4.08/1.81	YES
4.08/1.82	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
4.08/1.82	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.08/1.82	
4.08/1.82	
4.08/1.82	Termination of the given RelTRS could be proven:
4.08/1.82	
4.08/1.82	(0) RelTRS
4.08/1.82	(1) RelTRSRRRProof [EQUIVALENT, 56 ms]
4.08/1.82	(2) RelTRS
4.08/1.82	(3) RIsEmptyProof [EQUIVALENT, 0 ms]
4.08/1.82	(4) YES
4.08/1.82	
4.08/1.82	
4.08/1.82	----------------------------------------
4.08/1.82	
4.08/1.82	(0)
4.08/1.82	Obligation:
4.08/1.82	Relative term rewrite system:
4.08/1.82	The relative TRS consists of the following R rules:
4.08/1.82	
4.08/1.82	   f(x, 0) -> s(x)
4.08/1.82	   g(x) -> h(x, gen)
4.08/1.82	   h(0, x) -> f(x, x)
4.08/1.82	   a -> b
4.08/1.82	
4.08/1.82	The relative TRS consists of the following S rules:
4.08/1.82	
4.08/1.82	   gen -> s(gen)
4.08/1.82	
4.08/1.82	
4.08/1.82	----------------------------------------
4.08/1.82	
4.08/1.82	(1) RelTRSRRRProof (EQUIVALENT)
4.08/1.82	We used the following monotonic ordering for rule removal:
4.08/1.82	f/2(YES,YES)
4.08/1.82	0/0)
4.08/1.82	s/1)YES(
4.08/1.82	g/1(YES)
4.08/1.82	h/2(YES,YES)
4.08/1.82	gen/0)
4.08/1.82	a/0)
4.08/1.82	b/0)
4.08/1.82	
4.08/1.82	Quasi precedence:
4.08/1.82	0 > f_2 > gen
4.08/1.82	g_1 > h_2 > f_2 > gen
4.08/1.82	a > b > gen
4.08/1.82	
4.08/1.82	
4.08/1.82	Status:
4.08/1.82	f_2: [2,1]
4.08/1.82	0: multiset status
4.08/1.82	g_1: [1]
4.08/1.82	h_2: [2,1]
4.08/1.82	gen: multiset status
4.08/1.82	a: multiset status
4.08/1.82	b: multiset status
4.08/1.82	
4.08/1.82	With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
4.08/1.82	Rules from R:
4.08/1.82	
4.08/1.82	   f(x, 0) -> s(x)
4.08/1.82	   g(x) -> h(x, gen)
4.08/1.82	   h(0, x) -> f(x, x)
4.08/1.82	   a -> b
4.08/1.82	Rules from S:
4.08/1.82	none
4.08/1.82	
4.08/1.82	
4.08/1.82	
4.08/1.82	
4.08/1.82	----------------------------------------
4.08/1.82	
4.08/1.82	(2)
4.08/1.82	Obligation:
4.08/1.82	Relative term rewrite system:
4.08/1.82	R is empty.
4.08/1.82	The relative TRS consists of the following S rules:
4.08/1.82	
4.08/1.82	   gen -> s(gen)
4.08/1.82	
4.08/1.82	
4.08/1.82	----------------------------------------
4.08/1.82	
4.08/1.82	(3) RIsEmptyProof (EQUIVALENT)
4.08/1.82	The TRS R is empty. Hence, termination is trivially proven.
4.08/1.82	----------------------------------------
4.08/1.82	
4.08/1.82	(4)
4.08/1.82	YES
4.08/1.86	EOF