TRS_Equational 2019-03-21 05.09 pair #429997267

details

property	value
status	complete
benchmark	AC18.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	AProVE_AC_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	5.39235 seconds
cpu usage	11.0365
user time	10.6544
system time	0.382148
max virtual memory	1.8341604E7
max residence set size	627632.0

stage attributes

key	value
starexec-result	YES

output

10.83/5.34	YES
10.83/5.35	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
10.83/5.35	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
10.83/5.35	
10.83/5.35	
10.83/5.35	Termination of the given ETRS could be proven:
10.83/5.35	
10.83/5.35	(0) ETRS
10.83/5.35	(1) RRRPoloETRSProof [EQUIVALENT, 154 ms]
10.83/5.35	(2) ETRS
10.83/5.35	(3) RRRPoloETRSProof [EQUIVALENT, 45 ms]
10.83/5.35	(4) ETRS
10.83/5.35	(5) RRRPoloETRSProof [EQUIVALENT, 40 ms]
10.83/5.35	(6) ETRS
10.83/5.35	(7) RRRPoloETRSProof [EQUIVALENT, 1052 ms]
10.83/5.35	(8) ETRS
10.83/5.35	(9) EquationalDependencyPairsProof [EQUIVALENT, 66 ms]
10.83/5.35	(10) EDP
10.83/5.35	(11) EUsableRulesReductionPairsProof [EQUIVALENT, 17 ms]
10.83/5.35	(12) EDP
10.83/5.35	(13) ERuleRemovalProof [EQUIVALENT, 2 ms]
10.83/5.35	(14) EDP
10.83/5.35	(15) EDPPoloProof [EQUIVALENT, 0 ms]
10.83/5.35	(16) EDP
10.83/5.35	(17) PisEmptyProof [EQUIVALENT, 0 ms]
10.83/5.35	(18) YES
10.83/5.35	
10.83/5.35	
10.83/5.35	----------------------------------------
10.83/5.35	
10.83/5.35	(0)
10.83/5.35	Obligation:
10.83/5.35	Equational rewrite system:
10.83/5.35	The TRS R consists of the following rules:
10.83/5.35	
10.83/5.35	   0(S) -> S
10.83/5.35	   plus(S, x) -> x
10.83/5.35	   plus(0(x), 0(y)) -> 0(plus(x, y))
10.83/5.35	   plus(0(x), 1(y)) -> 1(plus(x, y))
10.83/5.35	   plus(0(x), j(y)) -> j(plus(x, y))
10.83/5.35	   plus(1(x), 1(y)) -> j(plus(1(S), plus(x, y)))
10.83/5.35	   plus(j(x), j(y)) -> 1(plus(j(S), plus(x, y)))
10.83/5.35	   plus(1(x), j(y)) -> 0(plus(x, y))
10.83/5.35	   opp(S) -> S
10.83/5.35	   opp(0(x)) -> 0(opp(x))
10.83/5.35	   opp(1(x)) -> j(opp(x))
10.83/5.35	   opp(j(x)) -> 1(opp(x))
10.83/5.35	   minus(x, y) -> plus(opp(y), x)
10.83/5.35	   times(S, x) -> S
10.83/5.35	   times(0(x), y) -> 0(times(x, y))
10.83/5.35	   times(1(x), y) -> plus(0(times(x, y)), y)
10.83/5.35	   times(j(x), y) -> minus(0(times(x, y)), y)
10.83/5.35	
10.83/5.35	The set E consists of the following equations:
10.83/5.35	
10.83/5.35	   plus(x, y) == plus(y, x)
10.83/5.35	   times(x, y) == times(y, x)
10.83/5.35	   plus(plus(x, y), z) == plus(x, plus(y, z))
10.83/5.35	   times(times(x, y), z) == times(x, times(y, z))
10.83/5.35	
10.83/5.35	
10.83/5.35	----------------------------------------
10.83/5.35	
10.83/5.35	(1) RRRPoloETRSProof (EQUIVALENT)
10.83/5.35	The following E TRS is given: Equational rewrite system:
10.83/5.35	The TRS R consists of the following rules:
10.83/5.35	
10.83/5.35	   0(S) -> S
10.83/5.35	   plus(S, x) -> x
10.83/5.35	   plus(0(x), 0(y)) -> 0(plus(x, y))
10.83/5.35	   plus(0(x), 1(y)) -> 1(plus(x, y))
10.83/5.35	   plus(0(x), j(y)) -> j(plus(x, y))
10.83/5.35	   plus(1(x), 1(y)) -> j(plus(1(S), plus(x, y)))
10.83/5.35	   plus(j(x), j(y)) -> 1(plus(j(S), plus(x, y)))
10.83/5.35	   plus(1(x), j(y)) -> 0(plus(x, y))
10.83/5.35	   opp(S) -> S
10.83/5.35	   opp(0(x)) -> 0(opp(x))
10.83/5.35	   opp(1(x)) -> j(opp(x))
10.83/5.35	   opp(j(x)) -> 1(opp(x))
10.83/5.35	   minus(x, y) -> plus(opp(y), x)
10.83/5.35	   times(S, x) -> S
10.83/5.35	   times(0(x), y) -> 0(times(x, y))
10.83/5.35	   times(1(x), y) -> plus(0(times(x, y)), y)
10.83/5.35	   times(j(x), y) -> minus(0(times(x, y)), y)
10.83/5.35	
10.83/5.35	The set E consists of the following equations:
10.83/5.35	
10.83/5.35	   plus(x, y) == plus(y, x)
10.83/5.35	   times(x, y) == times(y, x)
10.83/5.35	   plus(plus(x, y), z) == plus(x, plus(y, z))
10.83/5.35	   times(times(x, y), z) == times(x, times(y, z))
10.83/5.35	
10.83/5.35	The following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly by a polynomial ordering:
10.83/5.35	
10.83/5.35	   plus(1(x), j(y)) -> 0(plus(x, y))
10.83/5.35	   opp(1(x)) -> j(opp(x))
10.83/5.35	   opp(j(x)) -> 1(opp(x))
10.83/5.35	   minus(x, y) -> plus(opp(y), x)
10.83/5.35	   times(1(x), y) -> plus(0(times(x, y)), y)
10.83/5.35	Used ordering:

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