3.32/1.48	YES
3.32/1.49	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.32/1.49	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.32/1.49	
3.32/1.49	
3.32/1.49	Termination of the given CSR could be proven:
3.32/1.49	
3.32/1.49	(0) CSR
3.32/1.49	(1) CSRRRRProof [EQUIVALENT, 76 ms]
3.32/1.49	(2) CSR
3.32/1.49	(3) CSRRRRProof [EQUIVALENT, 9 ms]
3.32/1.49	(4) CSR
3.32/1.49	(5) CSRRRRProof [EQUIVALENT, 0 ms]
3.32/1.49	(6) CSR
3.32/1.49	(7) CSRRRRProof [EQUIVALENT, 0 ms]
3.32/1.49	(8) CSR
3.32/1.49	(9) CSRRRRProof [EQUIVALENT, 0 ms]
3.32/1.49	(10) CSR
3.32/1.49	(11) RisEmptyProof [EQUIVALENT, 0 ms]
3.32/1.49	(12) YES
3.32/1.49	
3.32/1.49	
3.32/1.49	----------------------------------------
3.32/1.49	
3.32/1.49	(0)
3.32/1.49	Obligation:
3.32/1.49	Context-sensitive rewrite system:
3.32/1.49	The TRS R consists of the following rules:
3.32/1.49	
3.32/1.49	   __(__(X, Y), Z) -> __(X, __(Y, Z))
3.32/1.49	   __(X, nil) -> X
3.32/1.49	   __(nil, X) -> X
3.32/1.49	   and(tt, X) -> X
3.32/1.49	   isList(V) -> isNeList(V)
3.32/1.49	   isList(nil) -> tt
3.32/1.49	   isList(__(V1, V2)) -> and(isList(V1), isList(V2))
3.32/1.49	   isNeList(V) -> isQid(V)
3.32/1.49	   isNeList(__(V1, V2)) -> and(isList(V1), isNeList(V2))
3.32/1.49	   isNeList(__(V1, V2)) -> and(isNeList(V1), isList(V2))
3.32/1.49	   isNePal(V) -> isQid(V)
3.32/1.49	   isNePal(__(I, __(P, I))) -> and(isQid(I), isPal(P))
3.32/1.49	   isPal(V) -> isNePal(V)
3.32/1.49	   isPal(nil) -> tt
3.32/1.49	   isQid(a) -> tt
3.32/1.49	   isQid(e) -> tt
3.32/1.49	   isQid(i) -> tt
3.32/1.49	   isQid(o) -> tt
3.32/1.49	   isQid(u) -> tt
3.32/1.49	
3.32/1.49	The replacement map contains the following entries:
3.32/1.49	
3.32/1.49	__: {1, 2}
3.32/1.49	nil: empty set
3.32/1.49	and: {1}
3.32/1.49	tt: empty set
3.32/1.49	isList: empty set
3.32/1.49	isNeList: empty set
3.32/1.49	isQid: empty set
3.32/1.49	isNePal: empty set
3.32/1.49	isPal: empty set
3.32/1.49	a: empty set
3.32/1.49	e: empty set
3.32/1.49	i: empty set
3.32/1.49	o: empty set
3.32/1.49	u: empty set
3.32/1.49	
3.32/1.49	----------------------------------------
3.32/1.49	
3.32/1.49	(1) CSRRRRProof (EQUIVALENT)
3.32/1.49	The following CSR is given: Context-sensitive rewrite system:
3.32/1.49	The TRS R consists of the following rules:
3.32/1.49	
3.32/1.49	   __(__(X, Y), Z) -> __(X, __(Y, Z))
3.32/1.49	   __(X, nil) -> X
3.32/1.49	   __(nil, X) -> X
3.32/1.49	   and(tt, X) -> X
3.32/1.49	   isList(V) -> isNeList(V)
3.32/1.49	   isList(nil) -> tt
3.32/1.49	   isList(__(V1, V2)) -> and(isList(V1), isList(V2))
3.32/1.49	   isNeList(V) -> isQid(V)
3.32/1.49	   isNeList(__(V1, V2)) -> and(isList(V1), isNeList(V2))
3.32/1.49	   isNeList(__(V1, V2)) -> and(isNeList(V1), isList(V2))
3.32/1.49	   isNePal(V) -> isQid(V)
3.32/1.49	   isNePal(__(I, __(P, I))) -> and(isQid(I), isPal(P))
3.32/1.49	   isPal(V) -> isNePal(V)
