Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307772

details

property	value
status	complete
benchmark	otto01.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n002.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.665 seconds
cpu usage	1001.63
user time	989.415
system time	12.2098
max virtual memory	5.6014552E7
max residence set size	1.50365E7

stage attributes

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

output

1001.04/291.49	WORST_CASE(Omega(n^1), O(n^1))
1001.36/291.56	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
1001.36/291.56	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
1001.36/291.56	
1001.36/291.56	
1001.36/291.56	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
1001.36/291.56	
1001.36/291.56	(0) CpxTRS
1001.36/291.56	(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
1001.36/291.56	(2) CpxTRS
1001.36/291.56	    (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
1001.36/291.56	    (4) CpxWeightedTrs
1001.36/291.56	    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
1001.36/291.56	    (6) CpxTypedWeightedTrs
1001.36/291.56	    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
1001.36/291.56	    (8) CpxTypedWeightedCompleteTrs
1001.36/291.56	    (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
1001.36/291.56	    (10) CpxRNTS
1001.36/291.56	    (11) CompleteCoflocoProof [FINISHED, 4047 ms]
1001.36/291.56	    (12) BOUNDS(1, n^1)
1001.36/291.56	(13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
1001.36/291.56	(14) TRS for Loop Detection
1001.36/291.56	    (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
1001.36/291.56	    (16) BEST
1001.36/291.56	        (17) proven lower bound
1001.36/291.56	            (18) LowerBoundPropagationProof [FINISHED, 0 ms]
1001.36/291.56	            (19) BOUNDS(n^1, INF)
1001.36/291.56	        (20) TRS for Loop Detection
1001.36/291.56	
1001.36/291.56	
1001.36/291.56	----------------------------------------
1001.36/291.56	
1001.36/291.56	(0)
1001.36/291.56	Obligation:
1001.36/291.56	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
1001.36/291.56	
1001.36/291.56	
1001.36/291.56	The TRS R consists of the following rules:
1001.36/291.56	
1001.36/291.56	   min(0, y) -> 0
1001.36/291.56	   min(s(x), 0) -> 0
1001.36/291.56	   min(s(x), s(y)) -> min(x, y)
1001.36/291.56	   len(nil) -> 0
1001.36/291.56	   len(cons(x, xs)) -> s(len(xs))
1001.36/291.56	   sum(x, 0) -> x
1001.36/291.56	   sum(x, s(y)) -> s(sum(x, y))
1001.36/291.56	   le(0, x) -> true
1001.36/291.56	   le(s(x), 0) -> false
1001.36/291.56	   le(s(x), s(y)) -> le(x, y)
1001.36/291.56	   take(0, cons(y, ys)) -> y
1001.36/291.56	   take(s(x), cons(y, ys)) -> take(x, ys)
1001.36/291.56	   addList(x, y) -> if(le(0, min(len(x), len(y))), 0, x, y, nil)
1001.36/291.56	   if(false, c, x, y, z) -> z
1001.36/291.56	   if(true, c, xs, ys, z) -> if(le(s(c), min(len(xs), len(ys))), s(c), xs, ys, cons(sum(take(c, xs), take(c, ys)), z))
1001.36/291.56	
1001.36/291.56	S is empty.
1001.36/291.56	Rewrite Strategy: FULL
1001.36/291.56	----------------------------------------
1001.36/291.56	
1001.36/291.56	(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
1001.36/291.56	Converted rc-obligation to irc-obligation.
1001.36/291.56	
1001.36/291.56	The duplicating contexts are:
1001.36/291.56	addList([], y)
1001.36/291.56	addList(x, [])
1001.36/291.56	if(true, [], xs, ys, z)
1001.36/291.56	if(true, c, [], ys, z)
1001.36/291.56	if(true, c, xs, [], z)
1001.36/291.56	
1001.36/291.56	
1001.36/291.56	The defined contexts are:
1001.36/291.56	if([], s(x1), x2, x3, cons(x4, x5))
1001.36/291.56	le(s(x0), [])
1001.36/291.56	min([], x1)
1001.36/291.56	min(x0, [])
1001.36/291.56	if(x0, s(x1), x2, x3, cons([], x5))
1001.36/291.56	sum([], x1)
1001.36/291.56	sum(x0, [])
1001.36/291.56	if([], 0, x1, x2, nil)
1001.36/291.56	le(0, [])
1001.36/291.56	le(x0, [])
1001.36/291.56	if(x0, s(x1), x2, x3, cons(x4, []))
1001.36/291.56	
1001.36/291.56	
1001.36/291.56	[] just represents basic- or constructor-terms in the following defined contexts:
1001.36/291.56	sum([], x1)
1001.36/291.56	sum(x0, [])
1001.36/291.56	
1001.36/291.56	
1001.36/291.56	As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc.
1001.36/291.56	----------------------------------------
1001.36/291.56	
1001.36/291.56	(2)
1001.36/291.56	Obligation:
1001.36/291.56	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
1001.36/291.56	
1001.36/291.56	
1001.36/291.56	The TRS R consists of the following rules:
1001.36/291.56	
1001.36/291.56	   min(0, y) -> 0

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