Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307994

details

property	value
status	complete
benchmark	Ex23_Luc06_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n007.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	8.30687 seconds
cpu usage	22.4531
user time	20.7606
system time	1.69242
max virtual memory	1.9248768E7
max residence set size	4129224.0

stage attributes

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

output

22.33/8.16	WORST_CASE(Omega(n^1), O(n^1))
22.33/8.17	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
22.33/8.17	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
22.33/8.17	
22.33/8.17	
22.33/8.17	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
22.33/8.17	
22.33/8.17	(0) CpxTRS
22.33/8.17	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
22.33/8.17	(2) CpxTRS
22.33/8.17	    (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
22.33/8.17	    (4) CpxTRS
22.33/8.17	    (5) CpxTrsMatchBoundsProof [FINISHED, 0 ms]
22.33/8.17	    (6) BOUNDS(1, n^1)
22.33/8.17	(7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
22.33/8.17	(8) TRS for Loop Detection
22.33/8.17	    (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
22.33/8.17	    (10) BEST
22.33/8.17	        (11) proven lower bound
22.33/8.17	            (12) LowerBoundPropagationProof [FINISHED, 0 ms]
22.33/8.17	            (13) BOUNDS(n^1, INF)
22.33/8.17	        (14) TRS for Loop Detection
22.33/8.17	
22.33/8.17	
22.33/8.17	----------------------------------------
22.33/8.17	
22.33/8.17	(0)
22.33/8.17	Obligation:
22.33/8.17	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
22.33/8.17	
22.33/8.17	
22.33/8.17	The TRS R consists of the following rules:
22.33/8.17	
22.33/8.17	   active(f(f(a))) -> mark(c(f(g(f(a)))))
22.33/8.17	   active(f(X)) -> f(active(X))
22.33/8.17	   active(g(X)) -> g(active(X))
22.33/8.17	   f(mark(X)) -> mark(f(X))
22.33/8.17	   g(mark(X)) -> mark(g(X))
22.33/8.17	   proper(f(X)) -> f(proper(X))
22.33/8.17	   proper(a) -> ok(a)
22.33/8.17	   proper(c(X)) -> c(proper(X))
22.33/8.17	   proper(g(X)) -> g(proper(X))
22.33/8.17	   f(ok(X)) -> ok(f(X))
22.33/8.17	   c(ok(X)) -> ok(c(X))
22.33/8.17	   g(ok(X)) -> ok(g(X))
22.33/8.17	   top(mark(X)) -> top(proper(X))
22.33/8.17	   top(ok(X)) -> top(active(X))
22.33/8.17	
22.33/8.17	S is empty.
22.33/8.17	Rewrite Strategy: FULL
22.33/8.17	----------------------------------------
22.33/8.17	
22.33/8.17	(1) NestedDefinedSymbolProof (UPPER BOUND(ID))
22.33/8.17	The following defined symbols can occur below the 0th argument of top: proper, active
22.33/8.17	The following defined symbols can occur below the 0th argument of proper: proper, active
22.33/8.17	The following defined symbols can occur below the 0th argument of active: proper, active
22.33/8.17	
22.33/8.17	Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
22.33/8.17	active(f(f(a))) -> mark(c(f(g(f(a)))))
22.33/8.17	active(f(X)) -> f(active(X))
22.33/8.17	active(g(X)) -> g(active(X))
22.33/8.17	proper(f(X)) -> f(proper(X))
22.33/8.17	proper(c(X)) -> c(proper(X))
22.33/8.17	proper(g(X)) -> g(proper(X))
22.33/8.17	
22.33/8.17	----------------------------------------
22.33/8.17	
22.33/8.17	(2)
22.33/8.17	Obligation:
22.33/8.17	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
22.33/8.17	
22.33/8.17	
22.33/8.17	The TRS R consists of the following rules:
22.33/8.17	
22.33/8.17	   f(mark(X)) -> mark(f(X))
22.33/8.17	   g(mark(X)) -> mark(g(X))
22.33/8.17	   proper(a) -> ok(a)
22.33/8.17	   f(ok(X)) -> ok(f(X))
22.33/8.17	   c(ok(X)) -> ok(c(X))
22.33/8.17	   g(ok(X)) -> ok(g(X))
22.33/8.17	   top(mark(X)) -> top(proper(X))
22.33/8.17	   top(ok(X)) -> top(active(X))
22.33/8.17	
22.33/8.17	S is empty.
22.33/8.17	Rewrite Strategy: FULL
22.33/8.17	----------------------------------------
22.33/8.17	
22.33/8.17	(3) RelTrsToTrsProof (UPPER BOUND(ID))
22.33/8.17	transformed relative TRS to TRS
22.33/8.17	----------------------------------------
22.33/8.17	
22.33/8.17	(4)
22.33/8.17	Obligation:
22.33/8.17	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
22.33/8.17	
22.33/8.17	
22.33/8.17	The TRS R consists of the following rules:
22.33/8.17	
22.33/8.17	   f(mark(X)) -> mark(f(X))
22.33/8.17	   g(mark(X)) -> mark(g(X))

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