3.56/1.74	YES
3.56/1.75	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.56/1.75	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.56/1.75	
3.56/1.75	
3.56/1.75	Termination w.r.t. Q of the given QTRS could be proven:
3.56/1.75	
3.56/1.75	(0) QTRS
3.56/1.75	(1) QTRSRRRProof [EQUIVALENT, 33 ms]
3.56/1.75	(2) QTRS
3.56/1.75	(3) RisEmptyProof [EQUIVALENT, 0 ms]
3.56/1.75	(4) YES
3.56/1.75	
3.56/1.75	
3.56/1.75	----------------------------------------
3.56/1.75	
3.56/1.75	(0)
3.56/1.75	Obligation:
3.56/1.75	Q restricted rewrite system:
3.56/1.75	The TRS R consists of the following rules:
3.56/1.75	
3.56/1.75	   a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z)))
3.56/1.75	   a____(X, nil) -> mark(X)
3.56/1.75	   a____(nil, X) -> mark(X)
3.56/1.75	   a__and(tt, X) -> mark(X)
3.56/1.75	   a__isList(V) -> a__isNeList(V)
3.56/1.75	   a__isList(nil) -> tt
3.56/1.75	   a__isList(__(V1, V2)) -> a__and(a__isList(V1), isList(V2))
3.56/1.75	   a__isNeList(V) -> a__isQid(V)
3.56/1.75	   a__isNeList(__(V1, V2)) -> a__and(a__isList(V1), isNeList(V2))
3.56/1.75	   a__isNeList(__(V1, V2)) -> a__and(a__isNeList(V1), isList(V2))
3.56/1.75	   a__isNePal(V) -> a__isQid(V)
3.56/1.75	   a__isNePal(__(I, __(P, I))) -> a__and(a__isQid(I), isPal(P))
3.56/1.75	   a__isPal(V) -> a__isNePal(V)
3.56/1.75	   a__isPal(nil) -> tt
3.56/1.75	   a__isQid(a) -> tt
3.56/1.75	   a__isQid(e) -> tt
3.56/1.75	   a__isQid(i) -> tt
3.56/1.75	   a__isQid(o) -> tt
3.56/1.75	   a__isQid(u) -> tt
3.56/1.75	   mark(__(X1, X2)) -> a____(mark(X1), mark(X2))
3.56/1.75	   mark(and(X1, X2)) -> a__and(mark(X1), X2)
3.56/1.75	   mark(isList(X)) -> a__isList(X)
3.56/1.75	   mark(isNeList(X)) -> a__isNeList(X)
3.56/1.75	   mark(isQid(X)) -> a__isQid(X)
3.56/1.75	   mark(isNePal(X)) -> a__isNePal(X)
3.56/1.75	   mark(isPal(X)) -> a__isPal(X)
3.56/1.75	   mark(nil) -> nil
3.56/1.75	   mark(tt) -> tt
3.56/1.75	   mark(a) -> a
3.56/1.75	   mark(e) -> e
3.56/1.75	   mark(i) -> i
3.56/1.75	   mark(o) -> o
3.56/1.75	   mark(u) -> u
3.56/1.75	   a____(X1, X2) -> __(X1, X2)
3.56/1.75	   a__and(X1, X2) -> and(X1, X2)
3.56/1.75	   a__isList(X) -> isList(X)
3.56/1.75	   a__isNeList(X) -> isNeList(X)
3.56/1.75	   a__isQid(X) -> isQid(X)
3.56/1.75	   a__isNePal(X) -> isNePal(X)
3.56/1.75	   a__isPal(X) -> isPal(X)
3.56/1.75	
3.56/1.75	The set Q consists of the following terms:
3.56/1.75	
3.56/1.75	   a__isList(x0)
3.56/1.75	   a__isNeList(x0)
3.56/1.75	   a__isNePal(x0)
3.56/1.75	   a__isPal(x0)
3.56/1.75	   mark(__(x0, x1))
3.56/1.75	   mark(and(x0, x1))
3.56/1.75	   mark(isList(x0))
3.56/1.75	   mark(isNeList(x0))
3.56/1.75	   mark(isQid(x0))
3.56/1.75	   mark(isNePal(x0))
3.56/1.75	   mark(isPal(x0))
3.56/1.75	   mark(nil)
3.56/1.75	   mark(tt)
3.56/1.75	   mark(a)
3.56/1.75	   mark(e)
3.56/1.75	   mark(i)
3.56/1.75	   mark(o)
3.56/1.75	   mark(u)
3.56/1.75	   a____(x0, x1)
3.56/1.75	   a__and(x0, x1)
3.56/1.75	   a__isQid(x0)
3.56/1.75	
3.56/1.75	
3.56/1.75	----------------------------------------
3.56/1.75	
3.56/1.75	(1) QTRSRRRProof (EQUIVALENT)
3.56/1.75	Used ordering:
3.56/1.75	Knuth-Bendix order [KBO] with precedence:mark_1 > a > nil > a__and_2 > and_2 > u > o > i > a__isNeList_1 > isNeList_1 > a__isNePal_1 > isNePal_1 > a__isQid_1 > isQid_1 > e > a_____2 > a__isPal_1 > a__isList_1 > isList_1 > ___2 > isPal_1 > tt
3.56/1.75	
3.56/1.75	and weight map:
3.56/1.75	
