2.92/1.38	YES
2.92/1.39	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.92/1.39	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.92/1.39	
2.92/1.39	
2.92/1.39	Termination of the given CSR could be proven:
2.92/1.39	
2.92/1.39	(0) CSR
2.92/1.39	(1) CSRRRRProof [EQUIVALENT, 65 ms]
2.92/1.39	(2) CSR
2.92/1.39	(3) CSRRRRProof [EQUIVALENT, 0 ms]
2.92/1.39	(4) CSR
2.92/1.39	(5) RisEmptyProof [EQUIVALENT, 0 ms]
2.92/1.39	(6) YES
2.92/1.39	
2.92/1.39	
2.92/1.39	----------------------------------------
2.92/1.39	
2.92/1.39	(0)
2.92/1.39	Obligation:
2.92/1.39	Context-sensitive rewrite system:
2.92/1.39	The TRS R consists of the following rules:
2.92/1.39	
2.92/1.39	   __(__(X, Y), Z) -> __(X, __(Y, Z))
2.92/1.39	   __(X, nil) -> X
2.92/1.39	   __(nil, X) -> X
2.92/1.39	   U11(tt) -> U12(tt)
2.92/1.39	   U12(tt) -> tt
2.92/1.39	   isNePal(__(I, __(P, I))) -> U11(tt)
2.92/1.39	
2.92/1.39	The replacement map contains the following entries:
2.92/1.39	
2.92/1.39	__: {1, 2}
2.92/1.39	nil: empty set
2.92/1.39	U11: {1}
2.92/1.39	tt: empty set
2.92/1.39	U12: {1}
2.92/1.39	isNePal: {1}
2.92/1.39	
2.92/1.39	----------------------------------------
2.92/1.39	
2.92/1.39	(1) CSRRRRProof (EQUIVALENT)
2.92/1.39	The following CSR is given: Context-sensitive rewrite system:
2.92/1.39	The TRS R consists of the following rules:
2.92/1.39	
2.92/1.39	   __(__(X, Y), Z) -> __(X, __(Y, Z))
2.92/1.39	   __(X, nil) -> X
2.92/1.39	   __(nil, X) -> X
2.92/1.39	   U11(tt) -> U12(tt)
2.92/1.39	   U12(tt) -> tt
2.92/1.39	   isNePal(__(I, __(P, I))) -> U11(tt)
2.92/1.39	
2.92/1.39	The replacement map contains the following entries:
2.92/1.39	
2.92/1.39	__: {1, 2}
2.92/1.39	nil: empty set
2.92/1.39	U11: {1}
2.92/1.39	tt: empty set
2.92/1.39	U12: {1}
2.92/1.39	isNePal: {1}
2.92/1.39	Used ordering:
2.92/1.39	Matrix interpretation [MATRO] to (N^2, +, *, >=, >) :
2.92/1.39	
2.92/1.39	   <<<
2.92/1.39	 POL(__(x_1, x_2)) =  	[[1], [1]] 	 +  	[[1, 1], [0, 1]] 	* 	x_1 	 +  	[[1, 0], [0, 1]] 	* 	x_2
2.92/1.39	>>>
2.92/1.39	
2.92/1.39	   <<<
2.92/1.39	 POL(nil) =  	[[0], [1]]
2.92/1.39	>>>
2.92/1.39	
2.92/1.39	   <<<
2.92/1.39	 POL(U11(x_1)) =  	[[1], [1]] 	 +  	[[1, 0], [1, 1]] 	* 	x_1
2.92/1.39	>>>
2.92/1.39	
2.92/1.39	   <<<
2.92/1.39	 POL(tt) =  	[[1], [1]]
2.92/1.39	>>>
2.92/1.39	
2.92/1.39	   <<<
2.92/1.39	 POL(U12(x_1)) =  	[[0], [1]] 	 +  	[[1, 1], [1, 1]] 	* 	x_1
2.92/1.39	>>>
2.92/1.39	
2.92/1.39	   <<<
2.92/1.39	 POL(isNePal(x_1)) =  	[[1], [1]] 	 +  	[[1, 1], [1, 1]] 	* 	x_1
2.92/1.39	>>>
2.92/1.39	
2.92/1.39	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
2.92/1.39	
2.92/1.39	   __(__(X, Y), Z) -> __(X, __(Y, Z))
2.92/1.39	   __(X, nil) -> X
2.92/1.39	   __(nil, X) -> X
2.92/1.39	   U12(tt) -> tt
2.92/1.39	   isNePal(__(I, __(P, I))) -> U11(tt)
2.92/1.39	
2.92/1.39	
2.92/1.39	
2.92/1.39	
2.92/1.39	----------------------------------------
2.92/1.39	
2.92/1.39	(2)
2.92/1.39	Obligation:
2.92/1.39	Context-sensitive rewrite system:
2.92/1.39	The TRS R consists of the following rules:
2.92/1.39	
2.92/1.39	   U11(tt) -> U12(tt)
2.92/1.39	
2.92/1.39	The replacement map contains the following entries:
2.92/1.39	
2.92/1.39	U11: {1}
2.92/1.39	tt: empty set
2.92/1.39	U12: {1}
2.92/1.39	
2.92/1.39	----------------------------------------
2.92/1.39	
2.92/1.39	(3) CSRRRRProof (EQUIVALENT)
2.92/1.39	The following CSR is given: Context-sensitive rewrite system:
2.92/1.39	The TRS R consists of the following rules:
2.92/1.39	
2.92/1.39	   U11(tt) -> U12(tt)
2.92/1.39	
2.92/1.39	The replacement map contains the following entries:
2.92/1.39	
2.92/1.39	U11: {1}
2.92/1.39	tt: empty set
2.92/1.39	U12: {1}
2.92/1.39	Used ordering:
2.92/1.39	Polynomial interpretation [POLO]:
2.92/1.39	
2.92/1.39	   POL(U11(x_1)) = 1 + x_1
2.92/1.39	   POL(U12(x_1)) = x_1
2.92/1.39	   POL(tt) = 0
2.92/1.39	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
2.92/1.39	
2.92/1.39	   U11(tt) -> U12(tt)
2.92/1.39	
2.92/1.39	
2.92/1.39	
2.92/1.39	
2.92/1.39	----------------------------------------
2.92/1.39	
2.92/1.39	(4)
2.92/1.39	Obligation:
2.92/1.39	Context-sensitive rewrite system:
2.92/1.39	R is empty.
2.92/1.39	
2.92/1.39	----------------------------------------
2.92/1.39	
2.92/1.39	(5) RisEmptyProof (EQUIVALENT)
2.92/1.39	The CSR R is empty. Hence, termination is trivially proven.
2.92/1.39	----------------------------------------
2.92/1.39	
2.92/1.39	(6)
2.92/1.39	YES
3.05/1.43	EOF