3.02/1.41	YES
3.02/1.42	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.02/1.42	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.02/1.42	
3.02/1.42	
3.02/1.42	Termination of the given CSR could be proven:
3.02/1.42	
3.02/1.42	(0) CSR
3.02/1.42	(1) CSRRRRProof [EQUIVALENT, 69 ms]
3.02/1.42	(2) CSR
3.02/1.42	(3) CSRRRRProof [EQUIVALENT, 0 ms]
3.02/1.42	(4) CSR
3.02/1.42	(5) CSRInnermostProof [EQUIVALENT, 0 ms]
3.02/1.42	(6) CSR
3.02/1.42	(7) CSDependencyPairsProof [EQUIVALENT, 0 ms]
3.02/1.42	(8) QCSDP
3.02/1.42	(9) QCSDependencyGraphProof [EQUIVALENT, 2 ms]
3.02/1.42	(10) TRUE
3.02/1.42	
3.02/1.42	
3.02/1.42	----------------------------------------
3.02/1.42	
3.02/1.42	(0)
3.02/1.42	Obligation:
3.02/1.42	Context-sensitive rewrite system:
3.02/1.42	The TRS R consists of the following rules:
3.02/1.42	
3.02/1.42	   f(a, b, X) -> f(X, X, X)
3.02/1.42	   c -> a
3.02/1.42	   c -> b
3.02/1.42	
3.02/1.42	The replacement map contains the following entries:
3.02/1.42	
3.02/1.42	f: {3}
3.02/1.42	a: empty set
3.02/1.42	b: empty set
3.02/1.42	c: empty set
3.02/1.42	
3.02/1.42	----------------------------------------
3.02/1.42	
3.02/1.42	(1) CSRRRRProof (EQUIVALENT)
3.02/1.42	The following CSR is given: Context-sensitive rewrite system:
3.02/1.42	The TRS R consists of the following rules:
3.02/1.42	
3.02/1.42	   f(a, b, X) -> f(X, X, X)
3.02/1.42	   c -> a
3.02/1.42	   c -> b
3.02/1.42	
3.02/1.42	The replacement map contains the following entries:
3.02/1.42	
3.02/1.42	f: {3}
3.02/1.42	a: empty set
3.02/1.42	b: empty set
3.02/1.42	c: empty set
3.02/1.42	Used ordering:
3.02/1.42	Polynomial interpretation [POLO]:
3.02/1.42	
3.02/1.42	   POL(a) = 1
3.02/1.42	   POL(b) = 0
3.02/1.42	   POL(c) = 1
3.02/1.42	   POL(f(x_1, x_2, x_3)) = x_3
3.02/1.42	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.02/1.42	
3.02/1.42	   c -> b
3.02/1.42	
3.02/1.42	
3.02/1.42	
3.02/1.42	
3.02/1.42	----------------------------------------
3.02/1.42	
3.02/1.42	(2)
3.02/1.42	Obligation:
3.02/1.42	Context-sensitive rewrite system:
3.02/1.42	The TRS R consists of the following rules:
3.02/1.42	
3.02/1.42	   f(a, b, X) -> f(X, X, X)
3.02/1.42	   c -> a
3.02/1.42	
3.02/1.42	The replacement map contains the following entries:
3.02/1.42	
3.02/1.42	f: {3}
3.02/1.42	a: empty set
3.02/1.42	b: empty set
3.02/1.42	c: empty set
3.02/1.42	
3.02/1.42	----------------------------------------
3.02/1.42	
3.02/1.42	(3) CSRRRRProof (EQUIVALENT)
3.02/1.42	The following CSR is given: Context-sensitive rewrite system:
3.02/1.42	The TRS R consists of the following rules:
3.02/1.42	
3.02/1.42	   f(a, b, X) -> f(X, X, X)
3.02/1.42	   c -> a
3.02/1.42	
3.02/1.42	The replacement map contains the following entries:
3.02/1.42	
