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Complexity_ITS 2019-03-21 04.46 pair #429991253
details
property
value
status
complete
benchmark
merge.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n061.star.cs.uiowa.edu
space
misc
run statistics
property
value
solver
CoFloCo 2018
configuration
its
runtime (wallclock)
0.213901 seconds
cpu usage
0.131906
user time
0.114473
system time
0.017433
max virtual memory
113176.0
max residence set size
11120.0
stage attributes
key
value
starexec-result
WORST_CASE(?,O(n^1))
output
0.03/0.11 WORST_CASE(?,O(n^1)) 0.03/0.11 0.03/0.11 Preprocessing Cost Relations 0.03/0.11 ===================================== 0.03/0.11 0.03/0.11 #### Computed strongly connected components 0.03/0.11 0. recursive : [merge/3] 0.03/0.11 1. non_recursive : [exit_location/1] 0.03/0.11 2. non_recursive : [merge_loop_cont/2] 0.03/0.11 3. non_recursive : [start/3] 0.03/0.11 0.03/0.11 #### Obtained direct recursion through partial evaluation 0.03/0.11 0. SCC is partially evaluated into merge/3 0.03/0.11 1. SCC is completely evaluated into other SCCs 0.03/0.11 2. SCC is completely evaluated into other SCCs 0.03/0.11 3. SCC is partially evaluated into start/3 0.03/0.11 0.03/0.11 Control-Flow Refinement of Cost Relations 0.03/0.11 ===================================== 0.03/0.11 0.03/0.11 ### Specialization of cost equations merge/3 0.03/0.11 * CE 4 is refined into CE [5] 0.03/0.11 * CE 2 is refined into CE [6] 0.03/0.11 * CE 3 is refined into CE [7] 0.03/0.11 0.03/0.11 0.03/0.11 ### Cost equations --> "Loop" of merge/3 0.03/0.11 * CEs [6] --> Loop 5 0.03/0.11 * CEs [7] --> Loop 6 0.03/0.11 * CEs [5] --> Loop 7 0.03/0.11 0.03/0.11 ### Ranking functions of CR merge(A,B,C) 0.03/0.11 * RF of phase [5,6]: [A+B-1] 0.03/0.11 0.03/0.11 #### Partial ranking functions of CR merge(A,B,C) 0.03/0.11 * Partial RF of phase [5,6]: 0.03/0.11 - RF of loop [5:1]: 0.03/0.11 A 0.03/0.11 - RF of loop [6:1]: 0.03/0.11 B 0.03/0.11 0.03/0.11 0.03/0.11 ### Specialization of cost equations start/3 0.03/0.11 * CE 1 is refined into CE [8,9] 0.03/0.11 0.03/0.11 0.03/0.11 ### Cost equations --> "Loop" of start/3 0.03/0.11 * CEs [9] --> Loop 8 0.03/0.11 * CEs [8] --> Loop 9 0.03/0.11 0.03/0.11 ### Ranking functions of CR start(A,B,C) 0.03/0.11 0.03/0.11 #### Partial ranking functions of CR start(A,B,C) 0.03/0.11 0.03/0.11 0.03/0.11 Computing Bounds 0.03/0.11 ===================================== 0.03/0.11 0.03/0.11 #### Cost of chains of merge(A,B,C): 0.03/0.11 * Chain [[5,6],7]: 1*it(5)+1*it(6)+0 0.03/0.11 Such that:it(5) =< A 0.03/0.11 it(6) =< B 0.03/0.11 aux(3) =< A+B 0.03/0.11 it(5) =< aux(3) 0.03/0.11 it(6) =< aux(3) 0.03/0.11 0.03/0.11 with precondition: [C=2,A>=1,B>=1] 0.03/0.11 0.03/0.11 * Chain [7]: 0 0.03/0.11 with precondition: [C=2] 0.03/0.11 0.03/0.11 0.03/0.11 #### Cost of chains of start(A,B,C): 0.03/0.11 * Chain [9]: 0 0.03/0.11 with precondition: [] 0.03/0.11 0.03/0.11 * Chain [8]: 1*s(1)+1*s(2)+0 0.03/0.11 Such that:s(1) =< A 0.03/0.11 s(3) =< A+B 0.03/0.11 s(2) =< B 0.03/0.11 s(1) =< s(3) 0.03/0.11 s(2) =< s(3) 0.03/0.11 0.03/0.11 with precondition: [A>=1,B>=1] 0.03/0.11 0.03/0.11 0.03/0.11 Closed-form bounds of start(A,B,C): 0.03/0.11 ------------------------------------- 0.03/0.11 * Chain [9] with precondition: [] 0.03/0.11 - Upper bound: 0 0.03/0.11 - Complexity: constant 0.03/0.11 * Chain [8] with precondition: [A>=1,B>=1] 0.03/0.11 - Upper bound: A+B 0.03/0.11 - Complexity: n 0.03/0.11 0.03/0.11 ### Maximum cost of start(A,B,C): nat(B)+nat(A) 0.03/0.11 Asymptotic class: n 0.03/0.11 * Total analysis performed in 51 ms. 0.03/0.11 0.03/0.21 EOF
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