3.50/1.55	YES
3.50/1.57	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.50/1.57	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.50/1.57	
3.50/1.57	
3.50/1.57	Termination of the given CSR could be proven:
3.50/1.57	
3.50/1.57	(0) CSR
3.50/1.57	(1) CSRRRRProof [EQUIVALENT, 101 ms]
3.50/1.57	(2) CSR
3.50/1.57	(3) CSRRRRProof [EQUIVALENT, 0 ms]
3.50/1.57	(4) CSR
3.50/1.57	(5) CSRRRRProof [EQUIVALENT, 0 ms]
3.50/1.57	(6) CSR
3.50/1.57	(7) CSRRRRProof [EQUIVALENT, 2 ms]
3.50/1.57	(8) CSR
3.50/1.57	(9) CSRRRRProof [EQUIVALENT, 0 ms]
3.50/1.57	(10) CSR
3.50/1.57	(11) RisEmptyProof [EQUIVALENT, 0 ms]
3.50/1.57	(12) YES
3.50/1.57	
3.50/1.57	
3.50/1.57	----------------------------------------
3.50/1.57	
3.50/1.57	(0)
3.50/1.57	Obligation:
3.50/1.57	Context-sensitive rewrite system:
3.50/1.57	The TRS R consists of the following rules:
3.50/1.57	
3.50/1.57	   __(__(X, Y), Z) -> __(X, __(Y, Z))
3.50/1.57	   __(X, nil) -> X
3.50/1.57	   __(nil, X) -> X
3.50/1.57	   U11(tt) -> tt
3.50/1.57	   U21(tt, V2) -> U22(isList(V2))
3.50/1.57	   U22(tt) -> tt
3.50/1.57	   U31(tt) -> tt
3.50/1.57	   U41(tt, V2) -> U42(isNeList(V2))
3.50/1.57	   U42(tt) -> tt
3.50/1.57	   U51(tt, V2) -> U52(isList(V2))
3.50/1.57	   U52(tt) -> tt
3.50/1.57	   U61(tt) -> tt
3.50/1.57	   U71(tt, P) -> U72(isPal(P))
3.50/1.57	   U72(tt) -> tt
3.50/1.57	   U81(tt) -> tt
3.50/1.57	   isList(V) -> U11(isNeList(V))
3.50/1.57	   isList(nil) -> tt
3.50/1.57	   isList(__(V1, V2)) -> U21(isList(V1), V2)
3.50/1.57	   isNeList(V) -> U31(isQid(V))
3.50/1.57	   isNeList(__(V1, V2)) -> U41(isList(V1), V2)
3.50/1.57	   isNeList(__(V1, V2)) -> U51(isNeList(V1), V2)
3.50/1.57	   isNePal(V) -> U61(isQid(V))
3.50/1.57	   isNePal(__(I, __(P, I))) -> U71(isQid(I), P)
3.50/1.57	   isPal(V) -> U81(isNePal(V))
3.50/1.57	   isPal(nil) -> tt
3.50/1.57	   isQid(a) -> tt
3.50/1.57	   isQid(e) -> tt
3.50/1.57	   isQid(i) -> tt
3.50/1.57	   isQid(o) -> tt
3.50/1.57	   isQid(u) -> tt
3.50/1.57	
3.50/1.57	The replacement map contains the following entries:
3.50/1.57	
3.50/1.57	__: {1, 2}
3.50/1.57	nil: empty set
3.50/1.57	U11: {1}
3.50/1.57	tt: empty set
3.50/1.57	U21: {1}
3.50/1.57	U22: {1}
3.50/1.57	isList: empty set
3.50/1.57	U31: {1}
3.50/1.57	U41: {1}
3.50/1.57	U42: {1}
3.50/1.57	isNeList: empty set
3.50/1.57	U51: {1}
3.50/1.57	U52: {1}
3.50/1.57	U61: {1}
3.50/1.57	U71: {1}
3.50/1.57	U72: {1}
3.50/1.57	isPal: empty set
3.50/1.57	U81: {1}
3.50/1.57	isQid: empty set
3.50/1.57	isNePal: empty set
3.50/1.57	a: empty set
