0.03/0.19 WORST_CASE(?,O(n^1)) 0.03/0.19 0.03/0.19 Preprocessing Cost Relations 0.03/0.19 ===================================== 0.03/0.19 0.03/0.19 #### Computed strongly connected components 0.03/0.19 0. recursive : [evalDis2bb1in/6,evalDis2bb2in/6,evalDis2bb3in/6,evalDis2bbin/6] 0.03/0.19 1. non_recursive : [evalDis2stop/4] 0.03/0.19 2. non_recursive : [evalDis2returnin/4] 0.03/0.19 3. non_recursive : [exit_location/1] 0.03/0.19 4. non_recursive : [evalDis2bb3in_loop_cont/5] 0.03/0.19 5. non_recursive : [evalDis2entryin/4] 0.03/0.19 6. non_recursive : [evalDis2start/4] 0.03/0.19 0.03/0.19 #### Obtained direct recursion through partial evaluation 0.03/0.19 0. SCC is partially evaluated into evalDis2bb3in/6 0.03/0.19 1. SCC is completely evaluated into other SCCs 0.03/0.19 2. SCC is completely evaluated into other SCCs 0.03/0.19 3. SCC is completely evaluated into other SCCs 0.03/0.19 4. SCC is partially evaluated into evalDis2bb3in_loop_cont/5 0.03/0.19 5. SCC is partially evaluated into evalDis2entryin/4 0.03/0.19 6. SCC is partially evaluated into evalDis2start/4 0.03/0.19 0.03/0.19 Control-Flow Refinement of Cost Relations 0.03/0.19 ===================================== 0.03/0.19 0.03/0.19 ### Specialization of cost equations evalDis2bb3in/6 0.03/0.19 * CE 6 is refined into CE [9] 0.03/0.19 * CE 5 is refined into CE [10] 0.03/0.19 * CE 3 is refined into CE [11] 0.03/0.19 * CE 4 is refined into CE [12] 0.03/0.19 0.03/0.19 0.03/0.19 ### Cost equations --> "Loop" of evalDis2bb3in/6 0.03/0.19 * CEs [11] --> Loop 9 0.03/0.19 * CEs [12] --> Loop 10 0.03/0.19 * CEs [9] --> Loop 11 0.03/0.19 * CEs [10] --> Loop 12 0.03/0.19 0.03/0.19 ### Ranking functions of CR evalDis2bb3in(A,B,C,D,E,F) 0.03/0.19 0.03/0.19 #### Partial ranking functions of CR evalDis2bb3in(A,B,C,D,E,F) 0.03/0.19 * Partial RF of phase [9,10]: 0.03/0.19 - RF of loop [9:1]: 0.03/0.19 A-C 0.03/0.19 B-C depends on loops [10:1] 0.03/0.19 - RF of loop [10:1]: 0.03/0.19 A-B 0.03/0.19 -B+C+1 depends on loops [9:1] 0.03/0.19 0.03/0.19 0.03/0.19 ### Specialization of cost equations evalDis2bb3in_loop_cont/5 0.03/0.19 * CE 8 is refined into CE [13] 0.03/0.19 * CE 7 is refined into CE [14] 0.03/0.19 0.03/0.19 0.03/0.19 ### Cost equations --> "Loop" of evalDis2bb3in_loop_cont/5 0.03/0.19 * CEs [13] --> Loop 13 0.03/0.19 * CEs [14] --> Loop 14 0.03/0.19 0.03/0.19 ### Ranking functions of CR evalDis2bb3in_loop_cont(A,B,C,D,E) 0.03/0.19 0.03/0.19 #### Partial ranking functions of CR evalDis2bb3in_loop_cont(A,B,C,D,E) 0.03/0.19 0.03/0.19 0.03/0.19 ### Specialization of cost equations evalDis2entryin/4 0.03/0.19 * CE 2 is refined into CE [15,16,17,18] 0.03/0.19 0.03/0.19 0.03/0.19 ### Cost equations --> "Loop" of evalDis2entryin/4 0.03/0.19 * CEs [15] --> Loop 15 0.03/0.19 * CEs [16,18] --> Loop 16 0.03/0.19 * CEs [17] --> Loop 17 0.03/0.19 0.03/0.19 ### Ranking functions of CR evalDis2entryin(A,B,C,D) 0.03/0.19 