Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313685

details

property	value
status	complete
benchmark	rta3.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n083.star.cs.uiowa.edu
space	AProVE_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.603 seconds
cpu usage	981.68
user time	976.234
system time	5.44564
max virtual memory	1.9120828E7
max residence set size	7390452.0

stage attributes

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

output

981.28/291.55	WORST_CASE(Omega(n^1), ?)
981.28/291.55	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
981.28/291.55	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
981.28/291.55	
981.28/291.55	
981.28/291.55	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
981.28/291.55	
981.28/291.55	(0) CpxTRS
981.28/291.55	(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
981.28/291.55	(2) CpxTRS
981.28/291.55	(3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
981.28/291.55	(4) typed CpxTrs
981.28/291.55	(5) OrderProof [LOWER BOUND(ID), 0 ms]
981.28/291.55	(6) typed CpxTrs
981.28/291.55	(7) RewriteLemmaProof [LOWER BOUND(ID), 931 ms]
981.28/291.55	(8) BEST
981.28/291.55	    (9) proven lower bound
981.28/291.55	        (10) LowerBoundPropagationProof [FINISHED, 0 ms]
981.28/291.55	        (11) BOUNDS(n^1, INF)
981.28/291.55	    (12) typed CpxTrs
981.28/291.55	
981.28/291.55	
981.28/291.55	----------------------------------------
981.28/291.55	
981.28/291.55	(0)
981.28/291.55	Obligation:
981.28/291.55	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
981.28/291.55	
981.28/291.55	
981.28/291.55	The TRS R consists of the following rules:
981.28/291.55	
981.28/291.55	   ack(0, y) -> s(y)
981.28/291.55	   ack(s(x), 0) -> ack(x, s(0))
981.28/291.55	   ack(s(x), s(y)) -> ack(x, ack(s(x), y))
981.28/291.55	   f(s(x), y) -> f(x, s(x))
981.28/291.55	   f(x, s(y)) -> f(y, x)
981.28/291.55	   f(x, y) -> ack(x, y)
981.28/291.55	   ack(s(x), y) -> f(x, x)
981.28/291.55	
981.28/291.55	S is empty.
981.28/291.55	Rewrite Strategy: INNERMOST
981.28/291.55	----------------------------------------
981.28/291.55	
981.28/291.55	(1) RenamingProof (BOTH BOUNDS(ID, ID))
981.28/291.55	Renamed function symbols to avoid clashes with predefined symbol.
981.28/291.55	----------------------------------------
981.28/291.55	
981.28/291.55	(2)
981.28/291.55	Obligation:
981.28/291.55	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
981.28/291.55	
981.28/291.55	
981.28/291.55	The TRS R consists of the following rules:
981.28/291.55	
981.28/291.55	   ack(0', y) -> s(y)
981.28/291.55	   ack(s(x), 0') -> ack(x, s(0'))
981.28/291.55	   ack(s(x), s(y)) -> ack(x, ack(s(x), y))
981.28/291.55	   f(s(x), y) -> f(x, s(x))
981.28/291.55	   f(x, s(y)) -> f(y, x)
981.28/291.55	   f(x, y) -> ack(x, y)
981.28/291.55	   ack(s(x), y) -> f(x, x)
981.28/291.55	
981.28/291.55	S is empty.
981.28/291.55	Rewrite Strategy: INNERMOST
981.28/291.55	----------------------------------------
981.28/291.55	
981.28/291.55	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
981.28/291.55	Infered types.
981.28/291.55	----------------------------------------
981.28/291.55	
981.28/291.55	(4)
981.28/291.55	Obligation:
981.28/291.55	Innermost TRS:
981.28/291.55	Rules:
981.28/291.55	ack(0', y) -> s(y)
981.28/291.55	ack(s(x), 0') -> ack(x, s(0'))
981.28/291.55	ack(s(x), s(y)) -> ack(x, ack(s(x), y))
981.28/291.55	f(s(x), y) -> f(x, s(x))
981.28/291.55	f(x, s(y)) -> f(y, x)
981.28/291.55	f(x, y) -> ack(x, y)
981.28/291.55	ack(s(x), y) -> f(x, x)
981.28/291.55	
981.28/291.55	Types:
981.28/291.55	ack :: 0':s -> 0':s -> 0':s
981.28/291.55	0' :: 0':s
981.28/291.55	s :: 0':s -> 0':s
981.28/291.55	f :: 0':s -> 0':s -> 0':s
981.28/291.55	hole_0':s1_0 :: 0':s
981.28/291.55	gen_0':s2_0 :: Nat -> 0':s
981.28/291.55	
981.28/291.55	----------------------------------------
981.28/291.55	
981.28/291.55	(5) OrderProof (LOWER BOUND(ID))
981.28/291.55	Heuristically decided to analyse the following defined symbols:
981.28/291.55	ack, f
981.28/291.55	
981.28/291.55	They will be analysed ascendingly in the following order:
981.28/291.55	ack = f
981.28/291.55	
981.28/291.55	----------------------------------------

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actions all output return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40