Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313292

details

property	value
status	complete
benchmark	logarquot.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n120.star.cs.uiowa.edu
space	Rubio_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.27224 seconds
cpu usage	21.081
user time	19.3737
system time	1.70727
max virtual memory	1.9143616E7
max residence set size	4084888.0

stage attributes

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

output

20.26/6.04	WORST_CASE(Omega(n^1), O(n^1))
20.76/6.11	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
20.76/6.11	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
20.76/6.11	
20.76/6.11	
20.76/6.11	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
20.76/6.11	
20.76/6.11	(0) CpxTRS
20.76/6.11	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
20.76/6.11	(2) CpxWeightedTrs
20.76/6.11	    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
20.76/6.11	    (4) CpxTypedWeightedTrs
20.76/6.11	    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
20.76/6.11	    (6) CpxTypedWeightedCompleteTrs
20.76/6.11	    (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
20.76/6.11	    (8) CpxRNTS
20.76/6.11	    (9) CompleteCoflocoProof [FINISHED, 411 ms]
20.76/6.11	    (10) BOUNDS(1, n^1)
20.76/6.11	(11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
20.76/6.11	(12) CpxTRS
20.76/6.11	    (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
20.76/6.11	    (14) typed CpxTrs
20.76/6.11	    (15) OrderProof [LOWER BOUND(ID), 0 ms]
20.76/6.11	    (16) typed CpxTrs
20.76/6.11	    (17) RewriteLemmaProof [LOWER BOUND(ID), 272 ms]
20.76/6.11	    (18) BEST
20.76/6.11	        (19) proven lower bound
20.76/6.11	            (20) LowerBoundPropagationProof [FINISHED, 0 ms]
20.76/6.11	            (21) BOUNDS(n^1, INF)
20.76/6.11	        (22) typed CpxTrs
20.76/6.11	
20.76/6.11	
20.76/6.11	----------------------------------------
20.76/6.11	
20.76/6.11	(0)
20.76/6.11	Obligation:
20.76/6.11	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
20.76/6.11	
20.76/6.11	
20.76/6.11	The TRS R consists of the following rules:
20.76/6.11	
20.76/6.11	   min(X, 0) -> X
20.76/6.11	   min(s(X), s(Y)) -> min(X, Y)
20.76/6.11	   quot(0, s(Y)) -> 0
20.76/6.11	   quot(s(X), s(Y)) -> s(quot(min(X, Y), s(Y)))
20.76/6.11	   log(s(0)) -> 0
20.76/6.11	   log(s(s(X))) -> s(log(s(quot(X, s(s(0))))))
20.76/6.11	
20.76/6.11	S is empty.
20.76/6.11	Rewrite Strategy: INNERMOST
20.76/6.11	----------------------------------------
20.76/6.11	
20.76/6.11	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
20.76/6.11	Transformed relative TRS to weighted TRS
20.76/6.11	----------------------------------------
20.76/6.11	
20.76/6.11	(2)
20.76/6.11	Obligation:
20.76/6.11	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
20.76/6.11	
20.76/6.11	
20.76/6.11	The TRS R consists of the following rules:
20.76/6.11	
20.76/6.11	   min(X, 0) -> X [1]
20.76/6.11	   min(s(X), s(Y)) -> min(X, Y) [1]
20.76/6.11	   quot(0, s(Y)) -> 0 [1]
20.76/6.11	   quot(s(X), s(Y)) -> s(quot(min(X, Y), s(Y))) [1]
20.76/6.11	   log(s(0)) -> 0 [1]
20.76/6.11	   log(s(s(X))) -> s(log(s(quot(X, s(s(0)))))) [1]
20.76/6.11	
20.76/6.11	Rewrite Strategy: INNERMOST
20.76/6.11	----------------------------------------
20.76/6.11	
20.76/6.11	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
20.76/6.11	Infered types.
20.76/6.11	----------------------------------------
20.76/6.11	
20.76/6.11	(4)
20.76/6.11	Obligation:
20.76/6.11	Runtime Complexity Weighted TRS with Types.
20.76/6.11	The TRS R consists of the following rules:
20.76/6.11	
20.76/6.11	   min(X, 0) -> X [1]
20.76/6.11	   min(s(X), s(Y)) -> min(X, Y) [1]
20.76/6.11	   quot(0, s(Y)) -> 0 [1]
20.76/6.11	   quot(s(X), s(Y)) -> s(quot(min(X, Y), s(Y))) [1]
20.76/6.11	   log(s(0)) -> 0 [1]
20.76/6.11	   log(s(s(X))) -> s(log(s(quot(X, s(s(0)))))) [1]
20.76/6.11	
20.76/6.11	The TRS has the following type information:
20.76/6.11	min :: 0:s -> 0:s -> 0:s
20.76/6.11	0 :: 0:s
20.76/6.11	s :: 0:s -> 0:s
20.76/6.11	quot :: 0:s -> 0:s -> 0:s
20.76/6.11	log :: 0:s -> 0:s
20.76/6.11	
20.76/6.11	Rewrite Strategy: INNERMOST
20.76/6.11	----------------------------------------
20.76/6.11	
20.76/6.11	(5) CompletionProof (UPPER BOUND(ID))

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