3.16/1.46	YES
3.16/1.47	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.16/1.47	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.16/1.47	
3.16/1.47	
3.16/1.47	Termination of the given CSR could be proven:
3.16/1.47	
3.16/1.47	(0) CSR
3.16/1.47	(1) CSRRRRProof [EQUIVALENT, 57 ms]
3.16/1.47	(2) CSR
3.16/1.47	(3) CSRRRRProof [EQUIVALENT, 0 ms]
3.16/1.47	(4) CSR
3.16/1.47	(5) RisEmptyProof [EQUIVALENT, 0 ms]
3.16/1.47	(6) YES
3.16/1.47	
3.16/1.47	
3.16/1.47	----------------------------------------
3.16/1.47	
3.16/1.47	(0)
3.16/1.47	Obligation:
3.16/1.47	Context-sensitive rewrite system:
3.16/1.47	The TRS R consists of the following rules:
3.16/1.47	
3.16/1.47	   from_2(x) -> cons_0(x, from_3(s_0(x)))
3.16/1.47	   from_3(x) -> cons_1(x, from_3(s_0(x)))
3.16/1.47	   from_1(x) -> cons_0(x, from_3(s_0(x)))
3.16/1.47	   cons_1(s_0(x), xs) -> overflow_0
3.16/1.47	
3.16/1.47	The replacement map contains the following entries:
3.16/1.47	
3.16/1.47	from_2: empty set
3.16/1.47	cons_0: {1, 2}
3.16/1.47	from_3: empty set
3.16/1.47	s_0: {1}
3.16/1.47	cons_1: empty set
3.16/1.47	from_1: empty set
3.16/1.47	overflow_0: empty set
3.16/1.47	
3.16/1.47	----------------------------------------
3.16/1.47	
3.16/1.47	(1) CSRRRRProof (EQUIVALENT)
3.16/1.47	The following CSR is given: Context-sensitive rewrite system:
3.16/1.47	The TRS R consists of the following rules:
3.16/1.47	
3.16/1.47	   from_2(x) -> cons_0(x, from_3(s_0(x)))
3.16/1.47	   from_3(x) -> cons_1(x, from_3(s_0(x)))
3.16/1.47	   from_1(x) -> cons_0(x, from_3(s_0(x)))
3.16/1.47	   cons_1(s_0(x), xs) -> overflow_0
3.16/1.47	
3.16/1.47	The replacement map contains the following entries:
3.16/1.47	
3.16/1.47	from_2: empty set
3.16/1.47	cons_0: {1, 2}
3.16/1.47	from_3: empty set
3.16/1.47	s_0: {1}
3.16/1.47	cons_1: empty set
3.16/1.47	from_1: empty set
3.16/1.47	overflow_0: empty set
3.16/1.47	Used ordering:
3.16/1.47	Polynomial interpretation [POLO]:
3.16/1.47	
3.16/1.47	   POL(cons_0(x_1, x_2)) = 2*x_1 + x_2
3.16/1.47	   POL(cons_1(x_1, x_2)) = 0
3.16/1.47	   POL(from_1(x_1)) = 2 + 2*x_1
3.16/1.47	   POL(from_2(x_1)) = 2 + 2*x_1
3.16/1.47	   POL(from_3(x_1)) = 1
3.16/1.47	   POL(overflow_0) = 0
3.16/1.47	   POL(s_0(x_1)) = x_1
3.16/1.47	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.16/1.47	
3.16/1.47	   from_2(x) -> cons_0(x, from_3(s_0(x)))
3.16/1.47	   from_3(x) -> cons_1(x, from_3(s_0(x)))
3.16/1.47	   from_1(x) -> cons_0(x, from_3(s_0(x)))
3.16/1.47	
3.16/1.47	
3.16/1.47	
3.16/1.47	
3.16/1.47	----------------------------------------
3.16/1.47	
3.16/1.47	(2)
3.16/1.47	Obligation:
3.16/1.47	Context-sensitive rewrite system:
3.16/1.47	The TRS R consists of the following rules:
3.16/1.47	
3.16/1.47	   cons_1(s_0(x), xs) -> overflow_0
3.16/1.47	
3.16/1.47	The replacement map contains the following entries:
3.16/1.47	
3.16/1.47	s_0: {1}
3.16/1.47	cons_1: empty set
3.16/1.47	overflow_0: empty set
3.16/1.47	
3.16/1.47	----------------------------------------
3.16/1.47	
3.16/1.47	(3) CSRRRRProof (EQUIVALENT)
3.16/1.47	The following CSR is given: Context-sensitive rewrite system:
3.16/1.47	The TRS R consists of the following rules:
3.16/1.47	
3.16/1.47	   cons_1(s_0(x), xs) -> overflow_0
3.16/1.47	
3.16/1.47	The replacement map contains the following entries:
3.16/1.47	
3.16/1.47	s_0: {1}
3.16/1.47	cons_1: empty set
3.16/1.47	overflow_0: empty set
3.16/1.47	Used ordering:
3.16/1.47	Polynomial interpretation [POLO]:
3.16/1.47	
3.16/1.47	   POL(cons_1(x_1, x_2)) = 2 + 2*x_1
3.16/1.47	   POL(overflow_0) = 0
3.16/1.47	   POL(s_0(x_1)) = 1 + x_1
3.16/1.47	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.16/1.47	
3.16/1.47	   cons_1(s_0(x), xs) -> overflow_0
3.16/1.47	
3.16/1.47	
3.16/1.47	
3.16/1.47	
3.16/1.47	----------------------------------------
3.16/1.47	
3.16/1.47	(4)
3.16/1.47	Obligation:
3.16/1.47	Context-sensitive rewrite system:
3.16/1.47	R is empty.
3.16/1.47	
3.16/1.47	----------------------------------------
3.16/1.47	
3.16/1.47	(5) RisEmptyProof (EQUIVALENT)
3.16/1.47	The CSR R is empty. Hence, termination is trivially proven.
3.16/1.47	----------------------------------------
3.16/1.47	
3.16/1.47	(6)
3.16/1.47	YES
3.16/1.48	EOF