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Complexity_ITS 2019-03-21 04.46 pair #429990613
details
property
value
status
complete
benchmark
232.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n057.star.cs.uiowa.edu
space
T2
run statistics
property
value
solver
CoFloCo 2018
configuration
its
runtime (wallclock)
0.230121 seconds
cpu usage
0.147862
user time
0.122168
system time
0.025694
max virtual memory
113176.0
max residence set size
11124.0
stage attributes
key
value
starexec-result
WORST_CASE(?,O(n^2))
output
0.03/0.12 WORST_CASE(?,O(n^2)) 0.03/0.12 0.03/0.12 Preprocessing Cost Relations 0.03/0.12 ===================================== 0.03/0.12 0.03/0.12 #### Computed strongly connected components 0.03/0.12 0. recursive : [f3/3] 0.03/0.12 1. non_recursive : [exit_location/1] 0.03/0.12 2. non_recursive : [f3_loop_cont/2] 0.03/0.12 3. non_recursive : [f1/3] 0.03/0.12 0.03/0.12 #### Obtained direct recursion through partial evaluation 0.03/0.12 0. SCC is partially evaluated into f3/3 0.03/0.12 1. SCC is completely evaluated into other SCCs 0.03/0.12 2. SCC is completely evaluated into other SCCs 0.03/0.12 3. SCC is partially evaluated into f1/3 0.03/0.12 0.03/0.12 Control-Flow Refinement of Cost Relations 0.03/0.12 ===================================== 0.03/0.12 0.03/0.12 ### Specialization of cost equations f3/3 0.03/0.12 * CE 4 is refined into CE [5] 0.03/0.12 * CE 3 is refined into CE [6] 0.03/0.12 * CE 2 is refined into CE [7] 0.03/0.12 0.03/0.12 0.03/0.12 ### Cost equations --> "Loop" of f3/3 0.03/0.12 * CEs [6] --> Loop 5 0.03/0.12 * CEs [7] --> Loop 6 0.03/0.12 * CEs [5] --> Loop 7 0.03/0.12 0.03/0.12 ### Ranking functions of CR f3(A,B,C) 0.03/0.12 0.03/0.12 #### Partial ranking functions of CR f3(A,B,C) 0.03/0.12 * Partial RF of phase [5,6]: 0.03/0.12 - RF of loop [5:1]: 0.03/0.12 A-1 0.03/0.12 -B+1 depends on loops [6:1] 0.03/0.12 - RF of loop [6:1]: 0.03/0.12 B depends on loops [5:1] 0.03/0.12 0.03/0.12 0.03/0.12 ### Specialization of cost equations f1/3 0.03/0.12 * CE 1 is refined into CE [8] 0.03/0.12 0.03/0.12 0.03/0.12 ### Cost equations --> "Loop" of f1/3 0.03/0.12 * CEs [8] --> Loop 8 0.03/0.12 0.03/0.12 ### Ranking functions of CR f1(A,B,C) 0.03/0.12 0.03/0.12 #### Partial ranking functions of CR f1(A,B,C) 0.03/0.12 0.03/0.12 0.03/0.12 Computing Bounds 0.03/0.12 ===================================== 0.03/0.12 0.03/0.12 #### Cost of chains of f3(A,B,C): 0.03/0.12 * Chain [[5,6],7]: 1*it(5)+1*it(6)+0 0.03/0.12 Such that:aux(4) =< B 0.03/0.12 aux(9) =< A 0.03/0.12 it(5) =< aux(9) 0.03/0.12 aux(3) =< it(5)*aux(9) 0.03/0.12 it(6) =< aux(3)+aux(4) 0.03/0.12 0.03/0.12 with precondition: [C=2,A>=1,A>=B] 0.03/0.12 0.03/0.12 * Chain [7]: 0 0.03/0.12 with precondition: [C=2,A>=1,A>=B] 0.03/0.12 0.03/0.12 0.03/0.12 #### Cost of chains of f1(A,B,C): 0.03/0.12 * Chain [8]: 1*s(8)+1*s(10)+0 0.03/0.12 Such that:aux(10) =< A 0.03/0.12 s(8) =< aux(10) 0.03/0.12 s(9) =< s(8)*aux(10) 0.03/0.12 s(10) =< s(9)+aux(10) 0.03/0.12 0.03/0.12 with precondition: [A>=1] 0.03/0.12 0.03/0.12 0.03/0.12 Closed-form bounds of f1(A,B,C): 0.03/0.12 ------------------------------------- 0.03/0.12 * Chain [8] with precondition: [A>=1] 0.03/0.12 - Upper bound: 2*A+A*A 0.03/0.12 - Complexity: n^2 0.03/0.12 0.03/0.12 ### Maximum cost of f1(A,B,C): 2*A+A*A 0.03/0.12 Asymptotic class: n^2 0.03/0.12 * Total analysis performed in 64 ms. 0.03/0.12 0.03/0.23 EOF
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