Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307774

details

property	value
status	complete
benchmark	thiemann23.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n177.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.648 seconds
cpu usage	931.746
user time	922.854
system time	8.89238
max virtual memory	1.9297916E7
max residence set size	1.140418E7

stage attributes

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

output

931.46/291.55	WORST_CASE(Omega(n^1), O(n^1))
931.46/291.58	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
931.46/291.58	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
931.46/291.58	
931.46/291.58	
931.46/291.58	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
931.46/291.58	
931.46/291.58	(0) CpxTRS
931.46/291.58	(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
931.46/291.58	(2) CpxTRS
931.46/291.58	    (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
931.46/291.58	    (4) CpxWeightedTrs
931.46/291.58	    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
931.46/291.58	    (6) CpxTypedWeightedTrs
931.46/291.58	    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
931.46/291.58	    (8) CpxTypedWeightedCompleteTrs
931.46/291.58	    (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 3 ms]
931.46/291.58	    (10) CpxRNTS
931.46/291.58	    (11) CompleteCoflocoProof [FINISHED, 189 ms]
931.46/291.58	    (12) BOUNDS(1, n^1)
931.46/291.58	(13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
931.46/291.58	(14) TRS for Loop Detection
931.46/291.58	    (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
931.46/291.58	    (16) BEST
931.46/291.58	        (17) proven lower bound
931.46/291.58	            (18) LowerBoundPropagationProof [FINISHED, 0 ms]
931.46/291.58	            (19) BOUNDS(n^1, INF)
931.46/291.58	        (20) TRS for Loop Detection
931.46/291.58	
931.46/291.58	
931.46/291.58	----------------------------------------
931.46/291.58	
931.46/291.58	(0)
931.46/291.58	Obligation:
931.46/291.58	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
931.46/291.58	
931.46/291.58	
931.46/291.58	The TRS R consists of the following rules:
931.46/291.58	
931.46/291.58	   digits -> d(0)
931.46/291.58	   d(x) -> if(le(x, s(s(s(s(s(s(s(s(s(0)))))))))), x)
931.46/291.58	   if(true, x) -> cons(x, d(s(x)))
931.46/291.58	   if(false, x) -> nil
931.46/291.58	   le(0, y) -> true
931.46/291.58	   le(s(x), 0) -> false
931.46/291.58	   le(s(x), s(y)) -> le(x, y)
931.46/291.58	
931.46/291.58	S is empty.
931.46/291.58	Rewrite Strategy: FULL
931.46/291.58	----------------------------------------
931.46/291.58	
931.46/291.58	(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
931.46/291.58	Converted rc-obligation to irc-obligation.
931.46/291.58	
931.46/291.58	The duplicating contexts are:
931.46/291.58	d([])
931.46/291.58	if(true, [])
931.46/291.58	
931.46/291.58	
931.46/291.58	The defined contexts are:
931.46/291.58	if([], x1)
931.46/291.58	
931.46/291.58	
931.46/291.58	[] just represents basic- or constructor-terms in the following defined contexts:
931.46/291.58	if([], x1)
931.46/291.58	
931.46/291.58	
931.46/291.58	As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc.
931.46/291.58	----------------------------------------
931.46/291.58	
931.46/291.58	(2)
931.46/291.58	Obligation:
931.46/291.58	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
931.46/291.58	
931.46/291.58	
931.46/291.58	The TRS R consists of the following rules:
931.46/291.58	
931.46/291.58	   digits -> d(0)
931.46/291.58	   d(x) -> if(le(x, s(s(s(s(s(s(s(s(s(0)))))))))), x)
931.46/291.58	   if(true, x) -> cons(x, d(s(x)))
931.46/291.58	   if(false, x) -> nil
931.46/291.58	   le(0, y) -> true
931.46/291.58	   le(s(x), 0) -> false
931.46/291.58	   le(s(x), s(y)) -> le(x, y)
931.46/291.58	
931.46/291.58	S is empty.
931.46/291.58	Rewrite Strategy: INNERMOST
931.46/291.58	----------------------------------------
931.46/291.58	
931.46/291.58	(3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
931.46/291.58	Transformed relative TRS to weighted TRS
931.46/291.58	----------------------------------------
931.46/291.58	
931.46/291.58	(4)
931.46/291.58	Obligation:
931.46/291.58	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
931.46/291.58	
931.46/291.58	
931.46/291.58	The TRS R consists of the following rules:
931.46/291.58

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