MAYBE

Problem:
 active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
 active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
 active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
 active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
 active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
 active(U16(tt())) -> mark(tt())
 active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
 active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
 active(U23(tt())) -> mark(tt())
 active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
 active(U32(tt())) -> mark(tt())
 active(U41(tt())) -> mark(tt())
 active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
 active(U52(tt(),N)) -> mark(N)
 active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
 active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
 active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
 active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
 active(isNat(0())) -> mark(tt())
 active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
 active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
 active(isNatKind(0())) -> mark(tt())
 active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
 active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
 active(plus(N,0())) -> mark(U51(isNat(N),N))
 active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
 active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
 active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
 active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
 active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
 active(U15(X1,X2)) -> U15(active(X1),X2)
 active(U16(X)) -> U16(active(X))
 active(U21(X1,X2)) -> U21(active(X1),X2)
 active(U22(X1,X2)) -> U22(active(X1),X2)
 active(U23(X)) -> U23(active(X))
 active(U31(X1,X2)) -> U31(active(X1),X2)
 active(U32(X)) -> U32(active(X))
 active(U41(X)) -> U41(active(X))
 active(U51(X1,X2)) -> U51(active(X1),X2)
 active(U52(X1,X2)) -> U52(active(X1),X2)
 active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
 active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
 active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
 active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
 U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
 U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
 U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
 U15(mark(X1),X2) -> mark(U15(X1,X2))
 U16(mark(X)) -> mark(U16(X))
 U21(mark(X1),X2) -> mark(U21(X1,X2))
 U22(mark(X1),X2) -> mark(U22(X1,X2))
 U23(mark(X)) -> mark(U23(X))
 U31(mark(X1),X2) -> mark(U31(X1,X2))
 U32(mark(X)) -> mark(U32(X))
 U41(mark(X)) -> mark(U41(X))
 U51(mark(X1),X2) -> mark(U51(X1,X2))
 U52(mark(X1),X2) -> mark(U52(X1,X2))
 U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
 U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
 U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
 U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
 proper(tt()) -> ok(tt())
 proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
 proper(isNatKind(X)) -> isNatKind(proper(X))
 proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
 proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
 proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
 proper(isNat(X)) -> isNat(proper(X))
 proper(U16(X)) -> U16(proper(X))
 proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
 proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
 proper(U23(X)) -> U23(proper(X))
 proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
 proper(U32(X)) -> U32(proper(X))
 proper(U41(X)) -> U41(proper(X))
 proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
 proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
 proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
 proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
 proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
 proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
 U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
 isNatKind(ok(X)) -> ok(isNatKind(X))
 U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
 U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
 U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
 isNat(ok(X)) -> ok(isNat(X))
 U16(ok(X)) -> ok(U16(X))
 U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
 U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
 U23(ok(X)) -> ok(U23(X))
 U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
 U32(ok(X)) -> ok(U32(X))
 U41(ok(X)) -> ok(U41(X))
 U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
 U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
 U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
 U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
 U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
 U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))

Proof:
 DP Processor:
  DPs:
   active#(U11(tt(),V1,V2)) -> isNatKind#(V1)
   active#(U11(tt(),V1,V2)) -> U12#(isNatKind(V1),V1,V2)
   active#(U12(tt(),V1,V2)) -> isNatKind#(V2)
   active#(U12(tt(),V1,V2)) -> U13#(isNatKind(V2),V1,V2)
   active#(U13(tt(),V1,V2)) -> isNatKind#(V2)
   active#(U13(tt(),V1,V2)) -> U14#(isNatKind(V2),V1,V2)
   active#(U14(tt(),V1,V2)) -> isNat#(V1)
   active#(U14(tt(),V1,V2)) -> U15#(isNat(V1),V2)
   active#(U15(tt(),V2)) -> isNat#(V2)
   active#(U15(tt(),V2)) -> U16#(isNat(V2))
   active#(U21(tt(),V1)) -> isNatKind#(V1)
   active#(U21(tt(),V1)) -> U22#(isNatKind(V1),V1)
   active#(U22(tt(),V1)) -> isNat#(V1)
   active#(U22(tt(),V1)) -> U23#(isNat(V1))
   active#(U31(tt(),V2)) -> isNatKind#(V2)
   active#(U31(tt(),V2)) -> U32#(isNatKind(V2))
   active#(U51(tt(),N)) -> isNatKind#(N)
   active#(U51(tt(),N)) -> U52#(isNatKind(N),N)
   active#(U61(tt(),M,N)) -> isNatKind#(M)
   active#(U61(tt(),M,N)) -> U62#(isNatKind(M),M,N)
   active#(U62(tt(),M,N)) -> isNat#(N)
   active#(U62(tt(),M,N)) -> U63#(isNat(N),M,N)
   active#(U63(tt(),M,N)) -> isNatKind#(N)
   active#(U63(tt(),M,N)) -> U64#(isNatKind(N),M,N)
   active#(U64(tt(),M,N)) -> plus#(N,M)
   active#(U64(tt(),M,N)) -> s#(plus(N,M))
   active#(isNat(plus(V1,V2))) -> isNatKind#(V1)
   active#(isNat(plus(V1,V2))) -> U11#(isNatKind(V1),V1,V2)
   active#(isNat(s(V1))) -> isNatKind#(V1)
   active#(isNat(s(V1))) -> U21#(isNatKind(V1),V1)
   active#(isNatKind(plus(V1,V2))) -> isNatKind#(V1)
   active#(isNatKind(plus(V1,V2))) -> U31#(isNatKind(V1),V2)
   active#(isNatKind(s(V1))) -> isNatKind#(V1)
   active#(isNatKind(s(V1))) -> U41#(isNatKind(V1))
   active#(plus(N,0())) -> isNat#(N)
   active#(plus(N,0())) -> U51#(isNat(N),N)
   active#(plus(N,s(M))) -> isNat#(M)
   active#(plus(N,s(M))) -> U61#(isNat(M),M,N)
   active#(U11(X1,X2,X3)) -> active#(X1)
   active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3)
   active#(U12(X1,X2,X3)) -> active#(X1)
   active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3)
   active#(U13(X1,X2,X3)) -> active#(X1)
   active#(U13(X1,X2,X3)) -> U13#(active(X1),X2,X3)
   active#(U14(X1,X2,X3)) -> active#(X1)
   active#(U14(X1,X2,X3)) -> U14#(active(X1),X2,X3)
   active#(U15(X1,X2)) -> active#(X1)
   active#(U15(X1,X2)) -> U15#(active(X1),X2)
   active#(U16(X)) -> active#(X)
   active#(U16(X)) -> U16#(active(X))
   active#(U21(X1,X2)) -> active#(X1)
   active#(U21(X1,X2)) -> U21#(active(X1),X2)
   active#(U22(X1,X2)) -> active#(X1)
   active#(U22(X1,X2)) -> U22#(active(X1),X2)
   active#(U23(X)) -> active#(X)
   active#(U23(X)) -> U23#(active(X))
   active#(U31(X1,X2)) -> active#(X1)
   active#(U31(X1,X2)) -> U31#(active(X1),X2)
   active#(U32(X)) -> active#(X)
   active#(U32(X)) -> U32#(active(X))
   active#(U41(X)) -> active#(X)
   active#(U41(X)) -> U41#(active(X))
   active#(U51(X1,X2)) -> active#(X1)
   active#(U51(X1,X2)) -> U51#(active(X1),X2)
   active#(U52(X1,X2)) -> active#(X1)
   active#(U52(X1,X2)) -> U52#(active(X1),X2)
   active#(U61(X1,X2,X3)) -> active#(X1)
   active#(U61(X1,X2,X3)) -> U61#(active(X1),X2,X3)
   active#(U62(X1,X2,X3)) -> active#(X1)
   active#(U62(X1,X2,X3)) -> U62#(active(X1),X2,X3)
   active#(U63(X1,X2,X3)) -> active#(X1)
   active#(U63(X1,X2,X3)) -> U63#(active(X1),X2,X3)
   active#(U64(X1,X2,X3)) -> active#(X1)
   active#(U64(X1,X2,X3)) -> U64#(active(X1),X2,X3)
   active#(s(X)) -> active#(X)
   active#(s(X)) -> s#(active(X))
   active#(plus(X1,X2)) -> active#(X1)
   active#(plus(X1,X2)) -> plus#(active(X1),X2)
   active#(plus(X1,X2)) -> active#(X2)
   active#(plus(X1,X2)) -> plus#(X1,active(X2))
   U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3)
   U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3)
   U13#(mark(X1),X2,X3) -> U13#(X1,X2,X3)
   U14#(mark(X1),X2,X3) -> U14#(X1,X2,X3)
   U15#(mark(X1),X2) -> U15#(X1,X2)
   U16#(mark(X)) -> U16#(X)
   U21#(mark(X1),X2) -> U21#(X1,X2)
   U22#(mark(X1),X2) -> U22#(X1,X2)
   U23#(mark(X)) -> U23#(X)
   U31#(mark(X1),X2) -> U31#(X1,X2)
   U32#(mark(X)) -> U32#(X)
   U41#(mark(X)) -> U41#(X)
   U51#(mark(X1),X2) -> U51#(X1,X2)
   U52#(mark(X1),X2) -> U52#(X1,X2)
   U61#(mark(X1),X2,X3) -> U61#(X1,X2,X3)
   U62#(mark(X1),X2,X3) -> U62#(X1,X2,X3)
   U63#(mark(X1),X2,X3) -> U63#(X1,X2,X3)
   U64#(mark(X1),X2,X3) -> U64#(X1,X2,X3)
   s#(mark(X)) -> s#(X)
   plus#(mark(X1),X2) -> plus#(X1,X2)
   plus#(X1,mark(X2)) -> plus#(X1,X2)
   proper#(U11(X1,X2,X3)) -> proper#(X3)
   proper#(U11(X1,X2,X3)) -> proper#(X2)
