2.69/1.32	YES
2.69/1.33	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.69/1.33	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.69/1.33	
2.69/1.33	
2.69/1.33	Termination of the given CSR could be proven:
2.69/1.33	
2.69/1.33	(0) CSR
2.69/1.33	(1) CSRRRRProof [EQUIVALENT, 61 ms]
2.69/1.33	(2) CSR
2.69/1.33	(3) RisEmptyProof [EQUIVALENT, 0 ms]
2.69/1.33	(4) YES
2.69/1.33	
2.69/1.33	
2.69/1.33	----------------------------------------
2.69/1.33	
2.69/1.33	(0)
2.69/1.33	Obligation:
2.69/1.33	Context-sensitive rewrite system:
2.69/1.33	The TRS R consists of the following rules:
2.69/1.33	
2.69/1.33	   f(f(a)) -> f(g(f(a)))
2.69/1.33	
2.69/1.33	The replacement map contains the following entries:
2.69/1.33	
2.69/1.33	f: {1}
2.69/1.33	a: empty set
2.69/1.33	g: empty set
2.69/1.33	
2.69/1.33	----------------------------------------
2.69/1.33	
2.69/1.33	(1) CSRRRRProof (EQUIVALENT)
2.69/1.33	The following CSR is given: Context-sensitive rewrite system:
2.69/1.33	The TRS R consists of the following rules:
2.69/1.33	
2.69/1.33	   f(f(a)) -> f(g(f(a)))
2.69/1.33	
2.69/1.33	The replacement map contains the following entries:
2.69/1.33	
2.69/1.33	f: {1}
2.69/1.33	a: empty set
2.69/1.33	g: empty set
2.69/1.33	Used ordering:
2.69/1.33	Polynomial interpretation [POLO]:
2.69/1.33	
2.69/1.33	   POL(a) = 2
2.69/1.33	   POL(f(x_1)) = 2 + x_1
2.69/1.33	   POL(g(x_1)) = 0
2.69/1.33	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
2.69/1.33	
2.69/1.33	   f(f(a)) -> f(g(f(a)))
2.69/1.33	
2.69/1.33	
2.69/1.33	
2.69/1.33	
2.69/1.33	----------------------------------------
2.69/1.33	
2.69/1.33	(2)
2.69/1.33	Obligation:
2.69/1.33	Context-sensitive rewrite system:
2.69/1.33	R is empty.
2.69/1.33	
2.69/1.33	----------------------------------------
2.69/1.33	
2.69/1.33	(3) RisEmptyProof (EQUIVALENT)
2.69/1.33	The CSR R is empty. Hence, termination is trivially proven.
2.69/1.33	----------------------------------------
2.69/1.33	
2.69/1.33	(4)
2.69/1.33	YES
2.69/1.34	EOF