3.32/1.49	   isPal(nil) -> tt
3.32/1.49	   isQid(a) -> tt
3.32/1.49	   isQid(e) -> tt
3.32/1.49	   isQid(i) -> tt
3.32/1.49	   isQid(o) -> tt
3.32/1.49	   isQid(u) -> tt
3.32/1.49	
3.32/1.49	The replacement map contains the following entries:
3.32/1.49	
3.32/1.49	__: {1, 2}
3.32/1.49	nil: empty set
3.32/1.49	and: {1}
3.32/1.49	tt: empty set
3.32/1.49	isList: empty set
3.32/1.49	isNeList: empty set
3.32/1.49	isQid: empty set
3.32/1.49	isNePal: empty set
3.32/1.49	isPal: empty set
3.32/1.49	a: empty set
3.32/1.49	e: empty set
3.32/1.49	i: empty set
3.32/1.49	o: empty set
3.32/1.49	u: empty set
3.32/1.49	Used ordering:
3.32/1.49	Polynomial interpretation [POLO]:
3.32/1.49	
3.32/1.49	   POL(__(x_1, x_2)) = 2 + 2*x_1 + x_2
3.32/1.49	   POL(a) = 2
3.32/1.49	   POL(and(x_1, x_2)) = 2 + 2*x_1 + x_2
3.32/1.49	   POL(e) = 2
3.32/1.49	   POL(i) = 2
3.32/1.49	   POL(isList(x_1)) = 1 + 2*x_1
3.32/1.49	   POL(isNeList(x_1)) = 2*x_1
3.32/1.49	   POL(isNePal(x_1)) = 2*x_1
3.32/1.49	   POL(isPal(x_1)) = 1 + 2*x_1
3.32/1.49	   POL(isQid(x_1)) = 2*x_1
3.32/1.49	   POL(nil) = 2
3.32/1.49	   POL(o) = 2
3.32/1.49	   POL(tt) = 2
3.32/1.49	   POL(u) = 2
3.32/1.49	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.32/1.49	
3.32/1.49	   __(__(X, Y), Z) -> __(X, __(Y, Z))
3.32/1.49	   __(X, nil) -> X
3.32/1.49	   __(nil, X) -> X
3.32/1.49	   and(tt, X) -> X
3.32/1.49	   isList(V) -> isNeList(V)
3.32/1.49	   isList(nil) -> tt
3.32/1.49	   isNeList(__(V1, V2)) -> and(isNeList(V1), isList(V2))
3.32/1.49	   isNePal(__(I, __(P, I))) -> and(isQid(I), isPal(P))
3.32/1.49	   isPal(V) -> isNePal(V)
3.32/1.49	   isPal(nil) -> tt
3.32/1.49	   isQid(a) -> tt
3.32/1.49	   isQid(e) -> tt
3.32/1.49	   isQid(i) -> tt
3.32/1.49	   isQid(o) -> tt
3.32/1.49	   isQid(u) -> tt
3.32/1.49	
3.32/1.49	
3.32/1.49	
3.32/1.49	
3.32/1.49	----------------------------------------
3.32/1.49	
3.32/1.49	(2)
3.32/1.49	Obligation:
3.32/1.49	Context-sensitive rewrite system:
3.32/1.49	The TRS R consists of the following rules:
3.32/1.49	
3.32/1.49	   isList(__(V1, V2)) -> and(isList(V1), isList(V2))
3.32/1.49	   isNeList(V) -> isQid(V)
3.32/1.49	   isNeList(__(V1, V2)) -> and(isList(V1), isNeList(V2))
3.32/1.49	   isNePal(V) -> isQid(V)
3.32/1.49	
3.32/1.49	The replacement map contains the following entries:
3.32/1.49	
3.32/1.49	__: {1, 2}
3.32/1.49	and: {1}
3.32/1.49	isList: empty set
3.32/1.49	isNeList: empty set
3.32/1.49	isQid: empty set
3.32/1.49	isNePal: empty set
3.32/1.49	
3.32/1.49	----------------------------------------
3.32/1.49	
3.32/1.49	(3) CSRRRRProof (EQUIVALENT)
3.32/1.49	The following CSR is given: Context-sensitive rewrite system:
3.32/1.49	The TRS R consists of the following rules:
3.32/1.49	
3.32/1.49	   isList(__(V1, V2)) -> and(isList(V1), isList(V2))
3.32/1.49	   isNeList(V) -> isQid(V)
