Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307763

details

property	value
status	complete
benchmark	thiemann29.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n103.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.522 seconds
cpu usage	313.825
user time	311.662
system time	2.16292
max virtual memory	1.8279388E7
max residence set size	5612540.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^2), ?)

output

313.76/291.47	WORST_CASE(Omega(n^2), ?)
313.76/291.48	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
313.76/291.48	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
313.76/291.48	
313.76/291.48	
313.76/291.48	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF).
313.76/291.48	
313.76/291.48	(0) CpxTRS
313.76/291.48	(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
313.76/291.48	(2) CpxTRS
313.76/291.48	(3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
313.76/291.48	(4) typed CpxTrs
313.76/291.48	(5) OrderProof [LOWER BOUND(ID), 0 ms]
313.76/291.48	(6) typed CpxTrs
313.76/291.48	(7) RewriteLemmaProof [LOWER BOUND(ID), 302 ms]
313.76/291.48	(8) BEST
313.76/291.48	    (9) proven lower bound
313.76/291.48	        (10) LowerBoundPropagationProof [FINISHED, 0 ms]
313.76/291.48	        (11) BOUNDS(n^1, INF)
313.76/291.48	    (12) typed CpxTrs
313.76/291.48	        (13) RewriteLemmaProof [LOWER BOUND(ID), 77 ms]
313.76/291.48	        (14) typed CpxTrs
313.76/291.48	        (15) RewriteLemmaProof [LOWER BOUND(ID), 45 ms]
313.76/291.48	        (16) BEST
313.76/291.48	            (17) proven lower bound
313.76/291.48	                (18) LowerBoundPropagationProof [FINISHED, 0 ms]
313.76/291.48	                (19) BOUNDS(n^2, INF)
313.76/291.48	            (20) typed CpxTrs
313.76/291.48	
313.76/291.48	
313.76/291.48	----------------------------------------
313.76/291.48	
313.76/291.48	(0)
313.76/291.48	Obligation:
313.76/291.48	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF).
313.76/291.48	
313.76/291.48	
313.76/291.48	The TRS R consists of the following rules:
313.76/291.48	
313.76/291.48	   le(s(x), 0) -> false
313.76/291.48	   le(0, y) -> true
313.76/291.48	   le(s(x), s(y)) -> le(x, y)
313.76/291.48	   plus(0, y) -> y
313.76/291.48	   plus(s(x), y) -> s(plus(x, y))
313.76/291.48	   times(0, y) -> 0
313.76/291.48	   times(s(x), y) -> plus(y, times(x, y))
313.76/291.48	   log(x, 0) -> baseError
313.76/291.48	   log(x, s(0)) -> baseError
313.76/291.48	   log(0, s(s(b))) -> logZeroError
313.76/291.48	   log(s(x), s(s(b))) -> loop(s(x), s(s(b)), s(0), 0)
313.76/291.48	   loop(x, s(s(b)), s(y), z) -> if(le(x, s(y)), x, s(s(b)), s(y), z)
313.76/291.48	   if(true, x, b, y, z) -> z
313.76/291.48	   if(false, x, b, y, z) -> loop(x, b, times(b, y), s(z))
313.76/291.48	
313.76/291.48	S is empty.
313.76/291.48	Rewrite Strategy: FULL
313.76/291.48	----------------------------------------
313.76/291.48	
313.76/291.48	(1) RenamingProof (BOTH BOUNDS(ID, ID))
313.76/291.48	Renamed function symbols to avoid clashes with predefined symbol.
313.76/291.48	----------------------------------------
313.76/291.48	
313.76/291.48	(2)
313.76/291.48	Obligation:
313.76/291.48	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF).
313.76/291.48	
313.76/291.48	
313.76/291.48	The TRS R consists of the following rules:
313.76/291.48	
313.76/291.48	   le(s(x), 0') -> false
313.76/291.48	   le(0', y) -> true
313.76/291.48	   le(s(x), s(y)) -> le(x, y)
313.76/291.48	   plus(0', y) -> y
313.76/291.48	   plus(s(x), y) -> s(plus(x, y))
313.76/291.48	   times(0', y) -> 0'
313.76/291.48	   times(s(x), y) -> plus(y, times(x, y))
313.76/291.48	   log(x, 0') -> baseError
313.76/291.48	   log(x, s(0')) -> baseError
313.76/291.48	   log(0', s(s(b))) -> logZeroError
313.76/291.48	   log(s(x), s(s(b))) -> loop(s(x), s(s(b)), s(0'), 0')
313.76/291.48	   loop(x, s(s(b)), s(y), z) -> if(le(x, s(y)), x, s(s(b)), s(y), z)
313.76/291.48	   if(true, x, b, y, z) -> z
313.76/291.48	   if(false, x, b, y, z) -> loop(x, b, times(b, y), s(z))
313.76/291.48	
313.76/291.48	S is empty.
313.76/291.48	Rewrite Strategy: FULL
313.76/291.48	----------------------------------------
313.76/291.48	
313.76/291.48	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
313.76/291.48	Infered types.
313.76/291.48	----------------------------------------
313.76/291.48	
313.76/291.48	(4)
313.76/291.48	Obligation:
313.76/291.48	TRS:
313.76/291.48	Rules:
313.76/291.48	le(s(x), 0') -> false
313.76/291.48	le(0', y) -> true
313.76/291.48	le(s(x), s(y)) -> le(x, y)
313.76/291.48	plus(0', y) -> y

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actions all output return to Runtime_Complexity_Full_Rewriting 2019-04-01 06.11