3.50/1.57	e: empty set
3.50/1.57	i: empty set
3.50/1.57	o: empty set
3.50/1.57	u: empty set
3.50/1.57	
3.50/1.57	----------------------------------------
3.50/1.57	
3.50/1.57	(1) CSRRRRProof (EQUIVALENT)
3.50/1.57	The following CSR is given: Context-sensitive rewrite system:
3.50/1.57	The TRS R consists of the following rules:
3.50/1.57	
3.50/1.57	   __(__(X, Y), Z) -> __(X, __(Y, Z))
3.50/1.57	   __(X, nil) -> X
3.50/1.57	   __(nil, X) -> X
3.50/1.57	   U11(tt) -> tt
3.50/1.57	   U21(tt, V2) -> U22(isList(V2))
3.50/1.57	   U22(tt) -> tt
3.50/1.57	   U31(tt) -> tt
3.50/1.57	   U41(tt, V2) -> U42(isNeList(V2))
3.50/1.57	   U42(tt) -> tt
3.50/1.57	   U51(tt, V2) -> U52(isList(V2))
3.50/1.57	   U52(tt) -> tt
3.50/1.57	   U61(tt) -> tt
3.50/1.57	   U71(tt, P) -> U72(isPal(P))
3.50/1.57	   U72(tt) -> tt
3.50/1.57	   U81(tt) -> tt
3.50/1.57	   isList(V) -> U11(isNeList(V))
3.50/1.57	   isList(nil) -> tt
3.50/1.57	   isList(__(V1, V2)) -> U21(isList(V1), V2)
3.50/1.57	   isNeList(V) -> U31(isQid(V))
3.50/1.57	   isNeList(__(V1, V2)) -> U41(isList(V1), V2)
3.50/1.57	   isNeList(__(V1, V2)) -> U51(isNeList(V1), V2)
3.50/1.57	   isNePal(V) -> U61(isQid(V))
3.50/1.57	   isNePal(__(I, __(P, I))) -> U71(isQid(I), P)
3.50/1.57	   isPal(V) -> U81(isNePal(V))
3.50/1.57	   isPal(nil) -> tt
3.50/1.57	   isQid(a) -> tt
3.50/1.57	   isQid(e) -> tt
3.50/1.57	   isQid(i) -> tt
3.50/1.57	   isQid(o) -> tt
3.50/1.57	   isQid(u) -> tt
3.50/1.57	
3.50/1.57	The replacement map contains the following entries:
3.50/1.57	
3.50/1.57	__: {1, 2}
3.50/1.57	nil: empty set
3.50/1.57	U11: {1}
3.50/1.57	tt: empty set
3.50/1.57	U21: {1}
3.50/1.57	U22: {1}
3.50/1.57	isList: empty set
3.50/1.57	U31: {1}
3.50/1.57	U41: {1}
3.50/1.57	U42: {1}
3.50/1.57	isNeList: empty set
3.50/1.57	U51: {1}
3.50/1.57	U52: {1}
3.50/1.57	U61: {1}
3.50/1.57	U71: {1}
3.50/1.57	U72: {1}
3.50/1.57	isPal: empty set
3.50/1.57	U81: {1}
3.50/1.57	isQid: empty set
3.50/1.57	isNePal: empty set
3.50/1.57	a: empty set
3.50/1.57	e: empty set
3.50/1.57	i: empty set
3.50/1.57	o: empty set
3.50/1.57	u: empty set
3.50/1.57	Used ordering:
3.50/1.57	Polynomial interpretation [POLO]:
3.50/1.57	
3.50/1.57	   POL(U11(x_1)) = x_1
3.50/1.57	   POL(U21(x_1, x_2)) = 1 + 2*x_1 + 2*x_2
3.50/1.57	   POL(U22(x_1)) = 1 + x_1
3.50/1.57	   POL(U31(x_1)) = x_1
3.50/1.57	   POL(U41(x_1, x_2)) = 1 + 2*x_1 + 2*x_2
3.50/1.57	   POL(U42(x_1)) = 1 + x_1
3.50/1.57	   POL(U51(x_1, x_2)) = 1 + 2*x_1 + 2*x_2
3.50/1.57	   POL(U52(x_1)) = 1 + x_1
