Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307707

details

property	value
status	complete
benchmark	#3.39.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n158.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	10.0879 seconds
cpu usage	22.9844
user time	21.3731
system time	1.61128
max virtual memory	1.9275108E7
max residence set size	3838436.0

stage attributes

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

output

22.70/8.02	WORST_CASE(Omega(n^1), O(n^1))
22.91/8.03	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
22.91/8.03	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
22.91/8.03	
22.91/8.03	
22.91/8.03	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
22.91/8.03	
22.91/8.03	(0) CpxTRS
22.91/8.03	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
22.91/8.03	(2) CpxTRS
22.91/8.03	    (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
22.91/8.03	    (4) CpxTRS
22.91/8.03	    (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
22.91/8.03	    (6) CpxWeightedTrs
22.91/8.03	    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
22.91/8.03	    (8) CpxTypedWeightedTrs
22.91/8.03	    (9) CompletionProof [UPPER BOUND(ID), 0 ms]
22.91/8.03	    (10) CpxTypedWeightedCompleteTrs
22.91/8.03	    (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
22.91/8.03	    (12) CpxRNTS
22.91/8.03	    (13) CompleteCoflocoProof [FINISHED, 290 ms]
22.91/8.03	    (14) BOUNDS(1, n^1)
22.91/8.03	(15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
22.91/8.03	(16) CpxTRS
22.91/8.03	    (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
22.91/8.03	    (18) typed CpxTrs
22.91/8.03	    (19) OrderProof [LOWER BOUND(ID), 0 ms]
22.91/8.03	    (20) typed CpxTrs
22.91/8.03	    (21) RewriteLemmaProof [LOWER BOUND(ID), 263 ms]
22.91/8.03	    (22) BEST
22.91/8.03	        (23) proven lower bound
22.91/8.03	            (24) LowerBoundPropagationProof [FINISHED, 0 ms]
22.91/8.03	            (25) BOUNDS(n^1, INF)
22.91/8.03	        (26) typed CpxTrs
22.91/8.03	            (27) RewriteLemmaProof [LOWER BOUND(ID), 61 ms]
22.91/8.03	            (28) BOUNDS(1, INF)
22.91/8.03	
22.91/8.03	
22.91/8.03	----------------------------------------
22.91/8.03	
22.91/8.03	(0)
22.91/8.03	Obligation:
22.91/8.03	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
22.91/8.03	
22.91/8.03	
22.91/8.03	The TRS R consists of the following rules:
22.91/8.03	
22.91/8.03	   minus(x, 0) -> x
22.91/8.03	   minus(s(x), s(y)) -> minus(x, y)
22.91/8.03	   quot(0, s(y)) -> 0
22.91/8.03	   quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
22.91/8.03	   plus(0, y) -> y
22.91/8.03	   plus(s(x), y) -> s(plus(x, y))
22.91/8.03	   plus(minus(x, s(0)), minus(y, s(s(z)))) -> plus(minus(y, s(s(z))), minus(x, s(0)))
22.91/8.03	
22.91/8.03	S is empty.
22.91/8.03	Rewrite Strategy: FULL
22.91/8.03	----------------------------------------
22.91/8.03	
22.91/8.03	(1) NestedDefinedSymbolProof (UPPER BOUND(ID))
22.91/8.03	The following defined symbols can occur below the 0th argument of quot: minus
22.91/8.03	The following defined symbols can occur below the 0th argument of minus: minus
22.91/8.03	
22.91/8.03	Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
22.91/8.03	plus(minus(x, s(0)), minus(y, s(s(z)))) -> plus(minus(y, s(s(z))), minus(x, s(0)))
22.91/8.03	
22.91/8.03	----------------------------------------
22.91/8.03	
22.91/8.03	(2)
22.91/8.03	Obligation:
22.91/8.03	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
22.91/8.03	
22.91/8.03	
22.91/8.03	The TRS R consists of the following rules:
22.91/8.03	
22.91/8.03	   minus(x, 0) -> x
22.91/8.03	   minus(s(x), s(y)) -> minus(x, y)
22.91/8.03	   quot(0, s(y)) -> 0
22.91/8.03	   quot(s(x), s(y)) -> s(quot(minus(x, y), s(y)))
22.91/8.03	   plus(0, y) -> y
22.91/8.03	   plus(s(x), y) -> s(plus(x, y))
22.91/8.03	
22.91/8.03	S is empty.
22.91/8.03	Rewrite Strategy: FULL
22.91/8.03	----------------------------------------
22.91/8.03	
22.91/8.03	(3) RcToIrcProof (BOTH BOUNDS(ID, ID))
22.91/8.03	Converted rc-obligation to irc-obligation.
22.91/8.03	
22.91/8.03	The duplicating contexts are:
22.91/8.03	quot(s(x), s([]))
22.91/8.03	
22.91/8.03	
22.91/8.03	The defined contexts are:
22.91/8.03	quot([], s(x1))
22.91/8.03	minus([], x1)
22.91/8.03	
22.91/8.03	
22.91/8.03	[] just represents basic- or constructor-terms in the following defined contexts:
22.91/8.03	quot([], s(x1))

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