(VAR V2 N M V1 X1 X2 X3 X)
(RULES 
a__U11(tt,V2) -> a__U12(a__isNat(V2))
a__U12(tt) -> tt
a__U21(tt) -> tt
a__U31(tt,V2) -> a__U32(a__isNat(V2))
a__U32(tt) -> tt
a__U41(tt,N) -> mark(N)
a__U51(tt,M,N) -> a__U52(a__isNat(N),M,N)
a__U52(tt,M,N) -> s(a__plus(mark(N),mark(M)))
a__U61(tt) -> 0
a__U71(tt,M,N) -> a__U72(a__isNat(N),M,N)
a__U72(tt,M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N))
a__isNat(0) -> tt
a__isNat(plus(V1,V2)) -> a__U11(a__isNat(V1),V2)
a__isNat(s(V1)) -> a__U21(a__isNat(V1))
a__isNat(x(V1,V2)) -> a__U31(a__isNat(V1),V2)
a__plus(N,0) -> a__U41(a__isNat(N),N)
a__plus(N,s(M)) -> a__U51(a__isNat(M),M,N)
a__x(N,0) -> a__U61(a__isNat(N))
a__x(N,s(M)) -> a__U71(a__isNat(M),M,N)
mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
mark(U12(X)) -> a__U12(mark(X))
mark(isNat(X)) -> a__isNat(X)
mark(U21(X)) -> a__U21(mark(X))
mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
mark(U32(X)) -> a__U32(mark(X))
mark(U41(X1,X2)) -> a__U41(mark(X1),X2)
mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3)
mark(U52(X1,X2,X3)) -> a__U52(mark(X1),X2,X3)
mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
mark(U61(X)) -> a__U61(mark(X))
mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3)
mark(U72(X1,X2,X3)) -> a__U72(mark(X1),X2,X3)
mark(x(X1,X2)) -> a__x(mark(X1),mark(X2))
mark(tt) -> tt
mark(s(X)) -> s(mark(X))
mark(0) -> 0
a__U11(X1,X2) -> U11(X1,X2)
a__U12(X) -> U12(X)
a__isNat(X) -> isNat(X)
a__U21(X) -> U21(X)
a__U31(X1,X2) -> U31(X1,X2)
a__U32(X) -> U32(X)
a__U41(X1,X2) -> U41(X1,X2)
a__U51(X1,X2,X3) -> U51(X1,X2,X3)
a__U52(X1,X2,X3) -> U52(X1,X2,X3)
a__plus(X1,X2) -> plus(X1,X2)
a__U61(X) -> U61(X)
a__U71(X1,X2,X3) -> U71(X1,X2,X3)
a__U72(X1,X2,X3) -> U72(X1,X2,X3)
a__x(X1,X2) -> x(X1,X2)
)