2.96/1.57	YES
2.96/1.57	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.96/1.57	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.96/1.57	
2.96/1.57	
2.96/1.57	Termination of the given ETRS could be proven:
2.96/1.57	
2.96/1.57	(0) ETRS
2.96/1.57	(1) EDirectTerminationProof [EQUIVALENT, 0 ms]
2.96/1.57	(2) YES
2.96/1.57	
2.96/1.57	
2.96/1.57	----------------------------------------
2.96/1.57	
2.96/1.57	(0)
2.96/1.57	Obligation:
2.96/1.57	Equational rewrite system:
2.96/1.57	The TRS R consists of the following rules:
2.96/1.57	
2.96/1.57	   s(p(x)) -> x
2.96/1.57	   p(s(x)) -> x
2.96/1.57	   plus(0, y) -> y
2.96/1.57	   plus(s(x), y) -> s(plus(x, y))
2.96/1.57	   plus(p(x), y) -> p(plus(x, y))
2.96/1.57	   plus(i(x), x) -> 0
2.96/1.57	   plus(x, plus(i(x), y)) -> y
2.96/1.57	   i(0) -> 0
2.96/1.57	   i(s(x)) -> p(i(x))
2.96/1.57	   i(p(x)) -> s(i(x))
2.96/1.57	   i(i(x)) -> x
2.96/1.57	   i(plus(x, y)) -> plus(i(y), i(x))
2.96/1.57	   times(0, y) -> 0
2.96/1.57	   times(s(x), y) -> plus(times(x, y), y)
2.96/1.57	   times(p(x), y) -> plus(times(x, y), i(y))
2.96/1.57	
2.96/1.57	The set E consists of the following equations:
2.96/1.57	
2.96/1.57	   plus(x, y) == plus(y, x)
2.96/1.57	   times(x, y) == times(y, x)
2.96/1.57	   plus(plus(x, y), z) == plus(x, plus(y, z))
2.96/1.57	   times(times(x, y), z) == times(x, times(y, z))
2.96/1.57	
2.96/1.57	
2.96/1.57	----------------------------------------
2.96/1.57	
2.96/1.57	(1) EDirectTerminationProof (EQUIVALENT)
2.96/1.57	We use [DA_FALKE] with the following order to prove termination.
2.96/1.57	
2.96/1.57	Precedence:
2.96/1.57	times_2 > i_1 > plus_2 > s_1
2.96/1.57	times_2 > i_1 > plus_2 > p_1
2.96/1.57	times_2 > i_1 > 0
2.96/1.57	
2.96/1.57	
2.96/1.57	Status:
2.96/1.57	plus_2: flat status
2.96/1.57	times_2: flat status
2.96/1.57	
2.96/1.57	
2.96/1.57	
2.96/1.57	----------------------------------------
2.96/1.57	
2.96/1.57	(2)
2.96/1.57	YES
2.96/1.60	EOF