3.11/1.45	NO
3.17/1.46	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.17/1.46	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.17/1.46	
3.17/1.46	
3.17/1.46	Termination of the given CSR could be disproven:
3.17/1.46	
3.17/1.46	(0) CSR
3.17/1.46	(1) CSRRRRProof [EQUIVALENT, 30 ms]
3.17/1.46	(2) CSR
3.17/1.46	(3) ContextSensitiveLoopProof [COMPLETE, 31 ms]
3.17/1.46	(4) NO
3.17/1.46	
3.17/1.46	
3.17/1.46	----------------------------------------
3.17/1.46	
3.17/1.46	(0)
3.17/1.46	Obligation:
3.17/1.46	Context-sensitive rewrite system:
3.17/1.46	The TRS R consists of the following rules:
3.17/1.46	
3.17/1.46	   zeros -> cons(0, zeros)
3.17/1.46	   and(tt, X) -> X
3.17/1.46	   length(nil) -> 0
3.17/1.46	   length(cons(N, L)) -> s(length(L))
3.17/1.46	
3.17/1.46	The replacement map contains the following entries:
3.17/1.46	
3.17/1.46	zeros: empty set
3.17/1.46	cons: {1}
3.17/1.46	0: empty set
3.17/1.46	and: {1}
3.17/1.46	tt: empty set
3.17/1.46	length: {1}
3.17/1.46	nil: empty set
3.17/1.46	s: {1}
3.17/1.46	
3.17/1.46	----------------------------------------
3.17/1.46	
3.17/1.46	(1) CSRRRRProof (EQUIVALENT)
3.17/1.46	The following CSR is given: Context-sensitive rewrite system:
3.17/1.46	The TRS R consists of the following rules:
3.17/1.46	
3.17/1.46	   zeros -> cons(0, zeros)
3.17/1.46	   and(tt, X) -> X
3.17/1.46	   length(nil) -> 0
3.17/1.46	   length(cons(N, L)) -> s(length(L))
3.17/1.46	
3.17/1.46	The replacement map contains the following entries:
3.17/1.46	
3.17/1.46	zeros: empty set
3.17/1.46	cons: {1}
3.17/1.46	0: empty set
3.17/1.46	and: {1}
3.17/1.46	tt: empty set
3.17/1.46	length: {1}
3.17/1.46	nil: empty set
3.17/1.46	s: {1}
3.17/1.46	Used ordering:
3.17/1.46	Polynomial interpretation [POLO]:
3.17/1.46	
3.17/1.46	   POL(0) = 0
3.17/1.46	   POL(and(x_1, x_2)) = 2*x_1 + x_2
3.17/1.46	   POL(cons(x_1, x_2)) = x_1 + 2*x_2
3.17/1.46	   POL(length(x_1)) = 2*x_1
3.17/1.46	   POL(nil) = 1
3.17/1.46	   POL(s(x_1)) = 2*x_1
3.17/1.46	   POL(tt) = 1
3.17/1.46	   POL(zeros) = 0
3.17/1.46	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.17/1.46	
3.17/1.46	   and(tt, X) -> X
3.17/1.46	   length(nil) -> 0
3.17/1.46	
3.17/1.46	
3.17/1.46	
3.17/1.46	
3.17/1.46	----------------------------------------
3.17/1.46	
3.17/1.46	(2)
3.17/1.46	Obligation:
3.17/1.46	Context-sensitive rewrite system:
3.17/1.46	The TRS R consists of the following rules:
3.17/1.46	
3.17/1.46	   zeros -> cons(0, zeros)
3.17/1.46	   length(cons(N, L)) -> s(length(L))
3.17/1.46	
3.17/1.46	The replacement map contains the following entries:
3.17/1.46	
3.17/1.46	zeros: empty set
3.17/1.46	cons: {1}
3.17/1.46	0: empty set
3.17/1.46	length: {1}
3.17/1.46	s: {1}
3.17/1.46	
3.17/1.46	----------------------------------------
3.17/1.46	
3.17/1.46	(3) ContextSensitiveLoopProof (COMPLETE)
3.17/1.46	
3.17/1.46	   zeros -> cons(0, zeros)
3.17/1.46	   length(cons(N, L)) -> s(length(L))
3.17/1.46	
3.17/1.46	---------- Loop: ----------
3.17/1.46	
3.17/1.46	length(zeros) -> length(cons(0, zeros)) with rule zeros -> cons(0, zeros) at position [0] and matcher [ ]
3.17/1.46	
3.17/1.46	length(cons(0, zeros)) -> s(length(zeros)) with rule length(cons(N, L)) -> s(length(L)) at position [] and matcher [N / 0, L / zeros]
3.17/1.46	
3.17/1.46	Now an instance of the first term with Matcher [ ] occurs in the last term at position [0].
3.17/1.46	
3.17/1.46	Context: s([])
3.17/1.46	
3.17/1.46	We used [[THIEMANN_LOOPS_UNDER_STRATEGIES], Theorem 1] to show that this loop is an context-sensitive loop.
3.17/1.46	----------------------------------------
3.17/1.46	
3.17/1.46	(4)
3.17/1.46	NO
3.17/1.48	EOF