3.50/1.57	   POL(U61(x_1)) = x_1
3.50/1.57	   POL(U71(x_1, x_2)) = 1 + 2*x_1 + 2*x_2
3.50/1.57	   POL(U72(x_1)) = 1 + x_1
3.50/1.57	   POL(U81(x_1)) = x_1
3.50/1.57	   POL(__(x_1, x_2)) = 2 + 2*x_1 + x_2
3.50/1.57	   POL(a) = 0
3.50/1.57	   POL(e) = 2
3.50/1.57	   POL(i) = 0
3.50/1.57	   POL(isList(x_1)) = 2 + 2*x_1
3.50/1.57	   POL(isNeList(x_1)) = 2 + 2*x_1
3.50/1.57	   POL(isNePal(x_1)) = 2 + 2*x_1
3.50/1.57	   POL(isPal(x_1)) = 2 + 2*x_1
3.50/1.57	   POL(isQid(x_1)) = 2 + 2*x_1
3.50/1.57	   POL(nil) = 0
3.50/1.57	   POL(o) = 2
3.50/1.57	   POL(tt) = 1
3.50/1.57	   POL(u) = 0
3.50/1.57	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.50/1.57	
3.50/1.57	   __(__(X, Y), Z) -> __(X, __(Y, Z))
3.50/1.57	   __(X, nil) -> X
3.50/1.57	   __(nil, X) -> X
3.50/1.57	   U22(tt) -> tt
3.50/1.57	   U42(tt) -> tt
3.50/1.57	   U52(tt) -> tt
3.50/1.57	   U72(tt) -> tt
3.50/1.57	   isList(nil) -> tt
3.50/1.57	   isList(__(V1, V2)) -> U21(isList(V1), V2)
3.50/1.57	   isNeList(__(V1, V2)) -> U41(isList(V1), V2)
3.50/1.57	   isNeList(__(V1, V2)) -> U51(isNeList(V1), V2)
3.50/1.57	   isNePal(__(I, __(P, I))) -> U71(isQid(I), P)
3.50/1.57	   isPal(nil) -> tt
3.50/1.57	   isQid(a) -> tt
3.50/1.57	   isQid(e) -> tt
3.50/1.57	   isQid(i) -> tt
3.50/1.57	   isQid(o) -> tt
3.50/1.57	   isQid(u) -> tt
3.50/1.57	
3.50/1.57	
3.50/1.57	
3.50/1.57	
3.50/1.57	----------------------------------------
3.50/1.57	
3.50/1.57	(2)
3.50/1.57	Obligation:
3.50/1.57	Context-sensitive rewrite system:
3.50/1.57	The TRS R consists of the following rules:
3.50/1.57	
3.50/1.57	   U11(tt) -> tt
3.50/1.57	   U21(tt, V2) -> U22(isList(V2))
3.50/1.57	   U31(tt) -> tt
3.50/1.57	   U41(tt, V2) -> U42(isNeList(V2))
3.50/1.57	   U51(tt, V2) -> U52(isList(V2))
3.50/1.57	   U61(tt) -> tt
3.50/1.57	   U71(tt, P) -> U72(isPal(P))
3.50/1.57	   U81(tt) -> tt
3.50/1.57	   isList(V) -> U11(isNeList(V))
3.50/1.57	   isNeList(V) -> U31(isQid(V))
3.50/1.57	   isNePal(V) -> U61(isQid(V))
3.50/1.57	   isPal(V) -> U81(isNePal(V))
3.50/1.57	
3.50/1.57	The replacement map contains the following entries:
3.50/1.57	
3.50/1.57	U11: {1}
3.50/1.57	tt: empty set
3.50/1.57	U21: {1}
3.50/1.57	U22: {1}
3.50/1.57	isList: empty set
3.50/1.57	U31: {1}
3.50/1.57	U41: {1}
3.50/1.57	U42: {1}
3.50/1.57	isNeList: empty set
3.50/1.57	U51: {1}
3.50/1.57	U52: {1}
3.50/1.57	U61: {1}
3.50/1.57	U71: {1}
3.50/1.57	U72: {1}
3.50/1.57	isPal: empty set
3.50/1.57	U81: {1}
3.50/1.57	isQid: empty set
3.50/1.57	isNePal: empty set
3.50/1.57	
