TRS_Relative 2019-03-21 03.54 pair #429988731

details

property	value
status	complete
benchmark	rt2-2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	Relative_05

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.76297 seconds
cpu usage	3.97482
user time	3.808
system time	0.166819
max virtual memory	1.8544064E7
max residence set size	271088.0

stage attributes

key	value
starexec-result	YES

output

3.58/1.70	YES
3.92/1.71	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.92/1.71	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.92/1.71	
3.92/1.71	
3.92/1.71	Termination of the given RelTRS could be proven:
3.92/1.71	
3.92/1.71	(0) RelTRS
3.92/1.71	(1) RelTRSRRRProof [EQUIVALENT, 32 ms]
3.92/1.71	(2) RelTRS
3.92/1.71	(3) RIsEmptyProof [EQUIVALENT, 0 ms]
3.92/1.71	(4) YES
3.92/1.71	
3.92/1.71	
3.92/1.71	----------------------------------------
3.92/1.71	
3.92/1.71	(0)
3.92/1.71	Obligation:
3.92/1.71	Relative term rewrite system:
3.92/1.71	The relative TRS consists of the following R rules:
3.92/1.71	
3.92/1.71	   R(x, B2) -> B2
3.92/1.71	
3.92/1.71	The relative TRS consists of the following S rules:
3.92/1.71	
3.92/1.71	   B1 -> R(T, B1)
3.92/1.71	
3.92/1.71	
3.92/1.71	----------------------------------------
3.92/1.71	
3.92/1.71	(1) RelTRSRRRProof (EQUIVALENT)
3.92/1.71	We used the following monotonic ordering for rule removal:
3.92/1.71	Matrix interpretation [MATRO] to (N^2, +, *, >=, >) :
3.92/1.71	
3.92/1.71	   <<<
3.92/1.71	 POL(R(x_1, x_2)) =  	[[0], [0]] 	 +  	[[1, 0], [1, 0]] 	* 	x_1 	 +  	[[1, 1], [1, 0]] 	* 	x_2
3.92/1.71	>>>
3.92/1.71	
3.92/1.71	   <<<
3.92/1.71	 POL(B2) =  	[[1], [1]]
3.92/1.71	>>>
3.92/1.71	
3.92/1.71	   <<<
3.92/1.71	 POL(B1) =  	[[0], [0]]
3.92/1.71	>>>
3.92/1.71	
3.92/1.71	   <<<
3.92/1.71	 POL(T) =  	[[0], [1]]
3.92/1.71	>>>
3.92/1.71	
3.92/1.71	With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
3.92/1.71	Rules from R:
3.92/1.71	
3.92/1.71	   R(x, B2) -> B2
3.92/1.71	Rules from S:
3.92/1.71	none
3.92/1.71	
3.92/1.71	
3.92/1.71	
3.92/1.71	
3.92/1.71	----------------------------------------
3.92/1.71	
3.92/1.71	(2)
3.92/1.71	Obligation:
3.92/1.71	Relative term rewrite system:
3.92/1.71	R is empty.
3.92/1.71	The relative TRS consists of the following S rules:
3.92/1.71	
3.92/1.71	   B1 -> R(T, B1)
3.92/1.71	
3.92/1.71	
3.92/1.71	----------------------------------------
3.92/1.71	
3.92/1.71	(3) RIsEmptyProof (EQUIVALENT)
3.92/1.71	The TRS R is empty. Hence, termination is trivially proven.
3.92/1.71	----------------------------------------
3.92/1.71	
3.92/1.71	(4)
3.92/1.71	YES
3.92/1.76	EOF

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