TRS_Equational 2019-03-21 05.09 pair #429997189

details

property	value
status	complete
benchmark	AC05.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	AProVE_AC_04

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.54615 seconds
cpu usage	6.2792
user time	6.0375
system time	0.241701
max virtual memory	1.8414284E7
max residence set size	360312.0

stage attributes

key	value
starexec-result	YES

output

6.08/2.50	YES
6.08/2.51	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
6.08/2.51	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.08/2.51	
6.08/2.51	
6.08/2.51	Termination of the given ETRS could be proven:
6.08/2.51	
6.08/2.51	(0) ETRS
6.08/2.51	(1) EquationalDependencyPairsProof [EQUIVALENT, 0 ms]
6.08/2.51	(2) EDP
6.08/2.51	(3) EDependencyGraphProof [EQUIVALENT, 0 ms]
6.08/2.51	(4) AND
6.08/2.51	    (5) EDP
6.08/2.51	        (6) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
6.08/2.51	        (7) EDP
6.08/2.51	        (8) EUsableRulesReductionPairsProof [EQUIVALENT, 8 ms]
6.08/2.51	        (9) EDP
6.08/2.51	        (10) EDPProblemToQDPProblemProof [EQUIVALENT, 0 ms]
6.08/2.51	        (11) QDP
6.08/2.51	        (12) MNOCProof [EQUIVALENT, 0 ms]
6.08/2.51	        (13) QDP
6.08/2.51	        (14) MRRProof [EQUIVALENT, 0 ms]
6.08/2.51	        (15) QDP
6.08/2.51	        (16) DependencyGraphProof [EQUIVALENT, 0 ms]
6.08/2.51	        (17) TRUE
6.08/2.51	    (18) EDP
6.08/2.51	        (19) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
6.08/2.51	        (20) EDP
6.08/2.51	        (21) EDPPoloProof [EQUIVALENT, 10 ms]
6.08/2.51	        (22) EDP
6.08/2.51	        (23) PisEmptyProof [EQUIVALENT, 0 ms]
6.08/2.51	        (24) YES
6.08/2.51	    (25) EDP
6.08/2.51	        (26) ESharpUsableEquationsProof [EQUIVALENT, 0 ms]
6.08/2.51	        (27) EDP
6.08/2.51	        (28) EUsableRulesReductionPairsProof [EQUIVALENT, 0 ms]
6.08/2.51	        (29) EDP
6.08/2.51	        (30) ERuleRemovalProof [EQUIVALENT, 0 ms]
6.08/2.51	        (31) EDP
6.08/2.51	        (32) EDPPoloProof [EQUIVALENT, 4 ms]
6.08/2.51	        (33) EDP
6.08/2.51	        (34) PisEmptyProof [EQUIVALENT, 0 ms]
6.08/2.51	        (35) YES
6.08/2.51	    (36) EDP
6.08/2.51	        (37) ESharpUsableEquationsProof [EQUIVALENT, 5 ms]
6.08/2.51	        (38) EDP
6.08/2.51	        (39) EDPPoloProof [EQUIVALENT, 0 ms]
6.08/2.51	        (40) EDP
6.08/2.51	        (41) EDPPoloProof [EQUIVALENT, 4 ms]
6.08/2.51	        (42) EDP
6.08/2.51	        (43) PisEmptyProof [EQUIVALENT, 0 ms]
6.08/2.51	        (44) YES
6.08/2.51	
6.08/2.51	
6.08/2.51	----------------------------------------
6.08/2.51	
6.08/2.51	(0)
6.08/2.51	Obligation:
6.08/2.51	Equational rewrite system:
6.08/2.51	The TRS R consists of the following rules:
6.08/2.51	
6.08/2.51	   p(s(x)) -> x
6.08/2.51	   plus(x, 0) -> x
6.08/2.51	   plus(x, s(y)) -> s(plus(x, y))
6.08/2.51	   times(x, 0) -> 0
6.08/2.51	   times(x, s(y)) -> plus(x, times(x, y))
6.08/2.51	   minus(x, 0) -> x
6.08/2.51	   minus(s(x), s(y)) -> minus(p(s(x)), p(s(y)))
6.08/2.51	   div(0, s(y)) -> 0
6.08/2.51	   div(s(x), s(y)) -> s(div(minus(x, y), s(y)))
6.08/2.51	
6.08/2.51	The set E consists of the following equations:
6.08/2.51	
6.08/2.51	   plus(x, y) == plus(y, x)
6.08/2.51	   times(x, y) == times(y, x)
6.08/2.51	   plus(plus(x, y), z) == plus(x, plus(y, z))
6.08/2.51	   times(times(x, y), z) == times(x, times(y, z))
6.08/2.51	
6.08/2.51	
6.08/2.51	----------------------------------------
6.08/2.51	
6.08/2.51	(1) EquationalDependencyPairsProof (EQUIVALENT)
6.08/2.51	Using Dependency Pairs [AG00,DA_STEIN] we result in the following initial EDP problem:
6.08/2.51	The TRS P consists of the following rules:
6.08/2.51	
6.08/2.51	   PLUS(x, s(y)) -> PLUS(x, y)
6.08/2.51	   TIMES(x, s(y)) -> PLUS(x, times(x, y))
6.08/2.51	   TIMES(x, s(y)) -> TIMES(x, y)
6.08/2.51	   MINUS(s(x), s(y)) -> MINUS(p(s(x)), p(s(y)))
6.08/2.51	   MINUS(s(x), s(y)) -> P(s(x))
6.08/2.51	   MINUS(s(x), s(y)) -> P(s(y))
6.08/2.51	   DIV(s(x), s(y)) -> DIV(minus(x, y), s(y))
6.08/2.51	   DIV(s(x), s(y)) -> MINUS(x, y)
6.08/2.51	   PLUS(plus(x, s(y)), ext) -> PLUS(s(plus(x, y)), ext)
6.08/2.51	   PLUS(plus(x, s(y)), ext) -> PLUS(x, y)
6.08/2.51	   TIMES(times(x, 0), ext) -> TIMES(0, ext)
6.08/2.51	   TIMES(times(x, s(y)), ext) -> TIMES(plus(x, times(x, y)), ext)
6.08/2.51	   TIMES(times(x, s(y)), ext) -> PLUS(x, times(x, y))
6.08/2.51	   TIMES(times(x, s(y)), ext) -> TIMES(x, y)
6.08/2.51

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