(VAR V1 V2 N M X1 X2 X3 X)
(RULES 
a__U11(tt,V1,V2) -> a__U12(a__isNatKind(V1),V1,V2)
a__U12(tt,V1,V2) -> a__U13(a__isNatKind(V2),V1,V2)
a__U13(tt,V1,V2) -> a__U14(a__isNatKind(V2),V1,V2)
a__U14(tt,V1,V2) -> a__U15(a__isNat(V1),V2)
a__U15(tt,V2) -> a__U16(a__isNat(V2))
a__U16(tt) -> tt
a__U21(tt,V1) -> a__U22(a__isNatKind(V1),V1)
a__U22(tt,V1) -> a__U23(a__isNat(V1))
a__U23(tt) -> tt
a__U31(tt,V2) -> a__U32(a__isNatKind(V2))
a__U32(tt) -> tt
a__U41(tt) -> tt
a__U51(tt,N) -> a__U52(a__isNatKind(N),N)
a__U52(tt,N) -> mark(N)
a__U61(tt,M,N) -> a__U62(a__isNatKind(M),M,N)
a__U62(tt,M,N) -> a__U63(a__isNat(N),M,N)
a__U63(tt,M,N) -> a__U64(a__isNatKind(N),M,N)
a__U64(tt,M,N) -> s(a__plus(mark(N),mark(M)))
a__isNat(0) -> tt
a__isNat(plus(V1,V2)) -> a__U11(a__isNatKind(V1),V1,V2)
a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1)
a__isNatKind(0) -> tt
a__isNatKind(plus(V1,V2)) -> a__U31(a__isNatKind(V1),V2)
a__isNatKind(s(V1)) -> a__U41(a__isNatKind(V1))
a__plus(N,0) -> a__U51(a__isNat(N),N)
a__plus(N,s(M)) -> a__U61(a__isNat(M),M,N)
mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
mark(U12(X1,X2,X3)) -> a__U12(mark(X1),X2,X3)
mark(isNatKind(X)) -> a__isNatKind(X)
mark(U13(X1,X2,X3)) -> a__U13(mark(X1),X2,X3)
mark(U14(X1,X2,X3)) -> a__U14(mark(X1),X2,X3)
mark(U15(X1,X2)) -> a__U15(mark(X1),X2)
mark(isNat(X)) -> a__isNat(X)
mark(U16(X)) -> a__U16(mark(X))
mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
mark(U22(X1,X2)) -> a__U22(mark(X1),X2)
mark(U23(X)) -> a__U23(mark(X))
mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
mark(U32(X)) -> a__U32(mark(X))
mark(U41(X)) -> a__U41(mark(X))
mark(U51(X1,X2)) -> a__U51(mark(X1),X2)
mark(U52(X1,X2)) -> a__U52(mark(X1),X2)
mark(U61(X1,X2,X3)) -> a__U61(mark(X1),X2,X3)
mark(U62(X1,X2,X3)) -> a__U62(mark(X1),X2,X3)
mark(U63(X1,X2,X3)) -> a__U63(mark(X1),X2,X3)
mark(U64(X1,X2,X3)) -> a__U64(mark(X1),X2,X3)
mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
mark(tt) -> tt
mark(s(X)) -> s(mark(X))
mark(0) -> 0
a__U11(X1,X2,X3) -> U11(X1,X2,X3)
a__U12(X1,X2,X3) -> U12(X1,X2,X3)
a__isNatKind(X) -> isNatKind(X)
a__U13(X1,X2,X3) -> U13(X1,X2,X3)
a__U14(X1,X2,X3) -> U14(X1,X2,X3)
a__U15(X1,X2) -> U15(X1,X2)
a__isNat(X) -> isNat(X)
a__U16(X) -> U16(X)
a__U21(X1,X2) -> U21(X1,X2)
a__U22(X1,X2) -> U22(X1,X2)
a__U23(X) -> U23(X)
a__U31(X1,X2) -> U31(X1,X2)
a__U32(X) -> U32(X)
a__U41(X) -> U41(X)
a__U51(X1,X2) -> U51(X1,X2)
a__U52(X1,X2) -> U52(X1,X2)
a__U61(X1,X2,X3) -> U61(X1,X2,X3)
a__U62(X1,X2,X3) -> U62(X1,X2,X3)
a__U63(X1,X2,X3) -> U63(X1,X2,X3)
a__U64(X1,X2,X3) -> U64(X1,X2,X3)
a__plus(X1,X2) -> plus(X1,X2)
)