0.00/0.01	YES
0.00/0.01	
0.00/0.01	Problem 1: 
0.00/0.01	
0.00/0.01	(VAR M N V1 V2)
0.00/0.01	(STRATEGY CONTEXTSENSITIVE
0.00/0.01	(U11 1)
0.00/0.01	(U12 1)
0.00/0.01	(U21 1)
0.00/0.01	(U31 1)
0.00/0.01	(U32 1)
0.00/0.01	(U41 1)
0.00/0.01	(U51 1)
0.00/0.01	(U52 1)
0.00/0.01	(U61 1)
0.00/0.01	(U71 1)
0.00/0.01	(U72 1)
0.00/0.01	(isNat)
0.00/0.01	(plus 1 2)
0.00/0.01	(x 1 2)
0.00/0.01	(0)
0.00/0.01	(s 1)
0.00/0.01	(tt)
0.00/0.01	)
0.00/0.01	(RULES
0.00/0.01	U11(tt,V2) -> U12(isNat(V2))
0.00/0.01	U12(tt) -> tt
0.00/0.01	U21(tt) -> tt
0.00/0.01	U31(tt,V2) -> U32(isNat(V2))
0.00/0.01	U32(tt) -> tt
0.00/0.01	U41(tt,N) -> N
0.00/0.01	U51(tt,M,N) -> U52(isNat(N),M,N)
0.00/0.01	U52(tt,M,N) -> s(plus(N,M))
0.00/0.01	U61(tt) -> 0
0.00/0.01	U71(tt,M,N) -> U72(isNat(N),M,N)
0.00/0.01	U72(tt,M,N) -> plus(x(N,M),N)
0.00/0.01	isNat(plus(V1,V2)) -> U11(isNat(V1),V2)
0.00/0.01	isNat(x(V1,V2)) -> U31(isNat(V1),V2)
0.00/0.01	isNat(0) -> tt
0.00/0.01	isNat(s(V1)) -> U21(isNat(V1))
0.00/0.01	plus(N,0) -> U41(isNat(N),N)
0.00/0.01	plus(N,s(M)) -> U51(isNat(M),M,N)
0.00/0.01	x(N,0) -> U61(isNat(N))
0.00/0.01	x(N,s(M)) -> U71(isNat(M),M,N)
0.00/0.01	)
0.00/0.01	
0.00/0.01	Problem 1: 
0.00/0.01	
0.00/0.01	Dependency Pairs Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 U11#(tt,V2) -> U12#(isNat(V2))
0.00/0.01	 U11#(tt,V2) -> ISNAT(V2)
0.00/0.01	 U31#(tt,V2) -> U32#(isNat(V2))
0.00/0.01	 U31#(tt,V2) -> ISNAT(V2)
0.00/0.01	 U41#(tt,N) -> N
0.00/0.01	 U51#(tt,M,N) -> U52#(isNat(N),M,N)
0.00/0.01	 U51#(tt,M,N) -> ISNAT(N)
0.00/0.01	 U52#(tt,M,N) -> PLUS(N,M)
0.00/0.01	 U52#(tt,M,N) -> M
0.00/0.01	 U52#(tt,M,N) -> N
0.00/0.01	 U71#(tt,M,N) -> U72#(isNat(N),M,N)
0.00/0.01	 U71#(tt,M,N) -> ISNAT(N)
0.00/0.01	 U72#(tt,M,N) -> PLUS(x(N,M),N)
0.00/0.01	 U72#(tt,M,N) -> X(N,M)
0.00/0.01	 U72#(tt,M,N) -> M
0.00/0.01	 U72#(tt,M,N) -> N
0.00/0.01	 ISNAT(plus(V1,V2)) -> U11#(isNat(V1),V2)
0.00/0.01	 ISNAT(plus(V1,V2)) -> ISNAT(V1)
0.00/0.01	 ISNAT(x(V1,V2)) -> U31#(isNat(V1),V2)
0.00/0.01	 ISNAT(x(V1,V2)) -> ISNAT(V1)
0.00/0.01	 ISNAT(s(V1)) -> U21#(isNat(V1))