0.03/0.19 #### Partial ranking functions of CR evalDis2entryin(A,B,C,D) 0.03/0.19 0.03/0.19 0.03/0.19 ### Specialization of cost equations evalDis2start/4 0.03/0.19 * CE 1 is refined into CE [19,20,21] 0.03/0.19 0.03/0.19 0.03/0.19 ### Cost equations --> "Loop" of evalDis2start/4 0.03/0.19 * CEs [21] --> Loop 18 0.03/0.19 * CEs [20] --> Loop 19 0.03/0.19 * CEs [19] --> Loop 20 0.03/0.19 0.03/0.19 ### Ranking functions of CR evalDis2start(A,B,C,D) 0.03/0.19 0.03/0.19 #### Partial ranking functions of CR evalDis2start(A,B,C,D) 0.03/0.19 0.03/0.19 0.03/0.19 Computing Bounds 0.03/0.19 ===================================== 0.03/0.19 0.03/0.19 #### Cost of chains of evalDis2bb3in(A,B,C,D,E,F): 0.03/0.19 * Chain [[9,10],12]: 1*it(9)+1*it(10)+0 0.03/0.19 Such that:it(10) =< A-B 0.03/0.19 it(9) =< A-C 0.03/0.19 it(10) =< -B+E 0.03/0.19 0.03/0.19 with precondition: [D=2,A=F,E>=A,E>=B,A>=C+1] 0.03/0.19 0.03/0.19 * Chain [[9,10],11]: 1*it(9)+1*it(10)+0 0.03/0.19 Such that:it(10) =< A-B 0.03/0.19 it(9) =< A-C 0.03/0.19 0.03/0.19 with precondition: [D=3,A>=C+1] 0.03/0.19 0.03/0.19 * Chain [12]: 0 0.03/0.19 with precondition: [D=2,E=B,C=F,C>=A] 0.03/0.19 0.03/0.19 * Chain [11]: 0 0.03/0.19 with precondition: [D=3] 0.03/0.19 0.03/0.19 0.03/0.19 #### Cost of chains of evalDis2bb3in_loop_cont(A,B,C,D,E): 0.03/0.19 * Chain [14]: 0 0.03/0.19 with precondition: [A=2] 0.03/0.19 0.03/0.19 * Chain [13]: 0 0.03/0.19 with precondition: [A=3] 0.03/0.19 0.03/0.19 0.03/0.19 #### Cost of chains of evalDis2entryin(A,B,C,D): 0.03/0.19 * Chain [17]: 0 0.03/0.19 with precondition: [] 0.03/0.19 0.03/0.19 * Chain [16]: 2*s(1)+2*s(2)+0 0.03/0.19 Such that:aux(5) =< -A+B 0.03/0.19 aux(6) =< B-C 0.03/0.19 s(2) =< aux(5) 0.03/0.19 s(1) =< aux(6) 0.03/0.19 0.03/0.19 with precondition: [B>=A+1] 0.03/0.19 0.03/0.19 * Chain [15]: 0 0.03/0.19 with precondition: [A>=B] 0.03/0.19 0.03/0.19 0.03/0.19 #### Cost of chains of evalDis2start(A,B,C,D): 0.03/0.19 * Chain [20]: 0 0.03/0.19 with precondition: [] 0.03/0.19 0.03/0.19 * Chain [19]: 2*s(7)+2*s(8)+0 0.03/0.19 Such that:s(5) =< -A+B 0.03/0.19 s(6) =< B-C 0.03/0.19 s(7) =< s(5) 0.03/0.19 s(8) =< s(6) 0.03/0.19 0.03/0.19 with precondition: [B>=A+1] 0.03/0.19 0.03/0.19 * Chain [18]: 0 0.03/0.19 with precondition: [A>=B] 0.03/0.19 0.03/0.19 0.03/0.19 Closed-form bounds of evalDis2start(A,B,C,D): 0.03/0.19 ------------------------------------- 0.03/0.19 * Chain [20] with precondition: [] 0.03/0.19 - Upper bound: 0 0.03/0.19 - Complexity: constant 0.03/0.19 * Chain [19] with precondition: [B>=A+1] 0.03/0.19 - Upper bound: -2*A+2*B+nat(B-C)*2 0.03/0.19 - Complexity: n 0.03/0.19 * Chain [18] with precondition: [A>=B] 0.03/0.19 - Upper bound: 0 0.03/0.19 - Complexity: constant 0.03/0.19 0.03/0.19 ### Maximum cost of evalDis2start(A,B,C,D): nat(B-C)*2+nat(-A+B)*2 0.03/0.19 Asymptotic class: n 0.03/0.19 * Total analysis performed in 129 ms. 0.03/0.19 0.03/0.29 EOF