Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313490

details

property	value
status	complete
benchmark	Ex4_Zan97_FR.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n094.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.593 seconds
cpu usage	1060.94
user time	1043.99
system time	16.9431
max virtual memory	3.8236856E7
max residence set size	1.4054456E7

stage attributes

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

output

1060.58/291.51	WORST_CASE(Omega(n^1), ?)
1060.82/291.53	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
1060.82/291.53	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
1060.82/291.53	
1060.82/291.53	
1060.82/291.53	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1060.82/291.53	
1060.82/291.53	(0) CpxTRS
1060.82/291.53	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
1060.82/291.53	(2) TRS for Loop Detection
1060.82/291.53	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
1060.82/291.53	(4) BEST
1060.82/291.53	    (5) proven lower bound
1060.82/291.53	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
1060.82/291.53	        (7) BOUNDS(n^1, INF)
1060.82/291.53	    (8) TRS for Loop Detection
1060.82/291.53	
1060.82/291.53	
1060.82/291.53	----------------------------------------
1060.82/291.53	
1060.82/291.53	(0)
1060.82/291.53	Obligation:
1060.82/291.53	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1060.82/291.53	
1060.82/291.53	
1060.82/291.53	The TRS R consists of the following rules:
1060.82/291.53	
1060.82/291.53	   f(X) -> cons(X, n__f(n__g(X)))
1060.82/291.53	   g(0) -> s(0)
1060.82/291.53	   g(s(X)) -> s(s(g(X)))
1060.82/291.53	   sel(0, cons(X, Y)) -> X
1060.82/291.53	   sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
1060.82/291.53	   f(X) -> n__f(X)
1060.82/291.53	   g(X) -> n__g(X)
1060.82/291.53	   activate(n__f(X)) -> f(activate(X))
1060.82/291.53	   activate(n__g(X)) -> g(activate(X))
1060.82/291.53	   activate(X) -> X
1060.82/291.53	
1060.82/291.53	S is empty.
1060.82/291.53	Rewrite Strategy: INNERMOST
1060.82/291.53	----------------------------------------
1060.82/291.53	
1060.82/291.53	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
1060.82/291.53	Transformed a relative TRS into a decreasing-loop problem.
1060.82/291.53	----------------------------------------
1060.82/291.53	
1060.82/291.53	(2)
1060.82/291.53	Obligation:
1060.82/291.53	Analyzing the following TRS for decreasing loops:
1060.82/291.53	
1060.82/291.53	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1060.82/291.53	
1060.82/291.53	
1060.82/291.53	The TRS R consists of the following rules:
1060.82/291.53	
1060.82/291.53	   f(X) -> cons(X, n__f(n__g(X)))
1060.82/291.53	   g(0) -> s(0)
1060.82/291.53	   g(s(X)) -> s(s(g(X)))
1060.82/291.53	   sel(0, cons(X, Y)) -> X
1060.82/291.53	   sel(s(X), cons(Y, Z)) -> sel(X, activate(Z))
1060.82/291.53	   f(X) -> n__f(X)
1060.82/291.53	   g(X) -> n__g(X)
1060.82/291.53	   activate(n__f(X)) -> f(activate(X))
1060.82/291.53	   activate(n__g(X)) -> g(activate(X))
1060.82/291.53	   activate(X) -> X
1060.82/291.53	
1060.82/291.53	S is empty.
1060.82/291.53	Rewrite Strategy: INNERMOST
1060.82/291.53	----------------------------------------
1060.82/291.53	
1060.82/291.53	(3) DecreasingLoopProof (LOWER BOUND(ID))
1060.82/291.53	The following loop(s) give(s) rise to the lower bound Omega(n^1):
1060.82/291.53	
1060.82/291.53	The rewrite sequence
1060.82/291.53	
1060.82/291.53	g(s(X)) ->^+ s(s(g(X)))
1060.82/291.53	
1060.82/291.53	gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0].
1060.82/291.53	
1060.82/291.53	The pumping substitution is [X / s(X)].
1060.82/291.53	
1060.82/291.53	The result substitution is [ ].
1060.82/291.53	
1060.82/291.53	
1060.82/291.53	
1060.82/291.53	
1060.82/291.53	----------------------------------------
1060.82/291.53	
1060.82/291.53	(4)
1060.82/291.53	Complex Obligation (BEST)
1060.82/291.53	
1060.82/291.53	----------------------------------------
1060.82/291.53	
1060.82/291.53	(5)
1060.82/291.53	Obligation:
1060.82/291.53	Proved the lower bound n^1 for the following obligation:
1060.82/291.53	
1060.82/291.53	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
1060.82/291.53	
1060.82/291.53

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40