MAYBE
0.18/0.28	MAYBE
0.18/0.29	
0.18/0.29	Problem:
0.18/0.29	 active(U11(tt(),V1,V2)) -> mark(U12(isNat(V1),V2))
0.18/0.29	 active(U12(tt(),V2)) -> mark(U13(isNat(V2)))
0.18/0.29	 active(U13(tt())) -> mark(tt())
0.18/0.29	 active(U21(tt(),V1)) -> mark(U22(isNat(V1)))
0.18/0.29	 active(U22(tt())) -> mark(tt())
0.18/0.29	 active(U31(tt(),V1,V2)) -> mark(U32(isNat(V1),V2))
0.18/0.29	 active(U32(tt(),V2)) -> mark(U33(isNat(V2)))
0.18/0.29	 active(U33(tt())) -> mark(tt())
0.18/0.29	 active(U41(tt(),N)) -> mark(N)
0.18/0.29	 active(U51(tt(),M,N)) -> mark(s(plus(N,M)))
0.18/0.29	 active(U61(tt())) -> mark(0())
0.18/0.29	 active(U71(tt(),M,N)) -> mark(plus(x(N,M),N))
0.18/0.29	 active(and(tt(),X)) -> mark(X)
0.18/0.29	 active(isNat(0())) -> mark(tt())
0.18/0.29	 active(isNat(plus(V1,V2))) -> mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2))
0.18/0.29	 active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
0.18/0.29	 active(isNat(x(V1,V2))) -> mark(U31(and(isNatKind(V1),isNatKind(V2)),V1,V2))
0.18/0.29	 active(isNatKind(0())) -> mark(tt())
0.18/0.29	 active(isNatKind(plus(V1,V2))) -> mark(and(isNatKind(V1),isNatKind(V2)))
0.18/0.29	 active(isNatKind(s(V1))) -> mark(isNatKind(V1))
0.18/0.29	 active(isNatKind(x(V1,V2))) -> mark(and(isNatKind(V1),isNatKind(V2)))
0.18/0.29	 active(plus(N,0())) -> mark(U41(and(isNat(N),isNatKind(N)),N))
0.18/0.30	 active(plus(N,s(M))) -> mark(U51(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))
0.18/0.30	 active(x(N,0())) -> mark(U61(and(isNat(N),isNatKind(N))))
0.18/0.30	 active(x(N,s(M))) -> mark(U71(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N))
0.18/0.30	 active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
0.18/0.30	 active(U12(X1,X2)) -> U12(active(X1),X2)
0.18/0.30	 active(U13(X)) -> U13(active(X))
0.18/0.30	 active(U21(X1,X2)) -> U21(active(X1),X2)
0.18/0.30	 active(U22(X)) -> U22(active(X))
0.18/0.30	 active(U31(X1,X2,X3)) -> U31(active(X1),X2,X3)
0.18/0.30	 active(U32(X1,X2)) -> U32(active(X1),X2)
0.18/0.30	 active(U33(X)) -> U33(active(X))
0.18/0.30	 active(U41(X1,X2)) -> U41(active(X1),X2)
0.18/0.30	 active(U51(X1,X2,X3)) -> U51(active(X1),X2,X3)
0.18/0.30	 active(s(X)) -> s(active(X))
0.18/0.30	 active(plus(X1,X2)) -> plus(active(X1),X2)
0.18/0.30	 active(plus(X1,X2)) -> plus(X1,active(X2))
0.18/0.30	 active(U61(X)) -> U61(active(X))
0.18/0.30	 active(U71(X1,X2,X3)) -> U71(active(X1),X2,X3)
0.18/0.30	 active(x(X1,X2)) -> x(active(X1),X2)
0.18/0.30	 active(x(X1,X2)) -> x(X1,active(X2))
0.18/0.30	 active(and(X1,X2)) -> and(active(X1),X2)
0.18/0.30	 U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
0.18/0.30	 U12(mark(X1),X2) -> mark(U12(X1,X2))
0.18/0.30	 U13(mark(X)) -> mark(U13(X))
0.18/0.30	 U21(mark(X1),X2) -> mark(U21(X1,X2))
0.18/0.30	 U22(mark(X)) -> mark(U22(X))
