Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308504

details

property	value
status	complete
benchmark	Ex26_Luc03b.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n087.star.cs.uiowa.edu
space	Strategy_removed_CSR_05

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	1.63205 seconds
cpu usage	3.23773
user time	3.08704
system time	0.15069
max virtual memory	1.8277336E7
max residence set size	219000.0

stage attributes

key	value
starexec-result	WORST_CASE(NON_POLY, ?)

output

2.81/1.58	WORST_CASE(NON_POLY, ?)
3.19/1.58	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.19/1.58	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.19/1.58	
3.19/1.58	
3.19/1.58	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.19/1.58	
3.19/1.58	(0) CpxTRS
3.19/1.58	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.19/1.58	(2) TRS for Loop Detection
3.19/1.58	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
3.19/1.58	(4) BEST
3.19/1.58	    (5) proven lower bound
3.19/1.58	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
3.19/1.58	        (7) BOUNDS(n^1, INF)
3.19/1.58	    (8) TRS for Loop Detection
3.19/1.58	        (9) InfiniteLowerBoundProof [FINISHED, 0 ms]
3.19/1.58	        (10) BOUNDS(INF, INF)
3.19/1.58	
3.19/1.58	
3.19/1.58	----------------------------------------
3.19/1.58	
3.19/1.58	(0)
3.19/1.58	Obligation:
3.19/1.58	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.19/1.58	
3.19/1.58	
3.19/1.58	The TRS R consists of the following rules:
3.19/1.58	
3.19/1.58	   terms(N) -> cons(recip(sqr(N)), terms(s(N)))
3.19/1.58	   sqr(0) -> 0
3.19/1.58	   sqr(s(X)) -> s(add(sqr(X), dbl(X)))
3.19/1.58	   dbl(0) -> 0
3.19/1.58	   dbl(s(X)) -> s(s(dbl(X)))
3.19/1.58	   add(0, X) -> X
3.19/1.58	   add(s(X), Y) -> s(add(X, Y))
3.19/1.58	   first(0, X) -> nil
3.19/1.58	   first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z))
3.19/1.58	
3.19/1.58	S is empty.
3.19/1.58	Rewrite Strategy: FULL
3.19/1.58	----------------------------------------
3.19/1.58	
3.19/1.58	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.19/1.58	Transformed a relative TRS into a decreasing-loop problem.
3.19/1.58	----------------------------------------
3.19/1.58	
3.19/1.58	(2)
3.19/1.58	Obligation:
3.19/1.58	Analyzing the following TRS for decreasing loops:
3.19/1.58	
3.19/1.58	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.19/1.58	
3.19/1.58	
3.19/1.58	The TRS R consists of the following rules:
3.19/1.58	
3.19/1.58	   terms(N) -> cons(recip(sqr(N)), terms(s(N)))
3.19/1.58	   sqr(0) -> 0
3.19/1.58	   sqr(s(X)) -> s(add(sqr(X), dbl(X)))
3.19/1.58	   dbl(0) -> 0
3.19/1.58	   dbl(s(X)) -> s(s(dbl(X)))
3.19/1.58	   add(0, X) -> X
3.19/1.58	   add(s(X), Y) -> s(add(X, Y))
3.19/1.58	   first(0, X) -> nil
3.19/1.58	   first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z))
3.19/1.58	
3.19/1.58	S is empty.
3.19/1.58	Rewrite Strategy: FULL
3.19/1.58	----------------------------------------
3.19/1.58	
3.19/1.58	(3) DecreasingLoopProof (LOWER BOUND(ID))
3.19/1.58	The following loop(s) give(s) rise to the lower bound Omega(n^1):
3.19/1.58	
3.19/1.58	The rewrite sequence
3.19/1.58	
3.19/1.58	first(s(X), cons(Y, Z)) ->^+ cons(Y, first(X, Z))
3.19/1.58	
3.19/1.58	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
3.19/1.58	
3.19/1.58	The pumping substitution is [X / s(X), Z / cons(Y, Z)].
3.19/1.58	
3.19/1.58	The result substitution is [ ].
3.19/1.58	
3.19/1.58	
3.19/1.58	
3.19/1.58	
3.19/1.58	----------------------------------------
3.19/1.58	
3.19/1.58	(4)
3.19/1.58	Complex Obligation (BEST)
3.19/1.58	
3.19/1.58	----------------------------------------
3.19/1.58	
3.19/1.58	(5)
3.19/1.58	Obligation:
3.19/1.58	Proved the lower bound n^1 for the following obligation:
3.19/1.58	
3.19/1.58	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.19/1.58	
3.19/1.58

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