   proper#(U11(X1,X2,X3)) -> proper#(X1)
   proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3))
   proper#(U12(X1,X2,X3)) -> proper#(X3)
   proper#(U12(X1,X2,X3)) -> proper#(X2)
   proper#(U12(X1,X2,X3)) -> proper#(X1)
   proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3))
   proper#(isNatKind(X)) -> proper#(X)
   proper#(isNatKind(X)) -> isNatKind#(proper(X))
   proper#(U13(X1,X2,X3)) -> proper#(X3)
   proper#(U13(X1,X2,X3)) -> proper#(X2)
   proper#(U13(X1,X2,X3)) -> proper#(X1)
   proper#(U13(X1,X2,X3)) -> U13#(proper(X1),proper(X2),proper(X3))
   proper#(U14(X1,X2,X3)) -> proper#(X3)
   proper#(U14(X1,X2,X3)) -> proper#(X2)
   proper#(U14(X1,X2,X3)) -> proper#(X1)
   proper#(U14(X1,X2,X3)) -> U14#(proper(X1),proper(X2),proper(X3))
   proper#(U15(X1,X2)) -> proper#(X2)
   proper#(U15(X1,X2)) -> proper#(X1)
   proper#(U15(X1,X2)) -> U15#(proper(X1),proper(X2))
   proper#(isNat(X)) -> proper#(X)
   proper#(isNat(X)) -> isNat#(proper(X))
   proper#(U16(X)) -> proper#(X)
   proper#(U16(X)) -> U16#(proper(X))
   proper#(U21(X1,X2)) -> proper#(X2)
   proper#(U21(X1,X2)) -> proper#(X1)
   proper#(U21(X1,X2)) -> U21#(proper(X1),proper(X2))
   proper#(U22(X1,X2)) -> proper#(X2)
   proper#(U22(X1,X2)) -> proper#(X1)
   proper#(U22(X1,X2)) -> U22#(proper(X1),proper(X2))
   proper#(U23(X)) -> proper#(X)
   proper#(U23(X)) -> U23#(proper(X))
   proper#(U31(X1,X2)) -> proper#(X2)
   proper#(U31(X1,X2)) -> proper#(X1)
   proper#(U31(X1,X2)) -> U31#(proper(X1),proper(X2))
   proper#(U32(X)) -> proper#(X)
   proper#(U32(X)) -> U32#(proper(X))
   proper#(U41(X)) -> proper#(X)
   proper#(U41(X)) -> U41#(proper(X))
   proper#(U51(X1,X2)) -> proper#(X2)
   proper#(U51(X1,X2)) -> proper#(X1)
   proper#(U51(X1,X2)) -> U51#(proper(X1),proper(X2))
   proper#(U52(X1,X2)) -> proper#(X2)
   proper#(U52(X1,X2)) -> proper#(X1)
   proper#(U52(X1,X2)) -> U52#(proper(X1),proper(X2))
   proper#(U61(X1,X2,X3)) -> proper#(X3)
   proper#(U61(X1,X2,X3)) -> proper#(X2)
   proper#(U61(X1,X2,X3)) -> proper#(X1)
   proper#(U61(X1,X2,X3)) -> U61#(proper(X1),proper(X2),proper(X3))
   proper#(U62(X1,X2,X3)) -> proper#(X3)
   proper#(U62(X1,X2,X3)) -> proper#(X2)
   proper#(U62(X1,X2,X3)) -> proper#(X1)
   proper#(U62(X1,X2,X3)) -> U62#(proper(X1),proper(X2),proper(X3))
   proper#(U63(X1,X2,X3)) -> proper#(X3)
   proper#(U63(X1,X2,X3)) -> proper#(X2)
   proper#(U63(X1,X2,X3)) -> proper#(X1)
   proper#(U63(X1,X2,X3)) -> U63#(proper(X1),proper(X2),proper(X3))
   proper#(U64(X1,X2,X3)) -> proper#(X3)
   proper#(U64(X1,X2,X3)) -> proper#(X2)
   proper#(U64(X1,X2,X3)) -> proper#(X1)
   proper#(U64(X1,X2,X3)) -> U64#(proper(X1),proper(X2),proper(X3))
   proper#(s(X)) -> proper#(X)
   proper#(s(X)) -> s#(proper(X))
   proper#(plus(X1,X2)) -> proper#(X2)
   proper#(plus(X1,X2)) -> proper#(X1)
   proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2))
   U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3)
   U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3)
   isNatKind#(ok(X)) -> isNatKind#(X)
   U13#(ok(X1),ok(X2),ok(X3)) -> U13#(X1,X2,X3)
   U14#(ok(X1),ok(X2),ok(X3)) -> U14#(X1,X2,X3)
   U15#(ok(X1),ok(X2)) -> U15#(X1,X2)
   isNat#(ok(X)) -> isNat#(X)
   U16#(ok(X)) -> U16#(X)
   U21#(ok(X1),ok(X2)) -> U21#(X1,X2)
   U22#(ok(X1),ok(X2)) -> U22#(X1,X2)
   U23#(ok(X)) -> U23#(X)
   U31#(ok(X1),ok(X2)) -> U31#(X1,X2)
   U32#(ok(X)) -> U32#(X)
   U41#(ok(X)) -> U41#(X)
   U51#(ok(X1),ok(X2)) -> U51#(X1,X2)
   U52#(ok(X1),ok(X2)) -> U52#(X1,X2)
   U61#(ok(X1),ok(X2),ok(X3)) -> U61#(X1,X2,X3)
   U62#(ok(X1),ok(X2),ok(X3)) -> U62#(X1,X2,X3)
   U63#(ok(X1),ok(X2),ok(X3)) -> U63#(X1,X2,X3)
   U64#(ok(X1),ok(X2),ok(X3)) -> U64#(X1,X2,X3)
   s#(ok(X)) -> s#(X)
   plus#(ok(X1),ok(X2)) -> plus#(X1,X2)
   top#(mark(X)) -> proper#(X)
   top#(mark(X)) -> top#(proper(X))
   top#(ok(X)) -> active#(X)
   top#(ok(X)) -> top#(active(X))
  TRS:
   active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
   active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
   active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
   active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
   active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
   active(U16(tt())) -> mark(tt())
   active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
   active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
   active(U23(tt())) -> mark(tt())
   active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
   active(U32(tt())) -> mark(tt())
   active(U41(tt())) -> mark(tt())
   active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
   active(U52(tt(),N)) -> mark(N)
   active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
   active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
   active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
   active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
   active(isNat(0())) -> mark(tt())
   active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
   active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
   active(isNatKind(0())) -> mark(tt())
   active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
   active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
   active(plus(N,0())) -> mark(U51(isNat(N),N))
   active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
   active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
   active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
   active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
   active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
   active(U15(X1,X2)) -> U15(active(X1),X2)
   active(U16(X)) -> U16(active(X))
   active(U21(X1,X2)) -> U21(active(X1),X2)
   active(U22(X1,X2)) -> U22(active(X1),X2)
   active(U23(X)) -> U23(active(X))
   active(U31(X1,X2)) -> U31(active(X1),X2)
   active(U32(X)) -> U32(active(X))
   active(U41(X)) -> U41(active(X))
   active(U51(X1,X2)) -> U51(active(X1),X2)
   active(U52(X1,X2)) -> U52(active(X1),X2)
   active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
   active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
   active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
   active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
   U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
   U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
   U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
   U15(mark(X1),X2) -> mark(U15(X1,X2))
   U16(mark(X)) -> mark(U16(X))
   U21(mark(X1),X2) -> mark(U21(X1,X2))
   U22(mark(X1),X2) -> mark(U22(X1,X2))
   U23(mark(X)) -> mark(U23(X))
   U31(mark(X1),X2) -> mark(U31(X1,X2))
   U32(mark(X)) -> mark(U32(X))
   U41(mark(X)) -> mark(U41(X))
   U51(mark(X1),X2) -> mark(U51(X1,X2))
   U52(mark(X1),X2) -> mark(U52(X1,X2))
   U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
   U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
   U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
   U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
   proper(tt()) -> ok(tt())
   proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
   proper(isNatKind(X)) -> isNatKind(proper(X))
   proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
   proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
   proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
   proper(isNat(X)) -> isNat(proper(X))
   proper(U16(X)) -> U16(proper(X))
   proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
   proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
   proper(U23(X)) -> U23(proper(X))
   proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
   proper(U32(X)) -> U32(proper(X))
   proper(U41(X)) -> U41(proper(X))
   proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
   proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
   proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
   proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
   proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
   proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
   U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
   isNatKind(ok(X)) -> ok(isNatKind(X))
   U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
   U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
   U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
   isNat(ok(X)) -> ok(isNat(X))
   U16(ok(X)) -> ok(U16(X))
   U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
   U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
   U23(ok(X)) -> ok(U23(X))
   U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
   U32(ok(X)) -> ok(U32(X))
   U41(ok(X)) -> ok(U41(X))
   U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
   U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
   U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
   U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
   U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
   U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
  Usable Rule Processor:
   DPs:
    active#(U11(tt(),V1,V2)) -> isNatKind#(V1)
    active#(U11(tt(),V1,V2)) -> U12#(isNatKind(V1),V1,V2)
    active#(U12(tt(),V1,V2)) -> isNatKind#(V2)
    active#(U12(tt(),V1,V2)) -> U13#(isNatKind(V2),V1,V2)
    active#(U13(tt(),V1,V2)) -> isNatKind#(V2)
    active#(U13(tt(),V1,V2)) -> U14#(isNatKind(V2),V1,V2)
    active#(U14(tt(),V1,V2)) -> isNat#(V1)
    active#(U14(tt(),V1,V2)) -> U15#(isNat(V1),V2)
