2.98/1.41	YES
2.98/1.42	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.98/1.42	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.98/1.42	
2.98/1.42	
2.98/1.42	Termination of the given CSR could be proven:
2.98/1.42	
2.98/1.42	(0) CSR
2.98/1.42	(1) CSRRRRProof [EQUIVALENT, 53 ms]
2.98/1.42	(2) CSR
2.98/1.42	(3) CSRRRRProof [EQUIVALENT, 0 ms]
2.98/1.42	(4) CSR
2.98/1.42	(5) RisEmptyProof [EQUIVALENT, 0 ms]
2.98/1.42	(6) YES
2.98/1.42	
2.98/1.42	
2.98/1.42	----------------------------------------
2.98/1.42	
2.98/1.42	(0)
2.98/1.42	Obligation:
2.98/1.42	Context-sensitive rewrite system:
2.98/1.42	The TRS R consists of the following rules:
2.98/1.42	
2.98/1.42	   c -> f(g(c))
2.98/1.42	   f(g(X)) -> g(X)
2.98/1.42	
2.98/1.42	The replacement map contains the following entries:
2.98/1.42	
2.98/1.42	c: empty set
2.98/1.42	f: empty set
2.98/1.42	g: empty set
2.98/1.42	
2.98/1.42	----------------------------------------
2.98/1.42	
2.98/1.42	(1) CSRRRRProof (EQUIVALENT)
2.98/1.42	The following CSR is given: Context-sensitive rewrite system:
2.98/1.42	The TRS R consists of the following rules:
2.98/1.42	
2.98/1.42	   c -> f(g(c))
2.98/1.42	   f(g(X)) -> g(X)
2.98/1.42	
2.98/1.42	The replacement map contains the following entries:
2.98/1.42	
2.98/1.42	c: empty set
2.98/1.42	f: empty set
2.98/1.42	g: empty set
2.98/1.42	Used ordering:
2.98/1.42	Polynomial interpretation [POLO]:
2.98/1.42	
2.98/1.42	   POL(c) = 1
2.98/1.42	   POL(f(x_1)) = 1 + x_1
2.98/1.42	   POL(g(x_1)) = 0
2.98/1.42	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
2.98/1.42	
2.98/1.42	   f(g(X)) -> g(X)
2.98/1.42	
2.98/1.42	
2.98/1.42	
2.98/1.42	
2.98/1.42	----------------------------------------
2.98/1.42	
2.98/1.42	(2)
2.98/1.42	Obligation:
2.98/1.42	Context-sensitive rewrite system:
2.98/1.42	The TRS R consists of the following rules:
2.98/1.42	
2.98/1.42	   c -> f(g(c))
2.98/1.42	
2.98/1.42	The replacement map contains the following entries:
2.98/1.42	
2.98/1.42	c: empty set
2.98/1.42	f: empty set
2.98/1.42	g: empty set
2.98/1.42	
2.98/1.42	----------------------------------------
2.98/1.42	
2.98/1.42	(3) CSRRRRProof (EQUIVALENT)
2.98/1.42	The following CSR is given: Context-sensitive rewrite system:
2.98/1.42	The TRS R consists of the following rules:
2.98/1.42	
2.98/1.42	   c -> f(g(c))
2.98/1.42	
2.98/1.42	The replacement map contains the following entries:
2.98/1.42	
2.98/1.42	c: empty set
2.98/1.42	f: empty set
2.98/1.42	g: empty set
2.98/1.42	Used ordering:
2.98/1.42	Polynomial interpretation [POLO]:
2.98/1.42	
2.98/1.42	   POL(c) = 2
2.98/1.42	   POL(f(x_1)) = 0
2.98/1.42	   POL(g(x_1)) = 1
2.98/1.42	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
2.98/1.42	
2.98/1.42	   c -> f(g(c))
2.98/1.42	
2.98/1.42	
2.98/1.42	
2.98/1.42	
2.98/1.42	----------------------------------------
2.98/1.42	
2.98/1.42	(4)
2.98/1.42	Obligation:
2.98/1.42	Context-sensitive rewrite system:
2.98/1.42	R is empty.
2.98/1.42	
2.98/1.42	----------------------------------------
2.98/1.42	
2.98/1.42	(5) RisEmptyProof (EQUIVALENT)
2.98/1.42	The CSR R is empty. Hence, termination is trivially proven.
2.98/1.42	----------------------------------------
2.98/1.42	
2.98/1.42	(6)
2.98/1.42	YES
2.98/1.43	EOF