0.03/0.21 MAYBE 0.03/0.21 0.03/0.21 Preprocessing Cost Relations 0.03/0.21 ===================================== 0.03/0.21 0.03/0.21 #### Computed strongly connected components 0.03/0.21 0. recursive : [eval/3] 0.03/0.21 1. non_recursive : [exit_location/1] 0.03/0.21 2. non_recursive : [eval_loop_cont/2] 0.03/0.21 3. non_recursive : [start/3] 0.03/0.21 0.03/0.21 #### Obtained direct recursion through partial evaluation 0.03/0.21 0. SCC is partially evaluated into eval/3 0.03/0.21 1. SCC is completely evaluated into other SCCs 0.03/0.21 2. SCC is completely evaluated into other SCCs 0.03/0.21 3. SCC is partially evaluated into start/3 0.03/0.21 0.03/0.21 Control-Flow Refinement of Cost Relations 0.03/0.21 ===================================== 0.03/0.21 0.03/0.21 ### Specialization of cost equations eval/3 0.03/0.21 * CE 4 is refined into CE [5] 0.03/0.21 * CE 2 is refined into CE [6] 0.03/0.21 * CE 3 is refined into CE [7] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of eval/3 0.03/0.21 * CEs [6] --> Loop 5 0.03/0.21 * CEs [7] --> Loop 6 0.03/0.21 * CEs [5] --> Loop 7 0.03/0.21 0.03/0.21 ### Ranking functions of CR eval(A,B,F) 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR eval(A,B,F) 0.03/0.21 * Partial RF of phase [5,6]: 0.03/0.21 - RF of loop [6:1]: 0.03/0.21 -2*A+2*B-1 depends on loops [5:1] 0.03/0.21 2*A+2*B-3 depends on loops [5:1] 0.03/0.21 2*B-2 0.03/0.21 0.03/0.21 0.03/0.21 ### Specialization of cost equations start/3 0.03/0.21 * CE 1 is refined into CE [8,9,10] 0.03/0.21 0.03/0.21 0.03/0.21 ### Cost equations --> "Loop" of start/3 0.03/0.21 * CEs [10] --> Loop 8 0.03/0.21 * CEs [9] --> Loop 9 0.03/0.21 * CEs [8] --> Loop 10 0.03/0.21 0.03/0.21 ### Ranking functions of CR start(A,B,F) 0.03/0.21 0.03/0.21 #### Partial ranking functions of CR start(A,B,F) 0.03/0.21 0.03/0.21 0.03/0.21 Computing Bounds 0.03/0.21 ===================================== 0.03/0.21 0.03/0.21 #### Cost of chains of eval(A,B,F): 0.03/0.21 * Chain [[5,6]]...: 1*it(5)+1*it(6)+0 0.03/0.21 Such that:aux(10) =< 2*B 0.03/0.21 it(6) =< aux(10) 0.03/0.21 0.03/0.21 with precondition: [A+B>=2,B>=A+1,A>=0,F=2] 0.03/0.21 0.03/0.21 * Chain [[5,6],7]: 1*it(5)+1*it(6)+0 0.03/0.21 Such that:aux(11) =< 2*B 0.03/0.21 it(6) =< aux(11) 0.03/0.21 0.03/0.21 with precondition: [F=2,A>=0,B>=A+1,A+B>=2] 0.03/0.21 0.03/0.21 * Chain [7]: 0 0.03/0.21 with precondition: [F=2] 0.03/0.21 0.03/0.21 0.03/0.21 #### Cost of chains of start(A,B,F): 0.03/0.21 * Chain [10]: 0 0.03/0.21 with precondition: [] 0.03/0.21 0.03/0.21 * Chain [9]: 1*s(2)+1*s(3)+0 0.03/0.21 Such that:s(1) =< 2*B 0.03/0.21 s(2) =< s(1) 0.03/0.21 0.03/0.21 with precondition: [A>=0,B>=A+1,A+B>=2] 0.03/0.21 0.03/0.21 * Chain [8]...: 1*s(5)+1*s(6)+0 0.03/0.21 Such that:s(4) =< 2*B 0.03/0.21 s(5) =< s(4) 0.03/0.21 0.03/0.21 with precondition: [A>=0,B>=A+1,A+B>=2] 0.03/0.21 0.03/0.21 0.03/0.21 Closed-form bounds of start(A,B,F): 0.03/0.21 ------------------------------------- 0.03/0.21 * Chain [10] with precondition: [] 0.03/0.21 - Upper bound: 0 0.03/0.21 - Complexity: constant 0.03/0.21 * Chain [9] with precondition: [A>=0,B>=A+1,A+B>=2] 0.03/0.21 - Upper bound: inf 0.03/0.21 - Complexity: infinity 0.03/0.21 * Chain [8]... with precondition: [A>=0,B>=A+1,A+B>=2] 0.03/0.21 - Upper bound: inf 0.03/0.21 - Complexity: infinity 0.03/0.21 0.03/0.21 ### Maximum cost of start(A,B,F): inf 0.03/0.21 Asymptotic class: infinity 0.03/0.21 * Total analysis performed in 148 ms. 0.03/0.21 0.03/0.31 EOF