    active#(U15(tt(),V2)) -> isNat#(V2)
    active#(U15(tt(),V2)) -> U16#(isNat(V2))
    active#(U21(tt(),V1)) -> isNatKind#(V1)
    active#(U21(tt(),V1)) -> U22#(isNatKind(V1),V1)
    active#(U22(tt(),V1)) -> isNat#(V1)
    active#(U22(tt(),V1)) -> U23#(isNat(V1))
    active#(U31(tt(),V2)) -> isNatKind#(V2)
    active#(U31(tt(),V2)) -> U32#(isNatKind(V2))
    active#(U51(tt(),N)) -> isNatKind#(N)
    active#(U51(tt(),N)) -> U52#(isNatKind(N),N)
    active#(U61(tt(),M,N)) -> isNatKind#(M)
    active#(U61(tt(),M,N)) -> U62#(isNatKind(M),M,N)
    active#(U62(tt(),M,N)) -> isNat#(N)
    active#(U62(tt(),M,N)) -> U63#(isNat(N),M,N)
    active#(U63(tt(),M,N)) -> isNatKind#(N)
    active#(U63(tt(),M,N)) -> U64#(isNatKind(N),M,N)
    active#(U64(tt(),M,N)) -> plus#(N,M)
    active#(U64(tt(),M,N)) -> s#(plus(N,M))
    active#(isNat(plus(V1,V2))) -> isNatKind#(V1)
    active#(isNat(plus(V1,V2))) -> U11#(isNatKind(V1),V1,V2)
    active#(isNat(s(V1))) -> isNatKind#(V1)
    active#(isNat(s(V1))) -> U21#(isNatKind(V1),V1)
    active#(isNatKind(plus(V1,V2))) -> isNatKind#(V1)
    active#(isNatKind(plus(V1,V2))) -> U31#(isNatKind(V1),V2)
    active#(isNatKind(s(V1))) -> isNatKind#(V1)
    active#(isNatKind(s(V1))) -> U41#(isNatKind(V1))
    active#(plus(N,0())) -> isNat#(N)
    active#(plus(N,0())) -> U51#(isNat(N),N)
    active#(plus(N,s(M))) -> isNat#(M)
    active#(plus(N,s(M))) -> U61#(isNat(M),M,N)
    active#(U11(X1,X2,X3)) -> active#(X1)
    active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3)
    active#(U12(X1,X2,X3)) -> active#(X1)
    active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3)
    active#(U13(X1,X2,X3)) -> active#(X1)
    active#(U13(X1,X2,X3)) -> U13#(active(X1),X2,X3)
    active#(U14(X1,X2,X3)) -> active#(X1)
    active#(U14(X1,X2,X3)) -> U14#(active(X1),X2,X3)
    active#(U15(X1,X2)) -> active#(X1)
    active#(U15(X1,X2)) -> U15#(active(X1),X2)
    active#(U16(X)) -> active#(X)
    active#(U16(X)) -> U16#(active(X))
    active#(U21(X1,X2)) -> active#(X1)
    active#(U21(X1,X2)) -> U21#(active(X1),X2)
    active#(U22(X1,X2)) -> active#(X1)
    active#(U22(X1,X2)) -> U22#(active(X1),X2)
    active#(U23(X)) -> active#(X)
    active#(U23(X)) -> U23#(active(X))
    active#(U31(X1,X2)) -> active#(X1)
    active#(U31(X1,X2)) -> U31#(active(X1),X2)
    active#(U32(X)) -> active#(X)
    active#(U32(X)) -> U32#(active(X))
    active#(U41(X)) -> active#(X)
    active#(U41(X)) -> U41#(active(X))
    active#(U51(X1,X2)) -> active#(X1)
    active#(U51(X1,X2)) -> U51#(active(X1),X2)
    active#(U52(X1,X2)) -> active#(X1)
    active#(U52(X1,X2)) -> U52#(active(X1),X2)
    active#(U61(X1,X2,X3)) -> active#(X1)
    active#(U61(X1,X2,X3)) -> U61#(active(X1),X2,X3)
    active#(U62(X1,X2,X3)) -> active#(X1)
    active#(U62(X1,X2,X3)) -> U62#(active(X1),X2,X3)
    active#(U63(X1,X2,X3)) -> active#(X1)
    active#(U63(X1,X2,X3)) -> U63#(active(X1),X2,X3)
    active#(U64(X1,X2,X3)) -> active#(X1)
    active#(U64(X1,X2,X3)) -> U64#(active(X1),X2,X3)
    active#(s(X)) -> active#(X)
    active#(s(X)) -> s#(active(X))
    active#(plus(X1,X2)) -> active#(X1)
    active#(plus(X1,X2)) -> plus#(active(X1),X2)
    active#(plus(X1,X2)) -> active#(X2)
    active#(plus(X1,X2)) -> plus#(X1,active(X2))
    U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3)
    U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3)
    U13#(mark(X1),X2,X3) -> U13#(X1,X2,X3)
    U14#(mark(X1),X2,X3) -> U14#(X1,X2,X3)
    U15#(mark(X1),X2) -> U15#(X1,X2)
    U16#(mark(X)) -> U16#(X)
    U21#(mark(X1),X2) -> U21#(X1,X2)
    U22#(mark(X1),X2) -> U22#(X1,X2)
    U23#(mark(X)) -> U23#(X)
    U31#(mark(X1),X2) -> U31#(X1,X2)
    U32#(mark(X)) -> U32#(X)
    U41#(mark(X)) -> U41#(X)
    U51#(mark(X1),X2) -> U51#(X1,X2)
    U52#(mark(X1),X2) -> U52#(X1,X2)
    U61#(mark(X1),X2,X3) -> U61#(X1,X2,X3)
    U62#(mark(X1),X2,X3) -> U62#(X1,X2,X3)
    U63#(mark(X1),X2,X3) -> U63#(X1,X2,X3)
    U64#(mark(X1),X2,X3) -> U64#(X1,X2,X3)
    s#(mark(X)) -> s#(X)
    plus#(mark(X1),X2) -> plus#(X1,X2)
    plus#(X1,mark(X2)) -> plus#(X1,X2)
    proper#(U11(X1,X2,X3)) -> proper#(X3)
    proper#(U11(X1,X2,X3)) -> proper#(X2)
    proper#(U11(X1,X2,X3)) -> proper#(X1)
    proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3))
    proper#(U12(X1,X2,X3)) -> proper#(X3)
    proper#(U12(X1,X2,X3)) -> proper#(X2)
    proper#(U12(X1,X2,X3)) -> proper#(X1)
    proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3))
    proper#(isNatKind(X)) -> proper#(X)
    proper#(isNatKind(X)) -> isNatKind#(proper(X))
    proper#(U13(X1,X2,X3)) -> proper#(X3)
    proper#(U13(X1,X2,X3)) -> proper#(X2)
    proper#(U13(X1,X2,X3)) -> proper#(X1)
    proper#(U13(X1,X2,X3)) -> U13#(proper(X1),proper(X2),proper(X3))
    proper#(U14(X1,X2,X3)) -> proper#(X3)
    proper#(U14(X1,X2,X3)) -> proper#(X2)
    proper#(U14(X1,X2,X3)) -> proper#(X1)
    proper#(U14(X1,X2,X3)) -> U14#(proper(X1),proper(X2),proper(X3))
    proper#(U15(X1,X2)) -> proper#(X2)
    proper#(U15(X1,X2)) -> proper#(X1)
    proper#(U15(X1,X2)) -> U15#(proper(X1),proper(X2))
    proper#(isNat(X)) -> proper#(X)
    proper#(isNat(X)) -> isNat#(proper(X))
    proper#(U16(X)) -> proper#(X)
    proper#(U16(X)) -> U16#(proper(X))
    proper#(U21(X1,X2)) -> proper#(X2)
    proper#(U21(X1,X2)) -> proper#(X1)
    proper#(U21(X1,X2)) -> U21#(proper(X1),proper(X2))
    proper#(U22(X1,X2)) -> proper#(X2)
    proper#(U22(X1,X2)) -> proper#(X1)
    proper#(U22(X1,X2)) -> U22#(proper(X1),proper(X2))
    proper#(U23(X)) -> proper#(X)
    proper#(U23(X)) -> U23#(proper(X))
    proper#(U31(X1,X2)) -> proper#(X2)
    proper#(U31(X1,X2)) -> proper#(X1)
    proper#(U31(X1,X2)) -> U31#(proper(X1),proper(X2))
    proper#(U32(X)) -> proper#(X)
    proper#(U32(X)) -> U32#(proper(X))
    proper#(U41(X)) -> proper#(X)
    proper#(U41(X)) -> U41#(proper(X))
    proper#(U51(X1,X2)) -> proper#(X2)
    proper#(U51(X1,X2)) -> proper#(X1)
    proper#(U51(X1,X2)) -> U51#(proper(X1),proper(X2))
    proper#(U52(X1,X2)) -> proper#(X2)
    proper#(U52(X1,X2)) -> proper#(X1)
    proper#(U52(X1,X2)) -> U52#(proper(X1),proper(X2))
    proper#(U61(X1,X2,X3)) -> proper#(X3)
    proper#(U61(X1,X2,X3)) -> proper#(X2)
    proper#(U61(X1,X2,X3)) -> proper#(X1)
    proper#(U61(X1,X2,X3)) -> U61#(proper(X1),proper(X2),proper(X3))
    proper#(U62(X1,X2,X3)) -> proper#(X3)
    proper#(U62(X1,X2,X3)) -> proper#(X2)
    proper#(U62(X1,X2,X3)) -> proper#(X1)
    proper#(U62(X1,X2,X3)) -> U62#(proper(X1),proper(X2),proper(X3))
    proper#(U63(X1,X2,X3)) -> proper#(X3)
    proper#(U63(X1,X2,X3)) -> proper#(X2)
    proper#(U63(X1,X2,X3)) -> proper#(X1)
    proper#(U63(X1,X2,X3)) -> U63#(proper(X1),proper(X2),proper(X3))
    proper#(U64(X1,X2,X3)) -> proper#(X3)
    proper#(U64(X1,X2,X3)) -> proper#(X2)
    proper#(U64(X1,X2,X3)) -> proper#(X1)
    proper#(U64(X1,X2,X3)) -> U64#(proper(X1),proper(X2),proper(X3))
    proper#(s(X)) -> proper#(X)
    proper#(s(X)) -> s#(proper(X))
    proper#(plus(X1,X2)) -> proper#(X2)
    proper#(plus(X1,X2)) -> proper#(X1)
    proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2))
    U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3)
    U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3)
    isNatKind#(ok(X)) -> isNatKind#(X)
    U13#(ok(X1),ok(X2),ok(X3)) -> U13#(X1,X2,X3)
    U14#(ok(X1),ok(X2),ok(X3)) -> U14#(X1,X2,X3)
    U15#(ok(X1),ok(X2)) -> U15#(X1,X2)
    isNat#(ok(X)) -> isNat#(X)
    U16#(ok(X)) -> U16#(X)
    U21#(ok(X1),ok(X2)) -> U21#(X1,X2)
    U22#(ok(X1),ok(X2)) -> U22#(X1,X2)
    U23#(ok(X)) -> U23#(X)
    U31#(ok(X1),ok(X2)) -> U31#(X1,X2)
    U32#(ok(X)) -> U32#(X)
    U41#(ok(X)) -> U41#(X)
    U51#(ok(X1),ok(X2)) -> U51#(X1,X2)
    U52#(ok(X1),ok(X2)) -> U52#(X1,X2)
    U61#(ok(X1),ok(X2),ok(X3)) -> U61#(X1,X2,X3)
    U62#(ok(X1),ok(X2),ok(X3)) -> U62#(X1,X2,X3)
    U63#(ok(X1),ok(X2),ok(X3)) -> U63#(X1,X2,X3)
    U64#(ok(X1),ok(X2),ok(X3)) -> U64#(X1,X2,X3)
    s#(ok(X)) -> s#(X)
    plus#(ok(X1),ok(X2)) -> plus#(X1,X2)
    top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X))
   TRS:
    f54(x,y) -> x
    f54(x,y) -> y
    isNatKind(ok(X)) -> ok(isNatKind(X))
    isNat(ok(X)) -> ok(isNat(X))
    plus(mark(X1),X2) -> mark(plus(X1,X2))
    plus(X1,mark(X2)) -> mark(plus(X1,X2))
    plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
    active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
    active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
    active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
    active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
    active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
    active(U16(tt())) -> mark(tt())
    active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
    active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
    active(U23(tt())) -> mark(tt())
    active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
    active(U32(tt())) -> mark(tt())
    active(U41(tt())) -> mark(tt())
    active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
    active(U52(tt(),N)) -> mark(N)
    active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
    active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
    active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
    active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
    active(isNat(0())) -> mark(tt())
    active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
