Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307843

details

property	value
status	complete
benchmark	hydra.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n171.star.cs.uiowa.edu
space	Mixed_TRS

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	2.51934 seconds
cpu usage	6.6768
user time	6.42217
system time	0.254627
max virtual memory	1.8811208E7
max residence set size	505512.0

stage attributes

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

output

6.37/2.47	WORST_CASE(Omega(n^1), O(n^1))
6.37/2.48	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
6.37/2.48	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.37/2.48	
6.37/2.48	
6.37/2.48	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
6.37/2.48	
6.37/2.48	(0) CpxTRS
6.37/2.48	(1) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
6.37/2.48	(2) CpxRelTRS
6.37/2.48	    (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
6.37/2.48	    (4) CpxRelTRS
6.37/2.48	    (5) CpxTrsToCdtProof [UPPER BOUND(ID), 2 ms]
6.37/2.48	    (6) CdtProblem
6.37/2.48	    (7) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
6.37/2.48	    (8) CdtProblem
6.37/2.48	    (9) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
6.37/2.48	    (10) CdtProblem
6.37/2.48	    (11) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
6.37/2.48	    (12) CdtProblem
6.37/2.48	    (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 61 ms]
6.37/2.48	    (14) CdtProblem
6.37/2.48	    (15) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms]
6.37/2.48	    (16) BOUNDS(1, 1)
6.37/2.48	(17) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
6.37/2.48	(18) TRS for Loop Detection
6.37/2.48	    (19) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
6.37/2.48	    (20) BEST
6.37/2.48	        (21) proven lower bound
6.37/2.48	            (22) LowerBoundPropagationProof [FINISHED, 0 ms]
6.37/2.48	            (23) BOUNDS(n^1, INF)
6.37/2.48	        (24) TRS for Loop Detection
6.37/2.48	
6.37/2.48	
6.37/2.48	----------------------------------------
6.37/2.48	
6.37/2.48	(0)
6.37/2.48	Obligation:
6.37/2.48	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
6.37/2.48	
6.37/2.48	
6.37/2.48	The TRS R consists of the following rules:
6.37/2.48	
6.37/2.48	   f(cons(nil, y)) -> y
6.37/2.48	   f(cons(f(cons(nil, y)), z)) -> copy(n, y, z)
6.37/2.48	   copy(0, y, z) -> f(z)
6.37/2.48	   copy(s(x), y, z) -> copy(x, y, cons(f(y), z))
6.37/2.48	
6.37/2.48	S is empty.
6.37/2.48	Rewrite Strategy: FULL
6.37/2.48	----------------------------------------
6.37/2.48	
6.37/2.48	(1) NonCtorToCtorProof (UPPER BOUND(ID))
6.37/2.48	transformed non-ctor to ctor-system
6.37/2.48	----------------------------------------
6.37/2.48	
6.37/2.48	(2)
6.37/2.48	Obligation:
6.37/2.48	The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1).
6.37/2.48	
6.37/2.48	
6.37/2.48	The TRS R consists of the following rules:
6.37/2.48	
6.37/2.48	   f(cons(nil, y)) -> y
6.37/2.48	   copy(0, y, z) -> f(z)
6.37/2.48	   copy(s(x), y, z) -> copy(x, y, cons(f(y), z))
6.37/2.48	   f(cons(c_f(cons(nil, y)), z)) -> copy(n, y, z)
6.37/2.48	
6.37/2.48	The (relative) TRS S consists of the following rules:
6.37/2.48	
6.37/2.48	   f(x0) -> c_f(x0)
6.37/2.48	
6.37/2.48	Rewrite Strategy: FULL
6.37/2.48	----------------------------------------
6.37/2.48	
6.37/2.48	(3) RcToIrcProof (BOTH BOUNDS(ID, ID))
6.37/2.48	Converted rc-obligation to irc-obligation.
6.37/2.48	
6.37/2.48	The duplicating contexts are:
6.37/2.48	copy(s(x), [], z)
6.37/2.48	
6.37/2.48	
6.37/2.48	The defined contexts are:
6.37/2.48	copy(x0, x1, cons([], x3))
6.37/2.48	f([])
6.37/2.48	copy(x0, x1, cons(x2, []))
6.37/2.48	copy(n, [], x1)
6.37/2.48	copy(n, x0, [])
6.37/2.48	
6.37/2.48	
6.37/2.48	As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc.
6.37/2.48	----------------------------------------
6.37/2.48	
6.37/2.48	(4)
6.37/2.48	Obligation:
6.37/2.48	The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1).
6.37/2.48	
6.37/2.48	
6.37/2.48	The TRS R consists of the following rules:
6.37/2.48

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