(VAR V2 N M V1 X1 X2 X3 X) (RULES active(U11(tt,V2)) -> mark(U12(isNat(V2))) active(U12(tt)) -> mark(tt) active(U21(tt)) -> mark(tt) active(U31(tt,N)) -> mark(N) active(U41(tt,M,N)) -> mark(U42(isNat(N),M,N)) active(U42(tt,M,N)) -> mark(s(plus(N,M))) active(isNat(0)) -> mark(tt) active(isNat(plus(V1,V2))) -> mark(U11(isNat(V1),V2)) active(isNat(s(V1))) -> mark(U21(isNat(V1))) active(plus(N,0)) -> mark(U31(isNat(N),N)) active(plus(N,s(M))) -> mark(U41(isNat(M),M,N)) active(U11(X1,X2)) -> U11(active(X1),X2) active(U12(X)) -> U12(active(X)) active(U21(X)) -> U21(active(X)) active(U31(X1,X2)) -> U31(active(X1),X2) active(U41(X1,X2,X3)) -> U41(active(X1),X2,X3) active(U42(X1,X2,X3)) -> U42(active(X1),X2,X3) active(s(X)) -> s(active(X)) active(plus(X1,X2)) -> plus(active(X1),X2) active(plus(X1,X2)) -> plus(X1,active(X2)) U11(mark(X1),X2) -> mark(U11(X1,X2)) U12(mark(X)) -> mark(U12(X)) U21(mark(X)) -> mark(U21(X)) U31(mark(X1),X2) -> mark(U31(X1,X2)) U41(mark(X1),X2,X3) -> mark(U41(X1,X2,X3)) U42(mark(X1),X2,X3) -> mark(U42(X1,X2,X3)) s(mark(X)) -> mark(s(X)) plus(mark(X1),X2) -> mark(plus(X1,X2)) plus(X1,mark(X2)) -> mark(plus(X1,X2)) proper(U11(X1,X2)) -> U11(proper(X1),proper(X2)) proper(tt) -> ok(tt) proper(U12(X)) -> U12(proper(X)) proper(isNat(X)) -> isNat(proper(X)) proper(U21(X)) -> U21(proper(X)) proper(U31(X1,X2)) -> U31(proper(X1),proper(X2)) proper(U41(X1,X2,X3)) -> U41(proper(X1),proper(X2),proper(X3)) proper(U42(X1,X2,X3)) -> U42(proper(X1),proper(X2),proper(X3)) proper(s(X)) -> s(proper(X)) proper(plus(X1,X2)) -> plus(proper(X1),proper(X2)) proper(0) -> ok(0) U11(ok(X1),ok(X2)) -> ok(U11(X1,X2)) U12(ok(X)) -> ok(U12(X)) isNat(ok(X)) -> ok(isNat(X)) U21(ok(X)) -> ok(U21(X)) U31(ok(X1),ok(X2)) -> ok(U31(X1,X2)) U41(ok(X1),ok(X2),ok(X3)) -> ok(U41(X1,X2,X3)) U42(ok(X1),ok(X2),ok(X3)) -> ok(U42(X1,X2,X3)) s(ok(X)) -> ok(s(X)) plus(ok(X1),ok(X2)) -> ok(plus(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) )