Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308401

details

property	value
status	complete
benchmark	4.53.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n049.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	11.6287 seconds
cpu usage	31.1182
user time	29.6328
system time	1.48544
max virtual memory	3.8099688E7
max residence set size	4009588.0

stage attributes

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

output

30.92/8.86	WORST_CASE(Omega(n^1), O(n^1))
30.92/8.88	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
30.92/8.88	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
30.92/8.88	
30.92/8.88	
30.92/8.88	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
30.92/8.88	
30.92/8.88	(0) CpxTRS
30.92/8.88	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
30.92/8.88	(2) CpxTRS
30.92/8.88	    (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
30.92/8.88	    (4) CpxTRS
30.92/8.88	    (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
30.92/8.88	    (6) CpxWeightedTrs
30.92/8.88	    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
30.92/8.88	    (8) CpxTypedWeightedTrs
30.92/8.88	    (9) CompletionProof [UPPER BOUND(ID), 0 ms]
30.92/8.88	    (10) CpxTypedWeightedCompleteTrs
30.92/8.88	    (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
30.92/8.88	    (12) CpxRNTS
30.92/8.88	    (13) CompleteCoflocoProof [FINISHED, 209 ms]
30.92/8.88	    (14) BOUNDS(1, n^1)
30.92/8.88	(15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
30.92/8.88	(16) TRS for Loop Detection
30.92/8.88	    (17) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
30.92/8.88	    (18) BEST
30.92/8.88	        (19) proven lower bound
30.92/8.88	            (20) LowerBoundPropagationProof [FINISHED, 0 ms]
30.92/8.88	            (21) BOUNDS(n^1, INF)
30.92/8.88	        (22) TRS for Loop Detection
30.92/8.88	
30.92/8.88	
30.92/8.88	----------------------------------------
30.92/8.88	
30.92/8.88	(0)
30.92/8.88	Obligation:
30.92/8.88	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
30.92/8.88	
30.92/8.88	
30.92/8.88	The TRS R consists of the following rules:
30.92/8.88	
30.92/8.88	   f(a) -> b
30.92/8.88	   f(c) -> d
30.92/8.88	   f(g(x, y)) -> g(f(x), f(y))
30.92/8.88	   f(h(x, y)) -> g(h(y, f(x)), h(x, f(y)))
30.92/8.88	   g(x, x) -> h(e, x)
30.92/8.88	
30.92/8.88	S is empty.
30.92/8.88	Rewrite Strategy: FULL
30.92/8.88	----------------------------------------
30.92/8.88	
30.92/8.88	(1) NestedDefinedSymbolProof (UPPER BOUND(ID))
30.92/8.88	The following defined symbols can occur below the 0th argument of g: f, g
30.92/8.88	The following defined symbols can occur below the 1th argument of g: f, g
30.92/8.88	
30.92/8.88	Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
30.92/8.88	f(g(x, y)) -> g(f(x), f(y))
30.92/8.88	
30.92/8.88	----------------------------------------
30.92/8.88	
30.92/8.88	(2)
30.92/8.88	Obligation:
30.92/8.88	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
30.92/8.88	
30.92/8.88	
30.92/8.88	The TRS R consists of the following rules:
30.92/8.88	
30.92/8.88	   f(a) -> b
30.92/8.88	   f(c) -> d
30.92/8.88	   f(h(x, y)) -> g(h(y, f(x)), h(x, f(y)))
30.92/8.88	   g(x, x) -> h(e, x)
30.92/8.88	
30.92/8.88	S is empty.
30.92/8.88	Rewrite Strategy: FULL
30.92/8.88	----------------------------------------
30.92/8.88	
30.92/8.88	(3) RcToIrcProof (BOTH BOUNDS(ID, ID))
30.92/8.88	Converted rc-obligation to irc-obligation.
30.92/8.88	
30.92/8.88	The duplicating contexts are:
30.92/8.88	f(h(x, []))
30.92/8.88	f(h([], y))
30.92/8.88	
30.92/8.88	
30.92/8.88	The defined contexts are:
30.92/8.88	g(h(x0, []), h(x2, x3))
30.92/8.88	g(h(x0, x1), h(x2, []))
30.92/8.88	
30.92/8.88	
30.92/8.88	As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc.
30.92/8.88	----------------------------------------
30.92/8.88	
30.92/8.88	(4)
30.92/8.88	Obligation:
30.92/8.88	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
30.92/8.88	
30.92/8.88	
30.92/8.88	The TRS R consists of the following rules:
30.92/8.88	
30.92/8.88	   f(a) -> b

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actions all output return to Runtime_Complexity_Full_Rewriting 2019-04-01 06.11