Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313791

details

property	value
status	complete
benchmark	nestdec.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n083.star.cs.uiowa.edu
space	Frederiksen_Glenstrup

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	4.64026 seconds
cpu usage	14.6067
user time	13.6423
system time	0.964406
max virtual memory	5.5541084E7
max residence set size	3122444.0

stage attributes

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

output

14.29/4.59	WORST_CASE(Omega(n^1), O(n^1))
14.29/4.60	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
14.29/4.60	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
14.29/4.60	
14.29/4.60	
14.29/4.60	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
14.29/4.60	
14.29/4.60	(0) CpxTRS
14.29/4.60	(1) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
14.29/4.60	(2) CpxTRS
14.29/4.60	    (3) CpxTrsMatchBoundsTAProof [FINISHED, 107 ms]
14.29/4.60	    (4) BOUNDS(1, n^1)
14.29/4.60	(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
14.29/4.60	(6) CpxTRS
14.29/4.60	    (7) SlicingProof [LOWER BOUND(ID), 0 ms]
14.29/4.60	    (8) CpxTRS
14.29/4.60	    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
14.29/4.60	    (10) typed CpxTrs
14.29/4.60	    (11) OrderProof [LOWER BOUND(ID), 0 ms]
14.29/4.60	    (12) typed CpxTrs
14.29/4.60	    (13) RewriteLemmaProof [LOWER BOUND(ID), 240 ms]
14.29/4.60	    (14) BEST
14.29/4.60	        (15) proven lower bound
14.29/4.60	            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
14.29/4.60	            (17) BOUNDS(n^1, INF)
14.29/4.60	        (18) typed CpxTrs
14.29/4.60	
14.29/4.60	
14.29/4.60	----------------------------------------
14.29/4.60	
14.29/4.60	(0)
14.29/4.60	Obligation:
14.29/4.60	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
14.29/4.60	
14.29/4.60	
14.29/4.60	The TRS R consists of the following rules:
14.29/4.60	
14.29/4.60	   dec(Cons(Nil, Nil)) -> Nil
14.29/4.60	   dec(Cons(Nil, Cons(x, xs))) -> dec(Cons(x, xs))
14.29/4.60	   dec(Cons(Cons(x, xs), Nil)) -> dec(Nil)
14.29/4.60	   dec(Cons(Cons(x', xs'), Cons(x, xs))) -> dec(Cons(x, xs))
14.29/4.60	   isNilNil(Cons(Nil, Nil)) -> True
14.29/4.60	   isNilNil(Cons(Nil, Cons(x, xs))) -> False
14.29/4.60	   isNilNil(Cons(Cons(x, xs), Nil)) -> False
14.29/4.60	   isNilNil(Cons(Cons(x', xs'), Cons(x, xs))) -> False
14.29/4.60	   nestdec(Nil) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil)))))))))))))))))
14.29/4.60	   nestdec(Cons(x, xs)) -> nestdec(dec(Cons(x, xs)))
14.29/4.60	   number17(n) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil)))))))))))))))))
14.29/4.60	   goal(x) -> nestdec(x)
14.29/4.60	
14.29/4.60	S is empty.
14.29/4.60	Rewrite Strategy: INNERMOST
14.29/4.60	----------------------------------------
14.29/4.60	
14.29/4.60	(1) RelTrsToTrsProof (UPPER BOUND(ID))
14.29/4.60	transformed relative TRS to TRS
14.29/4.60	----------------------------------------
14.29/4.60	
14.29/4.60	(2)
14.29/4.60	Obligation:
14.29/4.60	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
14.29/4.60	
14.29/4.60	
14.29/4.60	The TRS R consists of the following rules:
14.29/4.60	
14.29/4.60	   dec(Cons(Nil, Nil)) -> Nil
14.29/4.60	   dec(Cons(Nil, Cons(x, xs))) -> dec(Cons(x, xs))
14.29/4.60	   dec(Cons(Cons(x, xs), Nil)) -> dec(Nil)
14.29/4.60	   dec(Cons(Cons(x', xs'), Cons(x, xs))) -> dec(Cons(x, xs))
14.29/4.60	   isNilNil(Cons(Nil, Nil)) -> True
14.29/4.60	   isNilNil(Cons(Nil, Cons(x, xs))) -> False
14.29/4.60	   isNilNil(Cons(Cons(x, xs), Nil)) -> False
14.29/4.60	   isNilNil(Cons(Cons(x', xs'), Cons(x, xs))) -> False
14.29/4.60	   nestdec(Nil) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil)))))))))))))))))
14.29/4.60	   nestdec(Cons(x, xs)) -> nestdec(dec(Cons(x, xs)))
14.29/4.60	   number17(n) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil)))))))))))))))))
14.29/4.60	   goal(x) -> nestdec(x)
14.29/4.60	
14.29/4.60	S is empty.
14.29/4.60	Rewrite Strategy: INNERMOST
14.29/4.60	----------------------------------------
14.29/4.60	
14.29/4.60	(3) CpxTrsMatchBoundsTAProof (FINISHED)
14.29/4.60	A linear upper bound on the runtime complexity of the TRS R could be shown with a Match-Bound[TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] (for contructor-based start-terms) of 2. 
14.29/4.60	
14.29/4.60	The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: 
14.29/4.60	final states : [1, 2, 3, 4, 5]
14.29/4.60	transitions: 
14.29/4.60	Cons0(0, 0) -> 0
14.29/4.60	Nil0() -> 0
14.29/4.60	True0() -> 0
14.29/4.60	False0() -> 0
14.29/4.60	dec0(0) -> 1
14.29/4.60	isNilNil0(0) -> 2
14.29/4.60	nestdec0(0) -> 3
14.29/4.60	number170(0) -> 4
14.29/4.60	goal0(0) -> 5
14.29/4.60	Nil1() -> 1
14.29/4.60	Cons1(0, 0) -> 6
14.29/4.60	dec1(6) -> 1

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