2.89/1.55	YES
2.89/1.55	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.89/1.55	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.89/1.55	
2.89/1.55	
2.89/1.55	Termination of the given ETRS could be proven:
2.89/1.55	
2.89/1.55	(0) ETRS
2.89/1.55	(1) EDirectTerminationProof [EQUIVALENT, 0 ms]
2.89/1.55	(2) YES
2.89/1.55	
2.89/1.55	
2.89/1.55	----------------------------------------
2.89/1.55	
2.89/1.55	(0)
2.89/1.55	Obligation:
2.89/1.55	Equational rewrite system:
2.89/1.55	The TRS R consists of the following rules:
2.89/1.55	
2.89/1.55	   +(0, x) -> x
2.89/1.55	   +(s(x), s(y)) -> s(s(+(x, y)))
2.89/1.55	   *(0, x) -> 0
2.89/1.55	   *(s(x), s(y)) -> s(+(+(x, y), *(x, y)))
2.89/1.55	   U(empty, b) -> b
2.89/1.55	   sum(empty) -> 0
2.89/1.55	   sum(singl(x)) -> x
2.89/1.55	   sum(U(x, y)) -> +(sum(x), sum(y))
2.89/1.55	   prod(empty) -> s(0)
2.89/1.55	   prod(singl(x)) -> x
2.89/1.55	   prod(U(x, y)) -> *(prod(x), prod(y))
2.89/1.55	
2.89/1.55	The set E consists of the following equations:
2.89/1.55	
2.89/1.55	   *(x, y) == *(y, x)
2.89/1.55	   +(x, y) == +(y, x)
2.89/1.55	   U(x, y) == U(y, x)
2.89/1.55	   *(*(x, y), z) == *(x, *(y, z))
2.89/1.55	   +(+(x, y), z) == +(x, +(y, z))
2.89/1.55	   U(U(x, y), z) == U(x, U(y, z))
2.89/1.55	
2.89/1.55	
2.89/1.55	----------------------------------------
2.89/1.55	
2.89/1.55	(1) EDirectTerminationProof (EQUIVALENT)
2.89/1.55	We use [DA_FALKE] with the following order to prove termination.
2.89/1.55	
2.89/1.55	Precedence:
2.89/1.55	U_2 > +_2 > s_1
2.89/1.55	U_2 > sum_1
2.89/1.55	empty > 0
2.89/1.55	prod_1 > *_2 > +_2 > s_1
2.89/1.55	
2.89/1.55	
2.89/1.55	Status:
2.89/1.55	*_2: flat status
2.89/1.55	+_2: flat status
2.89/1.55	U_2: flat status
2.89/1.55	
2.89/1.55	
2.89/1.55	
2.89/1.55	----------------------------------------
2.89/1.55	
2.89/1.55	(2)
2.89/1.55	YES
3.22/1.58	EOF