3.50/1.57	----------------------------------------
3.50/1.57	
3.50/1.57	(3) CSRRRRProof (EQUIVALENT)
3.50/1.57	The following CSR is given: Context-sensitive rewrite system:
3.50/1.57	The TRS R consists of the following rules:
3.50/1.57	
3.50/1.57	   U11(tt) -> tt
3.50/1.57	   U21(tt, V2) -> U22(isList(V2))
3.50/1.57	   U31(tt) -> tt
3.50/1.57	   U41(tt, V2) -> U42(isNeList(V2))
3.50/1.57	   U51(tt, V2) -> U52(isList(V2))
3.50/1.57	   U61(tt) -> tt
3.50/1.57	   U71(tt, P) -> U72(isPal(P))
3.50/1.57	   U81(tt) -> tt
3.50/1.57	   isList(V) -> U11(isNeList(V))
3.50/1.57	   isNeList(V) -> U31(isQid(V))
3.50/1.57	   isNePal(V) -> U61(isQid(V))
3.50/1.57	   isPal(V) -> U81(isNePal(V))
3.50/1.57	
3.50/1.57	The replacement map contains the following entries:
3.50/1.57	
3.50/1.57	U11: {1}
3.50/1.57	tt: empty set
3.50/1.57	U21: {1}
3.50/1.57	U22: {1}
3.50/1.57	isList: empty set
3.50/1.57	U31: {1}
3.50/1.57	U41: {1}
3.50/1.57	U42: {1}
3.50/1.57	isNeList: empty set
3.50/1.57	U51: {1}
3.50/1.57	U52: {1}
3.50/1.57	U61: {1}
3.50/1.57	U71: {1}
3.50/1.57	U72: {1}
3.50/1.57	isPal: empty set
3.50/1.57	U81: {1}
3.50/1.57	isQid: empty set
3.50/1.57	isNePal: empty set
3.50/1.57	Used ordering:
3.50/1.57	Polynomial interpretation [POLO]:
3.50/1.57	
3.50/1.57	   POL(U11(x_1)) = x_1
3.50/1.57	   POL(U21(x_1, x_2)) = 2 + 2*x_1 + 2*x_2
3.50/1.57	   POL(U22(x_1)) = 2*x_1
3.50/1.57	   POL(U31(x_1)) = 2*x_1
3.50/1.57	   POL(U41(x_1, x_2)) = 1 + x_1 + 2*x_2
3.50/1.57	   POL(U42(x_1)) = x_1
3.50/1.57	   POL(U51(x_1, x_2)) = 2 + 2*x_1 + 2*x_2
3.50/1.57	   POL(U52(x_1)) = 1 + x_1
3.50/1.57	   POL(U61(x_1)) = 2*x_1
3.50/1.57	   POL(U71(x_1, x_2)) = 1 + x_1 + 2*x_2
3.50/1.57	   POL(U72(x_1)) = x_1
3.50/1.57	   POL(U81(x_1)) = 2*x_1
3.50/1.57	   POL(isList(x_1)) = 2 + x_1
3.50/1.57	   POL(isNeList(x_1)) = 1 + x_1
3.50/1.57	   POL(isNePal(x_1)) = x_1
3.50/1.57	   POL(isPal(x_1)) = 1 + 2*x_1
3.50/1.57	   POL(isQid(x_1)) = 0
3.50/1.57	   POL(tt) = 1
3.50/1.57	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.50/1.57	
3.50/1.57	   U31(tt) -> tt
3.50/1.57	   U41(tt, V2) -> U42(isNeList(V2))
3.50/1.57	   U51(tt, V2) -> U52(isList(V2))
3.50/1.57	   U61(tt) -> tt
3.50/1.57	   U71(tt, P) -> U72(isPal(P))
3.50/1.57	   U81(tt) -> tt
3.50/1.57	   isList(V) -> U11(isNeList(V))
3.50/1.57	   isNeList(V) -> U31(isQid(V))
3.50/1.57	   isPal(V) -> U81(isNePal(V))
3.50/1.57	
3.50/1.57	
3.50/1.57	
3.50/1.57	
3.50/1.57	----------------------------------------
3.50/1.57	
3.50/1.57	(4)
3.50/1.57	Obligation:
