28 Preprocessing Cost Relations 0.03/0.28 ===================================== 0.03/0.28 0.03/0.28 #### Computed strongly connected components 0.03/0.28 0. recursive : [a/7,b/7,cont1/7,start/7] 0.03/0.28 1. non_recursive : [exit_location/1] 0.03/0.28 2. non_recursive : [stop1/5] 0.03/0.28 3. non_recursive : [stop2/5] 0.03/0.28 4. non_recursive : [stop3/5] 0.03/0.28 5. non_recursive : [start_loop_cont/6] 0.03/0.28 6. non_recursive : [start0/5] 0.03/0.28 0.03/0.28 #### Obtained direct recursion through partial evaluation 0.03/0.28 0. SCC is partially evaluated into start/7 0.03/0.28 1. SCC is completely evaluated into other SCCs 0.03/0.28 2. SCC is completely evaluated into other SCCs 0.03/0.28 3. SCC is completely evaluated into other SCCs 0.03/0.28 4. SCC is completely evaluated into other SCCs 0.03/0.28 5. SCC is partially evaluated into start_loop_cont/6 0.03/0.28 6. SCC is partially evaluated into start0/5 0.03/0.28 0.03/0.28 Control-Flow Refinement of Cost Relations 0.03/0.28 ===================================== 0.03/0.28 0.03/0.28 ### Specialization of cost equations start/7 0.03/0.28 * CE 6 is refined into CE [11] 0.03/0.28 * CE 2 is refined into CE [12] 0.03/0.28 * CE 5 is refined into CE [13] 0.03/0.28 * CE 4 is refined into CE [14] 0.03/0.28 * CE 3 is refined into CE [15] 0.03/0.28 0.03/0.28 0.03/0.28 ### Cost equations --> "Loop" of start/7 0.03/0.28 * CEs [15] --> Loop 11 0.03/0.28 * CEs [11] --> Loop 12 0.03/0.28 * CEs [12] --> Loop 13 0.03/0.28 * CEs [13] --> Loop 14 0.03/0.28 * CEs [14] --> Loop 15 0.03/0.28 0.03/0.28 ### Ranking functions of CR start(A,B,C,D,F,G,H) 0.03/0.28 * RF of phase [11]: [D] 0.03/0.28 0.03/0.28 #### Partial ranking functions of CR start(A,B,C,D,F,G,H) 0.03/0.28 * Partial RF of phase [11]: 0.03/0.28 - RF of loop [11:1]: 0.03/0.28 D 0.03/0.28 0.03/0.28 0.03/0.28 ### Specialization of cost equations start_loop_cont/6 0.03/0.28 * CE 10 is refined into CE [16] 0.03/0.28 * CE 9 is refined into CE [17] 0.03/0.28 * CE 8 is refined into CE [18] 0.03/0.28 * CE 7 is refined into CE [19] 0.03/0.28 0.03/0.28 0.03/0.28 ### Cost equations --> "Loop" of start_loop_cont/6 0.03/0.28 * CEs [16] --> Loop 16 0.03/0.28 * CEs [17] --> Loop 17 0.03/0.28 * CEs [18] --> Loop 18 0.03/0.28 * CEs [19] --> Loop 19 0.03/0.28 0.03/0.28 ### Ranking functions of CR start_loop_cont(A,B,C,D,E,F) 0.03/0.28 0.03/0.28 #### Partial ranking functions of CR start_loop_cont(A,B,C,D,E,F) 0.03/0.28 0.03/0.28 0.03/0.28 ### Specialization of cost equations start0/5 0.03/0.28 * CE 1 is refined into CE [20,21,22,23,24,25,26,27] 0.03/0.28 0.03/0.28 0.03/0.28 ### Cost equations --> "Loop" of start0/5 0.03/0.28 * CEs [23,24] --> Loop 20 0.03/0.28 * CEs [22,25,26] --> Loop 21 0.03/0.28 * CEs [27] --> Loop 22 0.03/0.28 * CEs [20] --> Loop 23 0.03/0.28 * CEs [21] --> Loop 24 0.03/0.28 0.03/0.28 ### Ranking functions of CR start0(A,B,C,D,F) 0.03/0.28 0.03/0.28 #### Partial ranking functions of CR start0(A,B,C,D,F) 0.03/0.28 0.03/0.28 