3.02/1.42	f: {3}
3.02/1.42	a: empty set
3.02/1.42	b: empty set
3.02/1.42	c: empty set
3.02/1.42	Used ordering:
3.02/1.42	Polynomial interpretation [POLO]:
3.02/1.42	
3.02/1.42	   POL(a) = 0
3.02/1.42	   POL(b) = 0
3.02/1.42	   POL(c) = 1
3.02/1.42	   POL(f(x_1, x_2, x_3)) = x_3
3.02/1.42	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.02/1.42	
3.02/1.42	   c -> a
3.02/1.42	
3.02/1.42	
3.02/1.42	
3.02/1.42	
3.02/1.42	----------------------------------------
3.02/1.42	
3.02/1.42	(4)
3.02/1.42	Obligation:
3.02/1.42	Context-sensitive rewrite system:
3.02/1.42	The TRS R consists of the following rules:
3.02/1.42	
3.02/1.42	   f(a, b, X) -> f(X, X, X)
3.02/1.42	
3.02/1.42	The replacement map contains the following entries:
3.02/1.42	
3.02/1.42	f: {3}
3.02/1.42	a: empty set
3.02/1.42	b: empty set
3.02/1.42	
3.02/1.42	----------------------------------------
3.02/1.42	
3.02/1.42	(5) CSRInnermostProof (EQUIVALENT)
3.02/1.42	The CSR is orthogonal. By [CS_Inn] we can switch to innermost.
3.02/1.42	----------------------------------------
3.02/1.42	
3.02/1.42	(6)
3.02/1.42	Obligation:
3.02/1.42	Context-sensitive rewrite system:
3.02/1.42	The TRS R consists of the following rules:
3.02/1.42	
3.02/1.42	   f(a, b, X) -> f(X, X, X)
3.02/1.42	
3.02/1.42	The replacement map contains the following entries:
3.02/1.42	
3.02/1.42	f: {3}
3.02/1.42	a: empty set
3.02/1.42	b: empty set
3.02/1.42	
3.02/1.42	
3.02/1.42	Innermost Strategy.
3.02/1.42	
3.02/1.42	----------------------------------------
3.02/1.42	
3.02/1.42	(7) CSDependencyPairsProof (EQUIVALENT)
3.02/1.42	Using Improved CS-DPs [LPAR08] we result in the following initial Q-CSDP problem.
3.02/1.42	----------------------------------------
3.02/1.42	
3.02/1.42	(8)
3.02/1.42	Obligation:
3.02/1.42	Q-restricted context-sensitive dependency pair problem:
3.02/1.42	For all symbols f in {f_3, F_3} we have mu(f) = {3}.
3.02/1.42	
3.02/1.42	The ordinary context-sensitive dependency pairs DP_o are:
3.02/1.42	   F(a, b, X) -> F(X, X, X)
3.02/1.42	
3.02/1.42	The TRS R consists of the following rules:
3.02/1.42	
3.02/1.42	   f(a, b, X) -> f(X, X, X)
3.02/1.42	
3.02/1.42	The set Q consists of the following terms:
3.02/1.42	
3.02/1.42	   f(a, b, x0)
3.02/1.42	
3.02/1.42	
3.02/1.42	----------------------------------------
3.02/1.42	
3.02/1.42	(9) QCSDependencyGraphProof (EQUIVALENT)
3.02/1.42	The approximation of the Context-Sensitive Dependency Graph [LPAR08] contains 0 SCCs.
3.02/1.42	The rules F(a, b, z0) -> F(z0, z0, z0) and F(a, b, x0) -> F(x0, x0, x0) form no chain, because ECap^mu(F(z0, z0, z0)) = F(z0, z0, z0) does not unify with F(a, b, x0). 
3.02/1.42	----------------------------------------
3.02/1.42	
3.02/1.42	(10)
3.02/1.42	TRUE
3.14/1.81	EOF