5.32/2.20	YES
5.32/2.22	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
5.32/2.22	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.32/2.22	
5.32/2.22	
5.32/2.22	Termination w.r.t. Q of the given QTRS could be proven:
5.32/2.22	
5.32/2.22	(0) QTRS
5.32/2.22	(1) QTRSRRRProof [EQUIVALENT, 30 ms]
5.32/2.22	(2) QTRS
5.32/2.22	(3) RisEmptyProof [EQUIVALENT, 2 ms]
5.32/2.22	(4) YES
5.32/2.22	
5.32/2.22	
5.32/2.22	----------------------------------------
5.32/2.22	
5.32/2.22	(0)
5.32/2.22	Obligation:
5.32/2.22	Q restricted rewrite system:
5.32/2.22	The TRS R consists of the following rules:
5.32/2.22	
5.32/2.22	   a(a(a(x1))) -> b(b(x1))
5.32/2.22	   b(b(b(x1))) -> c(d(x1))
5.32/2.22	   c(x1) -> a(a(x1))
5.32/2.22	   d(x1) -> c(x1)
5.32/2.22	
5.32/2.22	Q is empty.
5.32/2.22	
5.32/2.22	----------------------------------------
5.32/2.22	
5.32/2.22	(1) QTRSRRRProof (EQUIVALENT)
5.32/2.22	Used ordering:
5.32/2.22	Polynomial interpretation [POLO]:
5.32/2.22	
5.32/2.22	   POL(a(x_1)) = 11 + x_1
5.32/2.22	   POL(b(x_1)) = 16 + x_1
5.32/2.22	   POL(c(x_1)) = 23 + x_1
5.32/2.22	   POL(d(x_1)) = 24 + x_1
5.32/2.22	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
5.32/2.22	
5.32/2.22	   a(a(a(x1))) -> b(b(x1))
5.32/2.22	   b(b(b(x1))) -> c(d(x1))
5.32/2.22	   c(x1) -> a(a(x1))
5.32/2.22	   d(x1) -> c(x1)
5.32/2.22	
5.32/2.22	
5.32/2.22	
5.32/2.22	
5.32/2.22	----------------------------------------
5.32/2.22	
5.32/2.22	(2)
5.32/2.22	Obligation:
5.32/2.22	Q restricted rewrite system:
5.32/2.22	R is empty.
5.32/2.22	Q is empty.
5.32/2.22	
5.32/2.22	----------------------------------------
5.32/2.22	
5.32/2.22	(3) RisEmptyProof (EQUIVALENT)
5.32/2.22	The TRS R is empty. Hence, termination is trivially proven.
5.32/2.22	----------------------------------------
5.32/2.22	
5.32/2.22	(4)
5.32/2.22	YES
5.68/2.24	EOF