0.03/0.28 Computing Bounds 0.03/0.28 ===================================== 0.03/0.28 0.03/0.28 #### Cost of chains of start(A,B,C,D,F,G,H): 0.03/0.28 * Chain [[11],15]: 1*it(11)+0 0.03/0.28 Such that:it(11) =< D-H 0.03/0.28 0.03/0.28 with precondition: [F=3,G=1,B>=0,C>=1,H>=0,A>=D,D>=H+2] 0.03/0.28 0.03/0.28 * Chain [[11],14]: 1*it(11)+0 0.03/0.28 Such that:it(11) =< D 0.03/0.28 0.03/0.28 with precondition: [F=4,H=0,B>=0,C>=1,D>=1,G>=0,A>=D] 0.03/0.28 0.03/0.28 * Chain [[11],13]: 1*it(11)+0 0.03/0.28 Such that:it(11) =< D-H 0.03/0.28 0.03/0.28 with precondition: [F=2,0>=G+1,B>=0,C>=1,H>=0,A>=D,D>=H+2] 0.03/0.28 0.03/0.28 * Chain [[11],12]: 1*it(11)+0 0.03/0.28 Such that:it(11) =< D 0.03/0.28 0.03/0.28 with precondition: [F=5,B>=0,C>=1,D>=1,A>=D] 0.03/0.28 0.03/0.28 * Chain [15]: 0 0.03/0.28 with precondition: [C=0,F=3,G=1,D=H+1,B>=0,D>=1,A>=D] 0.03/0.28 0.03/0.28 * Chain [14]: 0 0.03/0.28 with precondition: [D=0,F=4,H=0,C=G,A>=0,B>=0,C>=0] 0.03/0.28 0.03/0.28 * Chain [13]: 0 0.03/0.28 with precondition: [F=2,D=H+1,0>=G+1,B>=0,C>=1,D>=1,A>=D] 0.03/0.28 0.03/0.28 * Chain [12]: 0 0.03/0.28 with precondition: [F=5,C>=0,D>=0,A>=D] 0.03/0.28 0.03/0.28 0.03/0.28 #### Cost of chains of start_loop_cont(A,B,C,D,E,F): 0.03/0.28 * Chain [19]: 0 0.03/0.28 with precondition: [A=2,B>=0,C>=0] 0.03/0.28 0.03/0.28 * Chain [18]: 0 0.03/0.28 with precondition: [A=3,B>=0,C>=0] 0.03/0.28 0.03/0.28 * Chain [17]: 0 0.03/0.28 with precondition: [A=4,B>=0,C>=0] 0.03/0.28 0.03/0.28 * Chain [16]: 0 0.03/0.28 with precondition: [A=5,B>=0,C>=0] 0.03/0.28 0.03/0.28 0.03/0.28 #### Cost of chains of start0(A,B,C,D,F): 0.03/0.28 * Chain [24]: 0 0.03/0.28 with precondition: [A=0,B>=0] 0.03/0.28 0.03/0.28 * Chain [23]: 0 0.03/0.28 with precondition: [B=0,A>=1] 0.03/0.28 0.03/0.28 * Chain [22]: 0 0.03/0.28 with precondition: [A>=0,B>=0] 0.03/0.28 0.03/0.28 * Chain [21]: 2*s(1)+0 0.03/0.28 Such that:aux(1) =< A 0.03/0.28 s(1) =< aux(1) 0.03/0.28 0.03/0.28 with precondition: [A>=1,B>=1] 0.03/0.28 0.03/0.28 * Chain [20]: 2*s(3)+0 0.03/0.28 Such that:aux(2) =< A 0.03/0.28 s(3) =< aux(2) 0.03/0.28 0.03/0.28 with precondition: [A>=2,B>=1] 0.03/0.28 0.03/0.28 0.03/0.28 Closed-form bounds of start0(A,B,C,D,F): 0.03/0.28 ------------------------------------- 0.03/0.28 * Chain [24] with precondition: [A=0,B>=0] 0.03/0.28 - Upper bound: 0 0.03/0.28 - Complexity: constant 0.03/0.28 * Chain [23] with precondition: [B=0,A>=1] 0.03/0.28 - Upper bound: 0 0.03/0.28 - Complexity: constant 0.03/0.28 * Chain [22] with precondition: [A>=0,B>=0] 0.03/0.28 - Upper bound: 0 0.03/0.28 - Complexity: constant 0.03/0.28 * Chain [21] with precondition: [A>=1,B>=1] 0.03/0.28 - Upper bound: 2*A 0.03/0.28 - Complexity: n 0.03/0.28 * Chain [20] with precondition: [A>=2,B>=1] 0.03/0.28 - Upper bound: 2*A 0.03/0.28 - Complexity: n 0.03/0.28 0.03/0.28 ### Maximum cost of start0(A,B,C,D,F): 2*A 0.03/0.28 Asymptotic class: n 0.03/0.28 * Total analysis performed in 213 ms. 0.03/0.28 0.03/0.38 EOF