3.10/1.95	YES
3.10/1.96	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.10/1.96	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.10/1.96	
3.10/1.96	
3.10/1.96	Termination of the given CSR could be proven:
3.10/1.96	
3.10/1.96	(0) CSR
3.10/1.96	(1) CSDependencyPairsProof [EQUIVALENT, 0 ms]
3.10/1.96	(2) QCSDP
3.10/1.96	(3) QCSDPForwardInstantiationProcessor [EQUIVALENT, 0 ms]
3.10/1.96	(4) QCSDP
3.10/1.96	(5) PIsEmptyProof [EQUIVALENT, 0 ms]
3.10/1.96	(6) YES
3.10/1.96	
3.10/1.96	
3.10/1.96	----------------------------------------
3.10/1.96	
3.10/1.96	(0)
3.10/1.96	Obligation:
3.10/1.96	Context-sensitive rewrite system:
3.10/1.96	The TRS R consists of the following rules:
3.10/1.96	
3.10/1.96	   f(a, b, X) -> f(X, X, X)
3.10/1.96	   c -> a
3.10/1.96	   c -> b
3.10/1.96	
3.10/1.96	The replacement map contains the following entries:
3.10/1.96	
3.10/1.96	f: {1, 3}
3.10/1.96	a: empty set
3.10/1.96	b: empty set
3.10/1.96	c: empty set
3.10/1.96	
3.10/1.96	----------------------------------------
3.10/1.96	
3.10/1.96	(1) CSDependencyPairsProof (EQUIVALENT)
3.10/1.96	Using Improved CS-DPs [LPAR08] we result in the following initial Q-CSDP problem.
3.10/1.96	----------------------------------------
3.10/1.96	
3.10/1.96	(2)
3.10/1.96	Obligation:
3.10/1.96	Q-restricted context-sensitive dependency pair problem:
3.10/1.96	For all symbols f in {f_3, F_3} we have mu(f) = {1, 3}.
3.10/1.96	
3.10/1.96	The ordinary context-sensitive dependency pairs DP_o are:
3.10/1.96	   F(a, b, X) -> F(X, X, X)
3.10/1.96	
3.10/1.96	The TRS R consists of the following rules:
3.10/1.96	
3.10/1.96	   f(a, b, X) -> f(X, X, X)
3.10/1.96	   c -> a
3.10/1.96	   c -> b
3.10/1.96	
3.10/1.96	Q is empty.
3.10/1.96	
3.10/1.96	----------------------------------------
3.10/1.96	
3.10/1.96	(3) QCSDPForwardInstantiationProcessor (EQUIVALENT)
3.10/1.96	Using the Context-Sensitive Forward Instantiation[DA_EMMES] Processor
3.10/1.96	
3.10/1.96	the pair F(a, b, X) -> F(X, X, X)
3.10/1.96	
3.10/1.96	was transformed to the following new pairs: 
3.10/1.96	   F(a, b, b) -> F(b, b, b)
3.10/1.96	
3.10/1.96	
3.10/1.96	
3.10/1.96	----------------------------------------
3.10/1.96	
3.10/1.96	(4)
3.10/1.96	Obligation:
3.10/1.96	Q-restricted context-sensitive dependency pair problem:
3.10/1.96	For all symbols f in {f_3} we have mu(f) = {1, 3}.
3.10/1.96	
3.10/1.96	The TRS P consists of the following rules:
3.10/1.96	none
3.10/1.96	
3.10/1.96	The TRS R consists of the following rules:
3.10/1.96	
3.10/1.96	   f(a, b, X) -> f(X, X, X)
3.10/1.96	   c -> a
3.10/1.96	   c -> b
3.10/1.96	
3.10/1.96	Q is empty.
3.10/1.96	
3.10/1.96	----------------------------------------
3.10/1.96	
3.10/1.96	(5) PIsEmptyProof (EQUIVALENT)
3.10/1.96	The TRS P is empty. Hence, there is no (P,Q,R,mu)-chain.
3.10/1.96	----------------------------------------
3.10/1.96	
3.10/1.96	(6)
3.10/1.96	YES
3.10/2.00	EOF