Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307820

details

property	value
status	complete
benchmark	gm.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n143.star.cs.uiowa.edu
space	Rubio_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	9.45883 seconds
cpu usage	23.3761
user time	21.7753
system time	1.60077
max virtual memory	1.9174132E7
max residence set size	3891664.0

stage attributes

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

output

23.14/9.41	WORST_CASE(Omega(n^1), O(n^1))
23.30/9.42	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
23.30/9.42	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
23.30/9.42	
23.30/9.42	
23.30/9.42	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
23.30/9.42	
23.30/9.42	(0) CpxTRS
23.30/9.42	(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
23.30/9.42	(2) CpxTRS
23.30/9.42	    (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
23.30/9.42	    (4) CpxWeightedTrs
23.30/9.42	    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
23.30/9.42	    (6) CpxTypedWeightedTrs
23.30/9.42	    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
23.30/9.42	    (8) CpxTypedWeightedCompleteTrs
23.30/9.42	    (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 9 ms]
23.30/9.42	    (10) CpxRNTS
23.30/9.42	    (11) CompleteCoflocoProof [FINISHED, 289 ms]
23.30/9.42	    (12) BOUNDS(1, n^1)
23.30/9.42	(13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
23.30/9.42	(14) CpxTRS
23.30/9.42	    (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
23.30/9.42	    (16) typed CpxTrs
23.30/9.42	    (17) OrderProof [LOWER BOUND(ID), 0 ms]
23.30/9.42	    (18) typed CpxTrs
23.30/9.42	    (19) RewriteLemmaProof [LOWER BOUND(ID), 1129 ms]
23.30/9.42	    (20) BEST
23.30/9.42	        (21) proven lower bound
23.30/9.42	            (22) LowerBoundPropagationProof [FINISHED, 0 ms]
23.30/9.42	            (23) BOUNDS(n^1, INF)
23.30/9.42	        (24) typed CpxTrs
23.30/9.42	            (25) RewriteLemmaProof [LOWER BOUND(ID), 38 ms]
23.30/9.42	            (26) BOUNDS(1, INF)
23.30/9.42	
23.30/9.42	
23.30/9.42	----------------------------------------
23.30/9.42	
23.30/9.42	(0)
23.30/9.42	Obligation:
23.30/9.42	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
23.30/9.42	
23.30/9.42	
23.30/9.42	The TRS R consists of the following rules:
23.30/9.42	
23.30/9.42	   minus(X, 0) -> X
23.30/9.42	   minus(s(X), s(Y)) -> p(minus(X, Y))
23.30/9.42	   p(s(X)) -> X
23.30/9.42	   div(0, s(Y)) -> 0
23.30/9.42	   div(s(X), s(Y)) -> s(div(minus(X, Y), s(Y)))
23.30/9.42	
23.30/9.42	S is empty.
23.30/9.42	Rewrite Strategy: FULL
23.30/9.42	----------------------------------------
23.30/9.42	
23.30/9.42	(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
23.30/9.42	Converted rc-obligation to irc-obligation.
23.30/9.42	
23.30/9.42	The duplicating contexts are:
23.30/9.42	div(s(X), s([]))
23.30/9.42	
23.30/9.42	
23.30/9.42	The defined contexts are:
23.30/9.42	p([])
23.30/9.42	div([], s(x1))
23.30/9.42	minus([], x1)
23.30/9.42	
23.30/9.42	
23.30/9.42	As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc.
23.30/9.42	----------------------------------------
23.30/9.42	
23.30/9.42	(2)
23.30/9.42	Obligation:
23.30/9.42	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
23.30/9.42	
23.30/9.42	
23.30/9.42	The TRS R consists of the following rules:
23.30/9.42	
23.30/9.42	   minus(X, 0) -> X
23.30/9.42	   minus(s(X), s(Y)) -> p(minus(X, Y))
23.30/9.42	   p(s(X)) -> X
23.30/9.42	   div(0, s(Y)) -> 0
23.30/9.42	   div(s(X), s(Y)) -> s(div(minus(X, Y), s(Y)))
23.30/9.42	
23.30/9.42	S is empty.
23.30/9.42	Rewrite Strategy: INNERMOST
23.30/9.42	----------------------------------------
23.30/9.42	
23.30/9.42	(3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
23.30/9.42	Transformed relative TRS to weighted TRS
23.30/9.42	----------------------------------------
23.30/9.42	
23.30/9.42	(4)
23.30/9.42	Obligation:
23.30/9.42	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
23.30/9.42	
23.30/9.42	
23.30/9.42	The TRS R consists of the following rules:
23.30/9.42	
23.30/9.42	   minus(X, 0) -> X [1]

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