3.22/1.70	YES
3.27/1.70	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.27/1.70	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.27/1.70	
3.27/1.70	
3.27/1.70	Termination of the given CSR could be proven:
3.27/1.70	
3.27/1.70	(0) CSR
3.27/1.70	(1) CSDependencyPairsProof [EQUIVALENT, 0 ms]
3.27/1.70	(2) QCSDP
3.27/1.70	(3) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
3.27/1.70	(4) QCSDP
3.27/1.70	(5) QCSUsableRulesProof [EQUIVALENT, 0 ms]
3.27/1.70	(6) QCSDP
3.27/1.70	(7) QCSDPInstantiationProcessor [EQUIVALENT, 0 ms]
3.27/1.70	(8) QCSDP
3.27/1.70	(9) PIsEmptyProof [EQUIVALENT, 0 ms]
3.27/1.70	(10) YES
3.27/1.70	
3.27/1.70	
3.27/1.70	----------------------------------------
3.27/1.70	
3.27/1.70	(0)
3.27/1.70	Obligation:
3.27/1.70	Context-sensitive rewrite system:
3.27/1.70	The TRS R consists of the following rules:
3.27/1.70	
3.27/1.70	   f(a, X, X) -> f(X, b, b)
3.27/1.70	   b -> a
3.27/1.70	
3.27/1.70	The replacement map contains the following entries:
3.27/1.70	
3.27/1.70	f: {2}
3.27/1.70	a: empty set
3.27/1.70	b: empty set
3.27/1.70	
3.27/1.70	----------------------------------------
3.27/1.70	
3.27/1.70	(1) CSDependencyPairsProof (EQUIVALENT)
3.27/1.70	Using Improved CS-DPs [LPAR08] we result in the following initial Q-CSDP problem.
3.27/1.70	----------------------------------------
3.27/1.70	
3.27/1.70	(2)
3.27/1.70	Obligation:
3.27/1.70	Q-restricted context-sensitive dependency pair problem:
3.27/1.70	For all symbols f in {f_3, F_3} we have mu(f) = {2}.
3.27/1.70	
3.27/1.70	The ordinary context-sensitive dependency pairs DP_o are:
3.27/1.70	   F(a, X, X) -> F(X, b, b)
3.27/1.70	   F(a, X, X) -> B
3.27/1.70	
3.27/1.70	The TRS R consists of the following rules:
3.27/1.70	
3.27/1.70	   f(a, X, X) -> f(X, b, b)
3.27/1.70	   b -> a
3.27/1.70	
3.27/1.70	Q is empty.
3.27/1.70	
3.27/1.70	----------------------------------------
3.27/1.70	
3.27/1.70	(3) QCSDependencyGraphProof (EQUIVALENT)
3.27/1.70	The approximation of the Context-Sensitive Dependency Graph [LPAR08] contains 1 SCC with 1 less node.
3.27/1.70	
3.27/1.70	----------------------------------------
3.27/1.70	
3.27/1.70	(4)
3.27/1.70	Obligation:
3.27/1.70	Q-restricted context-sensitive dependency pair problem:
3.27/1.70	For all symbols f in {f_3, F_3} we have mu(f) = {2}.
3.27/1.70	
3.27/1.70	The TRS P consists of the following rules:
3.27/1.70	
3.27/1.70	   F(a, X, X) -> F(X, b, b)
3.27/1.70	
3.27/1.70	The TRS R consists of the following rules:
3.27/1.70	
3.27/1.70	   f(a, X, X) -> f(X, b, b)
3.27/1.70	   b -> a
3.27/1.70	
3.27/1.70	Q is empty.
3.27/1.70	
3.27/1.70	----------------------------------------
3.27/1.70	
3.27/1.70	(5) QCSUsableRulesProof (EQUIVALENT)
3.27/1.70	The following rules are not useable [DA_EMMES] and can be deleted:
3.27/1.70	
3.27/1.70	   f(a, x0, x0) -> f(x0, b, b)
3.27/1.70	
3.27/1.70	----------------------------------------
3.27/1.70	
3.27/1.70	(6)
3.27/1.70	Obligation:
3.27/1.70	Q-restricted context-sensitive dependency pair problem:
3.27/1.70	For all symbols f in {F_3} we have mu(f) = {2}.
3.27/1.70	
3.27/1.70	The TRS P consists of the following rules:
3.27/1.70	
3.27/1.70	   F(a, X, X) -> F(X, b, b)
3.27/1.70	
3.27/1.70	The TRS R consists of the following rules:
3.27/1.70	
3.27/1.70	   b -> a
3.27/1.70	
3.27/1.70	Q is empty.
3.27/1.70	
3.27/1.70	----------------------------------------
3.27/1.70	
3.27/1.70	(7) QCSDPInstantiationProcessor (EQUIVALENT)
3.27/1.70	Using the Context-Sensitive Instantiation[LPAR08,DA_EMMES] Processor
3.27/1.70	
3.27/1.70	the pair F(a, X, X) -> F(X, b, b)
3.27/1.70	
3.27/1.70	was transformed to the following new pairs: 
3.27/1.70	   F(a, b, b) -> F(b, b, b)
3.27/1.70	
3.27/1.70	
3.27/1.70	
3.27/1.70	----------------------------------------
3.27/1.70	
3.27/1.70	(8)
3.27/1.70	Obligation:
3.27/1.70	Q-restricted context-sensitive dependency pair problem:
3.27/1.70	
3.27/1.70	The TRS P consists of the following rules:
3.27/1.70	none
3.27/1.70	
3.27/1.70	The TRS R consists of the following rules:
3.27/1.70	
3.27/1.70	   b -> a
3.27/1.70	
3.27/1.70	Q is empty.
3.27/1.70	
3.27/1.70	----------------------------------------
3.27/1.70	
3.27/1.70	(9) PIsEmptyProof (EQUIVALENT)
3.27/1.70	The TRS P is empty. Hence, there is no (P,Q,R,mu)-chain.
3.27/1.70	----------------------------------------
3.27/1.70	
3.27/1.70	(10)
3.27/1.70	YES
3.29/1.80	EOF