Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313285

details

property	value
status	complete
benchmark	gm.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n165.star.cs.uiowa.edu
space	Rubio_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.62496 seconds
cpu usage	21.9503
user time	20.5391
system time	1.41115
max virtual memory	1.8973876E7
max residence set size	3878784.0

stage attributes

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

output

21.48/6.55	WORST_CASE(Omega(n^1), O(n^1))
21.48/6.56	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
21.48/6.56	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
21.48/6.56	
21.48/6.56	
21.48/6.56	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
21.48/6.56	
21.48/6.56	(0) CpxTRS
21.48/6.56	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
21.48/6.56	(2) CpxWeightedTrs
21.48/6.56	    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
21.48/6.56	    (4) CpxTypedWeightedTrs
21.48/6.56	    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
21.48/6.56	    (6) CpxTypedWeightedCompleteTrs
21.48/6.56	    (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
21.48/6.56	    (8) CpxRNTS
21.48/6.56	    (9) CompleteCoflocoProof [FINISHED, 291 ms]
21.48/6.56	    (10) BOUNDS(1, n^1)
21.48/6.56	(11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
21.48/6.56	(12) CpxTRS
21.48/6.56	    (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
21.48/6.56	    (14) typed CpxTrs
21.48/6.56	    (15) OrderProof [LOWER BOUND(ID), 0 ms]
21.48/6.56	    (16) typed CpxTrs
21.48/6.56	    (17) RewriteLemmaProof [LOWER BOUND(ID), 1186 ms]
21.48/6.56	    (18) BEST
21.48/6.56	        (19) proven lower bound
21.48/6.56	            (20) LowerBoundPropagationProof [FINISHED, 0 ms]
21.48/6.56	            (21) BOUNDS(n^1, INF)
21.48/6.56	        (22) typed CpxTrs
21.48/6.56	            (23) RewriteLemmaProof [LOWER BOUND(ID), 0 ms]
21.48/6.56	            (24) BOUNDS(1, INF)
21.48/6.56	
21.48/6.56	
21.48/6.56	----------------------------------------
21.48/6.56	
21.48/6.56	(0)
21.48/6.56	Obligation:
21.48/6.56	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
21.48/6.56	
21.48/6.56	
21.48/6.56	The TRS R consists of the following rules:
21.48/6.56	
21.48/6.56	   minus(X, 0) -> X
21.48/6.56	   minus(s(X), s(Y)) -> p(minus(X, Y))
21.48/6.56	   p(s(X)) -> X
21.48/6.56	   div(0, s(Y)) -> 0
21.48/6.56	   div(s(X), s(Y)) -> s(div(minus(X, Y), s(Y)))
21.48/6.56	
21.48/6.56	S is empty.
21.48/6.56	Rewrite Strategy: INNERMOST
21.48/6.56	----------------------------------------
21.48/6.56	
21.48/6.56	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
21.48/6.56	Transformed relative TRS to weighted TRS
21.48/6.56	----------------------------------------
21.48/6.56	
21.48/6.56	(2)
21.48/6.56	Obligation:
21.48/6.56	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
21.48/6.56	
21.48/6.56	
21.48/6.56	The TRS R consists of the following rules:
21.48/6.56	
21.48/6.56	   minus(X, 0) -> X [1]
21.48/6.56	   minus(s(X), s(Y)) -> p(minus(X, Y)) [1]
21.48/6.56	   p(s(X)) -> X [1]
21.48/6.56	   div(0, s(Y)) -> 0 [1]
21.48/6.56	   div(s(X), s(Y)) -> s(div(minus(X, Y), s(Y))) [1]
21.48/6.56	
21.48/6.56	Rewrite Strategy: INNERMOST
21.48/6.56	----------------------------------------
21.48/6.56	
21.48/6.56	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
21.48/6.56	Infered types.
21.48/6.56	----------------------------------------
21.48/6.56	
21.48/6.56	(4)
21.48/6.56	Obligation:
21.48/6.56	Runtime Complexity Weighted TRS with Types.
21.48/6.56	The TRS R consists of the following rules:
21.48/6.56	
21.48/6.56	   minus(X, 0) -> X [1]
21.48/6.56	   minus(s(X), s(Y)) -> p(minus(X, Y)) [1]
21.48/6.56	   p(s(X)) -> X [1]
21.48/6.56	   div(0, s(Y)) -> 0 [1]
21.48/6.56	   div(s(X), s(Y)) -> s(div(minus(X, Y), s(Y))) [1]
21.48/6.56	
21.48/6.56	The TRS has the following type information:
21.48/6.56	minus :: 0:s -> 0:s -> 0:s
21.48/6.56	0 :: 0:s
21.48/6.56	s :: 0:s -> 0:s
21.48/6.56	p :: 0:s -> 0:s
21.48/6.56	div :: 0:s -> 0:s -> 0:s
21.48/6.56	
21.48/6.56	Rewrite Strategy: INNERMOST
21.48/6.56	----------------------------------------
21.48/6.56	
21.48/6.56	(5) CompletionProof (UPPER BOUND(ID))
21.48/6.56	The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added:

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