Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307855

details

property	value
status	complete
benchmark	perfect.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n180.star.cs.uiowa.edu
space	Mixed_TRS

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	11.6578 seconds
cpu usage	40.1523
user time	38.4291
system time	1.72326
max virtual memory	3.7574868E7
max residence set size	3928548.0

stage attributes

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

output

39.89/11.60	WORST_CASE(Omega(n^1), O(n^1))
39.89/11.61	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
39.89/11.61	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
39.89/11.61	
39.89/11.61	
39.89/11.61	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
39.89/11.61	
39.89/11.61	(0) CpxTRS
39.89/11.61	(1) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
39.89/11.61	(2) CpxTRS
39.89/11.61	    (3) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
39.89/11.61	    (4) CdtProblem
39.89/11.61	    (5) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
39.89/11.61	    (6) CdtProblem
39.89/11.61	    (7) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
39.89/11.61	    (8) CdtProblem
39.89/11.61	    (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
39.89/11.61	    (10) CdtProblem
39.89/11.61	    (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 49 ms]
39.89/11.61	    (12) CdtProblem
39.89/11.61	    (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 6 ms]
39.89/11.61	    (14) CdtProblem
39.89/11.61	    (15) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms]
39.89/11.61	    (16) BOUNDS(1, 1)
39.89/11.61	(17) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
39.89/11.61	(18) TRS for Loop Detection
39.89/11.61	    (19) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
39.89/11.61	    (20) BEST
39.89/11.61	        (21) proven lower bound
39.89/11.61	            (22) LowerBoundPropagationProof [FINISHED, 1 ms]
39.89/11.61	            (23) BOUNDS(n^1, INF)
39.89/11.61	        (24) TRS for Loop Detection
39.89/11.61	
39.89/11.61	
39.89/11.61	----------------------------------------
39.89/11.61	
39.89/11.61	(0)
39.89/11.61	Obligation:
39.89/11.61	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
39.89/11.61	
39.89/11.61	
39.89/11.61	The TRS R consists of the following rules:
39.89/11.61	
39.89/11.61	   perfectp(0) -> false
39.89/11.61	   perfectp(s(x)) -> f(x, s(0), s(x), s(x))
39.89/11.61	   f(0, y, 0, u) -> true
39.89/11.61	   f(0, y, s(z), u) -> false
39.89/11.61	   f(s(x), 0, z, u) -> f(x, u, minus(z, s(x)), u)
39.89/11.61	   f(s(x), s(y), z, u) -> if(le(x, y), f(s(x), minus(y, x), z, u), f(x, u, z, u))
39.89/11.61	
39.89/11.61	S is empty.
39.89/11.61	Rewrite Strategy: FULL
39.89/11.61	----------------------------------------
39.89/11.61	
39.89/11.61	(1) RcToIrcProof (BOTH BOUNDS(ID, ID))
39.89/11.61	Converted rc-obligation to irc-obligation.
39.89/11.61	
39.89/11.61	As the TRS does not nest defined symbols, we have rc = irc.
39.89/11.61	----------------------------------------
39.89/11.61	
39.89/11.61	(2)
39.89/11.61	Obligation:
39.89/11.61	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
39.89/11.61	
39.89/11.61	
39.89/11.61	The TRS R consists of the following rules:
39.89/11.61	
39.89/11.61	   perfectp(0) -> false
39.89/11.61	   perfectp(s(x)) -> f(x, s(0), s(x), s(x))
39.89/11.61	   f(0, y, 0, u) -> true
39.89/11.61	   f(0, y, s(z), u) -> false
39.89/11.61	   f(s(x), 0, z, u) -> f(x, u, minus(z, s(x)), u)
39.89/11.61	   f(s(x), s(y), z, u) -> if(le(x, y), f(s(x), minus(y, x), z, u), f(x, u, z, u))
39.89/11.61	
39.89/11.61	S is empty.
39.89/11.61	Rewrite Strategy: INNERMOST
39.89/11.61	----------------------------------------
39.89/11.61	
39.89/11.61	(3) CpxTrsToCdtProof (UPPER BOUND(ID))
39.89/11.61	Converted Cpx (relative) TRS to CDT
39.89/11.61	----------------------------------------
39.89/11.61	
39.89/11.61	(4)
39.89/11.61	Obligation:
39.89/11.61	Complexity Dependency Tuples Problem
39.89/11.61	
39.89/11.61	Rules:
39.89/11.61	   perfectp(0) -> false
39.89/11.61	   perfectp(s(z0)) -> f(z0, s(0), s(z0), s(z0))
39.89/11.61	   f(0, z0, 0, z1) -> true
39.89/11.61	   f(0, z0, s(z1), z2) -> false
39.89/11.61	   f(s(z0), 0, z1, z2) -> f(z0, z2, minus(z1, s(z0)), z2)
39.89/11.61	   f(s(z0), s(z1), z2, z3) -> if(le(z0, z1), f(s(z0), minus(z1, z0), z2, z3), f(z0, z3, z2, z3))
39.89/11.61	Tuples:
39.89/11.61	   PERFECTP(0) -> c
39.89/11.61	   PERFECTP(s(z0)) -> c1(F(z0, s(0), s(z0), s(z0)))
39.89/11.61	   F(0, z0, 0, z1) -> c2
39.89/11.61	   F(0, z0, s(z1), z2) -> c3
39.89/11.61	   F(s(z0), 0, z1, z2) -> c4(F(z0, z2, minus(z1, s(z0)), z2))
39.89/11.61	   F(s(z0), s(z1), z2, z3) -> c5(F(s(z0), minus(z1, z0), z2, z3), F(z0, z3, z2, z3))

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