7.11/2.47	NO
7.11/2.47	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
7.11/2.47	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
7.11/2.47	
7.11/2.47	
7.11/2.47	Outermost Termination of the given OTRS could be disproven:
7.11/2.47	
7.11/2.47	(0) OTRS
7.11/2.47	(1) OutermostNonTerminationProof [COMPLETE, 693 ms]
7.11/2.47	(2) NO
7.11/2.47	
7.11/2.47	
7.11/2.47	----------------------------------------
7.11/2.47	
7.11/2.47	(0)
7.11/2.47	Obligation:
7.11/2.47	Term rewrite system R:
7.11/2.47	The TRS R consists of the following rules:
7.11/2.47	
7.11/2.47	   f(f(f(a, x), y), z) -> f(f(x, z), f(y, z))
7.11/2.47	   f(f(b, x), y) -> x
7.11/2.47	   f(c, y) -> y
7.11/2.47	
7.11/2.47	
7.11/2.47	
7.11/2.47	Outermost Strategy.
7.11/2.47	
7.11/2.47	----------------------------------------
7.11/2.47	
7.11/2.47	(1) OutermostNonTerminationProof (COMPLETE)
7.11/2.47	Term rewrite system R:
7.11/2.47	The TRS R consists of the following rules:
7.11/2.47	
7.11/2.47	   f(f(f(a, x), y), z) -> f(f(x, z), f(y, z))
7.11/2.47	   f(f(b, x), y) -> x
7.11/2.47	   f(c, y) -> y
7.11/2.47	
7.11/2.47	
7.11/2.47	
7.11/2.47	Outermost Strategy.
7.11/2.47	
7.11/2.47	---------- Loop: ----------
7.11/2.47	
7.11/2.47	f(f(f(f(b, f(f(a, a), b)), y'), f(f(b, f(a, f(f(b, f(f(a, a), b)), y'''))), y'')), y'''') -> f(f(f(f(b, f(f(a, a), b)), y'), f(a, f(f(b, f(f(a, a), b)), y'''))), y'''') with rule f(f(b, x'), y''1) -> x' at position [0,1] and matcher [x' / f(a, f(f(b, f(f(a, a), b)), y''')), y''1 / y'']
7.11/2.47	
7.11/2.47	f(f(f(f(b, f(f(a, a), b)), y'), f(a, f(f(b, f(f(a, a), b)), y'''))), y'''') -> f(f(f(f(a, a), b), f(a, f(f(b, f(f(a, a), b)), y'''))), y'''') with rule f(f(b, x'), y'') -> x' at position [0,0] and matcher [x' / f(f(a, a), b), y'' / y']
7.11/2.47	
7.11/2.47	f(f(f(f(a, a), b), f(a, f(f(b, f(f(a, a), b)), y'''))), y'''') -> f(f(f(a, f(a, f(f(b, f(f(a, a), b)), y'''))), f(b, f(a, f(f(b, f(f(a, a), b)), y''')))), y'''') with rule f(f(f(a, x'), y), z) -> f(f(x', z), f(y, z)) at position [0] and matcher [x' / a, y / b, z / f(a, f(f(b, f(f(a, a), b)), y'''))]
7.11/2.47	
7.11/2.47	f(f(f(a, f(a, f(f(b, f(f(a, a), b)), y'''))), f(b, f(a, f(f(b, f(f(a, a), b)), y''')))), y'''') -> f(f(f(a, f(f(b, f(f(a, a), b)), y''')), y''''), f(f(b, f(a, f(f(b, f(f(a, a), b)), y'''))), y'''')) with rule f(f(f(a, x), y), z) -> f(f(x, z), f(y, z)) at position [] and matcher [x / f(a, f(f(b, f(f(a, a), b)), y''')), y / f(b, f(a, f(f(b, f(f(a, a), b)), y'''))), z / y'''']
7.11/2.47	
7.11/2.47	f(f(f(a, f(f(b, f(f(a, a), b)), y''')), y''''), f(f(b, f(a, f(f(b, f(f(a, a), b)), y'''))), y'''')) -> f(f(f(f(b, f(f(a, a), b)), y'''), f(f(b, f(a, f(f(b, f(f(a, a), b)), y'''))), y'''')), f(y'''', f(f(b, f(a, f(f(b, f(f(a, a), b)), y'''))), y''''))) with rule f(f(f(a, x), y), z) -> f(f(x, z), f(y, z)) at position [] and matcher [x / f(f(b, f(f(a, a), b)), y'''), y / y'''', z / f(f(b, f(a, f(f(b, f(f(a, a), b)), y'''))), y'''')]
7.11/2.47	
7.11/2.47	Now an instance of the first term with Matcher [y' / y''', y'' / y'''', y'''' / f(y'''', f(f(b, f(a, f(f(b, f(f(a, a), b)), y'''))), y''''))] occurs in the last term at position [].
7.11/2.47	
7.11/2.47	Context: []
7.11/2.47	
7.11/2.47	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
7.11/2.47	----------------------------------------
7.11/2.47	
7.11/2.47	(2)
7.11/2.47	NO
7.11/2.51	EOF