Complexity_ITS 2019-03-21 04.46 pair #429990938

details

property	value
status	complete
benchmark	poly2.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n101.star.cs.uiowa.edu
space	VMCAI05

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.61785 seconds
cpu usage	6.90047
user time	6.44771
system time	0.452763
max virtual memory	1.871014E7
max residence set size	229200.0

stage attributes

key	value
starexec-result	MAYBE

output

6.83/4.57	MAYBE
6.83/4.58	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
6.83/4.58	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.83/4.58	
6.83/4.58	
6.83/4.58	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, INF).
6.83/4.58	
6.83/4.58	(0) CpxIntTrs
6.83/4.58	(1) Loat Proof [FINISHED, 233 ms]
6.83/4.58	(2) BOUNDS(1, INF)
6.83/4.58	
6.83/4.58	
6.83/4.58	----------------------------------------
6.83/4.58	
6.83/4.58	(0)
6.83/4.58	Obligation:
6.83/4.58	Complexity Int TRS consisting of the following rules:
6.83/4.58	eval(A, B, C) -> Com_1(eval(A + B, B - 2, C + 1)) :|: A >= 0
6.83/4.58	eval(A, B, C) -> Com_1(eval(A + C, B, C - 2)) :|: A >= 0
6.83/4.58	start(A, B, C) -> Com_1(eval(A, B, C)) :|: TRUE
6.83/4.58	
6.83/4.58	The start-symbols are:[start_3]
6.83/4.58	
6.83/4.58	
6.83/4.58	----------------------------------------
6.83/4.58	
6.83/4.58	(1) Loat Proof (FINISHED)
6.83/4.58	
6.83/4.58	
6.83/4.58	### Pre-processing the ITS problem ###
6.83/4.58	
6.83/4.58	
6.83/4.58	
6.83/4.58	Initial linear ITS problem
6.83/4.58	
6.83/4.58	   Start location: start
6.83/4.58	
6.83/4.58	      0: eval -> eval : A'=A+B, B'=-2+B, C'=1+C, [ A>=0 ], cost: 1
6.83/4.58	
6.83/4.58	      1: eval -> eval : A'=C+A, C'=-2+C, [ A>=0 ], cost: 1
6.83/4.58	
6.83/4.58	      2: start -> eval : [], cost: 1
6.83/4.58	
6.83/4.58	
6.83/4.58	
6.83/4.58	### Simplification by acceleration and chaining ###
6.83/4.58	
6.83/4.58	
6.83/4.58	
6.83/4.58	Accelerating simple loops of location 0.
6.83/4.58	
6.83/4.58	   Accelerating the following rules:
6.83/4.58	
6.83/4.58	      0: eval -> eval : A'=A+B, B'=-2+B, C'=1+C, [ A>=0 ], cost: 1
6.83/4.58	
6.83/4.58	      1: eval -> eval : A'=C+A, C'=-2+C, [ A>=0 ], cost: 1
6.83/4.58	
6.83/4.58	
6.83/4.58	
6.83/4.58	   Found no metering function for rule 0.
6.83/4.58	
6.83/4.58	   Found no metering function for rule 1.
6.83/4.58	
6.83/4.58	   Removing the simple loops:.
6.83/4.58	
6.83/4.58	
6.83/4.58	
6.83/4.58	Accelerated all simple loops using metering functions (where possible):
6.83/4.58	
6.83/4.58	   Start location: start
6.83/4.58	
6.83/4.58	      0: eval -> eval : A'=A+B, B'=-2+B, C'=1+C, [ A>=0 ], cost: 1
6.83/4.58	
6.83/4.58	      1: eval -> eval : A'=C+A, C'=-2+C, [ A>=0 ], cost: 1
6.83/4.58	
6.83/4.58	      2: start -> eval : [], cost: 1
6.83/4.58	
6.83/4.58	
6.83/4.58	
6.83/4.58	Chained accelerated rules (with incoming rules):
6.83/4.58	
6.83/4.58	   Start location: start
6.83/4.58	
6.83/4.58	      2: start -> eval : [], cost: 1
6.83/4.58	
6.83/4.58	      3: start -> eval : A'=A+B, B'=-2+B, C'=1+C, [ A>=0 ], cost: 2
6.83/4.58	
6.83/4.58	      4: start -> eval : A'=C+A, C'=-2+C, [ A>=0 ], cost: 2
6.83/4.58	
6.83/4.58	
6.83/4.58	
6.83/4.58	Removed unreachable locations (and leaf rules with constant cost):
6.83/4.58	
6.83/4.58	   Start location: start
6.83/4.58	
6.83/4.58	
6.83/4.58	
6.83/4.58	### Computing asymptotic complexity ###
6.83/4.58	
6.83/4.58

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