3.12/1.59	YES
3.12/1.60	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.12/1.60	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.12/1.60	
3.12/1.60	
3.12/1.60	Termination w.r.t. Q of the given QTRS could be proven:
3.12/1.60	
3.12/1.60	(0) QTRS
3.12/1.60	(1) QTRS Reverse [EQUIVALENT, 0 ms]
3.12/1.60	(2) QTRS
3.12/1.60	(3) QTRSRoofMatchBoundsTAProof [EQUIVALENT, 0 ms]
3.12/1.60	(4) YES
3.12/1.60	
3.12/1.60	
3.12/1.60	----------------------------------------
3.12/1.60	
3.12/1.60	(0)
3.12/1.60	Obligation:
3.12/1.60	Q restricted rewrite system:
3.12/1.60	The TRS R consists of the following rules:
3.12/1.60	
3.12/1.60	   f(f(a)) -> f(g)
3.12/1.60	
3.12/1.60	The set Q consists of the following terms:
3.12/1.60	
3.12/1.60	   f(f(a))
3.12/1.60	
3.12/1.60	
3.12/1.60	----------------------------------------
3.12/1.60	
3.12/1.60	(1) QTRS Reverse (EQUIVALENT)
3.12/1.60	We applied the QTRS Reverse Processor [REVERSE].
3.12/1.60	----------------------------------------
3.12/1.60	
3.12/1.60	(2)
3.12/1.60	Obligation:
3.12/1.60	Q restricted rewrite system:
3.12/1.60	The TRS R consists of the following rules:
3.12/1.60	
3.12/1.60	   a'(f(f(x))) -> g'(f(x))
3.12/1.60	
3.12/1.60	Q is empty.
3.12/1.60	
3.12/1.60	----------------------------------------
3.12/1.60	
3.12/1.60	(3) QTRSRoofMatchBoundsTAProof (EQUIVALENT)
3.12/1.60	The TRS R could be shown to be Match-Bounded [TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] by  1. Therefore it terminates.
3.12/1.60	
3.12/1.60	The compatible tree automaton used to show the Match-Boundedness is represented by: 
3.12/1.60	final states : [0, 1, 2]
3.12/1.60	transitions: 
3.12/1.60	a'0(0) -> 0
3.12/1.60	a'0(1) -> 0
3.12/1.60	a'0(2) -> 0
3.12/1.60	f0(0) -> 1
3.12/1.60	f0(1) -> 1
3.12/1.60	f0(2) -> 1
3.12/1.60	g'0(0) -> 2
3.12/1.60	g'0(1) -> 2
3.12/1.60	g'0(2) -> 2
3.12/1.60	f1(0) -> 3
3.12/1.60	g'1(3) -> 0
3.12/1.60	f1(1) -> 3
3.12/1.60	f1(2) -> 3
3.12/1.60	
3.12/1.60	----------------------------------------
3.12/1.60	
3.12/1.60	(4)
3.12/1.60	YES
3.34/1.64	EOF