Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313733

details

property	value
status	complete
benchmark	thiemann28.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n057.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	14.2963 seconds
cpu usage	51.4514
user time	48.8273
system time	2.62415
max virtual memory	3.790442E7
max residence set size	4261788.0

stage attributes

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

output

51.31/14.23	WORST_CASE(Omega(n^1), O(n^1))
51.31/14.24	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
51.31/14.24	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
51.31/14.24	
51.31/14.24	
51.31/14.24	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
51.31/14.24	
51.31/14.24	(0) CpxTRS
51.31/14.24	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
51.31/14.24	(2) CpxWeightedTrs
51.31/14.24	    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
51.31/14.24	    (4) CpxTypedWeightedTrs
51.31/14.24	    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
51.31/14.24	    (6) CpxTypedWeightedCompleteTrs
51.31/14.24	    (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 2 ms]
51.31/14.24	    (8) CpxRNTS
51.31/14.24	    (9) CompleteCoflocoProof [FINISHED, 643 ms]
51.31/14.24	    (10) BOUNDS(1, n^1)
51.31/14.24	(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
51.31/14.24	(12) TRS for Loop Detection
51.31/14.24	    (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
51.31/14.24	    (14) BEST
51.31/14.24	        (15) proven lower bound
51.31/14.24	            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
51.31/14.24	            (17) BOUNDS(n^1, INF)
51.31/14.24	        (18) TRS for Loop Detection
51.31/14.24	
51.31/14.24	
51.31/14.24	----------------------------------------
51.31/14.24	
51.31/14.24	(0)
51.31/14.24	Obligation:
51.31/14.24	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
51.31/14.24	
51.31/14.24	
51.31/14.24	The TRS R consists of the following rules:
51.31/14.24	
51.31/14.24	   ge(x, 0) -> true
51.31/14.24	   ge(0, s(y)) -> false
51.31/14.24	   ge(s(x), s(y)) -> ge(x, y)
51.31/14.24	   minus(x, 0) -> x
51.31/14.24	   minus(0, y) -> 0
51.31/14.24	   minus(s(x), s(y)) -> minus(x, y)
51.31/14.24	   id_inc(x) -> x
51.31/14.24	   id_inc(x) -> s(x)
51.31/14.24	   div(x, y) -> if(ge(y, s(0)), ge(x, y), x, y)
51.31/14.24	   if(false, b, x, y) -> div_by_zero
51.31/14.24	   if(true, false, x, y) -> 0
51.31/14.24	   if(true, true, x, y) -> id_inc(div(minus(x, y), y))
51.31/14.24	
51.31/14.24	S is empty.
51.31/14.24	Rewrite Strategy: INNERMOST
51.31/14.24	----------------------------------------
51.31/14.24	
51.31/14.24	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
51.31/14.24	Transformed relative TRS to weighted TRS
51.31/14.24	----------------------------------------
51.31/14.24	
51.31/14.24	(2)
51.31/14.24	Obligation:
51.31/14.24	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).
51.31/14.24	
51.31/14.24	
51.31/14.24	The TRS R consists of the following rules:
51.31/14.24	
51.31/14.24	   ge(x, 0) -> true [1]
51.31/14.24	   ge(0, s(y)) -> false [1]
51.31/14.24	   ge(s(x), s(y)) -> ge(x, y) [1]
51.31/14.24	   minus(x, 0) -> x [1]
51.31/14.24	   minus(0, y) -> 0 [1]
51.31/14.24	   minus(s(x), s(y)) -> minus(x, y) [1]
51.31/14.24	   id_inc(x) -> x [1]
51.31/14.24	   id_inc(x) -> s(x) [1]
51.31/14.24	   div(x, y) -> if(ge(y, s(0)), ge(x, y), x, y) [1]
51.31/14.24	   if(false, b, x, y) -> div_by_zero [1]
51.31/14.24	   if(true, false, x, y) -> 0 [1]
51.31/14.24	   if(true, true, x, y) -> id_inc(div(minus(x, y), y)) [1]
51.31/14.24	
51.31/14.24	Rewrite Strategy: INNERMOST
51.31/14.24	----------------------------------------
51.31/14.24	
51.31/14.24	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
51.31/14.24	Infered types.
51.31/14.24	----------------------------------------
51.31/14.24	
51.31/14.24	(4)
51.31/14.24	Obligation:
51.31/14.24	Runtime Complexity Weighted TRS with Types.
51.31/14.24	The TRS R consists of the following rules:
51.31/14.24	
51.31/14.24	   ge(x, 0) -> true [1]
51.31/14.24	   ge(0, s(y)) -> false [1]
51.31/14.24	   ge(s(x), s(y)) -> ge(x, y) [1]
51.31/14.24	   minus(x, 0) -> x [1]
51.31/14.24	   minus(0, y) -> 0 [1]
51.31/14.24	   minus(s(x), s(y)) -> minus(x, y) [1]
51.31/14.24	   id_inc(x) -> x [1]
51.31/14.24	   id_inc(x) -> s(x) [1]
51.31/14.24	   div(x, y) -> if(ge(y, s(0)), ge(x, y), x, y) [1]
51.31/14.24	   if(false, b, x, y) -> div_by_zero [1]

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