2.68/1.43	YES
2.81/1.44	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.81/1.44	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.81/1.44	
2.81/1.44	
2.81/1.44	Termination of the given CSR could be proven:
2.81/1.44	
2.81/1.44	(0) CSR
2.81/1.44	(1) CSRRRRProof [EQUIVALENT, 47 ms]
2.81/1.44	(2) CSR
2.81/1.44	(3) CSRRRRProof [EQUIVALENT, 0 ms]
2.81/1.44	(4) CSR
2.81/1.44	(5) CSRRRRProof [EQUIVALENT, 0 ms]
2.81/1.44	(6) CSR
2.81/1.44	(7) RisEmptyProof [EQUIVALENT, 0 ms]
2.81/1.44	(8) YES
2.81/1.44	
2.81/1.44	
2.81/1.44	----------------------------------------
2.81/1.44	
2.81/1.44	(0)
2.81/1.44	Obligation:
2.81/1.44	Context-sensitive rewrite system:
2.81/1.44	The TRS R consists of the following rules:
2.81/1.44	
2.81/1.44	   g(X) -> h(X)
2.81/1.44	   c -> d
2.81/1.44	   h(d) -> g(c)
2.81/1.44	
2.81/1.44	The replacement map contains the following entries:
2.81/1.44	
2.81/1.44	g: empty set
2.81/1.44	h: empty set
2.81/1.44	c: empty set
2.81/1.44	d: empty set
2.81/1.44	
2.81/1.44	----------------------------------------
2.81/1.44	
2.81/1.44	(1) CSRRRRProof (EQUIVALENT)
2.81/1.44	The following CSR is given: Context-sensitive rewrite system:
2.81/1.44	The TRS R consists of the following rules:
2.81/1.44	
2.81/1.44	   g(X) -> h(X)
2.81/1.44	   c -> d
2.81/1.44	   h(d) -> g(c)
2.81/1.44	
2.81/1.44	The replacement map contains the following entries:
2.81/1.44	
2.81/1.44	g: empty set
2.81/1.44	h: empty set
2.81/1.44	c: empty set
2.81/1.44	d: empty set
2.81/1.44	Used ordering:
2.81/1.44	Polynomial interpretation [POLO]:
2.81/1.44	
2.81/1.44	   POL(c) = 1
2.81/1.44	   POL(d) = 0
2.81/1.44	   POL(g(x_1)) = 0
2.81/1.44	   POL(h(x_1)) = 0
2.81/1.44	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
2.81/1.44	
2.81/1.44	   c -> d
2.81/1.44	
2.81/1.44	
2.81/1.44	
2.81/1.44	
2.81/1.44	----------------------------------------
2.81/1.44	
2.81/1.44	(2)
2.81/1.44	Obligation:
2.81/1.44	Context-sensitive rewrite system:
2.81/1.44	The TRS R consists of the following rules:
2.81/1.44	
2.81/1.44	   g(X) -> h(X)
2.81/1.44	   h(d) -> g(c)
2.81/1.44	
2.81/1.44	The replacement map contains the following entries:
2.81/1.44	
2.81/1.44	g: empty set
2.81/1.44	h: empty set
2.81/1.44	c: empty set
2.81/1.44	d: empty set
2.81/1.44	
2.81/1.44	----------------------------------------
2.81/1.44	
2.81/1.44	(3) CSRRRRProof (EQUIVALENT)
2.81/1.44	The following CSR is given: Context-sensitive rewrite system:
2.81/1.44	The TRS R consists of the following rules:
2.81/1.44	
2.81/1.44	   g(X) -> h(X)
2.81/1.44	   h(d) -> g(c)
2.81/1.44	
2.81/1.44	The replacement map contains the following entries:
2.81/1.44	
2.81/1.44	g: empty set
2.81/1.44	h: empty set
2.81/1.44	c: empty set
2.81/1.44	d: empty set
2.81/1.44	Used ordering:
2.81/1.44	Polynomial interpretation [POLO]:
2.81/1.44	
2.81/1.44	   POL(c) = 0
2.81/1.44	   POL(d) = 1
2.81/1.44	   POL(g(x_1)) = 1 + x_1
2.81/1.44	   POL(h(x_1)) = 1 + x_1
2.81/1.44	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
2.81/1.44	
2.81/1.44	   h(d) -> g(c)
2.81/1.44	
2.81/1.44	
2.81/1.44	
2.81/1.44	
2.81/1.44	----------------------------------------
2.81/1.44	
2.81/1.44	(4)
2.81/1.44	Obligation:
2.81/1.44	Context-sensitive rewrite system:
2.81/1.44	The TRS R consists of the following rules:
2.81/1.44	
2.81/1.44	   g(X) -> h(X)
2.81/1.44	
2.81/1.44	The replacement map contains the following entries:
2.81/1.44	
2.81/1.44	g: empty set
2.81/1.44	h: empty set
2.81/1.44	
2.81/1.44	----------------------------------------
2.81/1.44	
2.81/1.44	(5) CSRRRRProof (EQUIVALENT)
2.81/1.44	The following CSR is given: Context-sensitive rewrite system:
2.81/1.44	The TRS R consists of the following rules:
2.81/1.44	
2.81/1.44	   g(X) -> h(X)
2.81/1.44	
2.81/1.44	The replacement map contains the following entries:
2.81/1.44	
2.81/1.44	g: empty set
2.81/1.44	h: empty set
2.81/1.44	Used ordering:
2.81/1.44	Polynomial interpretation [POLO]:
2.81/1.44	
2.81/1.44	   POL(g(x_1)) = 1 + 2*x_1
2.81/1.44	   POL(h(x_1)) = 2*x_1
2.81/1.44	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
2.81/1.44	
2.81/1.44	   g(X) -> h(X)
2.81/1.44	
2.81/1.44	
2.81/1.44	
2.81/1.44	
2.81/1.44	----------------------------------------
2.81/1.44	
2.81/1.44	(6)
2.81/1.44	Obligation:
2.81/1.44	Context-sensitive rewrite system:
2.81/1.44	R is empty.
2.81/1.44	
2.81/1.44	----------------------------------------
2.81/1.44	
2.81/1.44	(7) RisEmptyProof (EQUIVALENT)
2.81/1.44	The CSR R is empty. Hence, termination is trivially proven.
2.81/1.44	----------------------------------------
2.81/1.44	
2.81/1.44	(8)
2.81/1.44	YES
2.83/1.46	EOF