3.56/1.75	   nil=1
3.56/1.75	   tt=3
3.56/1.75	   a=2
3.56/1.75	   e=2
3.56/1.75	   i=2
3.56/1.75	   o=2
3.56/1.75	   u=2
3.56/1.75	   mark_1=0
3.56/1.75	   a__isList_1=3
3.56/1.75	   a__isNeList_1=2
3.56/1.75	   isList_1=3
3.56/1.75	   a__isQid_1=1
3.56/1.75	   isNeList_1=2
3.56/1.75	   a__isNePal_1=2
3.56/1.75	   isPal_1=9
3.56/1.75	   a__isPal_1=9
3.56/1.75	   isQid_1=1
3.56/1.75	   isNePal_1=2
3.56/1.75	   ___2=4
3.56/1.75	   a_____2=4
3.56/1.75	   a__and_2=0
3.56/1.75	   and_2=0
3.56/1.75	
3.56/1.75	The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.56/1.75	
3.56/1.75	   a____(__(X, Y), Z) -> a____(mark(X), a____(mark(Y), mark(Z)))
3.56/1.75	   a____(X, nil) -> mark(X)
3.56/1.75	   a____(nil, X) -> mark(X)
3.56/1.75	   a__and(tt, X) -> mark(X)
3.56/1.75	   a__isList(V) -> a__isNeList(V)
3.56/1.75	   a__isList(nil) -> tt
3.56/1.75	   a__isList(__(V1, V2)) -> a__and(a__isList(V1), isList(V2))
3.56/1.75	   a__isNeList(V) -> a__isQid(V)
3.56/1.75	   a__isNeList(__(V1, V2)) -> a__and(a__isList(V1), isNeList(V2))
3.56/1.75	   a__isNeList(__(V1, V2)) -> a__and(a__isNeList(V1), isList(V2))
3.56/1.75	   a__isNePal(V) -> a__isQid(V)
3.56/1.75	   a__isNePal(__(I, __(P, I))) -> a__and(a__isQid(I), isPal(P))
3.56/1.75	   a__isPal(V) -> a__isNePal(V)
3.56/1.75	   a__isPal(nil) -> tt
3.56/1.75	   a__isQid(a) -> tt
3.56/1.75	   a__isQid(e) -> tt
3.56/1.75	   a__isQid(i) -> tt
3.56/1.75	   a__isQid(o) -> tt
3.56/1.75	   a__isQid(u) -> tt
3.56/1.75	   mark(__(X1, X2)) -> a____(mark(X1), mark(X2))
3.56/1.75	   mark(and(X1, X2)) -> a__and(mark(X1), X2)
3.56/1.75	   mark(isList(X)) -> a__isList(X)
3.56/1.75	   mark(isNeList(X)) -> a__isNeList(X)
3.56/1.75	   mark(isQid(X)) -> a__isQid(X)
3.56/1.75	   mark(isNePal(X)) -> a__isNePal(X)
3.56/1.75	   mark(isPal(X)) -> a__isPal(X)
3.56/1.75	   mark(nil) -> nil
3.56/1.75	   mark(tt) -> tt
3.56/1.75	   mark(a) -> a
3.56/1.75	   mark(e) -> e
3.56/1.75	   mark(i) -> i
3.56/1.75	   mark(o) -> o
3.56/1.75	   mark(u) -> u
3.56/1.75	   a____(X1, X2) -> __(X1, X2)
3.56/1.75	   a__and(X1, X2) -> and(X1, X2)
3.56/1.75	   a__isList(X) -> isList(X)
3.56/1.75	   a__isNeList(X) -> isNeList(X)
3.56/1.75	   a__isQid(X) -> isQid(X)
3.56/1.75	   a__isNePal(X) -> isNePal(X)
3.56/1.75	   a__isPal(X) -> isPal(X)
3.56/1.75	
3.56/1.75	
3.56/1.75	
3.56/1.75	
3.56/1.75	----------------------------------------
3.56/1.75	
3.56/1.75	(2)
3.56/1.75	Obligation:
3.56/1.75	Q restricted rewrite system:
3.56/1.75	R is empty.
3.56/1.75	The set Q consists of the following terms:
3.56/1.75	
3.56/1.75	   a__isList(x0)
3.56/1.75	   a__isNeList(x0)
3.56/1.75	   a__isNePal(x0)
3.56/1.75	   a__isPal(x0)
3.56/1.75	   mark(__(x0, x1))
3.56/1.75	   mark(and(x0, x1))
3.56/1.75	   mark(isList(x0))
3.56/1.75	   mark(isNeList(x0))
3.56/1.75	   mark(isQid(x0))
3.56/1.75	   mark(isNePal(x0))
3.56/1.75	   mark(isPal(x0))
3.56/1.75	   mark(nil)
3.56/1.75	   mark(tt)
3.56/1.75	   mark(a)
3.56/1.75	   mark(e)
3.56/1.75	   mark(i)
3.56/1.75	   mark(o)
3.56/1.75	   mark(u)
3.56/1.75	   a____(x0, x1)
3.56/1.75	   a__and(x0, x1)
3.56/1.75	   a__isQid(x0)
3.56/1.75	
3.56/1.75	
3.56/1.75	----------------------------------------
3.56/1.75	
3.56/1.75	(3) RisEmptyProof (EQUIVALENT)
3.56/1.75	The TRS R is empty. Hence, termination is trivially proven.
3.56/1.75	----------------------------------------
3.56/1.75	
3.56/1.75	(4)
3.56/1.75	YES
3.56/1.76	EOF