    active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
    active(isNatKind(0())) -> mark(tt())
    active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
    active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
    active(plus(N,0())) -> mark(U51(isNat(N),N))
    active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
    active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
    active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
    active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
    active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
    active(U15(X1,X2)) -> U15(active(X1),X2)
    active(U16(X)) -> U16(active(X))
    active(U21(X1,X2)) -> U21(active(X1),X2)
    active(U22(X1,X2)) -> U22(active(X1),X2)
    active(U23(X)) -> U23(active(X))
    active(U31(X1,X2)) -> U31(active(X1),X2)
    active(U32(X)) -> U32(active(X))
    active(U41(X)) -> U41(active(X))
    active(U51(X1,X2)) -> U51(active(X1),X2)
    active(U52(X1,X2)) -> U52(active(X1),X2)
    active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
    active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
    active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
    active(U64(X1,X2,X3)) -> U64(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))
    U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
    U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
    U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
    U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
    U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
    U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
    U15(mark(X1),X2) -> mark(U15(X1,X2))
    U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
    U16(mark(X)) -> mark(U16(X))
    U16(ok(X)) -> ok(U16(X))
    U22(mark(X1),X2) -> mark(U22(X1,X2))
    U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
    U23(mark(X)) -> mark(U23(X))
    U23(ok(X)) -> ok(U23(X))
    U32(mark(X)) -> mark(U32(X))
    U32(ok(X)) -> ok(U32(X))
    U52(mark(X1),X2) -> mark(U52(X1,X2))
    U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
    U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
    U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
    U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
    U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
    U64(mark(X1),X2,X3) -> mark(U64(X1,X2,X3))
    U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(X1,X2,X3))
    s(mark(X)) -> mark(s(X))
    s(ok(X)) -> ok(s(X))
    U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
    U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
    U21(mark(X1),X2) -> mark(U21(X1,X2))
    U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
    U31(mark(X1),X2) -> mark(U31(X1,X2))
    U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
    U41(mark(X)) -> mark(U41(X))
    U41(ok(X)) -> ok(U41(X))
    U51(mark(X1),X2) -> mark(U51(X1,X2))
    U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
    U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
    U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
    proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
    proper(tt()) -> ok(tt())
    proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
    proper(isNatKind(X)) -> isNatKind(proper(X))
    proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
    proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
    proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
    proper(isNat(X)) -> isNat(proper(X))
    proper(U16(X)) -> U16(proper(X))
    proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
    proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
    proper(U23(X)) -> U23(proper(X))
    proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
    proper(U32(X)) -> U32(proper(X))
    proper(U41(X)) -> U41(proper(X))
    proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
    proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
    proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
    proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
    proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
    proper(U64(X1,X2,X3)) -> U64(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())
   CDG Processor:
    DPs:
     active#(U11(tt(),V1,V2)) -> isNatKind#(V1)
     active#(U11(tt(),V1,V2)) -> U12#(isNatKind(V1),V1,V2)
     active#(U12(tt(),V1,V2)) -> isNatKind#(V2)
     active#(U12(tt(),V1,V2)) -> U13#(isNatKind(V2),V1,V2)
     active#(U13(tt(),V1,V2)) -> isNatKind#(V2)
     active#(U13(tt(),V1,V2)) -> U14#(isNatKind(V2),V1,V2)
     active#(U14(tt(),V1,V2)) -> isNat#(V1)
     active#(U14(tt(),V1,V2)) -> U15#(isNat(V1),V2)
     active#(U15(tt(),V2)) -> isNat#(V2)
     active#(U15(tt(),V2)) -> U16#(isNat(V2))
     active#(U21(tt(),V1)) -> isNatKind#(V1)
     active#(U21(tt(),V1)) -> U22#(isNatKind(V1),V1)
     active#(U22(tt(),V1)) -> isNat#(V1)
     active#(U22(tt(),V1)) -> U23#(isNat(V1))
     active#(U31(tt(),V2)) -> isNatKind#(V2)
     active#(U31(tt(),V2)) -> U32#(isNatKind(V2))
     active#(U51(tt(),N)) -> isNatKind#(N)
     active#(U51(tt(),N)) -> U52#(isNatKind(N),N)
     active#(U61(tt(),M,N)) -> isNatKind#(M)
     active#(U61(tt(),M,N)) -> U62#(isNatKind(M),M,N)
     active#(U62(tt(),M,N)) -> isNat#(N)
     active#(U62(tt(),M,N)) -> U63#(isNat(N),M,N)
     active#(U63(tt(),M,N)) -> isNatKind#(N)
     active#(U63(tt(),M,N)) -> U64#(isNatKind(N),M,N)
     active#(U64(tt(),M,N)) -> plus#(N,M)
     active#(U64(tt(),M,N)) -> s#(plus(N,M))
     active#(isNat(plus(V1,V2))) -> isNatKind#(V1)
     active#(isNat(plus(V1,V2))) -> U11#(isNatKind(V1),V1,V2)
     active#(isNat(s(V1))) -> isNatKind#(V1)
     active#(isNat(s(V1))) -> U21#(isNatKind(V1),V1)
     active#(isNatKind(plus(V1,V2))) -> isNatKind#(V1)
     active#(isNatKind(plus(V1,V2))) -> U31#(isNatKind(V1),V2)
     active#(isNatKind(s(V1))) -> isNatKind#(V1)
     active#(isNatKind(s(V1))) -> U41#(isNatKind(V1))
     active#(plus(N,0())) -> isNat#(N)
     active#(plus(N,0())) -> U51#(isNat(N),N)
     active#(plus(N,s(M))) -> isNat#(M)
     active#(plus(N,s(M))) -> U61#(isNat(M),M,N)
     active#(U11(X1,X2,X3)) -> active#(X1)
     active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3)
     active#(U12(X1,X2,X3)) -> active#(X1)
     active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3)
     active#(U13(X1,X2,X3)) -> active#(X1)
     active#(U13(X1,X2,X3)) -> U13#(active(X1),X2,X3)
     active#(U14(X1,X2,X3)) -> active#(X1)
     active#(U14(X1,X2,X3)) -> U14#(active(X1),X2,X3)
     active#(U15(X1,X2)) -> active#(X1)
     active#(U15(X1,X2)) -> U15#(active(X1),X2)
     active#(U16(X)) -> active#(X)
     active#(U16(X)) -> U16#(active(X))
     active#(U21(X1,X2)) -> active#(X1)
     active#(U21(X1,X2)) -> U21#(active(X1),X2)
     active#(U22(X1,X2)) -> active#(X1)
     active#(U22(X1,X2)) -> U22#(active(X1),X2)
     active#(U23(X)) -> active#(X)
     active#(U23(X)) -> U23#(active(X))
     active#(U31(X1,X2)) -> active#(X1)
     active#(U31(X1,X2)) -> U31#(active(X1),X2)
     active#(U32(X)) -> active#(X)
     active#(U32(X)) -> U32#(active(X))
     active#(U41(X)) -> active#(X)
     active#(U41(X)) -> U41#(active(X))
     active#(U51(X1,X2)) -> active#(X1)
     active#(U51(X1,X2)) -> U51#(active(X1),X2)
     active#(U52(X1,X2)) -> active#(X1)
     active#(U52(X1,X2)) -> U52#(active(X1),X2)
     active#(U61(X1,X2,X3)) -> active#(X1)
     active#(U61(X1,X2,X3)) -> U61#(active(X1),X2,X3)
     active#(U62(X1,X2,X3)) -> active#(X1)
     active#(U62(X1,X2,X3)) -> U62#(active(X1),X2,X3)
     active#(U63(X1,X2,X3)) -> active#(X1)
     active#(U63(X1,X2,X3)) -> U63#(active(X1),X2,X3)
     active#(U64(X1,X2,X3)) -> active#(X1)
     active#(U64(X1,X2,X3)) -> U64#(active(X1),X2,X3)
     active#(s(X)) -> active#(X)
     active#(s(X)) -> s#(active(X))
     active#(plus(X1,X2)) -> active#(X1)
     active#(plus(X1,X2)) -> plus#(active(X1),X2)
     active#(plus(X1,X2)) -> active#(X2)
     active#(plus(X1,X2)) -> plus#(X1,active(X2))
     U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3)
     U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3)
     U13#(mark(X1),X2,X3) -> U13#(X1,X2,X3)
     U14#(mark(X1),X2,X3) -> U14#(X1,X2,X3)
     U15#(mark(X1),X2) -> U15#(X1,X2)
     U16#(mark(X)) -> U16#(X)
     U21#(mark(X1),X2) -> U21#(X1,X2)
     U22#(mark(X1),X2) -> U22#(X1,X2)
     U23#(mark(X)) -> U23#(X)
     U31#(mark(X1),X2) -> U31#(X1,X2)
     U32#(mark(X)) -> U32#(X)
     U41#(mark(X)) -> U41#(X)
     U51#(mark(X1),X2) -> U51#(X1,X2)
     U52#(mark(X1),X2) -> U52#(X1,X2)
     U61#(mark(X1),X2,X3) -> U61#(X1,X2,X3)
     U62#(mark(X1),X2,X3) -> U62#(X1,X2,X3)
     U63#(mark(X1),X2,X3) -> U63#(X1,X2,X3)
     U64#(mark(X1),X2,X3) -> U64#(X1,X2,X3)
     s#(mark(X)) -> s#(X)
     plus#(mark(X1),X2) -> plus#(X1,X2)
     plus#(X1,mark(X2)) -> plus#(X1,X2)
     proper#(U11(X1,X2,X3)) -> proper#(X3)
     proper#(U11(X1,X2,X3)) -> proper#(X2)
     proper#(U11(X1,X2,X3)) -> proper#(X1)
     proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3))
     proper#(U12(X1,X2,X3)) -> proper#(X3)
     proper#(U12(X1,X2,X3)) -> proper#(X2)
     proper#(U12(X1,X2,X3)) -> proper#(X1)
     proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3))
     proper#(isNatKind(X)) -> proper#(X)
     proper#(isNatKind(X)) -> isNatKind#(proper(X))
     proper#(U13(X1,X2,X3)) -> proper#(X3)
