(VAR M N V1 V2 X X1 X2 X3 )
(RULES 
        a__U11(tt, V2) -> a__U12(a__isNat(V2))
        a__U12(tt) -> tt
        a__U21(tt) -> tt
        a__U31(tt, N) -> mark(N)
        a__U41(tt, M, N) -> a__U42(a__isNat(N), M, N)
        a__U42(tt, M, N) -> s(a__plus(mark(N), mark(M)))
        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__plus(N, 0) -> a__U31(a__isNat(N), N)
        a__plus(N, s(M)) -> a__U41(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(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
        mark(U42(X1, X2, X3)) -> a__U42(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) -> 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__U41(X1, X2, X3) -> U41(X1, X2, X3)
        a__U42(X1, X2, X3) -> U42(X1, X2, X3)
        a__plus(X1, X2) -> plus(X1, X2)
        
)