4.34/1.94	YES
4.34/1.95	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
4.34/1.95	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.34/1.95	
4.34/1.95	
4.34/1.95	Termination w.r.t. Q of the given QTRS could be proven:
4.34/1.95	
4.34/1.95	(0) QTRS
4.34/1.95	(1) DependencyPairsProof [EQUIVALENT, 0 ms]
4.34/1.95	(2) QDP
4.34/1.95	(3) DependencyGraphProof [EQUIVALENT, 0 ms]
4.34/1.95	(4) TRUE
4.34/1.95	
4.34/1.95	
4.34/1.95	----------------------------------------
4.34/1.95	
4.34/1.95	(0)
4.34/1.95	Obligation:
4.34/1.95	Q restricted rewrite system:
4.34/1.95	The TRS R consists of the following rules:
4.34/1.95	
4.34/1.95	   a(b(a(b(x)))) -> b(a(b(a(a(b(x))))))
4.34/1.95	
4.34/1.95	The set Q consists of the following terms:
4.34/1.95	
4.34/1.95	   a(b(a(b(x0))))
4.34/1.95	
4.34/1.95	
4.34/1.95	----------------------------------------
4.34/1.95	
4.34/1.95	(1) DependencyPairsProof (EQUIVALENT)
4.34/1.95	Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
4.34/1.95	----------------------------------------
4.34/1.95	
4.34/1.95	(2)
4.34/1.95	Obligation:
4.34/1.95	Q DP problem:
4.34/1.95	The TRS P consists of the following rules:
4.34/1.95	
4.34/1.95	   A(b(a(b(x)))) -> A(b(a(a(b(x)))))
4.34/1.95	   A(b(a(b(x)))) -> A(a(b(x)))
4.34/1.95	
4.34/1.95	The TRS R consists of the following rules:
4.34/1.95	
4.34/1.95	   a(b(a(b(x)))) -> b(a(b(a(a(b(x))))))
4.34/1.95	
4.34/1.95	The set Q consists of the following terms:
4.34/1.95	
4.34/1.95	   a(b(a(b(x0))))
4.34/1.95	
4.34/1.95	We have to consider all minimal (P,Q,R)-chains.
4.34/1.95	----------------------------------------
4.34/1.95	
4.34/1.95	(3) DependencyGraphProof (EQUIVALENT)
4.34/1.95	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 2 less nodes.
4.34/1.95	----------------------------------------
4.34/1.95	
4.34/1.95	(4)
4.34/1.95	TRUE
4.34/1.98	EOF