Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308471

details

property	value
status	complete
benchmark	aprove01.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n155.star.cs.uiowa.edu
space	Secret_07_TRS

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.556 seconds
cpu usage	311.384
user time	309.64
system time	1.74402
max virtual memory	1.8281712E7
max residence set size	5195060.0

stage attributes

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

output

311.30/291.52	WORST_CASE(Omega(n^1), ?)
311.30/291.52	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
311.30/291.52	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
311.30/291.52	
311.30/291.52	
311.30/291.52	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
311.30/291.52	
311.30/291.52	(0) CpxTRS
311.30/291.52	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
311.30/291.52	(2) TRS for Loop Detection
311.30/291.52	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
311.30/291.52	(4) BEST
311.30/291.52	    (5) proven lower bound
311.30/291.52	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
311.30/291.52	        (7) BOUNDS(n^1, INF)
311.30/291.52	    (8) TRS for Loop Detection
311.30/291.52	
311.30/291.52	
311.30/291.52	----------------------------------------
311.30/291.52	
311.30/291.52	(0)
311.30/291.52	Obligation:
311.30/291.52	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
311.30/291.52	
311.30/291.52	
311.30/291.52	The TRS R consists of the following rules:
311.30/291.52	
311.30/291.52	   times(x, y) -> sum(generate(x, y))
311.30/291.52	   generate(x, y) -> gen(x, y, 0)
311.30/291.52	   gen(x, y, z) -> if(ge(z, x), x, y, z)
311.30/291.52	   if(true, x, y, z) -> nil
311.30/291.52	   if(false, x, y, z) -> cons(y, gen(x, y, s(z)))
311.30/291.52	   sum(xs) -> sum2(xs, 0)
311.30/291.52	   sum2(xs, y) -> ifsum(isNil(xs), isZero(head(xs)), xs, y)
311.30/291.52	   ifsum(true, b, xs, y) -> y
311.30/291.52	   ifsum(false, b, xs, y) -> ifsum2(b, xs, y)
311.30/291.52	   ifsum2(true, xs, y) -> sum2(tail(xs), y)
311.30/291.52	   ifsum2(false, xs, y) -> sum2(cons(p(head(xs)), tail(xs)), s(y))
311.30/291.52	   isNil(nil) -> true
311.30/291.52	   isNil(cons(x, xs)) -> false
311.30/291.52	   tail(nil) -> nil
311.30/291.52	   tail(cons(x, xs)) -> xs
311.30/291.52	   head(cons(x, xs)) -> x
311.30/291.52	   head(nil) -> error
311.30/291.52	   isZero(0) -> true
311.30/291.52	   isZero(s(0)) -> false
311.30/291.52	   isZero(s(s(x))) -> isZero(s(x))
311.30/291.52	   p(0) -> s(s(0))
311.30/291.52	   p(s(0)) -> 0
311.30/291.52	   p(s(s(x))) -> s(p(s(x)))
311.30/291.52	   ge(x, 0) -> true
311.30/291.52	   ge(0, s(y)) -> false
311.30/291.52	   ge(s(x), s(y)) -> ge(x, y)
311.30/291.52	   a -> c
311.30/291.52	   a -> d
311.30/291.52	
311.30/291.52	S is empty.
311.30/291.52	Rewrite Strategy: FULL
311.30/291.52	----------------------------------------
311.30/291.52	
311.30/291.52	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
311.30/291.52	Transformed a relative TRS into a decreasing-loop problem.
311.30/291.52	----------------------------------------
311.30/291.52	
311.30/291.52	(2)
311.30/291.52	Obligation:
311.30/291.52	Analyzing the following TRS for decreasing loops:
311.30/291.52	
311.30/291.52	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
311.30/291.52	
311.30/291.52	
311.30/291.52	The TRS R consists of the following rules:
311.30/291.52	
311.30/291.52	   times(x, y) -> sum(generate(x, y))
311.30/291.53	   generate(x, y) -> gen(x, y, 0)
311.30/291.53	   gen(x, y, z) -> if(ge(z, x), x, y, z)
311.30/291.53	   if(true, x, y, z) -> nil
311.30/291.53	   if(false, x, y, z) -> cons(y, gen(x, y, s(z)))
311.30/291.53	   sum(xs) -> sum2(xs, 0)
311.30/291.53	   sum2(xs, y) -> ifsum(isNil(xs), isZero(head(xs)), xs, y)
311.30/291.53	   ifsum(true, b, xs, y) -> y
311.30/291.53	   ifsum(false, b, xs, y) -> ifsum2(b, xs, y)
311.30/291.53	   ifsum2(true, xs, y) -> sum2(tail(xs), y)
311.30/291.53	   ifsum2(false, xs, y) -> sum2(cons(p(head(xs)), tail(xs)), s(y))
311.30/291.53	   isNil(nil) -> true
311.30/291.53	   isNil(cons(x, xs)) -> false
311.30/291.53	   tail(nil) -> nil
311.30/291.53	   tail(cons(x, xs)) -> xs
311.30/291.53	   head(cons(x, xs)) -> x
311.30/291.53	   head(nil) -> error
311.30/291.53	   isZero(0) -> true
311.30/291.53	   isZero(s(0)) -> false
311.30/291.53	   isZero(s(s(x))) -> isZero(s(x))
311.30/291.53	   p(0) -> s(s(0))
311.30/291.53	   p(s(0)) -> 0
311.30/291.53	   p(s(s(x))) -> s(p(s(x)))
311.30/291.53	   ge(x, 0) -> true
311.30/291.53	   ge(0, s(y)) -> false
311.30/291.53	   ge(s(x), s(y)) -> ge(x, y)
311.30/291.53	   a -> c

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