(VAR N M X V1 V2 X1 X2) (RULES U11(tt,N) -> activate(N) U21(tt,M,N) -> s(plus(activate(N),activate(M))) and(tt,X) -> activate(X) isNat(n__0) -> tt isNat(n__plus(V1,V2)) -> and(isNat(activate(V1)),n__isNat(activate(V2))) isNat(n__s(V1)) -> isNat(activate(V1)) plus(N,0) -> U11(isNat(N),N) plus(N,s(M)) -> U21(and(isNat(M),n__isNat(N)),M,N) 0 -> n__0 plus(X1,X2) -> n__plus(X1,X2) isNat(X) -> n__isNat(X) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2)) activate(n__isNat(X)) -> isNat(X) activate(n__s(X)) -> s(activate(X)) activate(X) -> X )