TRS_Innermost 2019-03-28 22.12 pair #432271438

details

property	value
status	complete
benchmark	#4.20.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n004.star.cs.uiowa.edu
space	AG01_innermost

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.57845 seconds
cpu usage	3.28771
user time	3.11792
system time	0.169789
max virtual memory	1.8273204E7
max residence set size	227064.0

stage attributes

key	value
starexec-result	YES

output

3.00/1.54	YES
3.00/1.55	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.00/1.55	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.00/1.55	
3.00/1.55	
3.00/1.55	Termination w.r.t. Q of the given QTRS could be proven:
3.00/1.55	
3.00/1.55	(0) QTRS
3.00/1.55	(1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
3.00/1.55	(2) YES
3.00/1.55	
3.00/1.55	
3.00/1.55	----------------------------------------
3.00/1.55	
3.00/1.55	(0)
3.00/1.55	Obligation:
3.00/1.55	Q restricted rewrite system:
3.00/1.55	The TRS R consists of the following rules:
3.00/1.55	
3.00/1.55	   f(f(x)) -> f(x)
3.00/1.55	   g(0) -> g(f(0))
3.00/1.55	
3.00/1.55	The set Q consists of the following terms:
3.00/1.55	
3.00/1.55	   f(f(x0))
3.00/1.55	   g(0)
3.00/1.55	
3.00/1.55	
3.00/1.55	----------------------------------------
3.00/1.55	
3.00/1.55	(1) RFCMatchBoundsTRSProof (EQUIVALENT)
3.00/1.55	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
3.00/1.55	The following rules were used to construct the certificate:
3.00/1.55	
3.00/1.55	   f(f(x)) -> f(x)
3.00/1.55	   g(0) -> g(f(0))
3.00/1.55	
3.00/1.55	The certificate found is represented by the following graph.
3.00/1.55	The certificate consists of the following enumerated nodes:
3.00/1.55	1, 2, 3, 4
3.00/1.55	
3.00/1.55	Node 1 is start node and node 2 is final node.
3.00/1.55	
3.00/1.55	Those nodes are connected through the following edges:
3.00/1.55	
3.00/1.55	* 1 to 2 labelled f_1(0), f_1(1)* 1 to 3 labelled g_1(0)* 2 to 2 labelled #_1(0)* 3 to 4 labelled f_1(0)* 4 to 2 labelled 0(0)
3.00/1.55	
3.00/1.55	
3.00/1.55	----------------------------------------
3.00/1.55	
3.00/1.55	(2)
3.00/1.55	YES
3.00/1.57	EOF

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