     proper#(U13(X1,X2,X3)) -> proper#(X2)
     proper#(U13(X1,X2,X3)) -> proper#(X1)
     proper#(U13(X1,X2,X3)) -> U13#(proper(X1),proper(X2),proper(X3))
     proper#(U14(X1,X2,X3)) -> proper#(X3)
     proper#(U14(X1,X2,X3)) -> proper#(X2)
     proper#(U14(X1,X2,X3)) -> proper#(X1)
     proper#(U14(X1,X2,X3)) -> U14#(proper(X1),proper(X2),proper(X3))
     proper#(U15(X1,X2)) -> proper#(X2)
     proper#(U15(X1,X2)) -> proper#(X1)
     proper#(U15(X1,X2)) -> U15#(proper(X1),proper(X2))
     proper#(isNat(X)) -> proper#(X)
     proper#(isNat(X)) -> isNat#(proper(X))
     proper#(U16(X)) -> proper#(X)
     proper#(U16(X)) -> U16#(proper(X))
     proper#(U21(X1,X2)) -> proper#(X2)
     proper#(U21(X1,X2)) -> proper#(X1)
     proper#(U21(X1,X2)) -> U21#(proper(X1),proper(X2))
     proper#(U22(X1,X2)) -> proper#(X2)
     proper#(U22(X1,X2)) -> proper#(X1)
     proper#(U22(X1,X2)) -> U22#(proper(X1),proper(X2))
     proper#(U23(X)) -> proper#(X)
     proper#(U23(X)) -> U23#(proper(X))
     proper#(U31(X1,X2)) -> proper#(X2)
     proper#(U31(X1,X2)) -> proper#(X1)
     proper#(U31(X1,X2)) -> U31#(proper(X1),proper(X2))
     proper#(U32(X)) -> proper#(X)
     proper#(U32(X)) -> U32#(proper(X))
     proper#(U41(X)) -> proper#(X)
     proper#(U41(X)) -> U41#(proper(X))
     proper#(U51(X1,X2)) -> proper#(X2)
     proper#(U51(X1,X2)) -> proper#(X1)
     proper#(U51(X1,X2)) -> U51#(proper(X1),proper(X2))
     proper#(U52(X1,X2)) -> proper#(X2)
     proper#(U52(X1,X2)) -> proper#(X1)
     proper#(U52(X1,X2)) -> U52#(proper(X1),proper(X2))
     proper#(U61(X1,X2,X3)) -> proper#(X3)
     proper#(U61(X1,X2,X3)) -> proper#(X2)
     proper#(U61(X1,X2,X3)) -> proper#(X1)
     proper#(U61(X1,X2,X3)) -> U61#(proper(X1),proper(X2),proper(X3))
     proper#(U62(X1,X2,X3)) -> proper#(X3)
     proper#(U62(X1,X2,X3)) -> proper#(X2)
     proper#(U62(X1,X2,X3)) -> proper#(X1)
     proper#(U62(X1,X2,X3)) -> U62#(proper(X1),proper(X2),proper(X3))
     proper#(U63(X1,X2,X3)) -> proper#(X3)
     proper#(U63(X1,X2,X3)) -> proper#(X2)
     proper#(U63(X1,X2,X3)) -> proper#(X1)
     proper#(U63(X1,X2,X3)) -> U63#(proper(X1),proper(X2),proper(X3))
     proper#(U64(X1,X2,X3)) -> proper#(X3)
     proper#(U64(X1,X2,X3)) -> proper#(X2)
     proper#(U64(X1,X2,X3)) -> proper#(X1)
     proper#(U64(X1,X2,X3)) -> U64#(proper(X1),proper(X2),proper(X3))
     proper#(s(X)) -> proper#(X)
     proper#(s(X)) -> s#(proper(X))
     proper#(plus(X1,X2)) -> proper#(X2)
     proper#(plus(X1,X2)) -> proper#(X1)
     proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2))
     U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3)
     U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3)
     isNatKind#(ok(X)) -> isNatKind#(X)
     U13#(ok(X1),ok(X2),ok(X3)) -> U13#(X1,X2,X3)
     U14#(ok(X1),ok(X2),ok(X3)) -> U14#(X1,X2,X3)
     U15#(ok(X1),ok(X2)) -> U15#(X1,X2)
     isNat#(ok(X)) -> isNat#(X)
     U16#(ok(X)) -> U16#(X)
     U21#(ok(X1),ok(X2)) -> U21#(X1,X2)
     U22#(ok(X1),ok(X2)) -> U22#(X1,X2)
     U23#(ok(X)) -> U23#(X)
     U31#(ok(X1),ok(X2)) -> U31#(X1,X2)
     U32#(ok(X)) -> U32#(X)
     U41#(ok(X)) -> U41#(X)
     U51#(ok(X1),ok(X2)) -> U51#(X1,X2)
     U52#(ok(X1),ok(X2)) -> U52#(X1,X2)
     U61#(ok(X1),ok(X2),ok(X3)) -> U61#(X1,X2,X3)
     U62#(ok(X1),ok(X2),ok(X3)) -> U62#(X1,X2,X3)
     U63#(ok(X1),ok(X2),ok(X3)) -> U63#(X1,X2,X3)
     U64#(ok(X1),ok(X2),ok(X3)) -> U64#(X1,X2,X3)
     s#(ok(X)) -> s#(X)
     plus#(ok(X1),ok(X2)) -> plus#(X1,X2)
     top#(mark(X)) -> proper#(X)
     top#(mark(X)) -> top#(proper(X))
     top#(ok(X)) -> active#(X)
     top#(ok(X)) -> top#(active(X))
    TRS:
     f54(x,y) -> x
     f54(x,y) -> y
     isNatKind(ok(X)) -> ok(isNatKind(X))
     isNat(ok(X)) -> ok(isNat(X))
     plus(mark(X1),X2) -> mark(plus(X1,X2))
     plus(X1,mark(X2)) -> mark(plus(X1,X2))
     plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
     active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
     active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
     active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
     active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
     active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
     active(U16(tt())) -> mark(tt())
     active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
     active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
     active(U23(tt())) -> mark(tt())
     active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
     active(U32(tt())) -> mark(tt())
     active(U41(tt())) -> mark(tt())
     active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
     active(U52(tt(),N)) -> mark(N)
     active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
     active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
     active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
     active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
     active(isNat(0())) -> mark(tt())
     active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
     active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
     active(isNatKind(0())) -> mark(tt())
     active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
     active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
     active(plus(N,0())) -> mark(U51(isNat(N),N))
     active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
     active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
     active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
     active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
     active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
     active(U15(X1,X2)) -> U15(active(X1),X2)
     active(U16(X)) -> U16(active(X))
     active(U21(X1,X2)) -> U21(active(X1),X2)
     active(U22(X1,X2)) -> U22(active(X1),X2)
     active(U23(X)) -> U23(active(X))
     active(U31(X1,X2)) -> U31(active(X1),X2)
     active(U32(X)) -> U32(active(X))
     active(U41(X)) -> U41(active(X))
     active(U51(X1,X2)) -> U51(active(X1),X2)
     active(U52(X1,X2)) -> U52(active(X1),X2)
     active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
     active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
     active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
     active(U64(X1,X2,X3)) -> U64(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))
     U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
     U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
     U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
     U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
     U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
     U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
     U15(mark(X1),X2) -> mark(U15(X1,X2))
     U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
     U16(mark(X)) -> mark(U16(X))
     U16(ok(X)) -> ok(U16(X))
     U22(mark(X1),X2) -> mark(U22(X1,X2))
     U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
     U23(mark(X)) -> mark(U23(X))
     U23(ok(X)) -> ok(U23(X))
     U32(mark(X)) -> mark(U32(X))
     U32(ok(X)) -> ok(U32(X))
     U52(mark(X1),X2) -> mark(U52(X1,X2))
     U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
     U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
     U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
     U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
     U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
     U64(mark(X1),X2,X3) -> mark(U64(X1,X2,X3))
     U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(X1,X2,X3))
     s(mark(X)) -> mark(s(X))
     s(ok(X)) -> ok(s(X))
     U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
     U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
     U21(mark(X1),X2) -> mark(U21(X1,X2))
     U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
     U31(mark(X1),X2) -> mark(U31(X1,X2))
     U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
     U41(mark(X)) -> mark(U41(X))
     U41(ok(X)) -> ok(U41(X))
     U51(mark(X1),X2) -> mark(U51(X1,X2))
     U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
     U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
     U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
     proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
     proper(tt()) -> ok(tt())
     proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
     proper(isNatKind(X)) -> isNatKind(proper(X))
     proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
     proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
     proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
     proper(isNat(X)) -> isNat(proper(X))
     proper(U16(X)) -> U16(proper(X))
     proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
     proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
     proper(U23(X)) -> U23(proper(X))
     proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
     proper(U32(X)) -> U32(proper(X))
     proper(U41(X)) -> U41(proper(X))
     proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
     proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
     proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
     proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
     proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
     proper(U64(X1,X2,X3)) -> U64(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())
    graph:
     ...
