Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313759

details

property	value
status	complete
benchmark	#3.5a.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n092.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	10.9927 seconds
cpu usage	32.5814
user time	30.6726
system time	1.90873
max virtual memory	1.9174516E7
max residence set size	4464608.0

stage attributes

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

output

32.31/10.93	WORST_CASE(Omega(n^1), O(n^1))
32.31/10.94	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
32.31/10.94	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
32.31/10.94	
32.31/10.94	
32.31/10.94	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
32.31/10.94	
32.31/10.94	(0) CpxTRS
32.31/10.94	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
32.31/10.94	(2) CpxWeightedTrs
32.31/10.94	    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
32.31/10.94	    (4) CpxTypedWeightedTrs
32.31/10.94	    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
32.31/10.94	    (6) CpxTypedWeightedCompleteTrs
32.31/10.94	    (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
32.31/10.94	    (8) CpxRNTS
32.31/10.94	    (9) CompleteCoflocoProof [FINISHED, 544 ms]
32.31/10.94	    (10) BOUNDS(1, n^1)
32.31/10.94	(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
32.31/10.94	(12) TRS for Loop Detection
32.31/10.94	    (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
32.31/10.94	    (14) BEST
32.31/10.94	        (15) proven lower bound
32.31/10.94	            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
32.31/10.94	            (17) BOUNDS(n^1, INF)
32.31/10.94	        (18) TRS for Loop Detection
32.31/10.94	
32.31/10.94	
32.31/10.94	----------------------------------------
32.31/10.94	
32.31/10.94	(0)
32.31/10.94	Obligation:
32.31/10.94	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
32.31/10.94	
32.31/10.94	
32.31/10.94	The TRS R consists of the following rules:
32.31/10.94	
32.31/10.94	   le(0, y) -> true
32.31/10.94	   le(s(x), 0) -> false
32.31/10.94	   le(s(x), s(y)) -> le(x, y)
32.31/10.94	   pred(s(x)) -> x
32.31/10.94	   minus(x, 0) -> x
32.31/10.94	   minus(x, s(y)) -> pred(minus(x, y))
32.31/10.94	   mod(0, y) -> 0
32.31/10.94	   mod(s(x), 0) -> 0
32.31/10.94	   mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y))
32.31/10.94	   if_mod(true, s(x), s(y)) -> mod(minus(x, y), s(y))
32.31/10.94	   if_mod(false, s(x), s(y)) -> s(x)
32.31/10.94	
32.31/10.94	S is empty.
32.31/10.94	Rewrite Strategy: INNERMOST
32.31/10.94	----------------------------------------
32.31/10.94	
32.31/10.94	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
32.31/10.94	Transformed relative TRS to weighted TRS
32.31/10.94	----------------------------------------
32.31/10.94	
32.31/10.94	(2)
32.31/10.94	Obligation:
32.31/10.94	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
32.31/10.94	
32.31/10.94	
32.31/10.94	The TRS R consists of the following rules:
32.31/10.94	
32.31/10.94	   le(0, y) -> true [1]
32.31/10.94	   le(s(x), 0) -> false [1]
32.31/10.94	   le(s(x), s(y)) -> le(x, y) [1]
32.31/10.94	   pred(s(x)) -> x [1]
32.31/10.94	   minus(x, 0) -> x [1]
32.31/10.94	   minus(x, s(y)) -> pred(minus(x, y)) [1]
32.31/10.94	   mod(0, y) -> 0 [1]
32.31/10.94	   mod(s(x), 0) -> 0 [1]
32.31/10.94	   mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y)) [1]
32.31/10.94	   if_mod(true, s(x), s(y)) -> mod(minus(x, y), s(y)) [1]
32.31/10.94	   if_mod(false, s(x), s(y)) -> s(x) [1]
32.31/10.94	
32.31/10.94	Rewrite Strategy: INNERMOST
32.31/10.94	----------------------------------------
32.31/10.94	
32.31/10.94	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
32.31/10.94	Infered types.
32.31/10.94	----------------------------------------
32.31/10.94	
32.31/10.94	(4)
32.31/10.94	Obligation:
32.31/10.94	Runtime Complexity Weighted TRS with Types.
32.31/10.94	The TRS R consists of the following rules:
32.31/10.94	
32.31/10.94	   le(0, y) -> true [1]
32.31/10.94	   le(s(x), 0) -> false [1]
32.31/10.94	   le(s(x), s(y)) -> le(x, y) [1]
32.31/10.94	   pred(s(x)) -> x [1]
32.31/10.94	   minus(x, 0) -> x [1]
32.31/10.94	   minus(x, s(y)) -> pred(minus(x, y)) [1]
32.31/10.94	   mod(0, y) -> 0 [1]
32.31/10.94	   mod(s(x), 0) -> 0 [1]
32.31/10.94	   mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y)) [1]
32.31/10.94	   if_mod(true, s(x), s(y)) -> mod(minus(x, y), s(y)) [1]
32.31/10.94	   if_mod(false, s(x), s(y)) -> s(x) [1]
32.31/10.94

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