3.44/1.73	YES
3.44/1.74	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.44/1.74	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.44/1.74	
3.44/1.74	
3.44/1.74	Termination w.r.t. Q of the given QTRS could be proven:
3.44/1.74	
3.44/1.74	(0) QTRS
3.44/1.74	(1) DependencyPairsProof [EQUIVALENT, 0 ms]
3.44/1.74	(2) QDP
3.44/1.74	(3) DependencyGraphProof [EQUIVALENT, 0 ms]
3.44/1.74	(4) TRUE
3.44/1.74	
3.44/1.74	
3.44/1.74	----------------------------------------
3.44/1.74	
3.44/1.74	(0)
3.44/1.74	Obligation:
3.44/1.74	Q restricted rewrite system:
3.44/1.74	The TRS R consists of the following rules:
3.44/1.74	
3.44/1.74	   f(a(x), y) -> g(x, y)
3.44/1.74	   g(b, y) -> f(y, y)
3.44/1.74	   a(b) -> c
3.44/1.74	
3.44/1.74	The set Q consists of the following terms:
3.44/1.74	
3.44/1.74	   f(a(x0), x1)
3.44/1.74	   g(b, x0)
3.44/1.74	   a(b)
3.44/1.74	
3.44/1.74	
3.44/1.74	----------------------------------------
3.44/1.74	
3.44/1.74	(1) DependencyPairsProof (EQUIVALENT)
3.44/1.74	Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem.
3.44/1.74	----------------------------------------
3.44/1.74	
3.44/1.74	(2)
3.44/1.74	Obligation:
3.44/1.74	Q DP problem:
3.44/1.74	The TRS P consists of the following rules:
3.44/1.74	
3.44/1.74	   F(a(x), y) -> G(x, y)
3.44/1.74	   G(b, y) -> F(y, y)
3.44/1.74	
3.44/1.74	The TRS R consists of the following rules:
3.44/1.74	
3.44/1.74	   f(a(x), y) -> g(x, y)
3.44/1.74	   g(b, y) -> f(y, y)
3.44/1.74	   a(b) -> c
3.44/1.74	
3.44/1.74	The set Q consists of the following terms:
3.44/1.74	
3.44/1.74	   f(a(x0), x1)
3.44/1.74	   g(b, x0)
3.44/1.74	   a(b)
3.44/1.74	
3.44/1.74	We have to consider all minimal (P,Q,R)-chains.
3.44/1.74	----------------------------------------
3.44/1.74	
3.44/1.74	(3) DependencyGraphProof (EQUIVALENT)
3.44/1.74	The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 2 less nodes.
3.44/1.74	----------------------------------------
3.44/1.74	
3.44/1.74	(4)
3.44/1.74	TRUE
3.44/1.76	EOF