2.65/1.26	NO
2.65/1.27	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.65/1.27	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.65/1.27	
2.65/1.27	
2.65/1.27	Outermost Termination of the given OTRS could be disproven:
2.65/1.27	
2.65/1.27	(0) OTRS
2.65/1.27	(1) OutermostNonTerminationProof [COMPLETE, 0 ms]
2.65/1.27	(2) NO
2.65/1.27	
2.65/1.27	
2.65/1.27	----------------------------------------
2.65/1.27	
2.65/1.27	(0)
2.65/1.27	Obligation:
2.65/1.27	Term rewrite system R:
2.65/1.27	The TRS R consists of the following rules:
2.65/1.27	
2.65/1.27	   f(h(x), y) -> h(f(y, f(x, h(a))))
2.65/1.27	
2.65/1.27	
2.65/1.27	
2.65/1.27	Outermost Strategy.
2.65/1.27	
2.65/1.27	----------------------------------------
2.65/1.27	
2.65/1.27	(1) OutermostNonTerminationProof (COMPLETE)
2.65/1.27	Term rewrite system R:
2.65/1.27	The TRS R consists of the following rules:
2.65/1.27	
2.65/1.27	   f(h(x), y) -> h(f(y, f(x, h(a))))
2.65/1.27	
2.65/1.27	
2.65/1.27	
2.65/1.27	Outermost Strategy.
2.65/1.27	
2.65/1.27	---------- Loop: ----------
2.65/1.27	
2.65/1.27	f(f(f(h(x), y''), h(x'')), f(f(h(x'), y'''), h(x'''))) -> f(f(h(f(y'', f(x, h(a)))), h(x'')), f(f(h(x'), y'''), h(x'''))) with rule f(h(x1), y'''') -> h(f(y'''', f(x1, h(a)))) at position [0,0] and matcher [x1 / x, y'''' / y'']
2.65/1.27	
2.65/1.27	f(f(h(f(y'', f(x, h(a)))), h(x'')), f(f(h(x'), y'''), h(x'''))) -> f(h(f(h(x''), f(f(y'', f(x, h(a))), h(a)))), f(f(h(x'), y'''), h(x'''))) with rule f(h(x'1), y') -> h(f(y', f(x'1, h(a)))) at position [0] and matcher [x'1 / f(y'', f(x, h(a))), y' / h(x'')]
2.65/1.27	
2.65/1.27	f(h(f(h(x''), f(f(y'', f(x, h(a))), h(a)))), f(f(h(x'), y'''), h(x'''))) -> h(f(f(f(h(x'), y'''), h(x''')), f(f(h(x''), f(f(y'', f(x, h(a))), h(a))), h(a)))) with rule f(h(x1), y) -> h(f(y, f(x1, h(a)))) at position [] and matcher [x1 / f(h(x''), f(f(y'', f(x, h(a))), h(a))), y / f(f(h(x'), y'''), h(x'''))]
2.65/1.27	
2.65/1.27	Now an instance of the first term with Matcher [y'' / y''', x / x', x' / x'', x'' / x''', y''' / f(f(y'', f(x, h(a))), h(a)), x''' / a] occurs in the last term at position [0].
2.65/1.27	
2.65/1.27	Context: h([])
2.65/1.27	
2.65/1.27	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.65/1.27	----------------------------------------
2.65/1.27	
2.65/1.27	(2)
2.65/1.27	NO
2.65/1.31	EOF