Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307964

details

property	value
status	complete
benchmark	23.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n173.star.cs.uiowa.edu
space	Various_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	8.44192 seconds
cpu usage	22.7856
user time	21.2848
system time	1.50081
max virtual memory	1.9077896E7
max residence set size	3756904.0

stage attributes

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

output

22.64/8.38	WORST_CASE(Omega(n^1), O(n^1))
22.64/8.39	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
22.64/8.39	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
22.64/8.39	
22.64/8.39	
22.64/8.39	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
22.64/8.39	
22.64/8.39	(0) CpxTRS
22.64/8.39	(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
22.64/8.39	(2) CpxTRS
22.64/8.39	    (3) CpxTrsToCdtProof [UPPER BOUND(ID), 5 ms]
22.64/8.39	    (4) CdtProblem
22.64/8.39	    (5) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
22.64/8.39	    (6) CdtProblem
22.64/8.39	    (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
22.64/8.39	    (8) CdtProblem
22.64/8.39	    (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 28 ms]
22.64/8.39	    (10) CdtProblem
22.64/8.39	    (11) CdtKnowledgeProof [FINISHED, 0 ms]
22.64/8.39	    (12) BOUNDS(1, 1)
22.64/8.39	(13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
22.64/8.39	(14) CpxTRS
22.64/8.39	    (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
22.64/8.39	    (16) typed CpxTrs
22.64/8.39	    (17) OrderProof [LOWER BOUND(ID), 0 ms]
22.64/8.39	    (18) typed CpxTrs
22.64/8.39	    (19) RewriteLemmaProof [LOWER BOUND(ID), 873 ms]
22.64/8.39	    (20) proven lower bound
22.64/8.39	    (21) LowerBoundPropagationProof [FINISHED, 0 ms]
22.64/8.39	    (22) BOUNDS(n^1, INF)
22.64/8.39	
22.64/8.39	
22.64/8.39	----------------------------------------
22.64/8.39	
22.64/8.39	(0)
22.64/8.39	Obligation:
22.64/8.39	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
22.64/8.39	
22.64/8.39	
22.64/8.39	The TRS R consists of the following rules:
22.64/8.39	
22.64/8.39	   g(0, f(x, x)) -> x
22.64/8.39	   g(x, s(y)) -> g(f(x, y), 0)
22.64/8.39	   g(s(x), y) -> g(f(x, y), 0)
22.64/8.39	   g(f(x, y), 0) -> f(g(x, 0), g(y, 0))
22.64/8.39	
22.64/8.39	S is empty.
22.64/8.39	Rewrite Strategy: FULL
22.64/8.39	----------------------------------------
22.64/8.39	
22.64/8.39	(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
22.64/8.39	Converted rc-obligation to irc-obligation.
22.64/8.39	
22.64/8.39	As the TRS does not nest defined symbols, we have rc = irc.
22.64/8.39	----------------------------------------
22.64/8.39	
22.64/8.39	(2)
22.64/8.39	Obligation:
22.64/8.39	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
22.64/8.39	
22.64/8.39	
22.64/8.39	The TRS R consists of the following rules:
22.64/8.39	
22.64/8.39	   g(0, f(x, x)) -> x
22.64/8.39	   g(x, s(y)) -> g(f(x, y), 0)
22.64/8.39	   g(s(x), y) -> g(f(x, y), 0)
22.64/8.39	   g(f(x, y), 0) -> f(g(x, 0), g(y, 0))
22.64/8.39	
22.64/8.39	S is empty.
22.64/8.39	Rewrite Strategy: INNERMOST
22.64/8.39	----------------------------------------
22.64/8.39	
22.64/8.39	(3) CpxTrsToCdtProof (UPPER BOUND(ID))
22.64/8.39	Converted Cpx (relative) TRS to CDT
22.64/8.39	----------------------------------------
22.64/8.39	
22.64/8.39	(4)
22.64/8.39	Obligation:
22.64/8.39	Complexity Dependency Tuples Problem
22.64/8.39	
22.64/8.39	Rules:
22.64/8.39	   g(0, f(z0, z0)) -> z0
22.64/8.39	   g(z0, s(z1)) -> g(f(z0, z1), 0)
22.64/8.39	   g(s(z0), z1) -> g(f(z0, z1), 0)
22.64/8.39	   g(f(z0, z1), 0) -> f(g(z0, 0), g(z1, 0))
22.64/8.39	Tuples:
22.64/8.39	   G(0, f(z0, z0)) -> c
22.64/8.39	   G(z0, s(z1)) -> c1(G(f(z0, z1), 0))
22.64/8.39	   G(s(z0), z1) -> c2(G(f(z0, z1), 0))
22.64/8.39	   G(f(z0, z1), 0) -> c3(G(z0, 0), G(z1, 0))
22.64/8.39	S tuples:
22.64/8.39	   G(0, f(z0, z0)) -> c
22.64/8.39	   G(z0, s(z1)) -> c1(G(f(z0, z1), 0))
22.64/8.39	   G(s(z0), z1) -> c2(G(f(z0, z1), 0))
22.64/8.39	   G(f(z0, z1), 0) -> c3(G(z0, 0), G(z1, 0))
22.64/8.39	K tuples:none
22.64/8.39	Defined Rule Symbols:   g_2
22.64/8.39	
22.64/8.39	Defined Pair Symbols:   G_2
22.64/8.39

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