TRS_Innermost 2019-03-28 22.12 pair #432271428

details

property	value
status	complete
benchmark	#4.28.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n093.star.cs.uiowa.edu
space	AG01_innermost

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.60185 seconds
cpu usage	3.27842
user time	3.11195
system time	0.166469
max virtual memory	1.8544068E7
max residence set size	237876.0

stage attributes

key	value
starexec-result	YES

output

2.91/1.57	YES
2.91/1.58	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.91/1.58	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.91/1.58	
2.91/1.58	
2.91/1.58	Termination w.r.t. Q of the given QTRS could be proven:
2.91/1.58	
2.91/1.58	(0) QTRS
2.91/1.58	(1) QTRS Reverse [EQUIVALENT, 0 ms]
2.91/1.58	(2) QTRS
2.91/1.58	(3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
2.91/1.58	(4) YES
2.91/1.58	
2.91/1.58	
2.91/1.58	----------------------------------------
2.91/1.58	
2.91/1.58	(0)
2.91/1.58	Obligation:
2.91/1.58	Q restricted rewrite system:
2.91/1.58	The TRS R consists of the following rules:
2.91/1.58	
2.91/1.58	   half(0) -> 0
2.91/1.58	   half(s(0)) -> 0
2.91/1.58	   half(s(s(x))) -> s(half(x))
2.91/1.58	   bits(0) -> 0
2.91/1.58	   bits(s(x)) -> s(bits(half(s(x))))
2.91/1.58	
2.91/1.58	The set Q consists of the following terms:
2.91/1.58	
2.91/1.58	   half(0)
2.91/1.58	   half(s(0))
2.91/1.58	   half(s(s(x0)))
2.91/1.58	   bits(0)
2.91/1.58	   bits(s(x0))
2.91/1.58	
2.91/1.58	
2.91/1.58	----------------------------------------
2.91/1.58	
2.91/1.58	(1) QTRS Reverse (EQUIVALENT)
2.91/1.58	We applied the QTRS Reverse Processor [REVERSE].
2.91/1.58	----------------------------------------
2.91/1.58	
2.91/1.58	(2)
2.91/1.58	Obligation:
2.91/1.58	Q restricted rewrite system:
2.91/1.58	The TRS R consists of the following rules:
2.91/1.58	
2.91/1.58	   0'(half(x)) -> 0'(x)
2.91/1.58	   0'(s(half(x))) -> 0'(x)
2.91/1.58	   s(s(half(x))) -> half(s(x))
2.91/1.58	   0'(bits(x)) -> 0'(x)
2.91/1.58	   s(bits(x)) -> s(half(bits(s(x))))
2.91/1.58	
2.91/1.58	Q is empty.
2.91/1.58	
2.91/1.58	----------------------------------------
2.91/1.58	
2.91/1.58	(3) RFCMatchBoundsTRSProof (EQUIVALENT)
2.91/1.58	Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
2.91/1.58	The following rules were used to construct the certificate:
2.91/1.58	
2.91/1.58	   0'(half(x)) -> 0'(x)
2.91/1.58	   0'(s(half(x))) -> 0'(x)
2.91/1.58	   s(s(half(x))) -> half(s(x))
2.91/1.58	   0'(bits(x)) -> 0'(x)
2.91/1.58	   s(bits(x)) -> s(half(bits(s(x))))
2.91/1.58	
2.91/1.58	The certificate found is represented by the following graph.
2.91/1.58	The certificate consists of the following enumerated nodes:
2.91/1.58	3, 4, 9, 10, 11, 12, 17, 18, 19, 20
2.91/1.58	
2.91/1.58	Node 3 is start node and node 4 is final node.
2.91/1.58	
2.91/1.58	Those nodes are connected through the following edges:
2.91/1.58	
2.91/1.58	* 3 to 4 labelled 0'_1(0), 0'_1(1)* 3 to 9 labelled half_1(0)* 3 to 10 labelled s_1(0)* 4 to 4 labelled #_1(0)* 9 to 4 labelled s_1(0)* 9 to 17 labelled half_1(1)* 9 to 18 labelled s_1(1)* 10 to 11 labelled half_1(0)* 11 to 12 labelled bits_1(0)* 12 to 4 labelled s_1(0)* 12 to 17 labelled half_1(1)* 12 to 18 labelled s_1(1)* 17 to 4 labelled s_1(1)* 17 to 17 labelled half_1(1)* 17 to 18 labelled s_1(1)* 18 to 19 labelled half_1(1)* 19 to 20 labelled bits_1(1)* 20 to 4 labelled s_1(1)* 20 to 17 labelled half_1(1)* 20 to 18 labelled s_1(1)
2.91/1.58	
2.91/1.58	
2.91/1.58	----------------------------------------
2.91/1.58	
2.91/1.58	(4)
2.91/1.58	YES
3.26/1.60	EOF

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