    Restore Modifier:
     DPs:
      active#(U11(tt(),V1,V2)) -> isNatKind#(V1)
      active#(U11(tt(),V1,V2)) -> U12#(isNatKind(V1),V1,V2)
      active#(U12(tt(),V1,V2)) -> isNatKind#(V2)
      active#(U12(tt(),V1,V2)) -> U13#(isNatKind(V2),V1,V2)
      active#(U13(tt(),V1,V2)) -> isNatKind#(V2)
      active#(U13(tt(),V1,V2)) -> U14#(isNatKind(V2),V1,V2)
      active#(U14(tt(),V1,V2)) -> isNat#(V1)
      active#(U14(tt(),V1,V2)) -> U15#(isNat(V1),V2)
      active#(U15(tt(),V2)) -> isNat#(V2)
      active#(U15(tt(),V2)) -> U16#(isNat(V2))
      active#(U21(tt(),V1)) -> isNatKind#(V1)
      active#(U21(tt(),V1)) -> U22#(isNatKind(V1),V1)
      active#(U22(tt(),V1)) -> isNat#(V1)
      active#(U22(tt(),V1)) -> U23#(isNat(V1))
      active#(U31(tt(),V2)) -> isNatKind#(V2)
      active#(U31(tt(),V2)) -> U32#(isNatKind(V2))
      active#(U51(tt(),N)) -> isNatKind#(N)
      active#(U51(tt(),N)) -> U52#(isNatKind(N),N)
      active#(U61(tt(),M,N)) -> isNatKind#(M)
      active#(U61(tt(),M,N)) -> U62#(isNatKind(M),M,N)
      active#(U62(tt(),M,N)) -> isNat#(N)
      active#(U62(tt(),M,N)) -> U63#(isNat(N),M,N)
      active#(U63(tt(),M,N)) -> isNatKind#(N)
      active#(U63(tt(),M,N)) -> U64#(isNatKind(N),M,N)
      active#(U64(tt(),M,N)) -> plus#(N,M)
      active#(U64(tt(),M,N)) -> s#(plus(N,M))
      active#(isNat(plus(V1,V2))) -> isNatKind#(V1)
      active#(isNat(plus(V1,V2))) -> U11#(isNatKind(V1),V1,V2)
      active#(isNat(s(V1))) -> isNatKind#(V1)
      active#(isNat(s(V1))) -> U21#(isNatKind(V1),V1)
      active#(isNatKind(plus(V1,V2))) -> isNatKind#(V1)
      active#(isNatKind(plus(V1,V2))) -> U31#(isNatKind(V1),V2)
      active#(isNatKind(s(V1))) -> isNatKind#(V1)
      active#(isNatKind(s(V1))) -> U41#(isNatKind(V1))
      active#(plus(N,0())) -> isNat#(N)
      active#(plus(N,0())) -> U51#(isNat(N),N)
      active#(plus(N,s(M))) -> isNat#(M)
      active#(plus(N,s(M))) -> U61#(isNat(M),M,N)
      active#(U11(X1,X2,X3)) -> active#(X1)
      active#(U11(X1,X2,X3)) -> U11#(active(X1),X2,X3)
      active#(U12(X1,X2,X3)) -> active#(X1)
      active#(U12(X1,X2,X3)) -> U12#(active(X1),X2,X3)
      active#(U13(X1,X2,X3)) -> active#(X1)
      active#(U13(X1,X2,X3)) -> U13#(active(X1),X2,X3)
      active#(U14(X1,X2,X3)) -> active#(X1)
      active#(U14(X1,X2,X3)) -> U14#(active(X1),X2,X3)
      active#(U15(X1,X2)) -> active#(X1)
      active#(U15(X1,X2)) -> U15#(active(X1),X2)
      active#(U16(X)) -> active#(X)
      active#(U16(X)) -> U16#(active(X))
      active#(U21(X1,X2)) -> active#(X1)
      active#(U21(X1,X2)) -> U21#(active(X1),X2)
      active#(U22(X1,X2)) -> active#(X1)
      active#(U22(X1,X2)) -> U22#(active(X1),X2)
      active#(U23(X)) -> active#(X)
      active#(U23(X)) -> U23#(active(X))
      active#(U31(X1,X2)) -> active#(X1)
      active#(U31(X1,X2)) -> U31#(active(X1),X2)
      active#(U32(X)) -> active#(X)
      active#(U32(X)) -> U32#(active(X))
      active#(U41(X)) -> active#(X)
      active#(U41(X)) -> U41#(active(X))
      active#(U51(X1,X2)) -> active#(X1)
      active#(U51(X1,X2)) -> U51#(active(X1),X2)
      active#(U52(X1,X2)) -> active#(X1)
      active#(U52(X1,X2)) -> U52#(active(X1),X2)
      active#(U61(X1,X2,X3)) -> active#(X1)
      active#(U61(X1,X2,X3)) -> U61#(active(X1),X2,X3)
      active#(U62(X1,X2,X3)) -> active#(X1)
      active#(U62(X1,X2,X3)) -> U62#(active(X1),X2,X3)
      active#(U63(X1,X2,X3)) -> active#(X1)
      active#(U63(X1,X2,X3)) -> U63#(active(X1),X2,X3)
      active#(U64(X1,X2,X3)) -> active#(X1)
      active#(U64(X1,X2,X3)) -> U64#(active(X1),X2,X3)
      active#(s(X)) -> active#(X)
      active#(s(X)) -> s#(active(X))
      active#(plus(X1,X2)) -> active#(X1)
      active#(plus(X1,X2)) -> plus#(active(X1),X2)
      active#(plus(X1,X2)) -> active#(X2)
      active#(plus(X1,X2)) -> plus#(X1,active(X2))
      U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3)
      U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3)
      U13#(mark(X1),X2,X3) -> U13#(X1,X2,X3)
      U14#(mark(X1),X2,X3) -> U14#(X1,X2,X3)
      U15#(mark(X1),X2) -> U15#(X1,X2)
      U16#(mark(X)) -> U16#(X)
      U21#(mark(X1),X2) -> U21#(X1,X2)
      U22#(mark(X1),X2) -> U22#(X1,X2)
      U23#(mark(X)) -> U23#(X)
      U31#(mark(X1),X2) -> U31#(X1,X2)
      U32#(mark(X)) -> U32#(X)
      U41#(mark(X)) -> U41#(X)
      U51#(mark(X1),X2) -> U51#(X1,X2)
      U52#(mark(X1),X2) -> U52#(X1,X2)
      U61#(mark(X1),X2,X3) -> U61#(X1,X2,X3)
      U62#(mark(X1),X2,X3) -> U62#(X1,X2,X3)
      U63#(mark(X1),X2,X3) -> U63#(X1,X2,X3)
      U64#(mark(X1),X2,X3) -> U64#(X1,X2,X3)
      s#(mark(X)) -> s#(X)
      plus#(mark(X1),X2) -> plus#(X1,X2)
      plus#(X1,mark(X2)) -> plus#(X1,X2)
      proper#(U11(X1,X2,X3)) -> proper#(X3)
      proper#(U11(X1,X2,X3)) -> proper#(X2)
      proper#(U11(X1,X2,X3)) -> proper#(X1)
      proper#(U11(X1,X2,X3)) -> U11#(proper(X1),proper(X2),proper(X3))
      proper#(U12(X1,X2,X3)) -> proper#(X3)
      proper#(U12(X1,X2,X3)) -> proper#(X2)
      proper#(U12(X1,X2,X3)) -> proper#(X1)
      proper#(U12(X1,X2,X3)) -> U12#(proper(X1),proper(X2),proper(X3))
      proper#(isNatKind(X)) -> proper#(X)
      proper#(isNatKind(X)) -> isNatKind#(proper(X))
      proper#(U13(X1,X2,X3)) -> proper#(X3)
      proper#(U13(X1,X2,X3)) -> proper#(X2)
      proper#(U13(X1,X2,X3)) -> proper#(X1)
      proper#(U13(X1,X2,X3)) -> U13#(proper(X1),proper(X2),proper(X3))
      proper#(U14(X1,X2,X3)) -> proper#(X3)
      proper#(U14(X1,X2,X3)) -> proper#(X2)
      proper#(U14(X1,X2,X3)) -> proper#(X1)
      proper#(U14(X1,X2,X3)) -> U14#(proper(X1),proper(X2),proper(X3))
      proper#(U15(X1,X2)) -> proper#(X2)
      proper#(U15(X1,X2)) -> proper#(X1)
      proper#(U15(X1,X2)) -> U15#(proper(X1),proper(X2))
      proper#(isNat(X)) -> proper#(X)
      proper#(isNat(X)) -> isNat#(proper(X))
      proper#(U16(X)) -> proper#(X)
      proper#(U16(X)) -> U16#(proper(X))
      proper#(U21(X1,X2)) -> proper#(X2)
      proper#(U21(X1,X2)) -> proper#(X1)
      proper#(U21(X1,X2)) -> U21#(proper(X1),proper(X2))
      proper#(U22(X1,X2)) -> proper#(X2)
      proper#(U22(X1,X2)) -> proper#(X1)
      proper#(U22(X1,X2)) -> U22#(proper(X1),proper(X2))
      proper#(U23(X)) -> proper#(X)
      proper#(U23(X)) -> U23#(proper(X))
      proper#(U31(X1,X2)) -> proper#(X2)
      proper#(U31(X1,X2)) -> proper#(X1)
      proper#(U31(X1,X2)) -> U31#(proper(X1),proper(X2))
      proper#(U32(X)) -> proper#(X)
      proper#(U32(X)) -> U32#(proper(X))
      proper#(U41(X)) -> proper#(X)
      proper#(U41(X)) -> U41#(proper(X))
      proper#(U51(X1,X2)) -> proper#(X2)
      proper#(U51(X1,X2)) -> proper#(X1)
      proper#(U51(X1,X2)) -> U51#(proper(X1),proper(X2))
      proper#(U52(X1,X2)) -> proper#(X2)
      proper#(U52(X1,X2)) -> proper#(X1)
      proper#(U52(X1,X2)) -> U52#(proper(X1),proper(X2))
      proper#(U61(X1,X2,X3)) -> proper#(X3)
      proper#(U61(X1,X2,X3)) -> proper#(X2)
      proper#(U61(X1,X2,X3)) -> proper#(X1)
      proper#(U61(X1,X2,X3)) -> U61#(proper(X1),proper(X2),proper(X3))
      proper#(U62(X1,X2,X3)) -> proper#(X3)
      proper#(U62(X1,X2,X3)) -> proper#(X2)
      proper#(U62(X1,X2,X3)) -> proper#(X1)
      proper#(U62(X1,X2,X3)) -> U62#(proper(X1),proper(X2),proper(X3))
      proper#(U63(X1,X2,X3)) -> proper#(X3)
      proper#(U63(X1,X2,X3)) -> proper#(X2)
      proper#(U63(X1,X2,X3)) -> proper#(X1)
      proper#(U63(X1,X2,X3)) -> U63#(proper(X1),proper(X2),proper(X3))
      proper#(U64(X1,X2,X3)) -> proper#(X3)
      proper#(U64(X1,X2,X3)) -> proper#(X2)
      proper#(U64(X1,X2,X3)) -> proper#(X1)
      proper#(U64(X1,X2,X3)) -> U64#(proper(X1),proper(X2),proper(X3))
      proper#(s(X)) -> proper#(X)
      proper#(s(X)) -> s#(proper(X))
      proper#(plus(X1,X2)) -> proper#(X2)
      proper#(plus(X1,X2)) -> proper#(X1)
      proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2))
      U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3)
      U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3)
      isNatKind#(ok(X)) -> isNatKind#(X)
      U13#(ok(X1),ok(X2),ok(X3)) -> U13#(X1,X2,X3)
      U14#(ok(X1),ok(X2),ok(X3)) -> U14#(X1,X2,X3)
      U15#(ok(X1),ok(X2)) -> U15#(X1,X2)
      isNat#(ok(X)) -> isNat#(X)
      U16#(ok(X)) -> U16#(X)
      U21#(ok(X1),ok(X2)) -> U21#(X1,X2)
      U22#(ok(X1),ok(X2)) -> U22#(X1,X2)
      U23#(ok(X)) -> U23#(X)
      U31#(ok(X1),ok(X2)) -> U31#(X1,X2)
      U32#(ok(X)) -> U32#(X)
      U41#(ok(X)) -> U41#(X)
      U51#(ok(X1),ok(X2)) -> U51#(X1,X2)
      U52#(ok(X1),ok(X2)) -> U52#(X1,X2)
      U61#(ok(X1),ok(X2),ok(X3)) -> U61#(X1,X2,X3)
