0.03/0.27 WORST_CASE(?,O(n^2)) 0.03/0.27 0.03/0.27 Preprocessing Cost Relations 0.03/0.27 ===================================== 0.03/0.27 0.03/0.27 #### Computed strongly connected components 0.03/0.27 0. recursive : [evalaxbb1in/4,evalaxbb2in/4] 0.03/0.27 1. recursive : [evalaxbb2in_loop_cont/7,evalaxbb3in/6,evalaxbbin/6] 0.03/0.27 2. non_recursive : [evalaxstop/4] 0.03/0.27 3. non_recursive : [evalaxreturnin/4] 0.03/0.27 4. non_recursive : [exit_location/1] 0.03/0.27 5. non_recursive : [evalaxbbin_loop_cont/5] 0.03/0.27 6. non_recursive : [evalaxentryin/4] 0.03/0.27 7. non_recursive : [evalaxstart/4] 0.03/0.27 0.03/0.27 #### Obtained direct recursion through partial evaluation 0.03/0.27 0. SCC is partially evaluated into evalaxbb2in/4 0.03/0.27 1. SCC is partially evaluated into evalaxbbin/6 0.03/0.27 2. SCC is completely evaluated into other SCCs 0.03/0.27 3. SCC is completely evaluated into other SCCs 0.03/0.27 4. SCC is completely evaluated into other SCCs 0.03/0.27 5. SCC is partially evaluated into evalaxbbin_loop_cont/5 0.03/0.27 6. SCC is partially evaluated into evalaxentryin/4 0.03/0.27 7. SCC is partially evaluated into evalaxstart/4 0.03/0.27 0.03/0.27 Control-Flow Refinement of Cost Relations 0.03/0.27 ===================================== 0.03/0.27 0.03/0.27 ### Specialization of cost equations evalaxbb2in/4 0.03/0.27 * CE 12 is refined into CE [13] 0.03/0.27 * CE 11 is refined into CE [14] 0.03/0.27 * CE 10 is refined into CE [15] 0.03/0.27 0.03/0.27 0.03/0.27 ### Cost equations --> "Loop" of evalaxbb2in/4 0.03/0.27 * CEs [15] --> Loop 12 0.03/0.27 * CEs [13] --> Loop 13 0.03/0.27 * CEs [14] --> Loop 14 0.03/0.27 0.03/0.27 ### Ranking functions of CR evalaxbb2in(B,C,D,E) 0.03/0.27 * RF of phase [12]: [-B+C-1] 0.03/0.27 0.03/0.27 #### Partial ranking functions of CR evalaxbb2in(B,C,D,E) 0.03/0.27 * Partial RF of phase [12]: 0.03/0.27 - RF of loop [12:1]: 0.03/0.27 -B+C-1 0.03/0.27 0.03/0.27 0.03/0.27 ### Specialization of cost equations evalaxbbin/6 0.03/0.27 * CE 4 is discarded (unfeasible) 0.03/0.27 * CE 3 is refined into CE [16,17] 0.03/0.27 * CE 6 is refined into CE [18,19] 0.03/0.27 * CE 7 is refined into CE [20] 0.03/0.27 * CE 5 is refined into CE [21] 0.03/0.27 0.03/0.27 0.03/0.27 ### Cost equations --> "Loop" of evalaxbbin/6 0.03/0.27 * CEs [21] --> Loop 15 0.03/0.27 * CEs [17] --> Loop 16 0.03/0.27 * CEs [16] --> Loop 17 0.03/0.27 * CEs [19] --> Loop 18 0.03/0.27 * CEs [18,20] --> Loop 19 0.03/0.27 0.03/0.27 ### Ranking functions of CR evalaxbbin(A,B,C,D,E,F) 0.03/0.27 * RF of phase [15]: [-A+C-2] 0.03/0.27 0.03/0.27 #### Partial ranking functions of CR evalaxbbin(A,B,C,D,E,F) 0.03/0.27 * Partial RF of phase [15]: 0.03/0.27 - RF of loop [15:1]: 0.03/0.27 -A+C-2 0.03/0.27 0.03/0.27 0.03/0.27 ### Specialization of cost equations