3.50/1.57	Context-sensitive rewrite system:
3.50/1.57	The TRS R consists of the following rules:
3.50/1.57	
3.50/1.57	   U11(tt) -> tt
3.50/1.57	   U21(tt, V2) -> U22(isList(V2))
3.50/1.57	   isNePal(V) -> U61(isQid(V))
3.50/1.57	
3.50/1.57	The replacement map contains the following entries:
3.50/1.57	
3.50/1.57	U11: {1}
3.50/1.57	tt: empty set
3.50/1.57	U21: {1}
3.50/1.57	U22: {1}
3.50/1.57	isList: empty set
3.50/1.57	U61: {1}
3.50/1.57	isQid: empty set
3.50/1.57	isNePal: empty set
3.50/1.57	
3.50/1.57	----------------------------------------
3.50/1.57	
3.50/1.57	(5) CSRRRRProof (EQUIVALENT)
3.50/1.57	The following CSR is given: Context-sensitive rewrite system:
3.50/1.57	The TRS R consists of the following rules:
3.50/1.57	
3.50/1.57	   U11(tt) -> tt
3.50/1.57	   U21(tt, V2) -> U22(isList(V2))
3.50/1.57	   isNePal(V) -> U61(isQid(V))
3.50/1.57	
3.50/1.57	The replacement map contains the following entries:
3.50/1.57	
3.50/1.57	U11: {1}
3.50/1.57	tt: empty set
3.50/1.57	U21: {1}
3.50/1.57	U22: {1}
3.50/1.57	isList: empty set
3.50/1.57	U61: {1}
3.50/1.57	isQid: empty set
3.50/1.57	isNePal: empty set
3.50/1.57	Used ordering:
3.50/1.57	Polynomial interpretation [POLO]:
3.50/1.57	
3.50/1.57	   POL(U11(x_1)) = 1 + x_1
3.50/1.57	   POL(U21(x_1, x_2)) = 1 + x_1 + x_2
3.50/1.57	   POL(U22(x_1)) = 1 + x_1
3.50/1.57	   POL(U61(x_1)) = x_1
3.50/1.57	   POL(isList(x_1)) = 1 + x_1
3.50/1.57	   POL(isNePal(x_1)) = 1 + x_1
3.50/1.57	   POL(isQid(x_1)) = 1 + x_1
3.50/1.57	   POL(tt) = 1
3.50/1.57	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.50/1.57	
3.50/1.57	   U11(tt) -> tt
3.50/1.57	
3.50/1.57	
3.50/1.57	
3.50/1.57	
3.50/1.57	----------------------------------------
3.50/1.57	
3.50/1.57	(6)
3.50/1.57	Obligation:
3.50/1.57	Context-sensitive rewrite system:
3.50/1.57	The TRS R consists of the following rules:
3.50/1.57	
3.50/1.57	   U21(tt, V2) -> U22(isList(V2))
3.50/1.57	   isNePal(V) -> U61(isQid(V))
3.50/1.57	
3.50/1.57	The replacement map contains the following entries:
3.50/1.57	
3.50/1.57	tt: empty set
3.50/1.57	U21: {1}
3.50/1.57	U22: {1}
3.50/1.57	isList: empty set
3.50/1.57	U61: {1}
3.50/1.57	isQid: empty set
3.50/1.57	isNePal: empty set
3.50/1.57	
3.50/1.57	----------------------------------------
3.50/1.57	
3.50/1.57	(7) CSRRRRProof (EQUIVALENT)
3.50/1.57	The following CSR is given: Context-sensitive rewrite system:
3.50/1.57	The TRS R consists of the following rules:
3.50/1.57	
3.50/1.57	   U21(tt, V2) -> U22(isList(V2))
3.50/1.57	   isNePal(V) -> U61(isQid(V))