      U62#(ok(X1),ok(X2),ok(X3)) -> U62#(X1,X2,X3)
      U63#(ok(X1),ok(X2),ok(X3)) -> U63#(X1,X2,X3)
      U64#(ok(X1),ok(X2),ok(X3)) -> U64#(X1,X2,X3)
      s#(ok(X)) -> s#(X)
      plus#(ok(X1),ok(X2)) -> plus#(X1,X2)
      top#(mark(X)) -> proper#(X)
      top#(mark(X)) -> top#(proper(X))
      top#(ok(X)) -> active#(X)
      top#(ok(X)) -> top#(active(X))
     TRS:
      active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
      active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
      active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
      active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
      active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
      active(U16(tt())) -> mark(tt())
      active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
      active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
      active(U23(tt())) -> mark(tt())
      active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
      active(U32(tt())) -> mark(tt())
      active(U41(tt())) -> mark(tt())
      active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
      active(U52(tt(),N)) -> mark(N)
      active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
      active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
      active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
      active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
      active(isNat(0())) -> mark(tt())
      active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
      active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
      active(isNatKind(0())) -> mark(tt())
      active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
      active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
      active(plus(N,0())) -> mark(U51(isNat(N),N))
      active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
      active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
      active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
      active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
      active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
      active(U15(X1,X2)) -> U15(active(X1),X2)
      active(U16(X)) -> U16(active(X))
      active(U21(X1,X2)) -> U21(active(X1),X2)
      active(U22(X1,X2)) -> U22(active(X1),X2)
      active(U23(X)) -> U23(active(X))
      active(U31(X1,X2)) -> U31(active(X1),X2)
      active(U32(X)) -> U32(active(X))
      active(U41(X)) -> U41(active(X))
      active(U51(X1,X2)) -> U51(active(X1),X2)
      active(U52(X1,X2)) -> U52(active(X1),X2)
      active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
      active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
      active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
      active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
      U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
      U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
      U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
      U15(mark(X1),X2) -> mark(U15(X1,X2))
      U16(mark(X)) -> mark(U16(X))
      U21(mark(X1),X2) -> mark(U21(X1,X2))
      U22(mark(X1),X2) -> mark(U22(X1,X2))
      U23(mark(X)) -> mark(U23(X))
      U31(mark(X1),X2) -> mark(U31(X1,X2))
      U32(mark(X)) -> mark(U32(X))
      U41(mark(X)) -> mark(U41(X))
      U51(mark(X1),X2) -> mark(U51(X1,X2))
      U52(mark(X1),X2) -> mark(U52(X1,X2))
      U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
      U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
      U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
      U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
      proper(tt()) -> ok(tt())
      proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
      proper(isNatKind(X)) -> isNatKind(proper(X))
      proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
      proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
      proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
      proper(isNat(X)) -> isNat(proper(X))
      proper(U16(X)) -> U16(proper(X))
      proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
      proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
      proper(U23(X)) -> U23(proper(X))
      proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
      proper(U32(X)) -> U32(proper(X))
      proper(U41(X)) -> U41(proper(X))
      proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
      proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
      proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
      proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
      proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
      proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
      U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
      isNatKind(ok(X)) -> ok(isNatKind(X))
      U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
      U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
      U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
      isNat(ok(X)) -> ok(isNat(X))
      U16(ok(X)) -> ok(U16(X))
      U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
      U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
      U23(ok(X)) -> ok(U23(X))
      U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
      U32(ok(X)) -> ok(U32(X))
      U41(ok(X)) -> ok(U41(X))
      U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
      U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
      U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
      U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
      U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
      U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
     SCC Processor:
      #sccs: 25
      #rules: 111
      #arcs: 5065/37636
      DPs:
       top#(ok(X)) -> top#(active(X))
       top#(mark(X)) -> top#(proper(X))
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       proper#(plus(X1,X2)) -> proper#(X1)
       proper#(plus(X1,X2)) -> proper#(X2)
       proper#(s(X)) -> proper#(X)
       proper#(U64(X1,X2,X3)) -> proper#(X1)
       proper#(U64(X1,X2,X3)) -> proper#(X2)
       proper#(U64(X1,X2,X3)) -> proper#(X3)
       proper#(U63(X1,X2,X3)) -> proper#(X1)
       proper#(U63(X1,X2,X3)) -> proper#(X2)
       proper#(U63(X1,X2,X3)) -> proper#(X3)
       proper#(U62(X1,X2,X3)) -> proper#(X1)
       proper#(U62(X1,X2,X3)) -> proper#(X2)
       proper#(U62(X1,X2,X3)) -> proper#(X3)
       proper#(U61(X1,X2,X3)) -> proper#(X1)
       proper#(U61(X1,X2,X3)) -> proper#(X2)
       proper#(U61(X1,X2,X3)) -> proper#(X3)
       proper#(U52(X1,X2)) -> proper#(X1)
       proper#(U52(X1,X2)) -> proper#(X2)
       proper#(U51(X1,X2)) -> proper#(X1)
       proper#(U51(X1,X2)) -> proper#(X2)
       proper#(U41(X)) -> proper#(X)
       proper#(U32(X)) -> proper#(X)
       proper#(U31(X1,X2)) -> proper#(X1)
       proper#(U31(X1,X2)) -> proper#(X2)
       proper#(U23(X)) -> proper#(X)
       proper#(U22(X1,X2)) -> proper#(X1)
       proper#(U22(X1,X2)) -> proper#(X2)
       proper#(U21(X1,X2)) -> proper#(X1)
       proper#(U21(X1,X2)) -> proper#(X2)
       proper#(U16(X)) -> proper#(X)
       proper#(isNat(X)) -> proper#(X)
       proper#(U15(X1,X2)) -> proper#(X1)
       proper#(U15(X1,X2)) -> proper#(X2)
       proper#(U14(X1,X2,X3)) -> proper#(X1)
       proper#(U14(X1,X2,X3)) -> proper#(X2)
       proper#(U14(X1,X2,X3)) -> proper#(X3)
       proper#(U13(X1,X2,X3)) -> proper#(X1)
       proper#(U13(X1,X2,X3)) -> proper#(X2)
       proper#(U13(X1,X2,X3)) -> proper#(X3)
       proper#(isNatKind(X)) -> proper#(X)
       proper#(U12(X1,X2,X3)) -> proper#(X1)
       proper#(U12(X1,X2,X3)) -> proper#(X2)
       proper#(U12(X1,X2,X3)) -> proper#(X3)
       proper#(U11(X1,X2,X3)) -> proper#(X1)
       proper#(U11(X1,X2,X3)) -> proper#(X2)
       proper#(U11(X1,X2,X3)) -> proper#(X3)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       active#(plus(X1,X2)) -> active#(X2)
       active#(plus(X1,X2)) -> active#(X1)
       active#(s(X)) -> active#(X)
       active#(U64(X1,X2,X3)) -> active#(X1)
       active#(U63(X1,X2,X3)) -> active#(X1)
       active#(U62(X1,X2,X3)) -> active#(X1)
       active#(U61(X1,X2,X3)) -> active#(X1)
       active#(U52(X1,X2)) -> active#(X1)
       active#(U51(X1,X2)) -> active#(X1)
       active#(U41(X)) -> active#(X)
       active#(U32(X)) -> active#(X)
       active#(U31(X1,X2)) -> active#(X1)
       active#(U23(X)) -> active#(X)
       active#(U22(X1,X2)) -> active#(X1)
