2.63/1.36	YES
2.63/1.37	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.63/1.37	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.63/1.37	
2.63/1.37	
2.63/1.37	Termination of the given CSR could be proven:
2.63/1.37	
2.63/1.37	(0) CSR
2.63/1.37	(1) CSRRRRProof [EQUIVALENT, 35 ms]
2.63/1.37	(2) CSR
2.63/1.37	(3) RisEmptyProof [EQUIVALENT, 0 ms]
2.63/1.37	(4) YES
2.63/1.37	
2.63/1.37	
2.63/1.37	----------------------------------------
2.63/1.37	
2.63/1.37	(0)
2.63/1.37	Obligation:
2.63/1.37	Context-sensitive rewrite system:
2.63/1.37	The TRS R consists of the following rules:
2.63/1.37	
2.63/1.37	   f(X) -> g(h(f(X)))
2.63/1.37	
2.63/1.37	The replacement map contains the following entries:
2.63/1.37	
2.63/1.37	f: {1}
2.63/1.37	g: empty set
2.63/1.37	h: {1}
2.63/1.37	
2.63/1.37	----------------------------------------
2.63/1.37	
2.63/1.37	(1) CSRRRRProof (EQUIVALENT)
2.63/1.37	The following CSR is given: Context-sensitive rewrite system:
2.63/1.37	The TRS R consists of the following rules:
2.63/1.37	
2.63/1.37	   f(X) -> g(h(f(X)))
2.63/1.37	
2.63/1.37	The replacement map contains the following entries:
2.63/1.37	
2.63/1.37	f: {1}
2.63/1.37	g: empty set
2.63/1.37	h: {1}
2.63/1.37	Used ordering:
2.63/1.37	Polynomial interpretation [POLO]:
2.63/1.37	
2.63/1.37	   POL(f(x_1)) = 1 + x_1
2.63/1.37	   POL(g(x_1)) = 0
2.63/1.37	   POL(h(x_1)) = 1 + x_1
2.63/1.37	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
2.63/1.37	
2.63/1.37	   f(X) -> g(h(f(X)))
2.63/1.37	
2.63/1.37	
2.63/1.37	
2.63/1.37	
2.63/1.37	----------------------------------------
2.63/1.37	
2.63/1.37	(2)
2.63/1.37	Obligation:
2.63/1.37	Context-sensitive rewrite system:
2.63/1.37	R is empty.
2.63/1.37	
2.63/1.37	----------------------------------------
2.63/1.37	
2.63/1.37	(3) RisEmptyProof (EQUIVALENT)
2.63/1.37	The CSR R is empty. Hence, termination is trivially proven.
2.63/1.37	----------------------------------------
2.63/1.37	
2.63/1.37	(4)
2.63/1.37	YES
2.75/1.38	EOF