Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307773

details

property	value
status	complete
benchmark	kabasci03.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n166.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	1.54983 seconds
cpu usage	3.18779
user time	3.05158
system time	0.136205
max virtual memory	1.8277336E7
max residence set size	214848.0

stage attributes

key	value
starexec-result	WORST_CASE(?, O(1))

output

2.91/1.51	WORST_CASE(?, O(1))
2.91/1.52	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.91/1.52	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.91/1.52	
2.91/1.52	
2.91/1.52	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.91/1.52	
2.91/1.52	(0) CpxTRS
2.91/1.52	(1) DependencyGraphProof [UPPER BOUND(ID), 0 ms]
2.91/1.52	(2) CpxTRS
2.91/1.52	(3) NarrowingOnBasicTermsTerminatesProof [FINISHED, 0 ms]
2.91/1.52	(4) BOUNDS(1, 1)
2.91/1.52	
2.91/1.52	
2.91/1.52	----------------------------------------
2.91/1.52	
2.91/1.52	(0)
2.91/1.52	Obligation:
2.91/1.52	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.91/1.52	
2.91/1.52	
2.91/1.52	The TRS R consists of the following rules:
2.91/1.52	
2.91/1.52	   h(c(x, y), c(s(z), z), t(w)) -> h(z, c(y, x), t(t(c(x, c(y, t(w))))))
2.91/1.52	   h(x, c(y, z), t(w)) -> h(c(s(y), x), z, t(c(t(w), w)))
2.91/1.52	   h(c(s(x), c(s(0), y)), z, t(x)) -> h(y, c(s(0), c(x, z)), t(t(c(x, s(x)))))
2.91/1.52	   t(t(x)) -> t(c(t(x), x))
2.91/1.52	   t(x) -> x
2.91/1.52	   t(x) -> c(0, c(0, c(0, c(0, c(0, x)))))
2.91/1.52	
2.91/1.52	S is empty.
2.91/1.52	Rewrite Strategy: FULL
2.91/1.52	----------------------------------------
2.91/1.52	
2.91/1.52	(1) DependencyGraphProof (UPPER BOUND(ID))
2.91/1.52	The following rules are not reachable from basic terms in the dependency graph and can be removed:
2.91/1.52	
2.91/1.52	h(c(x, y), c(s(z), z), t(w)) -> h(z, c(y, x), t(t(c(x, c(y, t(w))))))
2.91/1.52	h(x, c(y, z), t(w)) -> h(c(s(y), x), z, t(c(t(w), w)))
2.91/1.52	h(c(s(x), c(s(0), y)), z, t(x)) -> h(y, c(s(0), c(x, z)), t(t(c(x, s(x)))))
2.91/1.52	t(t(x)) -> t(c(t(x), x))
2.91/1.52	
2.91/1.52	----------------------------------------
2.91/1.52	
2.91/1.52	(2)
2.91/1.52	Obligation:
2.91/1.52	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
2.91/1.52	
2.91/1.52	
2.91/1.52	The TRS R consists of the following rules:
2.91/1.52	
2.91/1.52	   t(x) -> x
2.91/1.52	   t(x) -> c(0, c(0, c(0, c(0, c(0, x)))))
2.91/1.52	
2.91/1.52	S is empty.
2.91/1.52	Rewrite Strategy: FULL
2.91/1.52	----------------------------------------
2.91/1.52	
2.91/1.52	(3) NarrowingOnBasicTermsTerminatesProof (FINISHED)
2.91/1.52	Constant runtime complexity proven by termination of constructor-based narrowing.
2.91/1.52	
2.91/1.52	The maximal most general narrowing sequences give rise to the following rewrite sequences:
2.91/1.52	
2.91/1.52	t(x0) ->^* c(0, c(0, c(0, c(0, c(0, x0)))))
2.91/1.52	
2.91/1.52	
2.91/1.52	
2.91/1.52	
2.91/1.52	----------------------------------------
2.91/1.52	
2.91/1.52	(4)
2.91/1.52	BOUNDS(1, 1)
3.16/1.54	EOF

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