       active#(U21(X1,X2)) -> active#(X1)
       active#(U16(X)) -> active#(X)
       active#(U15(X1,X2)) -> active#(X1)
       active#(U14(X1,X2,X3)) -> active#(X1)
       active#(U13(X1,X2,X3)) -> active#(X1)
       active#(U12(X1,X2,X3)) -> active#(X1)
       active#(U11(X1,X2,X3)) -> active#(X1)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       isNatKind#(ok(X)) -> isNatKind#(X)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       isNat#(ok(X)) -> isNat#(X)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       U11#(ok(X1),ok(X2),ok(X3)) -> U11#(X1,X2,X3)
       U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       U12#(ok(X1),ok(X2),ok(X3)) -> U12#(X1,X2,X3)
       U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       U13#(ok(X1),ok(X2),ok(X3)) -> U13#(X1,X2,X3)
       U13#(mark(X1),X2,X3) -> U13#(X1,X2,X3)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       U14#(ok(X1),ok(X2),ok(X3)) -> U14#(X1,X2,X3)
       U14#(mark(X1),X2,X3) -> U14#(X1,X2,X3)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       U15#(ok(X1),ok(X2)) -> U15#(X1,X2)
       U15#(mark(X1),X2) -> U15#(X1,X2)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       U16#(ok(X)) -> U16#(X)
       U16#(mark(X)) -> U16#(X)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       U21#(ok(X1),ok(X2)) -> U21#(X1,X2)
       U21#(mark(X1),X2) -> U21#(X1,X2)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       U22#(ok(X1),ok(X2)) -> U22#(X1,X2)
       U22#(mark(X1),X2) -> U22#(X1,X2)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       U23#(ok(X)) -> U23#(X)
       U23#(mark(X)) -> U23#(X)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       U31#(ok(X1),ok(X2)) -> U31#(X1,X2)
       U31#(mark(X1),X2) -> U31#(X1,X2)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       U32#(ok(X)) -> U32#(X)
       U32#(mark(X)) -> U32#(X)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       U41#(ok(X)) -> U41#(X)
       U41#(mark(X)) -> U41#(X)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       U51#(ok(X1),ok(X2)) -> U51#(X1,X2)
       U51#(mark(X1),X2) -> U51#(X1,X2)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       U52#(ok(X1),ok(X2)) -> U52#(X1,X2)
       U52#(mark(X1),X2) -> U52#(X1,X2)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       U61#(ok(X1),ok(X2),ok(X3)) -> U61#(X1,X2,X3)
       U61#(mark(X1),X2,X3) -> U61#(X1,X2,X3)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       U62#(ok(X1),ok(X2),ok(X3)) -> U62#(X1,X2,X3)
       U62#(mark(X1),X2,X3) -> U62#(X1,X2,X3)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       U63#(ok(X1),ok(X2),ok(X3)) -> U63#(X1,X2,X3)
       U63#(mark(X1),X2,X3) -> U63#(X1,X2,X3)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       U64#(ok(X1),ok(X2),ok(X3)) -> U64#(X1,X2,X3)
       U64#(mark(X1),X2,X3) -> U64#(X1,X2,X3)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       s#(ok(X)) -> s#(X)
       s#(mark(X)) -> s#(X)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open
      
      DPs:
       plus#(ok(X1),ok(X2)) -> plus#(X1,X2)
       plus#(X1,mark(X2)) -> plus#(X1,X2)
       plus#(mark(X1),X2) -> plus#(X1,X2)
      TRS:
       active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2))
       active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2))
       active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2))
       active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2))
       active(U15(tt(),V2)) -> mark(U16(isNat(V2)))
       active(U16(tt())) -> mark(tt())
       active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1))
       active(U22(tt(),V1)) -> mark(U23(isNat(V1)))
       active(U23(tt())) -> mark(tt())
       active(U31(tt(),V2)) -> mark(U32(isNatKind(V2)))
       active(U32(tt())) -> mark(tt())
       active(U41(tt())) -> mark(tt())
       active(U51(tt(),N)) -> mark(U52(isNatKind(N),N))
       active(U52(tt(),N)) -> mark(N)
       active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N))
       active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N))
       active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N))
       active(U64(tt(),M,N)) -> mark(s(plus(N,M)))
       active(isNat(0())) -> mark(tt())
       active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2))
       active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1))
       active(isNatKind(0())) -> mark(tt())
       active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2))
       active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1)))
       active(plus(N,0())) -> mark(U51(isNat(N),N))
       active(plus(N,s(M))) -> mark(U61(isNat(M),M,N))
       active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
       active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
       active(U13(X1,X2,X3)) -> U13(active(X1),X2,X3)
       active(U14(X1,X2,X3)) -> U14(active(X1),X2,X3)
       active(U15(X1,X2)) -> U15(active(X1),X2)
       active(U16(X)) -> U16(active(X))
       active(U21(X1,X2)) -> U21(active(X1),X2)
       active(U22(X1,X2)) -> U22(active(X1),X2)
       active(U23(X)) -> U23(active(X))
       active(U31(X1,X2)) -> U31(active(X1),X2)
       active(U32(X)) -> U32(active(X))
       active(U41(X)) -> U41(active(X))
       active(U51(X1,X2)) -> U51(active(X1),X2)
       active(U52(X1,X2)) -> U52(active(X1),X2)
       active(U61(X1,X2,X3)) -> U61(active(X1),X2,X3)
       active(U62(X1,X2,X3)) -> U62(active(X1),X2,X3)
       active(U63(X1,X2,X3)) -> U63(active(X1),X2,X3)
       active(U64(X1,X2,X3)) -> U64(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,X3) -> mark(U11(X1,X2,X3))
       U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
       U13(mark(X1),X2,X3) -> mark(U13(X1,X2,X3))
       U14(mark(X1),X2,X3) -> mark(U14(X1,X2,X3))
       U15(mark(X1),X2) -> mark(U15(X1,X2))
       U16(mark(X)) -> mark(U16(X))
       U21(mark(X1),X2) -> mark(U21(X1,X2))
       U22(mark(X1),X2) -> mark(U22(X1,X2))
       U23(mark(X)) -> mark(U23(X))
       U31(mark(X1),X2) -> mark(U31(X1,X2))
       U32(mark(X)) -> mark(U32(X))
       U41(mark(X)) -> mark(U41(X))
       U51(mark(X1),X2) -> mark(U51(X1,X2))
       U52(mark(X1),X2) -> mark(U52(X1,X2))
       U61(mark(X1),X2,X3) -> mark(U61(X1,X2,X3))
       U62(mark(X1),X2,X3) -> mark(U62(X1,X2,X3))
       U63(mark(X1),X2,X3) -> mark(U63(X1,X2,X3))
       U64(mark(X1),X2,X3) -> mark(U64(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,X3)) -> U11(proper(X1),proper(X2),proper(X3))
       proper(tt()) -> ok(tt())
       proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
       proper(isNatKind(X)) -> isNatKind(proper(X))
       proper(U13(X1,X2,X3)) -> U13(proper(X1),proper(X2),proper(X3))
       proper(U14(X1,X2,X3)) -> U14(proper(X1),proper(X2),proper(X3))
       proper(U15(X1,X2)) -> U15(proper(X1),proper(X2))
       proper(isNat(X)) -> isNat(proper(X))
       proper(U16(X)) -> U16(proper(X))
       proper(U21(X1,X2)) -> U21(proper(X1),proper(X2))
       proper(U22(X1,X2)) -> U22(proper(X1),proper(X2))
       proper(U23(X)) -> U23(proper(X))
       proper(U31(X1,X2)) -> U31(proper(X1),proper(X2))
       proper(U32(X)) -> U32(proper(X))
       proper(U41(X)) -> U41(proper(X))
       proper(U51(X1,X2)) -> U51(proper(X1),proper(X2))
       proper(U52(X1,X2)) -> U52(proper(X1),proper(X2))
       proper(U61(X1,X2,X3)) -> U61(proper(X1),proper(X2),proper(X3))
       proper(U62(X1,X2,X3)) -> U62(proper(X1),proper(X2),proper(X3))
       proper(U63(X1,X2,X3)) -> U63(proper(X1),proper(X2),proper(X3))
       proper(U64(X1,X2,X3)) -> U64(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(X3)) -> ok(U11(X1,X2,X3))
       U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
       isNatKind(ok(X)) -> ok(isNatKind(X))
       U13(ok(X1),ok(X2),ok(X3)) -> ok(U13(X1,X2,X3))
       U14(ok(X1),ok(X2),ok(X3)) -> ok(U14(X1,X2,X3))
       U15(ok(X1),ok(X2)) -> ok(U15(X1,X2))
       isNat(ok(X)) -> ok(isNat(X))
       U16(ok(X)) -> ok(U16(X))
       U21(ok(X1),ok(X2)) -> ok(U21(X1,X2))
       U22(ok(X1),ok(X2)) -> ok(U22(X1,X2))
       U23(ok(X)) -> ok(U23(X))
       U31(ok(X1),ok(X2)) -> ok(U31(X1,X2))
       U32(ok(X)) -> ok(U32(X))
       U41(ok(X)) -> ok(U41(X))
       U51(ok(X1),ok(X2)) -> ok(U51(X1,X2))
       U52(ok(X1),ok(X2)) -> ok(U52(X1,X2))
       U61(ok(X1),ok(X2),ok(X3)) -> ok(U61(X1,X2,X3))
       U62(ok(X1),ok(X2),ok(X3)) -> ok(U62(X1,X2,X3))
       U63(ok(X1),ok(X2),ok(X3)) -> ok(U63(X1,X2,X3))
       U64(ok(X1),ok(X2),ok(X3)) -> ok(U64(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))
      Open