0.18/0.30	 U31(mark(X1),X2,X3) -> mark(U31(X1,X2,X3))
0.18/0.30	 U32(mark(X1),X2) -> mark(U32(X1,X2))
0.18/0.30	 U33(mark(X)) -> mark(U33(X))
0.18/0.30	 U41(mark(X1),X2) -> mark(U41(X1,X2))
0.18/0.30	 U51(mark(X1),X2,X3) -> mark(U51(X1,X2,X3))
0.18/0.30	 s(mark(X)) -> mark(s(X))
0.18/0.30	 plus(mark(X1),X2) -> mark(plus(X1,X2))
0.18/0.30	 plus(X1,mark(X2)) -> mark(plus(X1,X2))
0.18/0.30	 U61(mark(X)) -> mark(U61(X))
0.18/0.30	 U71(mark(X1),X2,X3) -> mark(U71(X1,X2,X3))
0.18/0.30	 x(mark(X1),X2) -> mark(x(X1,X2))
0.18/0.30	 x(X1,mark(X2)) -> mark(x(X1,X2))
0.18/0.30	 and(mark(X1),X2) -> mark(and(X1,X2))
0.18/0.30	 proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
0.18/0.30	 proper(tt()) -> ok(tt())
0.18/0.30	 proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
0.18/0.30	 proper(isNat(X)) -> isNat(proper(X))
0.18/0.30	 proper(U13(X)) -> U13(proper(X))
0.18/0.30	 proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
0.18/0.30	 proper(U22(X)) -> U22(proper(X))
0.18/0.30	 proper(U31(X1,X2,X3)) -> U31(proper(X1),proper(X2),proper(X3))
0.18/0.30	 proper(U32(X1,X2)) -> U32(proper(X1),proper(X2))
0.18/0.30	 proper(U33(X)) -> U33(proper(X))
0.18/0.30	 proper(U41(X1,X2)) -> U41(proper(X1),proper(X2))
0.18/0.30	 proper(U51(X1,X2,X3)) -> U51(proper(X1),proper(X2),proper(X3))
0.18/0.30	 proper(s(X)) -> s(proper(X))
0.18/0.30	 proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
0.18/0.30	 proper(U61(X)) -> U61(proper(X))
0.18/0.30	 proper(0()) -> ok(0())
0.18/0.30	 proper(U71(X1,X2,X3)) -> U71(proper(X1),proper(X2),proper(X3))
0.18/0.30	 proper(x(X1,X2)) -> x(proper(X1),proper(X2))
0.18/0.30	 proper(and(X1,X2)) -> and(proper(X1),proper(X2))
0.18/0.30	 proper(isNatKind(X)) -> isNatKind(proper(X))
0.18/0.30	 U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
0.18/0.30	 U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
0.18/0.30	 isNat(ok(X)) -> ok(isNat(X))
0.18/0.30	 U13(ok(X)) -> ok(U13(X))
0.18/0.30	 U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
0.18/0.30	 U22(ok(X)) -> ok(U22(X))
0.18/0.30	 U31(ok(X1),ok(X2),ok(X3)) -> ok(U31(X1,X2,X3))
0.18/0.30	 U32(ok(X1),ok(X2)) -> ok(U32(X1,X2))
0.18/0.30	 U33(ok(X)) -> ok(U33(X))
0.18/0.30	 U41(ok(X1),ok(X2)) -> ok(U41(X1,X2))
0.18/0.30	 U51(ok(X1),ok(X2),ok(X3)) -> ok(U51(X1,X2,X3))
0.18/0.30	 s(ok(X)) -> ok(s(X))
0.18/0.30	 plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
0.18/0.30	 U61(ok(X)) -> ok(U61(X))
0.18/0.30	 U71(ok(X1),ok(X2),ok(X3)) -> ok(U71(X1,X2,X3))
0.18/0.30	 x(ok(X1),ok(X2)) -> ok(x(X1,X2))
0.18/0.30	 and(ok(X1),ok(X2)) -> ok(and(X1,X2))
0.18/0.30	 isNatKind(ok(X)) -> ok(isNatKind(X))
0.18/0.30	 top(mark(X)) -> top(proper(X))
0.18/0.30	 top(ok(X)) -> top(active(X))
0.18/0.30	
0.18/0.30	Proof:
0.18/0.30	 Open
0.18/0.30	EOF