Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313673

details

property	value
status	complete
benchmark	factorial1.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n030.star.cs.uiowa.edu
space	AProVE_06

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.598 seconds
cpu usage	1122.83
user time	1115.64
system time	7.18918
max virtual memory	3.79098E7
max residence set size	7664244.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^4), ?)

output

1122.38/291.48	WORST_CASE(Omega(n^4), ?)
1122.38/291.52	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
1122.38/291.52	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
1122.38/291.52	
1122.38/291.52	
1122.38/291.52	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^4, INF).
1122.38/291.52	
1122.38/291.52	(0) CpxTRS
1122.38/291.52	(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
1122.38/291.52	(2) CpxTRS
1122.38/291.52	(3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
1122.38/291.52	(4) typed CpxTrs
1122.38/291.52	(5) OrderProof [LOWER BOUND(ID), 0 ms]
1122.38/291.52	(6) typed CpxTrs
1122.38/291.52	(7) RewriteLemmaProof [LOWER BOUND(ID), 289 ms]
1122.38/291.52	(8) BEST
1122.38/291.52	    (9) proven lower bound
1122.38/291.52	        (10) LowerBoundPropagationProof [FINISHED, 0 ms]
1122.38/291.52	        (11) BOUNDS(n^1, INF)
1122.38/291.52	    (12) typed CpxTrs
1122.38/291.52	        (13) RewriteLemmaProof [LOWER BOUND(ID), 43 ms]
1122.38/291.52	        (14) BEST
1122.38/291.52	            (15) proven lower bound
1122.38/291.52	                (16) LowerBoundPropagationProof [FINISHED, 0 ms]
1122.38/291.52	                (17) BOUNDS(n^2, INF)
1122.38/291.52	            (18) typed CpxTrs
1122.38/291.52	                (19) RewriteLemmaProof [LOWER BOUND(ID), 38 ms]
1122.38/291.52	                (20) BEST
1122.38/291.52	                    (21) proven lower bound
1122.38/291.52	                        (22) LowerBoundPropagationProof [FINISHED, 0 ms]
1122.38/291.52	                        (23) BOUNDS(n^3, INF)
1122.38/291.52	                    (24) typed CpxTrs
1122.38/291.52	                        (25) RewriteLemmaProof [LOWER BOUND(ID), 1326 ms]
1122.38/291.52	                        (26) proven lower bound
1122.38/291.52	                        (27) LowerBoundPropagationProof [FINISHED, 0 ms]
1122.38/291.52	                        (28) BOUNDS(n^4, INF)
1122.38/291.52	
1122.38/291.52	
1122.38/291.52	----------------------------------------
1122.38/291.52	
1122.38/291.52	(0)
1122.38/291.52	Obligation:
1122.38/291.52	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^4, INF).
1122.38/291.52	
1122.38/291.52	
1122.38/291.52	The TRS R consists of the following rules:
1122.38/291.52	
1122.38/291.52	   plus(0, x) -> x
1122.38/291.52	   plus(s(x), y) -> s(plus(p(s(x)), y))
1122.38/291.52	   times(0, y) -> 0
1122.38/291.52	   times(s(x), y) -> plus(y, times(p(s(x)), y))
1122.38/291.52	   p(s(0)) -> 0
1122.38/291.52	   p(s(s(x))) -> s(p(s(x)))
1122.38/291.52	   fac(0, x) -> x
1122.38/291.52	   fac(s(x), y) -> fac(p(s(x)), times(s(x), y))
1122.38/291.52	   factorial(x) -> fac(x, s(0))
1122.38/291.52	
1122.38/291.52	S is empty.
1122.38/291.52	Rewrite Strategy: INNERMOST
1122.38/291.52	----------------------------------------
1122.38/291.52	
1122.38/291.52	(1) RenamingProof (BOTH BOUNDS(ID, ID))
1122.38/291.52	Renamed function symbols to avoid clashes with predefined symbol.
1122.38/291.52	----------------------------------------
1122.38/291.52	
1122.38/291.52	(2)
1122.38/291.52	Obligation:
1122.38/291.52	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^4, INF).
1122.38/291.52	
1122.38/291.52	
1122.38/291.52	The TRS R consists of the following rules:
1122.38/291.52	
1122.38/291.52	   plus(0', x) -> x
1122.38/291.52	   plus(s(x), y) -> s(plus(p(s(x)), y))
1122.38/291.52	   times(0', y) -> 0'
1122.38/291.52	   times(s(x), y) -> plus(y, times(p(s(x)), y))
1122.38/291.52	   p(s(0')) -> 0'
1122.38/291.52	   p(s(s(x))) -> s(p(s(x)))
1122.38/291.52	   fac(0', x) -> x
1122.38/291.52	   fac(s(x), y) -> fac(p(s(x)), times(s(x), y))
1122.38/291.52	   factorial(x) -> fac(x, s(0'))
1122.38/291.52	
1122.38/291.52	S is empty.
1122.38/291.52	Rewrite Strategy: INNERMOST
1122.38/291.52	----------------------------------------
1122.38/291.52	
1122.38/291.52	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
1122.38/291.52	Infered types.
1122.38/291.52	----------------------------------------
1122.38/291.52	
1122.38/291.52	(4)
1122.38/291.52	Obligation:
1122.38/291.52	Innermost TRS:
1122.38/291.52	Rules:
1122.38/291.52	plus(0', x) -> x
1122.38/291.52	plus(s(x), y) -> s(plus(p(s(x)), y))
1122.38/291.52	times(0', y) -> 0'
1122.38/291.52	times(s(x), y) -> plus(y, times(p(s(x)), y))
1122.38/291.52	p(s(0')) -> 0'
1122.38/291.52	p(s(s(x))) -> s(p(s(x)))

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