0.00/0.01	 ISNAT(s(V1)) -> ISNAT(V1)
0.00/0.01	 PLUS(N,0) -> U41#(isNat(N),N)
0.00/0.01	 PLUS(N,0) -> ISNAT(N)
0.00/0.01	 PLUS(N,s(M)) -> U51#(isNat(M),M,N)
0.00/0.01	 PLUS(N,s(M)) -> ISNAT(M)
0.00/0.01	 X(N,0) -> U61#(isNat(N))
0.00/0.01	 X(N,0) -> ISNAT(N)
0.00/0.01	 X(N,s(M)) -> U71#(isNat(M),M,N)
0.00/0.01	 X(N,s(M)) -> ISNAT(M)
0.00/0.01	-> Rules:
0.00/0.01	 U11(tt,V2) -> U12(isNat(V2))
0.00/0.01	 U12(tt) -> tt
0.00/0.01	 U21(tt) -> tt
0.00/0.01	 U31(tt,V2) -> U32(isNat(V2))
0.00/0.01	 U32(tt) -> tt
0.00/0.01	 U41(tt,N) -> N
0.00/0.01	 U51(tt,M,N) -> U52(isNat(N),M,N)
0.00/0.01	 U52(tt,M,N) -> s(plus(N,M))
0.00/0.01	 U61(tt) -> 0
0.00/0.01	 U71(tt,M,N) -> U72(isNat(N),M,N)
0.00/0.01	 U72(tt,M,N) -> plus(x(N,M),N)
0.00/0.01	 isNat(plus(V1,V2)) -> U11(isNat(V1),V2)
0.00/0.01	 isNat(x(V1,V2)) -> U31(isNat(V1),V2)
0.00/0.01	 isNat(0) -> tt
0.00/0.01	 isNat(s(V1)) -> U21(isNat(V1))
0.00/0.01	 plus(N,0) -> U41(isNat(N),N)
0.00/0.01	 plus(N,s(M)) -> U51(isNat(M),M,N)
0.00/0.01	 x(N,0) -> U61(isNat(N))
0.00/0.01	 x(N,s(M)) -> U71(isNat(M),M,N)
0.00/0.01	-> Unhiding Rules:
0.00/0.01	 Empty
0.00/0.01	
0.00/0.01	Problem 1: 
0.00/0.01	
0.00/0.01	SCC Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 U11#(tt,V2) -> U12#(isNat(V2))
0.00/0.01	 U11#(tt,V2) -> ISNAT(V2)
0.00/0.01	 U31#(tt,V2) -> U32#(isNat(V2))
0.00/0.01	 U31#(tt,V2) -> ISNAT(V2)
0.00/0.01	 U41#(tt,N) -> N
0.00/0.01	 U51#(tt,M,N) -> U52#(isNat(N),M,N)
0.00/0.01	 U51#(tt,M,N) -> ISNAT(N)
0.00/0.01	 U52#(tt,M,N) -> PLUS(N,M)
0.00/0.01	 U52#(tt,M,N) -> M
0.00/0.01	 U52#(tt,M,N) -> N
0.00/0.01	 U71#(tt,M,N) -> U72#(isNat(N),M,N)
0.00/0.01	 U71#(tt,M,N) -> ISNAT(N)
0.00/0.01	 U72#(tt,M,N) -> PLUS(x(N,M),N)
0.00/0.01	 U72#(tt,M,N) -> X(N,M)
0.00/0.01	 U72#(tt,M,N) -> M
0.00/0.01	 U72#(tt,M,N) -> N
0.00/0.01	 ISNAT(plus(V1,V2)) -> U11#(isNat(V1),V2)
0.00/0.01	 ISNAT(plus(V1,V2)) -> ISNAT(V1)
0.00/0.01	 ISNAT(x(V1,V2)) -> U31#(isNat(V1),V2)
0.00/0.01	 ISNAT(x(V1,V2)) -> ISNAT(V1)
0.00/0.01	 ISNAT(s(V1)) -> U21#(isNat(V1))
0.00/0.01	 ISNAT(s(V1)) -> ISNAT(V1)
0.00/0.01	 PLUS(N,0) -> U41#(isNat(N),N)
