Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313384

details

property	value
status	complete
benchmark	jones2.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n056.star.cs.uiowa.edu
space	Mixed_TRS

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	5.94186 seconds
cpu usage	19.9102
user time	18.7052
system time	1.20491
max virtual memory	1.8944008E7
max residence set size	3527312.0

stage attributes

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

output

19.42/5.86	WORST_CASE(Omega(n^1), O(n^1))
19.42/5.87	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
19.42/5.87	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
19.42/5.87	
19.42/5.87	
19.42/5.87	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
19.42/5.87	
19.42/5.87	(0) CpxTRS
19.42/5.87	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
19.42/5.87	(2) CpxWeightedTrs
19.42/5.87	    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
19.42/5.87	    (4) CpxTypedWeightedTrs
19.42/5.87	    (5) CompletionProof [UPPER BOUND(ID), 1 ms]
19.42/5.87	    (6) CpxTypedWeightedCompleteTrs
19.42/5.87	    (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
19.42/5.87	    (8) CpxRNTS
19.42/5.87	    (9) CompleteCoflocoProof [FINISHED, 28 ms]
19.42/5.87	    (10) BOUNDS(1, n^1)
19.42/5.87	(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
19.42/5.87	(12) TRS for Loop Detection
19.42/5.87	    (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
19.42/5.87	    (14) BEST
19.42/5.87	        (15) proven lower bound
19.42/5.87	            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
19.42/5.87	            (17) BOUNDS(n^1, INF)
19.42/5.87	        (18) TRS for Loop Detection
19.42/5.87	
19.42/5.87	
19.42/5.87	----------------------------------------
19.42/5.87	
19.42/5.87	(0)
19.42/5.87	Obligation:
19.42/5.87	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
19.42/5.87	
19.42/5.87	
19.42/5.87	The TRS R consists of the following rules:
19.42/5.87	
19.42/5.87	   f(empty, l) -> l
19.42/5.87	   f(cons(x, k), l) -> g(k, l, cons(x, k))
19.42/5.87	   g(a, b, c) -> f(a, cons(b, c))
19.42/5.87	
19.42/5.87	S is empty.
19.42/5.87	Rewrite Strategy: INNERMOST
19.42/5.87	----------------------------------------
19.42/5.87	
19.42/5.87	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
19.42/5.87	Transformed relative TRS to weighted TRS
19.42/5.87	----------------------------------------
19.42/5.87	
19.42/5.87	(2)
19.42/5.87	Obligation:
19.42/5.87	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
19.42/5.87	
19.42/5.87	
19.42/5.87	The TRS R consists of the following rules:
19.42/5.87	
19.42/5.87	   f(empty, l) -> l [1]
19.42/5.87	   f(cons(x, k), l) -> g(k, l, cons(x, k)) [1]
19.42/5.87	   g(a, b, c) -> f(a, cons(b, c)) [1]
19.42/5.87	
19.42/5.87	Rewrite Strategy: INNERMOST
19.42/5.87	----------------------------------------
19.42/5.87	
19.42/5.87	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
19.42/5.87	Infered types.
19.42/5.87	----------------------------------------
19.42/5.87	
19.42/5.87	(4)
19.42/5.87	Obligation:
19.42/5.87	Runtime Complexity Weighted TRS with Types.
19.42/5.87	The TRS R consists of the following rules:
19.42/5.87	
19.42/5.87	   f(empty, l) -> l [1]
19.42/5.87	   f(cons(x, k), l) -> g(k, l, cons(x, k)) [1]
19.42/5.87	   g(a, b, c) -> f(a, cons(b, c)) [1]
19.42/5.87	
19.42/5.87	The TRS has the following type information:
19.42/5.87	f :: empty:cons -> empty:cons -> empty:cons
19.42/5.87	empty :: empty:cons
19.42/5.87	cons :: empty:cons -> empty:cons -> empty:cons
19.42/5.87	g :: empty:cons -> empty:cons -> empty:cons -> empty:cons
19.42/5.87	
19.42/5.87	Rewrite Strategy: INNERMOST
19.42/5.87	----------------------------------------
19.42/5.87	
19.42/5.87	(5) CompletionProof (UPPER BOUND(ID))
19.42/5.87	The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added:
19.42/5.87	none
19.42/5.87	
19.42/5.87	And the following fresh constants: none
19.42/5.87	
19.42/5.87	----------------------------------------
19.42/5.87	
19.42/5.87	(6)
19.42/5.87	Obligation:
19.42/5.87	Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is:
19.42/5.87	
19.42/5.87	Runtime Complexity Weighted TRS with Types.
19.42/5.87	The TRS R consists of the following rules:
19.42/5.87

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