Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313755

details

property	value
status	complete
benchmark	#3.53b.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n106.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.41217 seconds
cpu usage	13.5599
user time	12.4527
system time	1.10717
max virtual memory	1.8938648E7
max residence set size	3732040.0

stage attributes

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

output

13.31/4.35	WORST_CASE(Omega(n^1), O(n^1))
13.31/4.36	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
13.31/4.36	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
13.31/4.36	
13.31/4.36	
13.31/4.36	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
13.31/4.36	
13.31/4.36	(0) CpxTRS
13.31/4.36	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
13.31/4.36	(2) CpxWeightedTrs
13.31/4.36	    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
13.31/4.36	    (4) CpxTypedWeightedTrs
13.31/4.36	    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
13.31/4.36	    (6) CpxTypedWeightedCompleteTrs
13.31/4.36	    (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
13.31/4.36	    (8) CpxRNTS
13.31/4.36	    (9) CompleteCoflocoProof [FINISHED, 168 ms]
13.31/4.36	    (10) BOUNDS(1, n^1)
13.31/4.36	(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
13.31/4.36	(12) TRS for Loop Detection
13.31/4.36	    (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
13.31/4.36	    (14) BEST
13.31/4.36	        (15) proven lower bound
13.31/4.36	            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
13.31/4.36	            (17) BOUNDS(n^1, INF)
13.31/4.36	        (18) TRS for Loop Detection
13.31/4.36	
13.31/4.36	
13.31/4.36	----------------------------------------
13.31/4.36	
13.31/4.36	(0)
13.31/4.36	Obligation:
13.31/4.36	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
13.31/4.36	
13.31/4.36	
13.31/4.36	The TRS R consists of the following rules:
13.31/4.36	
13.31/4.36	   g(x, y) -> x
13.31/4.36	   g(x, y) -> y
13.31/4.36	   f(0, 1, x) -> f(s(x), x, x)
13.31/4.36	   f(x, y, s(z)) -> s(f(0, 1, z))
13.31/4.36	
13.31/4.36	S is empty.
13.31/4.36	Rewrite Strategy: INNERMOST
13.31/4.36	----------------------------------------
13.31/4.36	
13.31/4.36	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
13.31/4.36	Transformed relative TRS to weighted TRS
13.31/4.36	----------------------------------------
13.31/4.36	
13.31/4.36	(2)
13.31/4.36	Obligation:
13.31/4.36	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
13.31/4.36	
13.31/4.36	
13.31/4.36	The TRS R consists of the following rules:
13.31/4.36	
13.31/4.36	   g(x, y) -> x [1]
13.31/4.36	   g(x, y) -> y [1]
13.31/4.36	   f(0, 1, x) -> f(s(x), x, x) [1]
13.31/4.36	   f(x, y, s(z)) -> s(f(0, 1, z)) [1]
13.31/4.36	
13.31/4.36	Rewrite Strategy: INNERMOST
13.31/4.36	----------------------------------------
13.31/4.36	
13.31/4.36	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
13.31/4.36	Infered types.
13.31/4.36	----------------------------------------
13.31/4.36	
13.31/4.36	(4)
13.31/4.36	Obligation:
13.31/4.36	Runtime Complexity Weighted TRS with Types.
13.31/4.36	The TRS R consists of the following rules:
13.31/4.36	
13.31/4.36	   g(x, y) -> x [1]
13.31/4.36	   g(x, y) -> y [1]
13.31/4.36	   f(0, 1, x) -> f(s(x), x, x) [1]
13.31/4.36	   f(x, y, s(z)) -> s(f(0, 1, z)) [1]
13.31/4.36	
13.31/4.36	The TRS has the following type information:
13.31/4.36	g :: g -> g -> g
13.31/4.36	f :: 0:1:s -> 0:1:s -> 0:1:s -> 0:1:s
13.31/4.36	0 :: 0:1:s
13.31/4.36	1 :: 0:1:s
13.31/4.36	s :: 0:1:s -> 0:1:s
13.31/4.36	
13.31/4.36	Rewrite Strategy: INNERMOST
13.31/4.36	----------------------------------------
13.31/4.36	
13.31/4.36	(5) CompletionProof (UPPER BOUND(ID))
13.31/4.36	The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added:
13.31/4.36	
13.31/4.36	   f(v0, v1, v2) -> null_f [0]
13.31/4.36	
13.31/4.36	And the following fresh constants:    null_f, const
13.31/4.36	
13.31/4.36	----------------------------------------
13.31/4.36	
13.31/4.36	(6)
13.31/4.36	Obligation:

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