0.00/0.01	 PLUS(N,0) -> ISNAT(N)
0.00/0.01	 PLUS(N,s(M)) -> U51#(isNat(M),M,N)
0.00/0.01	 PLUS(N,s(M)) -> ISNAT(M)
0.00/0.01	 X(N,0) -> U61#(isNat(N))
0.00/0.01	 X(N,0) -> ISNAT(N)
0.00/0.01	 X(N,s(M)) -> U71#(isNat(M),M,N)
0.00/0.01	 X(N,s(M)) -> ISNAT(M)
0.00/0.01	-> Rules:
0.00/0.01	 U11(tt,V2) -> U12(isNat(V2))
0.00/0.01	 U12(tt) -> tt
0.00/0.01	 U21(tt) -> tt
0.00/0.01	 U31(tt,V2) -> U32(isNat(V2))
0.00/0.01	 U32(tt) -> tt
0.00/0.01	 U41(tt,N) -> N
0.00/0.01	 U51(tt,M,N) -> U52(isNat(N),M,N)
0.00/0.01	 U52(tt,M,N) -> s(plus(N,M))
0.00/0.01	 U61(tt) -> 0
0.00/0.01	 U71(tt,M,N) -> U72(isNat(N),M,N)
0.00/0.01	 U72(tt,M,N) -> plus(x(N,M),N)
0.00/0.01	 isNat(plus(V1,V2)) -> U11(isNat(V1),V2)
0.00/0.01	 isNat(x(V1,V2)) -> U31(isNat(V1),V2)
0.00/0.01	 isNat(0) -> tt
0.00/0.01	 isNat(s(V1)) -> U21(isNat(V1))
0.00/0.01	 plus(N,0) -> U41(isNat(N),N)
0.00/0.01	 plus(N,s(M)) -> U51(isNat(M),M,N)
0.00/0.01	 x(N,0) -> U61(isNat(N))
0.00/0.01	 x(N,s(M)) -> U71(isNat(M),M,N)
0.00/0.01	-> Unhiding rules:
0.00/0.01	 Empty
0.00/0.01	->Strongly Connected Components:
0.00/0.01	->->Cycle:
0.00/0.01	->->-> Pairs:
0.00/0.01	 U11#(tt,V2) -> ISNAT(V2)
0.00/0.01	 U31#(tt,V2) -> ISNAT(V2)
0.00/0.01	 ISNAT(plus(V1,V2)) -> U11#(isNat(V1),V2)
0.00/0.01	 ISNAT(plus(V1,V2)) -> ISNAT(V1)
0.00/0.01	 ISNAT(x(V1,V2)) -> U31#(isNat(V1),V2)
0.00/0.01	 ISNAT(x(V1,V2)) -> ISNAT(V1)
0.00/0.01	 ISNAT(s(V1)) -> ISNAT(V1)
0.00/0.01	->->-> Rules:
0.00/0.01	 U11(tt,V2) -> U12(isNat(V2))
0.00/0.01	 U12(tt) -> tt
0.00/0.01	 U21(tt) -> tt
0.00/0.01	 U31(tt,V2) -> U32(isNat(V2))
0.00/0.01	 U32(tt) -> tt
0.00/0.01	 U41(tt,N) -> N
0.00/0.01	 U51(tt,M,N) -> U52(isNat(N),M,N)
0.00/0.01	 U52(tt,M,N) -> s(plus(N,M))
0.00/0.01	 U61(tt) -> 0
0.00/0.01	 U71(tt,M,N) -> U72(isNat(N),M,N)
0.00/0.01	 U72(tt,M,N) -> plus(x(N,M),N)
0.00/0.01	 isNat(plus(V1,V2)) -> U11(isNat(V1),V2)
0.00/0.01	 isNat(x(V1,V2)) -> U31(isNat(V1),V2)
0.00/0.01	 isNat(0) -> tt
0.00/0.01	 isNat(s(V1)) -> U21(isNat(V1))
0.00/0.01	 plus(N,0) -> U41(isNat(N),N)
0.00/0.01	 plus(N,s(M)) -> U51(isNat(M),M,N)
0.00/0.01	 x(N,0) -> U61(isNat(N))
