3.32/1.48	NO
3.32/1.49	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.32/1.49	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.32/1.49	
3.32/1.49	
3.32/1.49	Termination of the given CSR could be disproven:
3.32/1.49	
3.32/1.49	(0) CSR
3.32/1.49	(1) CSRRRRProof [EQUIVALENT, 46 ms]
3.32/1.49	(2) CSR
3.32/1.49	(3) ContextSensitiveLoopProof [COMPLETE, 4 ms]
3.32/1.49	(4) NO
3.32/1.49	
3.32/1.49	
3.32/1.49	----------------------------------------
3.32/1.49	
3.32/1.49	(0)
3.32/1.49	Obligation:
3.32/1.49	Context-sensitive rewrite system:
3.32/1.49	The TRS R consists of the following rules:
3.32/1.49	
3.32/1.49	   zeros -> cons(0, zeros)
3.32/1.49	   U11(tt, L) -> U12(tt, L)
3.32/1.49	   U12(tt, L) -> s(length(L))
3.32/1.49	   length(nil) -> 0
3.32/1.49	   length(cons(N, L)) -> U11(tt, L)
3.32/1.49	
3.32/1.49	The replacement map contains the following entries:
3.32/1.49	
3.32/1.49	zeros: empty set
3.32/1.49	cons: {1}
3.32/1.49	0: empty set
3.32/1.49	U11: {1}
3.32/1.49	tt: empty set
3.32/1.49	U12: {1}
3.32/1.49	s: {1}
3.32/1.49	length: {1}
3.32/1.49	nil: empty set
3.32/1.49	
3.32/1.49	----------------------------------------
3.32/1.49	
3.32/1.49	(1) CSRRRRProof (EQUIVALENT)
3.32/1.49	The following CSR is given: Context-sensitive rewrite system:
3.32/1.49	The TRS R consists of the following rules:
3.32/1.49	
3.32/1.49	   zeros -> cons(0, zeros)
3.32/1.49	   U11(tt, L) -> U12(tt, L)
3.32/1.49	   U12(tt, L) -> s(length(L))
3.32/1.49	   length(nil) -> 0
3.32/1.49	   length(cons(N, L)) -> U11(tt, L)
3.32/1.49	
3.32/1.49	The replacement map contains the following entries:
3.32/1.49	
3.32/1.49	zeros: empty set
3.32/1.49	cons: {1}
3.32/1.49	0: empty set
3.32/1.49	U11: {1}
3.32/1.49	tt: empty set
3.32/1.49	U12: {1}
3.32/1.49	s: {1}
3.32/1.49	length: {1}
3.32/1.49	nil: empty set
3.32/1.49	Used ordering:
3.32/1.49	Polynomial interpretation [POLO]:
3.32/1.49	
3.32/1.49	   POL(0) = 0
3.32/1.49	   POL(U11(x_1, x_2)) = x_1 + 2*x_2
3.32/1.49	   POL(U12(x_1, x_2)) = x_1 + 2*x_2
3.32/1.49	   POL(cons(x_1, x_2)) = 2*x_1 + 2*x_2
3.32/1.49	   POL(length(x_1)) = x_1
3.32/1.49	   POL(nil) = 1
3.32/1.49	   POL(s(x_1)) = 2*x_1
3.32/1.49	   POL(tt) = 0
3.32/1.49	   POL(zeros) = 0
3.32/1.49	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.32/1.49	
3.32/1.49	   length(nil) -> 0
3.32/1.49	
3.32/1.49	
3.32/1.49	
3.32/1.49	
3.32/1.49	----------------------------------------
3.32/1.49	
3.32/1.49	(2)
3.32/1.49	Obligation:
3.32/1.49	Context-sensitive rewrite system:
3.32/1.49	The TRS R consists of the following rules:
3.32/1.49	
3.32/1.49	   zeros -> cons(0, zeros)
3.32/1.49	   U11(tt, L) -> U12(tt, L)
3.32/1.49	   U12(tt, L) -> s(length(L))
3.32/1.49	   length(cons(N, L)) -> U11(tt, L)
3.32/1.49	
3.32/1.49	The replacement map contains the following entries:
3.32/1.49	
3.32/1.49	zeros: empty set
3.32/1.49	cons: {1}
3.32/1.49	0: empty set
3.32/1.49	U11: {1}
3.32/1.49	tt: empty set
3.32/1.49	U12: {1}
3.32/1.49	s: {1}
3.32/1.49	length: {1}
3.32/1.49	
3.32/1.49	----------------------------------------
3.32/1.49	
3.32/1.49	(3) ContextSensitiveLoopProof (COMPLETE)
3.32/1.49	
3.32/1.49	   zeros -> cons(0, zeros)
3.32/1.49	   U11(tt, L) -> U12(tt, L)
3.32/1.49	   U12(tt, L) -> s(length(L))
3.32/1.49	   length(cons(N, L)) -> U11(tt, L)
3.32/1.49	
3.32/1.49	---------- Loop: ----------
3.32/1.49	
3.32/1.49	U12(tt, zeros) -> s(length(zeros)) with rule U12(tt, L) -> s(length(L)) at position [] and matcher [L / zeros]
3.32/1.49	
3.32/1.49	s(length(zeros)) -> s(length(cons(0, zeros))) with rule zeros -> cons(0, zeros) at position [0,0] and matcher [ ]
3.32/1.49	
3.32/1.49	s(length(cons(0, zeros))) -> s(U11(tt, zeros)) with rule length(cons(N, L)) -> U11(tt, L) at position [0] and matcher [N / 0, L / zeros]
3.32/1.49	
3.32/1.49	s(U11(tt, zeros)) -> s(U12(tt, zeros)) with rule U11(tt, L) -> U12(tt, L) at position [0] and matcher [L / zeros]
3.32/1.49	
3.32/1.49	Now an instance of the first term with Matcher [ ] occurs in the last term at position [0].
3.32/1.49	
3.32/1.49	Context: s([])
3.32/1.49	
3.32/1.49	We used [[THIEMANN_LOOPS_UNDER_STRATEGIES], Theorem 1] to show that this loop is an context-sensitive loop.
3.32/1.49	----------------------------------------
3.32/1.49	
3.32/1.49	(4)
3.32/1.49	NO
3.32/1.51	EOF