3.32/1.49	   isNeList(__(V1, V2)) -> and(isList(V1), isNeList(V2))
3.32/1.49	   isNePal(V) -> isQid(V)
3.32/1.49	
3.32/1.49	The replacement map contains the following entries:
3.32/1.49	
3.32/1.49	__: {1, 2}
3.32/1.49	and: {1}
3.32/1.49	isList: empty set
3.32/1.49	isNeList: empty set
3.32/1.49	isQid: empty set
3.32/1.49	isNePal: empty set
3.32/1.49	Used ordering:
3.32/1.49	Polynomial interpretation [POLO]:
3.32/1.49	
3.32/1.49	   POL(__(x_1, x_2)) = 2*x_1 + x_2
3.32/1.49	   POL(and(x_1, x_2)) = x_1
3.32/1.49	   POL(isList(x_1)) = 2*x_1
3.32/1.49	   POL(isNeList(x_1)) = 2*x_1
3.32/1.49	   POL(isNePal(x_1)) = 1 + 2*x_1
3.32/1.49	   POL(isQid(x_1)) = 2*x_1
3.32/1.49	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.32/1.49	
3.32/1.49	   isNePal(V) -> isQid(V)
3.32/1.49	
3.32/1.49	
3.32/1.49	
3.32/1.49	
3.32/1.49	----------------------------------------
3.32/1.49	
3.32/1.49	(4)
3.32/1.49	Obligation:
3.32/1.49	Context-sensitive rewrite system:
3.32/1.49	The TRS R consists of the following rules:
3.32/1.49	
3.32/1.49	   isList(__(V1, V2)) -> and(isList(V1), isList(V2))
3.32/1.49	   isNeList(V) -> isQid(V)
3.32/1.49	   isNeList(__(V1, V2)) -> and(isList(V1), isNeList(V2))
3.32/1.49	
3.32/1.49	The replacement map contains the following entries:
3.32/1.49	
3.32/1.49	__: {1, 2}
3.32/1.49	and: {1}
3.32/1.49	isList: empty set
3.32/1.49	isNeList: empty set
3.32/1.49	isQid: empty set
3.32/1.49	
3.32/1.49	----------------------------------------
3.32/1.49	
3.32/1.49	(5) CSRRRRProof (EQUIVALENT)
3.32/1.49	The following CSR is given: Context-sensitive rewrite system:
3.32/1.49	The TRS R consists of the following rules:
3.32/1.49	
3.32/1.49	   isList(__(V1, V2)) -> and(isList(V1), isList(V2))
3.32/1.49	   isNeList(V) -> isQid(V)
3.32/1.49	   isNeList(__(V1, V2)) -> and(isList(V1), isNeList(V2))
3.32/1.49	
3.32/1.49	The replacement map contains the following entries:
3.32/1.49	
3.32/1.49	__: {1, 2}
3.32/1.49	and: {1}
3.32/1.49	isList: empty set
3.32/1.49	isNeList: empty set
3.32/1.49	isQid: empty set
3.32/1.49	Used ordering:
3.32/1.49	Polynomial interpretation [POLO]:
3.32/1.49	
3.32/1.49	   POL(__(x_1, x_2)) = x_1 + x_2
3.32/1.49	   POL(and(x_1, x_2)) = x_1
3.32/1.49	   POL(isList(x_1)) = 0
3.32/1.49	   POL(isNeList(x_1)) = 1
3.32/1.49	   POL(isQid(x_1)) = 1
3.32/1.49	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.32/1.49	
3.32/1.49	   isNeList(__(V1, V2)) -> and(isList(V1), isNeList(V2))
3.32/1.49	
3.32/1.49	
3.32/1.49	
3.32/1.49	
3.32/1.49	----------------------------------------
3.32/1.49	
3.32/1.49	(6)
3.32/1.49	Obligation:
3.32/1.49	Context-sensitive rewrite system:
3.32/1.49	The TRS R consists of the following rules:
3.32/1.49	
3.32/1.49	   isList(__(V1, V2)) -> and(isList(V1), isList(V2))
3.32/1.49	   isNeList(V) -> isQid(V)
3.32/1.49	
3.32/1.49	The replacement map contains the following entries:
3.32/1.49	