0.00/0.01	 x(N,s(M)) -> U71(isNat(M),M,N)
0.00/0.01	->->-> Unhiding rules:
0.00/0.01	 Empty
0.00/0.01	->->Cycle:
0.00/0.01	->->-> Pairs:
0.00/0.01	 U51#(tt,M,N) -> U52#(isNat(N),M,N)
0.00/0.01	 U52#(tt,M,N) -> PLUS(N,M)
0.00/0.01	 PLUS(N,s(M)) -> U51#(isNat(M),M,N)
0.00/0.01	->->-> Rules:
0.00/0.01	 U11(tt,V2) -> U12(isNat(V2))
0.00/0.01	 U12(tt) -> tt
0.00/0.01	 U21(tt) -> tt
0.00/0.01	 U31(tt,V2) -> U32(isNat(V2))
0.00/0.01	 U32(tt) -> tt
0.00/0.01	 U41(tt,N) -> N
0.00/0.01	 U51(tt,M,N) -> U52(isNat(N),M,N)
0.00/0.01	 U52(tt,M,N) -> s(plus(N,M))
0.00/0.01	 U61(tt) -> 0
0.00/0.01	 U71(tt,M,N) -> U72(isNat(N),M,N)
0.00/0.01	 U72(tt,M,N) -> plus(x(N,M),N)
0.00/0.01	 isNat(plus(V1,V2)) -> U11(isNat(V1),V2)
0.00/0.01	 isNat(x(V1,V2)) -> U31(isNat(V1),V2)
0.00/0.01	 isNat(0) -> tt
0.00/0.01	 isNat(s(V1)) -> U21(isNat(V1))
0.00/0.01	 plus(N,0) -> U41(isNat(N),N)
0.00/0.01	 plus(N,s(M)) -> U51(isNat(M),M,N)
0.00/0.01	 x(N,0) -> U61(isNat(N))
0.00/0.01	 x(N,s(M)) -> U71(isNat(M),M,N)
0.00/0.01	->->-> Unhiding rules:
0.00/0.01	 Empty
0.00/0.01	->->Cycle:
0.00/0.01	->->-> Pairs:
0.00/0.01	 U71#(tt,M,N) -> U72#(isNat(N),M,N)
0.00/0.01	 U72#(tt,M,N) -> X(N,M)
0.00/0.01	 X(N,s(M)) -> U71#(isNat(M),M,N)
0.00/0.01	->->-> Rules:
0.00/0.01	 U11(tt,V2) -> U12(isNat(V2))
0.00/0.01	 U12(tt) -> tt
0.00/0.01	 U21(tt) -> tt
0.00/0.01	 U31(tt,V2) -> U32(isNat(V2))
0.00/0.01	 U32(tt) -> tt
0.00/0.01	 U41(tt,N) -> N
0.00/0.01	 U51(tt,M,N) -> U52(isNat(N),M,N)
0.00/0.01	 U52(tt,M,N) -> s(plus(N,M))
0.00/0.01	 U61(tt) -> 0
0.00/0.01	 U71(tt,M,N) -> U72(isNat(N),M,N)
0.00/0.01	 U72(tt,M,N) -> plus(x(N,M),N)
0.00/0.01	 isNat(plus(V1,V2)) -> U11(isNat(V1),V2)
0.00/0.01	 isNat(x(V1,V2)) -> U31(isNat(V1),V2)
0.00/0.01	 isNat(0) -> tt
0.00/0.01	 isNat(s(V1)) -> U21(isNat(V1))
0.00/0.01	 plus(N,0) -> U41(isNat(N),N)
0.00/0.01	 plus(N,s(M)) -> U51(isNat(M),M,N)
0.00/0.01	 x(N,0) -> U61(isNat(N))
0.00/0.01	 x(N,s(M)) -> U71(isNat(M),M,N)
0.00/0.01	->->-> Unhiding rules:
0.00/0.01	 Empty
0.00/0.01	
0.00/0.01	
0.00/0.01	The problem is decomposed in 3 subproblems.
