3.18/1.63	YES
3.18/1.64	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.18/1.64	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.18/1.64	
3.18/1.64	
3.18/1.64	Termination w.r.t. Q of the given QTRS could be proven:
3.18/1.64	
3.18/1.64	(0) QTRS
3.18/1.64	(1) DependencyPairsProof [EQUIVALENT, 0 ms]
3.18/1.64	(2) QDP
3.18/1.64	(3) DependencyGraphProof [EQUIVALENT, 0 ms]
3.18/1.64	(4) TRUE
3.18/1.64	
3.18/1.64	
3.18/1.64	----------------------------------------
3.18/1.64	
3.18/1.64	(0)
3.18/1.64	Obligation:
3.18/1.64	Q restricted rewrite system:
3.18/1.64	The TRS R consists of the following rules:
3.18/1.64	
3.18/1.64	   f(X, g(X)) -> f(1, g(X))
3.18/1.64	   g(1) -> g(0)
3.18/1.64	
3.18/1.64	The set Q consists of the following terms:
3.18/1.64	
3.18/1.64	   f(x0, g(x0))
3.18/1.64	   g(1)
3.18/1.64	
3.18/1.64	
3.18/1.64	----------------------------------------
3.18/1.64	
3.18/1.64	(1) DependencyPairsProof (EQUIVALENT)
3.18/1.64	Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
3.18/1.64	----------------------------------------
3.18/1.64	
3.18/1.64	(2)
3.18/1.64	Obligation:
3.18/1.64	Q DP problem:
3.18/1.64	The TRS P consists of the following rules:
3.18/1.64	
3.18/1.64	   F(X, g(X)) -> F(1, g(X))
3.18/1.64	   G(1) -> G(0)
3.18/1.64	
3.18/1.64	The TRS R consists of the following rules:
3.18/1.64	
3.18/1.64	   f(X, g(X)) -> f(1, g(X))
3.18/1.64	   g(1) -> g(0)
3.18/1.64	
3.18/1.64	The set Q consists of the following terms:
3.18/1.64	
3.18/1.64	   f(x0, g(x0))
3.18/1.64	   g(1)
3.18/1.64	
3.18/1.64	We have to consider all minimal (P,Q,R)-chains.
3.18/1.64	----------------------------------------
3.18/1.64	
3.18/1.64	(3) DependencyGraphProof (EQUIVALENT)
3.18/1.64	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 2 less nodes.
3.18/1.64	----------------------------------------
3.18/1.64	
3.18/1.64	(4)
3.18/1.64	TRUE
3.22/1.65	EOF