3.50/1.57	
3.50/1.57	The replacement map contains the following entries:
3.50/1.57	
3.50/1.57	tt: empty set
3.50/1.57	U21: {1}
3.50/1.57	U22: {1}
3.50/1.57	isList: empty set
3.50/1.57	U61: {1}
3.50/1.57	isQid: empty set
3.50/1.57	isNePal: empty set
3.50/1.57	Used ordering:
3.50/1.57	Polynomial interpretation [POLO]:
3.50/1.57	
3.50/1.57	   POL(U21(x_1, x_2)) = x_1 + 2*x_2
3.50/1.57	   POL(U22(x_1)) = 2*x_1
3.50/1.57	   POL(U61(x_1)) = x_1
3.50/1.57	   POL(isList(x_1)) = x_1
3.50/1.57	   POL(isNePal(x_1)) = 1 + 2*x_1
3.50/1.57	   POL(isQid(x_1)) = 2*x_1
3.50/1.57	   POL(tt) = 0
3.50/1.57	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.50/1.57	
3.50/1.57	   isNePal(V) -> U61(isQid(V))
3.50/1.57	
3.50/1.57	
3.50/1.57	
3.50/1.57	
3.50/1.57	----------------------------------------
3.50/1.57	
3.50/1.57	(8)
3.50/1.57	Obligation:
3.50/1.57	Context-sensitive rewrite system:
3.50/1.57	The TRS R consists of the following rules:
3.50/1.57	
3.50/1.57	   U21(tt, V2) -> U22(isList(V2))
3.50/1.57	
3.50/1.57	The replacement map contains the following entries:
3.50/1.57	
3.50/1.57	tt: empty set
3.50/1.57	U21: {1}
3.50/1.57	U22: {1}
3.50/1.57	isList: empty set
3.50/1.57	
3.50/1.57	----------------------------------------
3.50/1.57	
3.50/1.57	(9) CSRRRRProof (EQUIVALENT)
3.50/1.57	The following CSR is given: Context-sensitive rewrite system:
3.50/1.57	The TRS R consists of the following rules:
3.50/1.57	
3.50/1.57	   U21(tt, V2) -> U22(isList(V2))
3.50/1.57	
3.50/1.57	The replacement map contains the following entries:
3.50/1.57	
3.50/1.57	tt: empty set
3.50/1.57	U21: {1}
3.50/1.57	U22: {1}
3.50/1.57	isList: empty set
3.50/1.57	Used ordering:
3.50/1.57	Polynomial interpretation [POLO]:
3.50/1.57	
3.50/1.57	   POL(U21(x_1, x_2)) = 1 + x_1 + 2*x_2
3.50/1.57	   POL(U22(x_1)) = x_1
3.50/1.57	   POL(isList(x_1)) = 2 + 2*x_1
3.50/1.57	   POL(tt) = 2
3.50/1.57	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
3.50/1.57	
3.50/1.57	   U21(tt, V2) -> U22(isList(V2))
3.50/1.57	
3.50/1.57	
3.50/1.57	
3.50/1.57	
3.50/1.57	----------------------------------------
3.50/1.57	
3.50/1.57	(10)
3.50/1.57	Obligation:
3.50/1.57	Context-sensitive rewrite system:
3.50/1.57	R is empty.
3.50/1.57	
3.50/1.57	----------------------------------------
3.50/1.57	
3.50/1.57	(11) RisEmptyProof (EQUIVALENT)
3.50/1.57	The CSR R is empty. Hence, termination is trivially proven.
3.50/1.57	----------------------------------------
3.50/1.57	
3.50/1.57	(12)
3.50/1.57	YES
3.50/1.61	EOF