0.00/0.01	
0.00/0.01	Problem 1.1: 
0.00/0.01	
0.00/0.01	SubNColl Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 U11#(tt,V2) -> ISNAT(V2)
0.00/0.01	 U31#(tt,V2) -> ISNAT(V2)
0.00/0.01	 ISNAT(plus(V1,V2)) -> U11#(isNat(V1),V2)
0.00/0.01	 ISNAT(plus(V1,V2)) -> ISNAT(V1)
0.00/0.01	 ISNAT(x(V1,V2)) -> U31#(isNat(V1),V2)
0.00/0.01	 ISNAT(x(V1,V2)) -> ISNAT(V1)
0.00/0.01	 ISNAT(s(V1)) -> ISNAT(V1)
0.00/0.01	-> Rules:
0.00/0.01	 U11(tt,V2) -> U12(isNat(V2))
0.00/0.01	 U12(tt) -> tt
0.00/0.01	 U21(tt) -> tt
0.00/0.01	 U31(tt,V2) -> U32(isNat(V2))
0.00/0.01	 U32(tt) -> tt
0.00/0.01	 U41(tt,N) -> N
0.00/0.01	 U51(tt,M,N) -> U52(isNat(N),M,N)
0.00/0.01	 U52(tt,M,N) -> s(plus(N,M))
0.00/0.01	 U61(tt) -> 0
0.00/0.01	 U71(tt,M,N) -> U72(isNat(N),M,N)
0.00/0.01	 U72(tt,M,N) -> plus(x(N,M),N)
0.00/0.01	 isNat(plus(V1,V2)) -> U11(isNat(V1),V2)
0.00/0.01	 isNat(x(V1,V2)) -> U31(isNat(V1),V2)
0.00/0.01	 isNat(0) -> tt
0.00/0.01	 isNat(s(V1)) -> U21(isNat(V1))
0.00/0.01	 plus(N,0) -> U41(isNat(N),N)
0.00/0.01	 plus(N,s(M)) -> U51(isNat(M),M,N)
0.00/0.01	 x(N,0) -> U61(isNat(N))
0.00/0.01	 x(N,s(M)) -> U71(isNat(M),M,N)
0.00/0.01	-> Unhiding rules:
0.00/0.01	 Empty
0.00/0.01	->Projection:
0.00/0.01	 pi(U11#) = 2
0.00/0.01	 pi(U31#) = 2
0.00/0.01	 pi(ISNAT) = 1
0.00/0.01	
0.00/0.01	Problem 1.1: 
0.00/0.01	
0.00/0.01	SCC Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 U11#(tt,V2) -> ISNAT(V2)
0.00/0.01	 U31#(tt,V2) -> ISNAT(V2)
0.00/0.01	-> Rules:
0.00/0.01	 U11(tt,V2) -> U12(isNat(V2))
0.00/0.01	 U12(tt) -> tt
0.00/0.01	 U21(tt) -> tt
0.00/0.01	 U31(tt,V2) -> U32(isNat(V2))
0.00/0.01	 U32(tt) -> tt
0.00/0.01	 U41(tt,N) -> N
0.00/0.01	 U51(tt,M,N) -> U52(isNat(N),M,N)
0.00/0.01	 U52(tt,M,N) -> s(plus(N,M))
0.00/0.01	 U61(tt) -> 0
0.00/0.01	 U71(tt,M,N) -> U72(isNat(N),M,N)
0.00/0.01	 U72(tt,M,N) -> plus(x(N,M),N)
0.00/0.01	 isNat(plus(V1,V2)) -> U11(isNat(V1),V2)
0.00/0.01	 isNat(x(V1,V2)) -> U31(isNat(V1),V2)
0.00/0.01	 isNat(0) -> tt
0.00/0.01	 isNat(s(V1)) -> U21(isNat(V1))
0.00/0.01	 plus(N,0) -> U41(isNat(N),N)
0.00/0.01	 plus(N,s(M)) -> U51(isNat(M),M,N)
0.00/0.01	 x(N,0) -> U61(isNat(N))
0.00/0.01	 x(N,s(M)) -> U71(isNat(M),M,N)
0.00/0.01	-> Unhiding rules:
0.00/0.01	 Empty
0.00/0.01	->Strongly Connected Components:
0.00/0.01	 There is no strongly connected component
0.00/0.01	
0.00/0.01	The problem is finite.