3.32/1.49	__: {1, 2}
3.32/1.49	and: {1}
3.32/1.49	isList: empty set
3.32/1.49	isNeList: empty set
3.32/1.49	isQid: empty set
3.32/1.49	
3.32/1.49	----------------------------------------
3.32/1.49	
3.32/1.49	(7) CSRRRRProof (EQUIVALENT)
3.32/1.49	The following CSR is given: Context-sensitive rewrite system:
3.32/1.49	The TRS R consists of the following rules:
3.32/1.49	
3.32/1.49	   isList(__(V1, V2)) -> and(isList(V1), isList(V2))
3.32/1.49	   isNeList(V) -> isQid(V)
3.32/1.49	
3.32/1.49	The replacement map contains the following entries:
3.32/1.49	
3.32/1.49	__: {1, 2}
3.32/1.49	and: {1}
3.32/1.49	isList: empty set
3.32/1.49	isNeList: empty set
3.32/1.49	isQid: empty set
3.32/1.49	Used ordering:
3.32/1.49	Polynomial interpretation [POLO]:
3.32/1.49	
3.32/1.49	   POL(__(x_1, x_2)) = 2*x_1 + x_2
3.32/1.49	   POL(and(x_1, x_2)) = x_1
3.32/1.49	   POL(isList(x_1)) = 2*x_1
3.32/1.49	   POL(isNeList(x_1)) = 1 + 2*x_1
3.32/1.49	   POL(isQid(x_1)) = 2*x_1
3.32/1.49	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.32/1.49	
3.32/1.49	   isNeList(V) -> isQid(V)
3.32/1.49	
3.32/1.49	
3.32/1.49	
3.32/1.49	
3.32/1.49	----------------------------------------
3.32/1.49	
3.32/1.49	(8)
3.32/1.49	Obligation:
3.32/1.49	Context-sensitive rewrite system:
3.32/1.49	The TRS R consists of the following rules:
3.32/1.49	
3.32/1.49	   isList(__(V1, V2)) -> and(isList(V1), isList(V2))
3.32/1.49	
3.32/1.49	The replacement map contains the following entries:
3.32/1.49	
3.32/1.49	__: {1, 2}
3.32/1.49	and: {1}
3.32/1.49	isList: empty set
3.32/1.49	
3.32/1.49	----------------------------------------
3.32/1.49	
3.32/1.49	(9) CSRRRRProof (EQUIVALENT)
3.32/1.49	The following CSR is given: Context-sensitive rewrite system:
3.32/1.49	The TRS R consists of the following rules:
3.32/1.49	
3.32/1.49	   isList(__(V1, V2)) -> and(isList(V1), isList(V2))
3.32/1.49	
3.32/1.49	The replacement map contains the following entries:
3.32/1.49	
3.32/1.49	__: {1, 2}
3.32/1.49	and: {1}
3.32/1.49	isList: empty set
3.32/1.49	Used ordering:
3.32/1.49	Polynomial interpretation [POLO]:
3.32/1.49	
3.32/1.49	   POL(__(x_1, x_2)) = 1 + x_1 + x_2
3.32/1.49	   POL(and(x_1, x_2)) = x_1
3.32/1.49	   POL(isList(x_1)) = 1 + x_1
3.32/1.49	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.32/1.49	
3.32/1.49	   isList(__(V1, V2)) -> and(isList(V1), isList(V2))
3.32/1.49	
3.32/1.49	
3.32/1.49	
3.32/1.49	
3.32/1.49	----------------------------------------
3.32/1.49	
3.32/1.49	(10)
3.32/1.49	Obligation:
3.32/1.49	Context-sensitive rewrite system:
3.32/1.49	R is empty.
3.32/1.49	
3.32/1.49	----------------------------------------
3.32/1.49	
3.32/1.49	(11) RisEmptyProof (EQUIVALENT)
3.32/1.49	The CSR R is empty. Hence, termination is trivially proven.
3.32/1.49	----------------------------------------
3.32/1.49	
3.32/1.49	(12)
3.32/1.49	YES
3.32/1.51	EOF