Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308387

details

property	value
status	complete
benchmark	2.40.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n118.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	7.40823 seconds
cpu usage	40.8772
user time	38.215
system time	2.66227
max virtual memory	1.8879904E7
max residence set size	3145872.0

stage attributes

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

output

20.39/7.35	WORST_CASE(Omega(n^1), O(n^1))
20.39/7.36	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
20.39/7.36	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
20.39/7.36	
20.39/7.36	
20.39/7.36	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
20.39/7.36	
20.39/7.36	(0) CpxTRS
20.39/7.36	(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
20.39/7.36	(2) CpxTRS
20.39/7.36	    (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
20.39/7.36	    (4) CpxWeightedTrs
20.39/7.36	    (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
20.39/7.36	    (6) CpxTypedWeightedTrs
20.39/7.36	    (7) CompletionProof [UPPER BOUND(ID), 0 ms]
20.39/7.36	    (8) CpxTypedWeightedCompleteTrs
20.39/7.36	    (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
20.39/7.36	    (10) CpxTypedWeightedCompleteTrs
20.39/7.36	    (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
20.39/7.36	    (12) CpxRNTS
20.39/7.36	    (13) InliningProof [UPPER BOUND(ID), 311 ms]
20.39/7.36	    (14) CpxRNTS
20.39/7.36	    (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
20.39/7.36	    (16) CpxRNTS
20.39/7.36	    (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
20.39/7.36	    (18) CpxRNTS
20.39/7.36	    (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
20.39/7.36	    (20) CpxRNTS
20.39/7.36	    (21) IntTrsBoundProof [UPPER BOUND(ID), 213 ms]
20.39/7.36	    (22) CpxRNTS
20.39/7.36	    (23) IntTrsBoundProof [UPPER BOUND(ID), 69 ms]
20.39/7.36	    (24) CpxRNTS
20.39/7.36	    (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
20.39/7.36	    (26) CpxRNTS
20.39/7.36	    (27) IntTrsBoundProof [UPPER BOUND(ID), 599 ms]
20.39/7.36	    (28) CpxRNTS
20.39/7.36	    (29) IntTrsBoundProof [UPPER BOUND(ID), 930 ms]
20.39/7.36	    (30) CpxRNTS
20.39/7.36	    (31) FinalProof [FINISHED, 0 ms]
20.39/7.36	    (32) BOUNDS(1, n^1)
20.39/7.36	(33) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
20.39/7.36	(34) TRS for Loop Detection
20.39/7.36	    (35) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
20.39/7.36	    (36) BEST
20.39/7.36	        (37) proven lower bound
20.39/7.36	            (38) LowerBoundPropagationProof [FINISHED, 0 ms]
20.39/7.36	            (39) BOUNDS(n^1, INF)
20.39/7.36	        (40) TRS for Loop Detection
20.39/7.36	
20.39/7.36	
20.39/7.36	----------------------------------------
20.39/7.36	
20.39/7.36	(0)
20.39/7.36	Obligation:
20.39/7.36	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
20.39/7.36	
20.39/7.36	
20.39/7.36	The TRS R consists of the following rules:
20.39/7.36	
20.39/7.36	   or(true, y) -> true
20.39/7.36	   or(x, true) -> true
20.39/7.36	   or(false, false) -> false
20.39/7.36	   mem(x, nil) -> false
20.39/7.36	   mem(x, set(y)) -> =(x, y)
20.39/7.36	   mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))
20.39/7.36	
20.39/7.36	S is empty.
20.39/7.36	Rewrite Strategy: FULL
20.39/7.36	----------------------------------------
20.39/7.36	
20.39/7.36	(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
20.39/7.36	Converted rc-obligation to irc-obligation.
20.39/7.36	
20.39/7.36	The duplicating contexts are:
20.39/7.36	mem([], union(y, z))
20.39/7.36	
20.39/7.36	
20.39/7.36	The defined contexts are:
20.39/7.36	or([], x1)
20.39/7.36	or(x0, [])
20.39/7.36	
20.39/7.36	
20.39/7.36	As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc.
20.39/7.36	----------------------------------------
20.39/7.36	
20.39/7.36	(2)
20.39/7.36	Obligation:
20.39/7.36	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
20.39/7.36	
20.39/7.36	
20.39/7.36	The TRS R consists of the following rules:
20.39/7.36	
20.39/7.36	   or(true, y) -> true
20.39/7.36	   or(x, true) -> true
20.39/7.36	   or(false, false) -> false
20.39/7.36	   mem(x, nil) -> false
20.39/7.36	   mem(x, set(y)) -> =(x, y)
20.39/7.36	   mem(x, union(y, z)) -> or(mem(x, y), mem(x, z))
20.39/7.36	
20.39/7.36	S is empty.

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