0.00/0.01	
0.00/0.01	Problem 1.2: 
0.00/0.01	
0.00/0.01	SubNColl Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 U51#(tt,M,N) -> U52#(isNat(N),M,N)
0.00/0.01	 U52#(tt,M,N) -> PLUS(N,M)
0.00/0.01	 PLUS(N,s(M)) -> U51#(isNat(M),M,N)
0.00/0.01	-> Rules:
0.00/0.01	 U11(tt,V2) -> U12(isNat(V2))
0.00/0.01	 U12(tt) -> tt
0.00/0.01	 U21(tt) -> tt
0.00/0.01	 U31(tt,V2) -> U32(isNat(V2))
0.00/0.01	 U32(tt) -> tt
0.00/0.01	 U41(tt,N) -> N
0.00/0.01	 U51(tt,M,N) -> U52(isNat(N),M,N)
0.00/0.01	 U52(tt,M,N) -> s(plus(N,M))
0.00/0.01	 U61(tt) -> 0
0.00/0.01	 U71(tt,M,N) -> U72(isNat(N),M,N)
0.00/0.01	 U72(tt,M,N) -> plus(x(N,M),N)
0.00/0.01	 isNat(plus(V1,V2)) -> U11(isNat(V1),V2)
0.00/0.01	 isNat(x(V1,V2)) -> U31(isNat(V1),V2)
0.00/0.01	 isNat(0) -> tt
0.00/0.01	 isNat(s(V1)) -> U21(isNat(V1))
0.00/0.01	 plus(N,0) -> U41(isNat(N),N)
0.00/0.01	 plus(N,s(M)) -> U51(isNat(M),M,N)
0.00/0.01	 x(N,0) -> U61(isNat(N))
0.00/0.01	 x(N,s(M)) -> U71(isNat(M),M,N)
0.00/0.01	-> Unhiding rules:
0.00/0.01	 Empty
0.00/0.01	->Projection:
0.00/0.01	 pi(U51#) = 2
0.00/0.01	 pi(U52#) = 2
0.00/0.01	 pi(PLUS) = 2
0.00/0.01	
0.00/0.01	Problem 1.2: 
0.00/0.01	
0.00/0.01	SCC Processor:
0.00/0.01	-> Pairs:
0.00/0.02	 U51#(tt,M,N) -> U52#(isNat(N),M,N)
0.00/0.02	 U52#(tt,M,N) -> PLUS(N,M)
0.00/0.02	-> Rules:
0.00/0.02	 U11(tt,V2) -> U12(isNat(V2))
0.00/0.02	 U12(tt) -> tt
0.00/0.02	 U21(tt) -> tt
0.00/0.02	 U31(tt,V2) -> U32(isNat(V2))
0.00/0.02	 U32(tt) -> tt
0.00/0.02	 U41(tt,N) -> N
0.00/0.02	 U51(tt,M,N) -> U52(isNat(N),M,N)
0.00/0.02	 U52(tt,M,N) -> s(plus(N,M))
0.00/0.02	 U61(tt) -> 0
0.00/0.02	 U71(tt,M,N) -> U72(isNat(N),M,N)
0.00/0.02	 U72(tt,M,N) -> plus(x(N,M),N)
0.00/0.02	 isNat(plus(V1,V2)) -> U11(isNat(V1),V2)
0.00/0.02	 isNat(x(V1,V2)) -> U31(isNat(V1),V2)
0.00/0.02	 isNat(0) -> tt
0.00/0.02	 isNat(s(V1)) -> U21(isNat(V1))
0.00/0.02	 plus(N,0) -> U41(isNat(N),N)
0.00/0.02	 plus(N,s(M)) -> U51(isNat(M),M,N)
0.00/0.02	 x(N,0) -> U61(isNat(N))
0.00/0.02	 x(N,s(M)) -> U71(isNat(M),M,N)
0.00/0.02	-> Unhiding rules:
0.00/0.02	 Empty
0.00/0.02	->Strongly Connected Components:
0.00/0.02	 There is no strongly connected component
0.00/0.02	
0.00/0.02	The problem is finite.