evalaxbbin_loop_cont/5 0.03/0.27 * CE 8 is refined into CE [22] 0.03/0.27 * CE 9 is refined into CE [23] 0.03/0.27 0.03/0.27 0.03/0.27 ### Cost equations --> "Loop" of evalaxbbin_loop_cont/5 0.03/0.27 * CEs [22] --> Loop 20 0.03/0.27 * CEs [23] --> Loop 21 0.03/0.27 0.03/0.27 ### Ranking functions of CR evalaxbbin_loop_cont(A,B,C,D,E) 0.03/0.27 0.03/0.27 #### Partial ranking functions of CR evalaxbbin_loop_cont(A,B,C,D,E) 0.03/0.27 0.03/0.27 0.03/0.27 ### Specialization of cost equations evalaxentryin/4 0.03/0.27 * CE 2 is refined into CE [24,25,26,27,28,29] 0.03/0.27 0.03/0.27 0.03/0.27 ### Cost equations --> "Loop" of evalaxentryin/4 0.03/0.27 * CEs [27,29] --> Loop 22 0.03/0.27 * CEs [26] --> Loop 23 0.03/0.27 * CEs [24] --> Loop 24 0.03/0.27 * CEs [28] --> Loop 25 0.03/0.27 * CEs [25] --> Loop 26 0.03/0.27 0.03/0.27 ### Ranking functions of CR evalaxentryin(A,B,C,D) 0.03/0.27 0.03/0.27 #### Partial ranking functions of CR evalaxentryin(A,B,C,D) 0.03/0.27 0.03/0.27 0.03/0.27 ### Specialization of cost equations evalaxstart/4 0.03/0.27 * CE 1 is refined into CE [30,31,32,33,34] 0.03/0.27 0.03/0.27 0.03/0.27 ### Cost equations --> "Loop" of evalaxstart/4 0.03/0.27 * CEs [34] --> Loop 27 0.03/0.27 * CEs [33] --> Loop 28 0.03/0.27 * CEs [32] --> Loop 29 0.03/0.27 * CEs [31] --> Loop 30 0.03/0.27 * CEs [30] --> Loop 31 0.03/0.27 0.03/0.27 ### Ranking functions of CR evalaxstart(A,B,C,D) 0.03/0.27 0.03/0.27 #### Partial ranking functions of CR evalaxstart(A,B,C,D) 0.03/0.27 0.03/0.27 0.03/0.27 Computing Bounds 0.03/0.27 ===================================== 0.03/0.27 0.03/0.27 #### Cost of chains of evalaxbb2in(B,C,D,E): 0.03/0.27 * Chain [[12],14]: 1*it(12)+0 0.03/0.27 Such that:it(12) =< -B+E 0.03/0.27 0.03/0.27 with precondition: [D=2,C=E+1,B>=0,C>=B+2] 0.03/0.27 0.03/0.27 * Chain [[12],13]: 1*it(12)+0 0.03/0.27 Such that:it(12) =< -B+C 0.03/0.27 0.03/0.27 with precondition: [D=3,B>=0,C>=B+2] 0.03/0.27 0.03/0.27 * Chain [14]: 0 0.03/0.27 with precondition: [D=2,B=E,B>=0,B+1>=C] 0.03/0.27 0.03/0.27 * Chain [13]: 0 0.03/0.27 with precondition: [D=3,B>=0] 0.03/0.27 0.03/0.27 0.03/0.27 #### Cost of chains of evalaxbbin(A,B,C,D,E,F): 0.03/0.27 * Chain [[15],19]: 1*it(15)+1*s(3)+0 0.03/0.27 Such that:it(15) =< -A+C 0.03/0.27 aux(1) =< C 0.03/0.27 s(3) =< it(15)*aux(1) 0.03/0.27 0.03/0.27 with precondition: [D=3,A>=0,C>=A+3] 0.03/0.27 0.03/0.27 * Chain [[15],18]: 1*it(15)+1*s(3)+1*s(4)+0 0.03/0.27 Such that:it(15) =< -A+C 0.03/0.27 aux(2) =< C 0.03/0.27 s(4) =< aux(2) 0.03/0.27 s(3) =< it(15)*aux(2) 0.03/0.27 0.03/0.27 with precondition: [D=3,A>=0,C>=A+3] 0.03/0.27 0.03/0.27 * Chain [[15],16]: 1*it(15)+1*s(3)+1*s(5)+0 0.03/0.27 Such that:it(15) =< -A+E 0.03/0.27 aux(3) =< E+2 0.03/0.27 s(5) =< aux(3) 0.03/0.27 s(3) =< it(15)*aux(3) 0.03/0.27 0.03/0.27 with precondition: [D=4,C=E+2,C=F+1,A>=0,C>=A+3] 0.03/0.27 0.03/0.27 * Chain [19]: 0 0.03/0.27 with precondition: [D=3,A>=0] 0.03/0.27 0.03/0.27 * Chain [18]: 1*s(4)+0 0.03/0.27 Such that:s(4) =< C 0.03/0.27 0.03/0.27 with precondition: [D=3,A>=0,C>=2] 0.03/0.27 0.03/0.27 * Chain [17]: 0 0.03/0.27 with precondition: [A=0,D=4,E=0,F=0,1>=C] 0.03/0.27 0.03/0.27 * Chain [16]: 1*s(5)+0 0.03/0.27 Such that:s(5) =< C 0.03/0.27 0.03/0.27 with precondition: [D=4,F+1=C,A=E,F>=1,A+1>=F] 0.03/0.27 0.03/0.27 0.03/0.27 #### Cost of chains of evalaxbbin_loop_cont(A,B,C,D,E): 0.03/0.27 * Chain [21]: 0 0.03/0.27 with precondition: [A=3] 0.03/0.27 0.03/0.27 * Chain [20]: 0 0.03/0.27 with precondition: [A=4] 0.03/0.27 0.03/0.27 0.03/0.27 #### Cost of chains of evalaxentryin(A,B,C,D): 0.03/0.27 * Chain [26]: 0 0.03/0.27 with precondition: [] 0.03/0.27 0.03/0.27 * Chain [25]: 1*s(13)+0 0.03/0.27 Such that:s(13) =< 2 0.03/0.27 0.03/0.27 with precondition: [C=2] 0.03/0.27 0.03/0.27 * Chain [24]: 0 0.03/0.27 with precondition: [1>=C] 0.03/0.27 0.03/0.27 * Chain [23]: 1*s(14)+0 0.03/0.27 Such that:s(14) =< C 0.03/0.27 0.03/0.27 with precondition: [C>=2] 0.03/0.27 0.03/0.27 * Chain [22]: 5*s(17)+3*s(19)+0 0.03/0.27 Such that:aux(8) =< C 0.03/0.27 s(17) =< aux(8) 0.03/0.27 s(19) =< s(17)*aux(8) 0.03/0.27 0.03/0.27 with precondition: [C>=3] 0.03/0.27 0.03/0.27 0.03/0.27 #### Cost of chains of evalaxstart(A,B,C,D): 0.03/0.27 * Chain [31]: 0 0.03/0.27 with precondition: [] 0.03/0.27 0.03/0.27 * Chain [30]: 1*s(24)+0 0.03/0.27 Such that:s(24) =< 2 0.03/0.27 0.03/0.27 with precondition: [C=2] 0.03/0.27 0.03/0.27 * Chain [29]: 0 0.03/0.27 with precondition: [1>=C] 0.03/0.27 0.03/0.27 * Chain [28]: 1*s(25)+0 0.03/0.27 Such that:s(25) =< C 0.03/0.27 0.03/0.27 with precondition: [C>=2] 0.03/0.27 0.03/0.27 * Chain [27]: 5*s(27)+3*s(28)+0 0.03/0.27 Such that:s(26) =< C 0.03/0.27 s(27) =< s(26) 0.03/0.27 s(28) =< s(27)*s(26) 0.03/0.27 0.03/0.27 with precondition: [C>=3] 0.03/0.27 0.03/0.27 0.03/0.27 Closed-form bounds of evalaxstart(A,B,C,D): 0.03/0.27 ------------------------------------- 0.03/0.27 * Chain [31] with precondition: [] 0.03/0.27 - Upper bound: 0 0.03/0.27 - Complexity: constant 0.03/0.27 * Chain [30] with precondition: [C=2] 0.03/0.27 - Upper bound: 2 0.03/0.27 - Complexity: constant 0.03/0.27 * Chain [29] with precondition: [1>=C] 0.03/0.27 - Upper bound: 0 0.03/0.27 - Complexity: constant 0.03/0.27 * Chain [28] with precondition: [C>=2] 0.03/0.27 - Upper bound: C 0.03/0.27 - Complexity: n 0.03/0.27 * Chain [27] with precondition: [C>=3] 0.03/0.27 - Upper bound: 3*C*C+5*C 0.03/0.27 - Complexity: n^2 0.03/0.27 0.03/0.27 ### Maximum cost of evalaxstart(A,B,C,D): max([2,nat(C)*3*nat(C)+nat(C)*4+nat(C)]) 0.03/0.27 Asymptotic class: n^2 0.03/0.27 * Total analysis performed in 206 ms. 0.03/0.27 0.03/0.37 EOF