Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313624

details

property	value
status	complete
benchmark	test830.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n018.star.cs.uiowa.edu
space	Strategy_removed_mixed_05

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	5.42008 seconds
cpu usage	17.0338
user time	15.8832
system time	1.15053
max virtual memory	1.9144324E7
max residence set size	3414220.0

stage attributes

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

output

16.57/5.30	WORST_CASE(Omega(n^1), O(n^1))
16.87/5.35	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
16.87/5.35	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
16.87/5.35	
16.87/5.35	
16.87/5.35	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
16.87/5.35	
16.87/5.35	(0) CpxTRS
16.87/5.35	(1) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
16.87/5.35	(2) CpxTRS
16.87/5.35	    (3) CpxTrsMatchBoundsTAProof [FINISHED, 0 ms]
16.87/5.35	    (4) BOUNDS(1, n^1)
16.87/5.35	(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
16.87/5.35	(6) CpxTRS
16.87/5.35	    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
16.87/5.35	    (8) typed CpxTrs
16.87/5.35	    (9) OrderProof [LOWER BOUND(ID), 0 ms]
16.87/5.35	    (10) typed CpxTrs
16.87/5.35	    (11) RewriteLemmaProof [LOWER BOUND(ID), 460 ms]
16.87/5.35	    (12) BEST
16.87/5.35	        (13) proven lower bound
16.87/5.35	            (14) LowerBoundPropagationProof [FINISHED, 0 ms]
16.87/5.35	            (15) BOUNDS(n^1, INF)
16.87/5.35	        (16) typed CpxTrs
16.87/5.35	
16.87/5.35	
16.87/5.35	----------------------------------------
16.87/5.35	
16.87/5.35	(0)
16.87/5.35	Obligation:
16.87/5.35	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
16.87/5.35	
16.87/5.35	
16.87/5.35	The TRS R consists of the following rules:
16.87/5.35	
16.87/5.35	   f(s(X)) -> f(X)
16.87/5.35	   g(cons(0, Y)) -> g(Y)
16.87/5.35	   g(cons(s(X), Y)) -> s(X)
16.87/5.35	   h(cons(X, Y)) -> h(g(cons(X, Y)))
16.87/5.35	
16.87/5.35	S is empty.
16.87/5.35	Rewrite Strategy: INNERMOST
16.87/5.35	----------------------------------------
16.87/5.35	
16.87/5.35	(1) RelTrsToTrsProof (UPPER BOUND(ID))
16.87/5.35	transformed relative TRS to TRS
16.87/5.35	----------------------------------------
16.87/5.35	
16.87/5.35	(2)
16.87/5.35	Obligation:
16.87/5.35	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).
16.87/5.35	
16.87/5.35	
16.87/5.35	The TRS R consists of the following rules:
16.87/5.35	
16.87/5.35	   f(s(X)) -> f(X)
16.87/5.35	   g(cons(0, Y)) -> g(Y)
16.87/5.35	   g(cons(s(X), Y)) -> s(X)
16.87/5.35	   h(cons(X, Y)) -> h(g(cons(X, Y)))
16.87/5.35	
16.87/5.35	S is empty.
16.87/5.35	Rewrite Strategy: INNERMOST
16.87/5.35	----------------------------------------
16.87/5.35	
16.87/5.35	(3) CpxTrsMatchBoundsTAProof (FINISHED)
16.87/5.35	A linear upper bound on the runtime complexity of the TRS R could be shown with a Match-Bound[TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] (for contructor-based start-terms) of 1. 
16.87/5.35	
16.87/5.35	The compatible tree automaton used to show the Match-Boundedness (for constructor-based start-terms) is represented by: 
16.87/5.35	final states : [1, 2, 3]
16.87/5.35	transitions: 
16.87/5.35	s0(0) -> 0
16.87/5.35	cons0(0, 0) -> 0
16.87/5.35	00() -> 0
16.87/5.35	f0(0) -> 1
16.87/5.35	g0(0) -> 2
16.87/5.35	h0(0) -> 3
16.87/5.35	f1(0) -> 1
16.87/5.35	g1(0) -> 2
16.87/5.35	s1(0) -> 2
16.87/5.35	cons1(0, 0) -> 5
16.87/5.35	g1(5) -> 4
16.87/5.35	h1(4) -> 3
16.87/5.35	g1(0) -> 4
16.87/5.35	s1(0) -> 4
16.87/5.35	
16.87/5.35	----------------------------------------
16.87/5.35	
16.87/5.35	(4)
16.87/5.35	BOUNDS(1, n^1)
16.87/5.35	
16.87/5.35	----------------------------------------
16.87/5.35	
16.87/5.35	(5) RenamingProof (BOTH BOUNDS(ID, ID))
16.87/5.35	Renamed function symbols to avoid clashes with predefined symbol.
16.87/5.35	----------------------------------------
16.87/5.35	
16.87/5.35	(6)
16.87/5.35	Obligation:
16.87/5.35	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).
16.87/5.35

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