0.00/0.02	
0.00/0.02	Problem 1.3: 
0.00/0.02	
0.00/0.02	SubNColl Processor:
0.00/0.02	-> Pairs:
0.00/0.02	 U71#(tt,M,N) -> U72#(isNat(N),M,N)
0.00/0.02	 U72#(tt,M,N) -> X(N,M)
0.00/0.02	 X(N,s(M)) -> U71#(isNat(M),M,N)
0.00/0.02	-> Rules:
0.00/0.02	 U11(tt,V2) -> U12(isNat(V2))
0.00/0.02	 U12(tt) -> tt
0.00/0.02	 U21(tt) -> tt
0.00/0.02	 U31(tt,V2) -> U32(isNat(V2))
0.00/0.02	 U32(tt) -> tt
0.00/0.02	 U41(tt,N) -> N
0.00/0.02	 U51(tt,M,N) -> U52(isNat(N),M,N)
0.00/0.02	 U52(tt,M,N) -> s(plus(N,M))
0.00/0.02	 U61(tt) -> 0
0.00/0.02	 U71(tt,M,N) -> U72(isNat(N),M,N)
0.00/0.02	 U72(tt,M,N) -> plus(x(N,M),N)
0.00/0.02	 isNat(plus(V1,V2)) -> U11(isNat(V1),V2)
0.00/0.02	 isNat(x(V1,V2)) -> U31(isNat(V1),V2)
0.00/0.02	 isNat(0) -> tt
0.00/0.02	 isNat(s(V1)) -> U21(isNat(V1))
0.00/0.02	 plus(N,0) -> U41(isNat(N),N)
0.00/0.02	 plus(N,s(M)) -> U51(isNat(M),M,N)
0.00/0.02	 x(N,0) -> U61(isNat(N))
0.00/0.02	 x(N,s(M)) -> U71(isNat(M),M,N)
0.00/0.02	-> Unhiding rules:
0.00/0.02	 Empty
0.00/0.02	->Projection:
0.00/0.02	 pi(U71#) = 2
0.00/0.02	 pi(U72#) = 2
0.00/0.02	 pi(X) = 2
0.00/0.02	
0.00/0.02	Problem 1.3: 
0.00/0.02	
0.00/0.02	SCC Processor:
0.00/0.02	-> Pairs:
0.00/0.02	 U71#(tt,M,N) -> U72#(isNat(N),M,N)
0.00/0.02	 U72#(tt,M,N) -> X(N,M)
0.00/0.02	-> Rules:
0.00/0.02	 U11(tt,V2) -> U12(isNat(V2))
0.00/0.02	 U12(tt) -> tt
0.00/0.02	 U21(tt) -> tt
0.00/0.02	 U31(tt,V2) -> U32(isNat(V2))
0.00/0.02	 U32(tt) -> tt
0.00/0.02	 U41(tt,N) -> N
0.00/0.02	 U51(tt,M,N) -> U52(isNat(N),M,N)
0.00/0.02	 U52(tt,M,N) -> s(plus(N,M))
0.00/0.02	 U61(tt) -> 0
0.00/0.02	 U71(tt,M,N) -> U72(isNat(N),M,N)
0.00/0.02	 U72(tt,M,N) -> plus(x(N,M),N)
0.00/0.02	 isNat(plus(V1,V2)) -> U11(isNat(V1),V2)
0.00/0.02	 isNat(x(V1,V2)) -> U31(isNat(V1),V2)
0.00/0.02	 isNat(0) -> tt
0.00/0.02	 isNat(s(V1)) -> U21(isNat(V1))
0.00/0.02	 plus(N,0) -> U41(isNat(N),N)
0.00/0.02	 plus(N,s(M)) -> U51(isNat(M),M,N)
0.00/0.02	 x(N,0) -> U61(isNat(N))
0.00/0.02	 x(N,s(M)) -> U71(isNat(M),M,N)
0.00/0.02	-> Unhiding rules:
0.00/0.02	 Empty
0.00/0.02	->Strongly Connected Components:
0.00/0.02	 There is no strongly connected component
0.00/0.02	
0.00/0.02	The problem is finite.
0.00/0.02	EOF