Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308312

details

property	value
status	complete
benchmark	Ex18_Luc06_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n016.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.75286 seconds
cpu usage	20.8983
user time	19.3668
system time	1.53143
max virtual memory	1.9272452E7
max residence set size	3770848.0

stage attributes

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

output

20.66/6.70	WORST_CASE(Omega(n^1), O(n^1))
20.66/6.70	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
20.66/6.70	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
20.66/6.70	
20.66/6.70	
20.66/6.70	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
20.66/6.70	
20.66/6.70	(0) CpxTRS
20.66/6.70	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
20.66/6.70	(2) CpxTRS
20.66/6.70	    (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
20.66/6.70	    (4) CpxTRS
20.66/6.70	    (5) CpxTrsMatchBoundsProof [FINISHED, 0 ms]
20.66/6.70	    (6) BOUNDS(1, n^1)
20.66/6.70	(7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
20.66/6.70	(8) TRS for Loop Detection
20.66/6.70	    (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
20.66/6.70	    (10) BEST
20.66/6.70	        (11) proven lower bound
20.66/6.70	            (12) LowerBoundPropagationProof [FINISHED, 0 ms]
20.66/6.70	            (13) BOUNDS(n^1, INF)
20.66/6.70	        (14) TRS for Loop Detection
20.66/6.70	
20.66/6.70	
20.66/6.70	----------------------------------------
20.66/6.70	
20.66/6.70	(0)
20.66/6.70	Obligation:
20.66/6.70	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
20.66/6.70	
20.66/6.70	
20.66/6.70	The TRS R consists of the following rules:
20.66/6.70	
20.66/6.70	   active(f(f(a))) -> mark(f(g(f(a))))
20.66/6.70	   active(f(X)) -> f(active(X))
20.66/6.70	   f(mark(X)) -> mark(f(X))
20.66/6.70	   proper(f(X)) -> f(proper(X))
20.66/6.70	   proper(a) -> ok(a)
20.66/6.70	   proper(g(X)) -> g(proper(X))
20.66/6.70	   f(ok(X)) -> ok(f(X))
20.66/6.70	   g(ok(X)) -> ok(g(X))
20.66/6.70	   top(mark(X)) -> top(proper(X))
20.66/6.70	   top(ok(X)) -> top(active(X))
20.66/6.70	
20.66/6.70	S is empty.
20.66/6.70	Rewrite Strategy: FULL
20.66/6.70	----------------------------------------
20.66/6.70	
20.66/6.70	(1) NestedDefinedSymbolProof (UPPER BOUND(ID))
20.66/6.70	The following defined symbols can occur below the 0th argument of top: proper, active
20.66/6.70	The following defined symbols can occur below the 0th argument of proper: proper, active
20.66/6.70	The following defined symbols can occur below the 0th argument of active: proper, active
20.66/6.70	
20.66/6.70	Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
20.66/6.70	active(f(f(a))) -> mark(f(g(f(a))))
20.66/6.70	active(f(X)) -> f(active(X))
20.66/6.70	proper(f(X)) -> f(proper(X))
20.66/6.70	proper(g(X)) -> g(proper(X))
20.66/6.70	
20.66/6.70	----------------------------------------
20.66/6.70	
20.66/6.70	(2)
20.66/6.70	Obligation:
20.66/6.70	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
20.66/6.70	
20.66/6.70	
20.66/6.70	The TRS R consists of the following rules:
20.66/6.70	
20.66/6.70	   f(mark(X)) -> mark(f(X))
20.66/6.70	   proper(a) -> ok(a)
20.66/6.70	   f(ok(X)) -> ok(f(X))
20.66/6.70	   g(ok(X)) -> ok(g(X))
20.66/6.70	   top(mark(X)) -> top(proper(X))
20.66/6.70	   top(ok(X)) -> top(active(X))
20.66/6.70	
20.66/6.70	S is empty.
20.66/6.70	Rewrite Strategy: FULL
20.66/6.70	----------------------------------------
20.66/6.70	
20.66/6.70	(3) RelTrsToTrsProof (UPPER BOUND(ID))
20.66/6.70	transformed relative TRS to TRS
20.66/6.70	----------------------------------------
20.66/6.70	
20.66/6.70	(4)
20.66/6.70	Obligation:
20.66/6.70	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
20.66/6.70	
20.66/6.70	
20.66/6.70	The TRS R consists of the following rules:
20.66/6.70	
20.66/6.70	   f(mark(X)) -> mark(f(X))
20.66/6.70	   proper(a) -> ok(a)
20.66/6.70	   f(ok(X)) -> ok(f(X))
20.66/6.70	   g(ok(X)) -> ok(g(X))
20.66/6.70	   top(mark(X)) -> top(proper(X))
20.66/6.70	   top(ok(X)) -> top(active(X))
20.66/6.70	
20.66/6.70	S is empty.
20.66/6.70	Rewrite Strategy: FULL
20.66/6.70	----------------------------------------

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