Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307597

details

property	value
status	complete
benchmark	zerolist.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n175.star.cs.uiowa.edu
space	AProVE_09_Inductive

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.685 seconds
cpu usage	912.221
user time	903.153
system time	9.06802
max virtual memory	3.8113272E7
max residence set size	7871924.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

911.90/291.59	WORST_CASE(Omega(n^1), O(n^2))
911.90/291.61	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
911.90/291.61	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
911.90/291.61	
911.90/291.61	
911.90/291.61	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).
911.90/291.61	
911.90/291.61	(0) CpxTRS
911.90/291.61	(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
911.90/291.61	(2) CpxTRS
911.90/291.61	    (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
911.90/291.61	    (4) CpxWeightedTrs
911.90/291.61	    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
911.90/291.61	    (6) CpxTypedWeightedTrs
911.90/291.61	    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
911.90/291.61	    (8) CpxTypedWeightedCompleteTrs
911.90/291.61	    (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
911.90/291.61	    (10) CpxRNTS
911.90/291.61	    (11) CompleteCoflocoProof [FINISHED, 282 ms]
911.90/291.61	    (12) BOUNDS(1, n^2)
911.90/291.61	(13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
911.90/291.61	(14) CpxTRS
911.90/291.61	    (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
911.90/291.61	    (16) typed CpxTrs
911.90/291.61	    (17) OrderProof [LOWER BOUND(ID), 0 ms]
911.90/291.61	    (18) typed CpxTrs
911.90/291.61	    (19) RewriteLemmaProof [LOWER BOUND(ID), 333 ms]
911.90/291.61	    (20) BEST
911.90/291.61	        (21) proven lower bound
911.90/291.61	            (22) LowerBoundPropagationProof [FINISHED, 0 ms]
911.90/291.61	            (23) BOUNDS(n^1, INF)
911.90/291.61	        (24) typed CpxTrs
911.90/291.61	            (25) RewriteLemmaProof [LOWER BOUND(ID), 65 ms]
911.90/291.61	            (26) BOUNDS(1, INF)
911.90/291.61	
911.90/291.61	
911.90/291.61	----------------------------------------
911.90/291.61	
911.90/291.61	(0)
911.90/291.61	Obligation:
911.90/291.61	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).
911.90/291.61	
911.90/291.61	
911.90/291.61	The TRS R consists of the following rules:
911.90/291.61	
911.90/291.61	   sub(0, 0) -> 0
911.90/291.61	   sub(s(x), 0) -> s(x)
911.90/291.61	   sub(0, s(x)) -> 0
911.90/291.61	   sub(s(x), s(y)) -> sub(x, y)
911.90/291.61	   zero(nil) -> zero2(0, nil)
911.90/291.61	   zero(cons(x, xs)) -> zero2(sub(x, x), cons(x, xs))
911.90/291.61	   zero2(0, nil) -> nil
911.90/291.61	   zero2(0, cons(x, xs)) -> cons(sub(x, x), zero(xs))
911.90/291.61	   zero2(s(y), nil) -> zero(nil)
911.90/291.61	   zero2(s(y), cons(x, xs)) -> zero(cons(x, xs))
911.90/291.61	
911.90/291.61	S is empty.
911.90/291.61	Rewrite Strategy: FULL
911.90/291.61	----------------------------------------
911.90/291.61	
911.90/291.61	(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
911.90/291.61	Converted rc-obligation to irc-obligation.
911.90/291.61	
911.90/291.61	The duplicating contexts are:
911.90/291.61	zero(cons([], xs))
911.90/291.61	zero2(0, cons([], xs))
911.90/291.61	
911.90/291.61	
911.90/291.61	The defined contexts are:
911.90/291.61	zero2([], cons(x1, x2))
911.90/291.61	
911.90/291.61	
911.90/291.61	[] just represents basic- or constructor-terms in the following defined contexts:
911.90/291.61	zero2([], cons(x1, x2))
911.90/291.61	
911.90/291.61	
911.90/291.61	As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc.
911.90/291.61	----------------------------------------
911.90/291.61	
911.90/291.61	(2)
911.90/291.61	Obligation:
911.90/291.61	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^2).
911.90/291.61	
911.90/291.61	
911.90/291.61	The TRS R consists of the following rules:
911.90/291.61	
911.90/291.61	   sub(0, 0) -> 0
911.90/291.61	   sub(s(x), 0) -> s(x)
911.90/291.61	   sub(0, s(x)) -> 0
911.90/291.61	   sub(s(x), s(y)) -> sub(x, y)
911.90/291.61	   zero(nil) -> zero2(0, nil)
911.90/291.61	   zero(cons(x, xs)) -> zero2(sub(x, x), cons(x, xs))
911.90/291.61	   zero2(0, nil) -> nil
911.90/291.61	   zero2(0, cons(x, xs)) -> cons(sub(x, x), zero(xs))
911.90/291.61	   zero2(s(y), nil) -> zero(nil)
911.90/291.61	   zero2(s(y), cons(x, xs)) -> zero(cons(x, xs))
911.90/291.61	
911.90/291.61	S is empty.
911.90/291.61	Rewrite Strategy: INNERMOST
911.90/291.61	----------------------------------------

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