(VAR V1 V2 N M X X1 X2 X3) (RULES a__U11(tt,V1,V2) -> a__U12(a__isNat(V1),V2) a__U12(tt,V2) -> a__U13(a__isNat(V2)) a__U13(tt) -> tt a__U21(tt,V1) -> a__U22(a__isNat(V1)) a__U22(tt) -> tt a__U31(tt,V1,V2) -> a__U32(a__isNat(V1),V2) a__U32(tt,V2) -> a__U33(a__isNat(V2)) a__U33(tt) -> tt a__U41(tt,N) -> mark(N) a__U51(tt,M,N) -> s(a__plus(mark(N),mark(M))) a__U61(tt) -> 0 a__U71(tt,M,N) -> a__plus(a__x(mark(N),mark(M)),mark(N)) a__and(tt,X) -> mark(X) a__isNat(0) -> tt a__isNat(plus(V1,V2)) -> a__U11(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNat(x(V1,V2)) -> a__U31(a__and(a__isNatKind(V1),isNatKind(V2)),V1,V2) a__isNatKind(0) -> tt a__isNatKind(plus(V1,V2)) -> a__and(a__isNatKind(V1),isNatKind(V2)) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatKind(x(V1,V2)) -> a__and(a__isNatKind(V1),isNatKind(V2)) a__plus(N,0) -> a__U41(a__and(a__isNat(N),isNatKind(N)),N) a__plus(N,s(M)) -> a__U51(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N) a__x(N,0) -> a__U61(a__and(a__isNat(N),isNatKind(N))) a__x(N,s(M)) -> a__U71(a__and(a__and(a__isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N) mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3) mark(U12(X1,X2)) -> a__U12(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(U13(X)) -> a__U13(mark(X)) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(U31(X1,X2,X3)) -> a__U31(mark(X1),X2,X3) mark(U32(X1,X2)) -> a__U32(mark(X1),X2) mark(U33(X)) -> a__U33(mark(X)) mark(U41(X1,X2)) -> a__U41(mark(X1),X2) mark(U51(X1,X2,X3)) -> a__U51(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(x(X1,X2)) -> a__x(mark(X1),mark(X2)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatKind(X)) -> a__isNatKind(X) 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) -> U12(X1,X2) a__isNat(X) -> isNat(X) a__U13(X) -> U13(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__U31(X1,X2,X3) -> U31(X1,X2,X3) a__U32(X1,X2) -> U32(X1,X2) a__U33(X) -> U33(X) a__U41(X1,X2) -> U41(X1,X2) a__U51(X1,X2,X3) -> U51(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__x(X1,X2) -> x(X1,X2) a__and(X1,X2) -> and(X1,X2) a__isNatKind(X) -> isNatKind(X) )