SRS_Standard 2019-03-29 03.29 pair #432294481

details

property	value
status	complete
benchmark	random-397.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	Waldmann_19

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	5.41722 seconds
cpu usage	17.7388
user time	16.9399
system time	0.798843
max virtual memory	1.00598368E8
max residence set size	2074392.0

stage attributes

key	value
starexec-result	YES

output

17.39/5.32	YES
17.39/5.33	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
17.39/5.33	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
17.39/5.33	
17.39/5.33	
17.39/5.33	Termination w.r.t. Q of the given QTRS could be proven:
17.39/5.33	
17.39/5.33	(0) QTRS
17.39/5.33	(1) DependencyPairsProof [EQUIVALENT, 4 ms]
17.39/5.33	(2) QDP
17.39/5.33	(3) DependencyGraphProof [EQUIVALENT, 2 ms]
17.39/5.33	(4) AND
17.39/5.33	    (5) QDP
17.39/5.33	        (6) UsableRulesProof [EQUIVALENT, 3 ms]
17.39/5.33	        (7) QDP
17.39/5.33	        (8) DependencyGraphProof [EQUIVALENT, 0 ms]
17.39/5.33	        (9) QDP
17.39/5.33	        (10) MRRProof [EQUIVALENT, 23 ms]
17.39/5.33	        (11) QDP
17.39/5.33	        (12) PisEmptyProof [EQUIVALENT, 0 ms]
17.39/5.33	        (13) YES
17.39/5.33	    (14) QDP
17.39/5.33	        (15) QDPOrderProof [EQUIVALENT, 10 ms]
17.39/5.33	        (16) QDP
17.39/5.33	        (17) PisEmptyProof [EQUIVALENT, 0 ms]
17.39/5.33	        (18) YES
17.39/5.33	
17.39/5.33	
17.39/5.33	----------------------------------------
17.39/5.33	
17.39/5.33	(0)
17.39/5.33	Obligation:
17.39/5.33	Q restricted rewrite system:
17.39/5.33	The TRS R consists of the following rules:
17.39/5.33	
17.39/5.33	   b(a(a(b(x1)))) -> b(b(b(b(x1))))
17.39/5.33	   b(b(b(a(x1)))) -> b(b(b(b(x1))))
17.39/5.33	   a(b(b(b(x1)))) -> b(a(a(a(x1))))
17.39/5.33	
17.39/5.33	Q is empty.
17.39/5.33	
17.39/5.33	----------------------------------------
17.39/5.33	
17.39/5.33	(1) DependencyPairsProof (EQUIVALENT)
17.39/5.33	Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
17.39/5.33	----------------------------------------
17.39/5.33	
17.39/5.33	(2)
17.39/5.33	Obligation:
17.39/5.33	Q DP problem:
17.39/5.33	The TRS P consists of the following rules:
17.39/5.33	
17.39/5.33	   B(a(a(b(x1)))) -> B(b(b(b(x1))))
17.39/5.33	   B(a(a(b(x1)))) -> B(b(b(x1)))
17.39/5.33	   B(a(a(b(x1)))) -> B(b(x1))
17.39/5.33	   B(b(b(a(x1)))) -> B(b(b(b(x1))))
17.39/5.33	   B(b(b(a(x1)))) -> B(b(b(x1)))
17.39/5.33	   B(b(b(a(x1)))) -> B(b(x1))
17.39/5.33	   B(b(b(a(x1)))) -> B(x1)
17.39/5.33	   A(b(b(b(x1)))) -> B(a(a(a(x1))))
17.39/5.33	   A(b(b(b(x1)))) -> A(a(a(x1)))
17.39/5.33	   A(b(b(b(x1)))) -> A(a(x1))
17.39/5.33	   A(b(b(b(x1)))) -> A(x1)
17.39/5.33	
17.39/5.33	The TRS R consists of the following rules:
17.39/5.33	
17.39/5.33	   b(a(a(b(x1)))) -> b(b(b(b(x1))))
17.39/5.33	   b(b(b(a(x1)))) -> b(b(b(b(x1))))
17.39/5.33	   a(b(b(b(x1)))) -> b(a(a(a(x1))))
17.39/5.33	
17.39/5.33	Q is empty.
17.39/5.33	We have to consider all minimal (P,Q,R)-chains.
17.39/5.33	----------------------------------------
17.39/5.33	
17.39/5.33	(3) DependencyGraphProof (EQUIVALENT)
17.39/5.33	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 1 less node.
17.39/5.33	----------------------------------------
17.39/5.33	
17.39/5.33	(4)
17.39/5.33	Complex Obligation (AND)
17.39/5.33	
17.39/5.33	----------------------------------------
17.39/5.33	
17.39/5.33	(5)
17.39/5.33	Obligation:
17.39/5.33	Q DP problem:
17.39/5.33	The TRS P consists of the following rules:
17.39/5.33	
17.39/5.33	   B(b(b(a(x1)))) -> B(b(b(b(x1))))
17.39/5.33	   B(b(b(a(x1)))) -> B(b(b(x1)))
17.39/5.33	   B(b(b(a(x1)))) -> B(b(x1))
17.39/5.33	   B(b(b(a(x1)))) -> B(x1)
17.39/5.33	   B(a(a(b(x1)))) -> B(b(b(b(x1))))
17.39/5.33	   B(a(a(b(x1)))) -> B(b(b(x1)))
17.39/5.33	   B(a(a(b(x1)))) -> B(b(x1))
17.39/5.33	
17.39/5.33	The TRS R consists of the following rules:
17.39/5.33	
17.39/5.33	   b(a(a(b(x1)))) -> b(b(b(b(x1))))
17.39/5.33	   b(b(b(a(x1)))) -> b(b(b(b(x1))))

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