2.66/1.24	NO
2.66/1.25	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.66/1.25	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.66/1.25	
2.66/1.25	
2.66/1.25	Outermost Termination of the given OTRS could be disproven:
2.66/1.25	
2.66/1.25	(0) OTRS
2.66/1.25	(1) OutermostNonTerminationProof [COMPLETE, 57 ms]
2.66/1.25	(2) NO
2.66/1.25	
2.66/1.25	
2.66/1.25	----------------------------------------
2.66/1.25	
2.66/1.25	(0)
2.66/1.25	Obligation:
2.66/1.25	Term rewrite system R:
2.66/1.25	The TRS R consists of the following rules:
2.66/1.25	
2.66/1.25	   f(x, h(y)) -> h(f(f(h(a), y), x))
2.66/1.25	
2.66/1.25	
2.66/1.25	
2.66/1.25	Outermost Strategy.
2.66/1.25	
2.66/1.25	----------------------------------------
2.66/1.25	
2.66/1.25	(1) OutermostNonTerminationProof (COMPLETE)
2.66/1.25	Term rewrite system R:
2.66/1.25	The TRS R consists of the following rules:
2.66/1.25	
2.66/1.25	   f(x, h(y)) -> h(f(f(h(a), y), x))
2.66/1.25	
2.66/1.25	
2.66/1.25	
2.66/1.25	Outermost Strategy.
2.66/1.25	
2.66/1.25	---------- Loop: ----------
2.66/1.25	
2.66/1.25	f(f(h(y'''), f(x''', h(y'))), f(h(y''), f(x'', h(y)))) -> f(f(h(y'''), f(x''', h(y'))), f(h(y''), h(f(f(h(a), y), x'')))) with rule f(x'''', h(y1)) -> h(f(f(h(a), y1), x'''')) at position [1,1] and matcher [x'''' / x'', y1 / y]
2.66/1.25	
2.66/1.25	f(f(h(y'''), f(x''', h(y'))), f(h(y''), h(f(f(h(a), y), x'')))) -> f(f(h(y'''), f(x''', h(y'))), h(f(f(h(a), f(f(h(a), y), x'')), h(y'')))) with rule f(x', h(y'1)) -> h(f(f(h(a), y'1), x')) at position [1] and matcher [x' / h(y''), y'1 / f(f(h(a), y), x'')]
2.66/1.25	
2.66/1.25	f(f(h(y'''), f(x''', h(y'))), h(f(f(h(a), f(f(h(a), y), x'')), h(y'')))) -> h(f(f(h(a), f(f(h(a), f(f(h(a), y), x'')), h(y''))), f(h(y'''), f(x''', h(y'))))) with rule f(x, h(y1)) -> h(f(f(h(a), y1), x)) at position [] and matcher [x / f(h(y'''), f(x''', h(y'))), y1 / f(f(h(a), f(f(h(a), y), x'')), h(y''))]
2.66/1.25	
2.66/1.25	Now an instance of the first term with Matcher [y / y', y' / y'', y'' / y''', x'' / x''', y''' / a, x''' / f(h(a), f(f(h(a), y), x''))] occurs in the last term at position [0].
2.66/1.25	
2.66/1.25	Context: h([])
2.66/1.25	
2.66/1.25	We used [THIEMANN_LOOPS_UNDER_STRATEGIES] to show that this Loop is an Outermost-Loop.
2.66/1.25	----------------------------------------
2.66/1.25	
2.66/1.25	(2)
2.66/1.25	NO
2.66/1.28	EOF