Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307710

details

property	value
status	complete
benchmark	#3.40.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n033.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	8.05713 seconds
cpu usage	23.8874
user time	22.2628
system time	1.62461
max virtual memory	1.9211664E7
max residence set size	3776816.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

23.61/8.00	WORST_CASE(Omega(n^1), O(n^1))
23.82/8.01	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
23.82/8.01	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
23.82/8.01	
23.82/8.01	
23.82/8.01	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
23.82/8.01	
23.82/8.01	(0) CpxTRS
23.82/8.01	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
23.82/8.01	(2) CpxTRS
23.82/8.01	    (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
23.82/8.01	    (4) CpxTRS
23.82/8.01	    (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
23.82/8.01	    (6) CpxWeightedTrs
23.82/8.01	    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 2 ms]
23.82/8.01	    (8) CpxTypedWeightedTrs
23.82/8.01	    (9) CompletionProof [UPPER BOUND(ID), 0 ms]
23.82/8.01	    (10) CpxTypedWeightedCompleteTrs
23.82/8.01	    (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
23.82/8.01	    (12) CpxRNTS
23.82/8.01	    (13) CompleteCoflocoProof [FINISHED, 290 ms]
23.82/8.01	    (14) BOUNDS(1, n^1)
23.82/8.01	(15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
23.82/8.01	(16) TRS for Loop Detection
23.82/8.01	    (17) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
23.82/8.01	    (18) BEST
23.82/8.01	        (19) proven lower bound
23.82/8.01	            (20) LowerBoundPropagationProof [FINISHED, 0 ms]
23.82/8.01	            (21) BOUNDS(n^1, INF)
23.82/8.01	        (22) TRS for Loop Detection
23.82/8.01	
23.82/8.01	
23.82/8.01	----------------------------------------
23.82/8.01	
23.82/8.01	(0)
23.82/8.01	Obligation:
23.82/8.01	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
23.82/8.01	
23.82/8.01	
23.82/8.01	The TRS R consists of the following rules:
23.82/8.01	
23.82/8.01	   minus(x, 0) -> x
23.82/8.01	   minus(s(x), s(y)) -> minus(x, y)
23.82/8.01	   quot(0, s(y)) -> 0
23.82/8.01	   quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
23.82/8.01	   plus(0, y) -> y
23.82/8.01	   plus(s(x), y) -> s(plus(x, y))
23.82/8.01	   plus(minus(x, s(0)), minus(y, s(s(z)))) -> plus(minus(y, s(s(z))), minus(x, s(0)))
23.82/8.01	   plus(plus(x, s(0)), plus(y, s(s(z)))) -> plus(plus(y, s(s(z))), plus(x, s(0)))
23.82/8.01	
23.82/8.01	S is empty.
23.82/8.01	Rewrite Strategy: FULL
23.82/8.01	----------------------------------------
23.82/8.01	
23.82/8.01	(1) NestedDefinedSymbolProof (UPPER BOUND(ID))
23.82/8.01	The following defined symbols can occur below the 0th argument of quot: minus
23.82/8.01	The following defined symbols can occur below the 0th argument of minus: minus
23.82/8.01	
23.82/8.01	Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
23.82/8.01	plus(minus(x, s(0)), minus(y, s(s(z)))) -> plus(minus(y, s(s(z))), minus(x, s(0)))
23.82/8.01	plus(plus(x, s(0)), plus(y, s(s(z)))) -> plus(plus(y, s(s(z))), plus(x, s(0)))
23.82/8.01	
23.82/8.01	----------------------------------------
23.82/8.01	
23.82/8.01	(2)
23.82/8.01	Obligation:
23.82/8.01	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
23.82/8.01	
23.82/8.01	
23.82/8.01	The TRS R consists of the following rules:
23.82/8.01	
23.82/8.01	   minus(x, 0) -> x
23.82/8.01	   minus(s(x), s(y)) -> minus(x, y)
23.82/8.01	   quot(0, s(y)) -> 0
23.82/8.01	   quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
23.82/8.01	   plus(0, y) -> y
23.82/8.01	   plus(s(x), y) -> s(plus(x, y))
23.82/8.01	
23.82/8.01	S is empty.
23.82/8.01	Rewrite Strategy: FULL
23.82/8.01	----------------------------------------
23.82/8.01	
23.82/8.01	(3) RcToIrcProof (BOTH BOUNDS(ID, ID))
23.82/8.01	Converted rc-obligation to irc-obligation.
23.82/8.01	
23.82/8.01	The duplicating contexts are:
23.82/8.01	quot(s(x), s([]))
23.82/8.01	
23.82/8.01	
23.82/8.01	The defined contexts are:
23.82/8.01	quot([], s(x1))
23.82/8.01	minus([], x1)
23.82/8.01	
23.82/8.01	
23.82/8.01	[] just represents basic- or constructor-terms in the following defined contexts:
23.82/8.01	quot([], s(x1))
23.82/8.01	
23.82/8.01	
23.82/8.01	As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc.
23.82/8.01	----------------------------------------

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