TRS_Equational 2019-03-21 05.09 pair #429997288

details

property	value
status	complete
benchmark	kusakari1.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n164.star.cs.uiowa.edu
space	Mixed_AC

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.80238 seconds
cpu usage	6.45411
user time	6.22537
system time	0.228737
max virtual memory	1.8311616E7
max residence set size	331004.0

stage attributes

key	value
starexec-result	YES

output

6.32/2.76	YES
6.32/2.77	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
6.32/2.77	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.32/2.77	
6.32/2.77	
6.32/2.77	Termination of the given ETRS could be proven:
6.32/2.77	
6.32/2.77	(0) ETRS
6.32/2.77	(1) EquationalDependencyPairsProof [EQUIVALENT, 51 ms]
6.32/2.77	(2) EDP
6.32/2.77	(3) ERuleRemovalProof [EQUIVALENT, 0 ms]
6.32/2.77	(4) EDP
6.32/2.77	(5) EDPPoloProof [EQUIVALENT, 0 ms]
6.32/2.77	(6) EDP
6.32/2.77	(7) PisEmptyProof [EQUIVALENT, 0 ms]
6.32/2.77	(8) YES
6.32/2.77	
6.32/2.77	
6.32/2.77	----------------------------------------
6.32/2.77	
6.32/2.77	(0)
6.32/2.77	Obligation:
6.32/2.77	Equational rewrite system:
6.32/2.77	The TRS R consists of the following rules:
6.32/2.77	
6.32/2.77	   +(g(x), g(y)) -> g(+(g(a), +(x, y)))
6.32/2.77	
6.32/2.77	The set E consists of the following equations:
6.32/2.77	
6.32/2.77	   +(x, y) == +(y, x)
6.32/2.77	   +(+(x, y), z) == +(x, +(y, z))
6.32/2.77	
6.32/2.77	
6.32/2.77	----------------------------------------
6.32/2.77	
6.32/2.77	(1) EquationalDependencyPairsProof (EQUIVALENT)
6.32/2.77	Using Dependency Pairs [AG00,DA_STEIN] we result in the following initial EDP problem:
6.32/2.77	The TRS P consists of the following rules:
6.32/2.77	
6.32/2.77	   +^1(g(x), g(y)) -> +^1(g(a), +(x, y))
6.32/2.77	   +^1(g(x), g(y)) -> +^1(x, y)
6.32/2.77	   +^1(+(g(x), g(y)), ext) -> +^1(g(+(g(a), +(x, y))), ext)
6.32/2.77	   +^1(+(g(x), g(y)), ext) -> +^1(g(a), +(x, y))
6.32/2.77	   +^1(+(g(x), g(y)), ext) -> +^1(x, y)
6.32/2.77	
6.32/2.77	The TRS R consists of the following rules:
6.32/2.77	
6.32/2.77	   +(g(x), g(y)) -> g(+(g(a), +(x, y)))
6.32/2.77	   +(+(g(x), g(y)), ext) -> +(g(+(g(a), +(x, y))), ext)
6.32/2.77	
6.32/2.77	The set E consists of the following equations:
6.32/2.77	
6.32/2.77	   +(x, y) == +(y, x)
6.32/2.77	   +(+(x, y), z) == +(x, +(y, z))
6.32/2.77	
6.32/2.77	The set E# consists of the following equations:
6.32/2.77	
6.32/2.77	   +^1(x, y) == +^1(y, x)
6.32/2.77	   +^1(+(x, y), z) == +^1(x, +(y, z))
6.32/2.77	
6.32/2.77	We have to consider all minimal (P,E#,R,E)-chains
6.32/2.77	
6.32/2.77	----------------------------------------
6.32/2.77	
6.32/2.77	(2)
6.32/2.77	Obligation:
6.32/2.77	The TRS P consists of the following rules:
6.32/2.77	
6.32/2.77	   +^1(g(x), g(y)) -> +^1(g(a), +(x, y))
6.32/2.77	   +^1(g(x), g(y)) -> +^1(x, y)
6.32/2.77	   +^1(+(g(x), g(y)), ext) -> +^1(g(+(g(a), +(x, y))), ext)
6.32/2.77	   +^1(+(g(x), g(y)), ext) -> +^1(g(a), +(x, y))
6.32/2.77	   +^1(+(g(x), g(y)), ext) -> +^1(x, y)
6.32/2.77	
6.32/2.77	The TRS R consists of the following rules:
6.32/2.77	
6.32/2.77	   +(g(x), g(y)) -> g(+(g(a), +(x, y)))
6.32/2.77	   +(+(g(x), g(y)), ext) -> +(g(+(g(a), +(x, y))), ext)
6.32/2.77	
6.32/2.77	The set E consists of the following equations:
6.32/2.77	
6.32/2.77	   +(x, y) == +(y, x)
6.32/2.77	   +(+(x, y), z) == +(x, +(y, z))
6.32/2.77	
6.32/2.77	The set E# consists of the following equations:
6.32/2.77	
6.32/2.77	   +^1(x, y) == +^1(y, x)
6.32/2.77	   +^1(+(x, y), z) == +^1(x, +(y, z))
6.32/2.77	
6.32/2.77	We have to consider all minimal (P,E#,R,E)-chains
6.32/2.77	----------------------------------------
6.32/2.77	
6.32/2.77	(3) ERuleRemovalProof (EQUIVALENT)
6.32/2.77	By using the rule removal processor [DA_STEIN] with the following polynomial ordering [POLO], at least one Dependency Pair or term rewrite system rule of this EDP problem can be strictly oriented.
6.32/2.77	
6.32/2.77	Strictly oriented dependency pairs:
6.32/2.77	
6.32/2.77	   +^1(g(x), g(y)) -> +^1(g(a), +(x, y))
6.32/2.77	   +^1(g(x), g(y)) -> +^1(x, y)
6.32/2.77	   +^1(+(g(x), g(y)), ext) -> +^1(g(a), +(x, y))

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actions all output return to TRS_Equational 2019-03-21 05.09