3.55/1.79	YES
3.55/1.80	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.55/1.80	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.55/1.80	
3.55/1.80	
3.55/1.80	Termination w.r.t. Q of the given QTRS could be proven:
3.55/1.80	
3.55/1.80	(0) QTRS
3.55/1.80	(1) QTRSRRRProof [EQUIVALENT, 34 ms]
3.55/1.80	(2) QTRS
3.55/1.80	(3) RisEmptyProof [EQUIVALENT, 0 ms]
3.55/1.80	(4) YES
3.55/1.80	
3.55/1.80	
3.55/1.80	----------------------------------------
3.55/1.80	
3.55/1.80	(0)
3.55/1.80	Obligation:
3.55/1.80	Q restricted rewrite system:
3.55/1.80	The TRS R consists of the following rules:
3.55/1.80	
3.55/1.80	   a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z)))
3.55/1.80	   a____(X, nil) -> mark(X)
3.55/1.80	   a____(nil, X) -> mark(X)
3.55/1.80	   a__U11(tt) -> a__U12(tt)
3.55/1.80	   a__U12(tt) -> tt
3.55/1.80	   a__isNePal(__(I, __(P, I))) -> a__U11(tt)
3.55/1.80	   mark(__(X1, X2)) -> a____(mark(X1), mark(X2))
3.55/1.80	   mark(U11(X)) -> a__U11(mark(X))
3.55/1.80	   mark(U12(X)) -> a__U12(mark(X))
3.55/1.80	   mark(isNePal(X)) -> a__isNePal(mark(X))
3.55/1.80	   mark(nil) -> nil
3.55/1.80	   mark(tt) -> tt
3.55/1.80	   a____(X1, X2) -> __(X1, X2)
3.55/1.80	   a__U11(X) -> U11(X)
3.55/1.80	   a__U12(X) -> U12(X)
3.55/1.80	   a__isNePal(X) -> isNePal(X)
3.55/1.80	
3.55/1.80	The set Q consists of the following terms:
3.55/1.80	
3.55/1.80	   mark(__(x0, x1))
3.55/1.80	   mark(U11(x0))
3.55/1.80	   mark(U12(x0))
3.55/1.80	   mark(isNePal(x0))
3.55/1.80	   mark(nil)
3.55/1.80	   mark(tt)
3.55/1.80	   a____(x0, x1)
3.55/1.80	   a__U11(x0)
3.55/1.80	   a__U12(x0)
3.55/1.80	   a__isNePal(x0)
3.55/1.80	
3.55/1.80	
3.55/1.80	----------------------------------------
3.55/1.80	
3.55/1.80	(1) QTRSRRRProof (EQUIVALENT)
3.55/1.80	Used ordering:
3.55/1.80	Knuth-Bendix order [KBO] with precedence:mark_1 > a_____2 > ___2 > nil > a__isNePal_1 > a__U11_1 > isNePal_1 > U11_1 > a__U12_1 > U12_1 > tt
3.55/1.80	
3.55/1.80	and weight map:
3.55/1.80	
3.55/1.80	   nil=1
3.55/1.80	   tt=4
3.55/1.80	   mark_1=0
3.55/1.80	   a__U11_1=1
3.55/1.80	   a__U12_1=1
3.55/1.80	   a__isNePal_1=2
3.55/1.80	   U11_1=1
3.55/1.80	   U12_1=1
3.55/1.80	   isNePal_1=2
3.55/1.80	   ___2=0
3.55/1.80	   a_____2=0
3.55/1.80	
3.55/1.80	The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.55/1.80	
3.55/1.80	   a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z)))
3.55/1.80	   a____(X, nil) -> mark(X)
3.55/1.80	   a____(nil, X) -> mark(X)
3.55/1.80	   a__U11(tt) -> a__U12(tt)
3.55/1.80	   a__U12(tt) -> tt
3.55/1.80	   a__isNePal(__(I, __(P, I))) -> a__U11(tt)
3.55/1.80	   mark(__(X1, X2)) -> a____(mark(X1), mark(X2))
3.55/1.80	   mark(U11(X)) -> a__U11(mark(X))
3.55/1.80	   mark(U12(X)) -> a__U12(mark(X))
3.55/1.80	   mark(isNePal(X)) -> a__isNePal(mark(X))
3.55/1.80	   mark(nil) -> nil
3.55/1.80	   mark(tt) -> tt
3.55/1.80	   a____(X1, X2) -> __(X1, X2)
3.55/1.80	   a__U11(X) -> U11(X)
3.55/1.80	   a__U12(X) -> U12(X)
3.55/1.80	   a__isNePal(X) -> isNePal(X)
3.55/1.80	
3.55/1.80	
3.55/1.80	
3.55/1.80	
3.55/1.80	----------------------------------------
3.55/1.80	
3.55/1.80	(2)
3.55/1.80	Obligation:
3.55/1.80	Q restricted rewrite system:
3.55/1.80	R is empty.
3.55/1.80	The set Q consists of the following terms:
3.55/1.80	
3.55/1.80	   mark(__(x0, x1))
3.55/1.80	   mark(U11(x0))
3.55/1.80	   mark(U12(x0))
3.55/1.80	   mark(isNePal(x0))
3.55/1.80	   mark(nil)
3.55/1.80	   mark(tt)
3.55/1.80	   a____(x0, x1)
3.55/1.80	   a__U11(x0)
3.55/1.80	   a__U12(x0)
3.55/1.80	   a__isNePal(x0)
3.55/1.80	
3.55/1.80	
3.55/1.80	----------------------------------------
3.55/1.80	
3.55/1.80	(3) RisEmptyProof (EQUIVALENT)
3.55/1.80	The TRS R is empty. Hence, termination is trivially proven.
3.55/1.80	----------------------------------------
3.55/1.80	
3.55/1.80	(4)
3.55/1.80	YES
3.60/1.86	EOF