TRS_Equational 2019-03-21 05.09 pair #429997264

details

property	value
status	complete
benchmark	AC23.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n175.star.cs.uiowa.edu
space	AProVE_AC_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.8893 seconds
cpu usage	3.94065
user time	3.75918
system time	0.181465
max virtual memory	1.8277816E7
max residence set size	236656.0

stage attributes

key	value
starexec-result	YES

output

3.86/1.84	YES
3.86/1.85	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.86/1.85	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.86/1.85	
3.86/1.85	
3.86/1.85	Termination of the given ETRS could be proven:
3.86/1.85	
3.86/1.85	(0) ETRS
3.86/1.85	(1) RRRPoloETRSProof [EQUIVALENT, 156 ms]
3.86/1.85	(2) ETRS
3.86/1.85	(3) RRRPoloETRSProof [EQUIVALENT, 0 ms]
3.86/1.85	(4) ETRS
3.86/1.85	(5) RisEmptyProof [EQUIVALENT, 0 ms]
3.86/1.85	(6) YES
3.86/1.85	
3.86/1.85	
3.86/1.85	----------------------------------------
3.86/1.85	
3.86/1.85	(0)
3.86/1.85	Obligation:
3.86/1.85	Equational rewrite system:
3.86/1.85	The TRS R consists of the following rules:
3.86/1.85	
3.86/1.85	   zero(S) -> S
3.86/1.85	   plus(x, S) -> x
3.86/1.85	   plus(zero(x), zero(y)) -> zero(plus(x, y))
3.86/1.85	   plus(zero(x), un(y)) -> un(plus(x, y))
3.86/1.85	   plus(un(x), un(y)) -> zero(plus(x, plus(y, un(S))))
3.86/1.85	   times(x, S) -> S
3.86/1.85	   times(x, times(S, z)) -> times(S, z)
3.86/1.85	   times(x, zero(y)) -> zero(times(x, y))
3.86/1.85	   times(x, times(zero(y), z)) -> times(zero(times(x, y)), z)
3.86/1.85	   times(x, un(y)) -> plus(x, zero(times(x, y)))
3.86/1.85	   times(x, times(un(y), z)) -> times(plus(x, zero(times(x, y))), z)
3.86/1.85	
3.86/1.85	The set E consists of the following equations:
3.86/1.85	
3.86/1.85	   plus(x, y) == plus(y, x)
3.86/1.85	   times(x, y) == times(y, x)
3.86/1.85	   plus(plus(x, y), z) == plus(x, plus(y, z))
3.86/1.85	   times(times(x, y), z) == times(x, times(y, z))
3.86/1.85	
3.86/1.85	
3.86/1.85	----------------------------------------
3.86/1.85	
3.86/1.85	(1) RRRPoloETRSProof (EQUIVALENT)
3.86/1.85	The following E TRS is given: Equational rewrite system:
3.86/1.85	The TRS R consists of the following rules:
3.86/1.85	
3.86/1.85	   zero(S) -> S
3.86/1.85	   plus(x, S) -> x
3.86/1.85	   plus(zero(x), zero(y)) -> zero(plus(x, y))
3.86/1.85	   plus(zero(x), un(y)) -> un(plus(x, y))
3.86/1.85	   plus(un(x), un(y)) -> zero(plus(x, plus(y, un(S))))
3.86/1.85	   times(x, S) -> S
3.86/1.85	   times(x, times(S, z)) -> times(S, z)
3.86/1.85	   times(x, zero(y)) -> zero(times(x, y))
3.86/1.85	   times(x, times(zero(y), z)) -> times(zero(times(x, y)), z)
3.86/1.85	   times(x, un(y)) -> plus(x, zero(times(x, y)))
3.86/1.85	   times(x, times(un(y), z)) -> times(plus(x, zero(times(x, y))), z)
3.86/1.85	
3.86/1.85	The set E consists of the following equations:
3.86/1.85	
3.86/1.85	   plus(x, y) == plus(y, x)
3.86/1.85	   times(x, y) == times(y, x)
3.86/1.85	   plus(plus(x, y), z) == plus(x, plus(y, z))
3.86/1.85	   times(times(x, y), z) == times(x, times(y, z))
3.86/1.85	
3.86/1.85	The following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly by a polynomial ordering:
3.86/1.85	
3.86/1.85	   plus(un(x), un(y)) -> zero(plus(x, plus(y, un(S))))
3.86/1.85	   times(x, un(y)) -> plus(x, zero(times(x, y)))
3.86/1.85	   times(x, times(un(y), z)) -> times(plus(x, zero(times(x, y))), z)
3.86/1.85	Used ordering:
3.86/1.85	Polynomial interpretation [POLO]:
3.86/1.85	
3.86/1.85	   POL(S) = 0
3.86/1.85	   POL(plus(x_1, x_2)) = x_1 + x_2
3.86/1.85	   POL(times(x_1, x_2)) = x_1 + x_1*x_2 + x_2
3.86/1.85	   POL(un(x_1)) = 2 + x_1
3.86/1.85	   POL(zero(x_1)) = x_1
3.86/1.85	
3.86/1.85	
3.86/1.85	
3.86/1.85	
3.86/1.85	----------------------------------------
3.86/1.85	
3.86/1.85	(2)
3.86/1.85	Obligation:
3.86/1.85	Equational rewrite system:
3.86/1.85	The TRS R consists of the following rules:
3.86/1.85	
3.86/1.85	   zero(S) -> S
3.86/1.85	   plus(x, S) -> x
3.86/1.85	   plus(zero(x), zero(y)) -> zero(plus(x, y))
3.86/1.85	   plus(zero(x), un(y)) -> un(plus(x, y))
3.86/1.85	   times(x, S) -> S
3.86/1.85	   times(x, times(S, z)) -> times(S, z)
3.86/1.85	   times(x, zero(y)) -> zero(times(x, y))
3.86/1.85	   times(x, times(zero(y), z)) -> times(zero(times(x, y)), z)

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