Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308070

details

property	value
status	complete
benchmark	Ex26_Luc03b_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n036.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	1.67949 seconds
cpu usage	3.57184
user time	3.41293
system time	0.158916
max virtual memory	1.8277336E7
max residence set size	221700.0

stage attributes

key	value
starexec-result	WORST_CASE(?, O(1))

output

3.49/1.64	WORST_CASE(?, O(1))
3.49/1.64	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.49/1.64	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.49/1.64	
3.49/1.64	
3.49/1.64	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.49/1.64	
3.49/1.64	(0) CpxTRS
3.49/1.64	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
3.49/1.64	(2) CpxTRS
3.49/1.64	(3) NarrowingOnBasicTermsTerminatesProof [FINISHED, 13 ms]
3.49/1.64	(4) BOUNDS(1, 1)
3.49/1.64	
3.49/1.64	
3.49/1.64	----------------------------------------
3.49/1.64	
3.49/1.64	(0)
3.49/1.64	Obligation:
3.49/1.64	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.49/1.64	
3.49/1.64	
3.49/1.64	The TRS R consists of the following rules:
3.49/1.64	
3.49/1.64	   terms(N) -> cons(recip(sqr(N)), n__terms(s(N)))
3.49/1.64	   sqr(0) -> 0
3.49/1.64	   sqr(s(X)) -> s(n__add(sqr(activate(X)), dbl(activate(X))))
3.49/1.64	   dbl(0) -> 0
3.49/1.64	   dbl(s(X)) -> s(n__s(n__dbl(activate(X))))
3.49/1.64	   add(0, X) -> X
3.49/1.64	   add(s(X), Y) -> s(n__add(activate(X), Y))
3.49/1.64	   first(0, X) -> nil
3.49/1.64	   first(s(X), cons(Y, Z)) -> cons(Y, n__first(activate(X), activate(Z)))
3.49/1.64	   terms(X) -> n__terms(X)
3.49/1.64	   add(X1, X2) -> n__add(X1, X2)
3.49/1.64	   s(X) -> n__s(X)
3.49/1.64	   dbl(X) -> n__dbl(X)
3.49/1.64	   first(X1, X2) -> n__first(X1, X2)
3.49/1.64	   activate(n__terms(X)) -> terms(X)
3.49/1.64	   activate(n__add(X1, X2)) -> add(X1, X2)
3.49/1.64	   activate(n__s(X)) -> s(X)
3.49/1.64	   activate(n__dbl(X)) -> dbl(X)
3.49/1.64	   activate(n__first(X1, X2)) -> first(X1, X2)
3.49/1.64	   activate(X) -> X
3.49/1.64	
3.49/1.64	S is empty.
3.49/1.64	Rewrite Strategy: FULL
3.49/1.64	----------------------------------------
3.49/1.64	
3.49/1.64	(1) NestedDefinedSymbolProof (UPPER BOUND(ID))
3.49/1.64	The TRS does not nest defined symbols.
3.49/1.64	Hence, the left-hand sides of the following rules are not basic-reachable and can be removed:
3.49/1.64	sqr(s(X)) -> s(n__add(sqr(activate(X)), dbl(activate(X))))
3.49/1.64	dbl(s(X)) -> s(n__s(n__dbl(activate(X))))
3.49/1.64	add(s(X), Y) -> s(n__add(activate(X), Y))
3.49/1.64	first(s(X), cons(Y, Z)) -> cons(Y, n__first(activate(X), activate(Z)))
3.49/1.64	
3.49/1.64	----------------------------------------
3.49/1.64	
3.49/1.64	(2)
3.49/1.64	Obligation:
3.49/1.64	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, 1).
3.49/1.64	
3.49/1.64	
3.49/1.64	The TRS R consists of the following rules:
3.49/1.64	
3.49/1.64	   terms(N) -> cons(recip(sqr(N)), n__terms(s(N)))
3.49/1.64	   sqr(0) -> 0
3.49/1.64	   dbl(0) -> 0
3.49/1.64	   add(0, X) -> X
3.49/1.64	   first(0, X) -> nil
3.49/1.64	   terms(X) -> n__terms(X)
3.49/1.64	   add(X1, X2) -> n__add(X1, X2)
3.49/1.64	   s(X) -> n__s(X)
3.49/1.64	   dbl(X) -> n__dbl(X)
3.49/1.64	   first(X1, X2) -> n__first(X1, X2)
3.49/1.64	   activate(n__terms(X)) -> terms(X)
3.49/1.64	   activate(n__add(X1, X2)) -> add(X1, X2)
3.49/1.64	   activate(n__s(X)) -> s(X)
3.49/1.64	   activate(n__dbl(X)) -> dbl(X)
3.49/1.64	   activate(n__first(X1, X2)) -> first(X1, X2)
3.49/1.64	   activate(X) -> X
3.49/1.64	
3.49/1.64	S is empty.
3.49/1.64	Rewrite Strategy: FULL
3.49/1.64	----------------------------------------
3.49/1.64	
3.49/1.64	(3) NarrowingOnBasicTermsTerminatesProof (FINISHED)
3.49/1.64	Constant runtime complexity proven by termination of constructor-based narrowing.
3.49/1.64	
3.49/1.64	The maximal most general narrowing sequences give rise to the following rewrite sequences:
3.49/1.64	
3.49/1.64	activate(n__first(x0, x1)) ->^* n__first(x0, x1)
3.49/1.64	
3.49/1.64	activate(n__first(0, x0)) ->^* nil
3.49/1.64	
3.49/1.64	activate(n__dbl(x0)) ->^* n__dbl(x0)
3.49/1.64	
3.49/1.64	activate(n__dbl(0)) ->^* 0
3.49/1.64	
3.49/1.64	activate(n__s(x0)) ->^* n__s(x0)

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