3.02/1.56	YES
3.02/1.56	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.02/1.56	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.02/1.56	
3.02/1.56	
3.02/1.56	Termination of the given ETRS could be proven:
3.02/1.56	
3.02/1.56	(0) ETRS
3.02/1.56	(1) EDirectTerminationProof [EQUIVALENT, 0 ms]
3.02/1.56	(2) YES
3.02/1.56	
3.02/1.56	
3.02/1.56	----------------------------------------
3.02/1.56	
3.02/1.56	(0)
3.02/1.56	Obligation:
3.02/1.56	Equational rewrite system:
3.02/1.56	The TRS R consists of the following rules:
3.02/1.56	
3.02/1.56	   1 -> s(0)
3.02/1.56	   2 -> s(1)
3.02/1.56	   3 -> s(2)
3.02/1.56	   4 -> s(3)
3.02/1.56	   5 -> s(4)
3.02/1.56	   6 -> s(5)
3.02/1.56	   7 -> s(6)
3.02/1.56	   8 -> s(7)
3.02/1.56	   9 -> s(8)
3.02/1.56	   max'(0, x) -> x
3.02/1.56	   max'(s(x), s(y)) -> s(max'(x, y))
3.02/1.56	   app(empty, X) -> X
3.02/1.56	   max(singl(x)) -> x
3.02/1.56	   max(app(singl(x), Y)) -> max2(x, Y)
3.02/1.56	   max2(x, empty) -> x
3.02/1.56	   max2(x, singl(y)) -> max'(x, y)
3.02/1.56	   max2(x, app(singl(y), Z)) -> max2(max'(x, y), Z)
3.02/1.56	
3.02/1.56	The set E consists of the following equations:
3.02/1.56	
3.02/1.56	   max'(x, y) == max'(y, x)
3.02/1.56	   app(x, y) == app(y, x)
3.02/1.56	   app(app(x, y), z) == app(x, app(y, z))
3.02/1.56	
3.02/1.56	
3.02/1.56	----------------------------------------
3.02/1.56	
3.02/1.56	(1) EDirectTerminationProof (EQUIVALENT)
3.02/1.56	We use [DA_FALKE] with the following order to prove termination.
3.02/1.56	
3.02/1.56	Precedence:
3.02/1.56	9 > 8 > 7 > 6 > 5 > 4 > 3 > 2 > 1 > s_1
3.02/1.56	9 > 8 > 7 > 6 > 5 > 4 > 3 > 2 > 1 > 0
3.02/1.56	app_2 > max2_2 > max'_2 > s_1
3.02/1.56	
3.02/1.56	
3.02/1.56	Status:
3.02/1.56	app_2: flat status
3.02/1.56	max2_2: [2,1]
3.02/1.56	max'_2: multiset status
3.02/1.56	
3.02/1.56	
3.02/1.56	
3.02/1.56	----------------------------------------
3.02/1.56	
3.02/1.56	(2)
3.02/1.56	YES
3.22/1.61	EOF