MAYBE Problem: U11(tt(),V1,V2) -> U12(isNat(activate(V1)),activate(V2)) U12(tt(),V2) -> U13(isNat(activate(V2))) U13(tt()) -> tt() U21(tt(),V1) -> U22(isNat(activate(V1))) U22(tt()) -> tt() U31(tt(),V1,V2) -> U32(isNat(activate(V1)),activate(V2)) U32(tt(),V2) -> U33(isNat(activate(V2))) U33(tt()) -> tt() U41(tt(),N) -> activate(N) U51(tt(),M,N) -> s(plus(activate(N),activate(M))) U61(tt()) -> 0() U71(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N)) and(tt(),X) -> activate(X) isNat(n__0()) -> tt() isNat(n__plus(V1,V2)) -> U11(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNat(n__x(V1,V2)) -> U31(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) isNatKind(n__0()) -> tt() isNatKind(n__plus(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNatKind(n__s(V1)) -> isNatKind(activate(V1)) isNatKind(n__x(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatKind(activate(V2))) plus(N,0()) -> U41(and(isNat(N),n__isNatKind(N)),N) plus(N,s(M)) -> U51(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) x(N,0()) -> U61(and(isNat(N),n__isNatKind(N))) x(N,s(M)) -> U71(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) 0() -> n__0() plus(X1,X2) -> n__plus(X1,X2) isNatKind(X) -> n__isNatKind(X) s(X) -> n__s(X) x(X1,X2) -> n__x(X1,X2) and(X1,X2) -> n__and(X1,X2) activate(n__0()) -> 0() activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__isNatKind(X)) -> isNatKind(X) activate(n__s(X)) -> s(X) activate(n__x(X1,X2)) -> x(X1,X2) activate(n__and(X1,X2)) -> and(X1,X2) activate(X) -> X Proof: DP Processor: DPs: U11#(tt(),V1,V2) -> activate#(V2) U11#(tt(),V1,V2) -> activate#(V1) U11#(tt(),V1,V2) -> isNat#(activate(V1)) U11#(tt(),V1,V2) -> U12#(isNat(activate(V1)),activate(V2)) U12#(tt(),V2) -> activate#(V2) U12#(tt(),V2) -> isNat#(activate(V2)) U12#(tt(),V2) -> U13#(isNat(activate(V2))) U21#(tt(),V1) -> activate#(V1) U21#(tt(),V1) -> isNat#(activate(V1)) U21#(tt(),V1) -> U22#(isNat(activate(V1))) U31#(tt(),V1,V2) -> activate#(V2) U31#(tt(),V1,V2) -> activate#(V1) U31#(tt(),V1,V2) -> isNat#(activate(V1)) U31#(tt(),V1,V2) -> U32#(isNat(activate(V1)),activate(V2)) U32#(tt(),V2) -> activate#(V2) U32#(tt(),V2) -> isNat#(activate(V2)) U32#(tt(),V2) -> U33#(isNat(activate(V2))) U41#(tt(),N) -> activate#(N) U51#(tt(),M,N) -> activate#(M) U51#(tt(),M,N) -> activate#(N) U51#(tt(),M,N) -> plus#(activate(N),activate(M)) U51#(tt(),M,N) -> s#(plus(activate(N),activate(M))) U61#(tt()) -> 0#() U71#(tt(),M,N) -> activate#(M) U71#(tt(),M,N) -> activate#(N) U71#(tt(),M,N) -> x#(activate(N),activate(M)) U71#(tt(),M,N) -> plus#(x(activate(N),activate(M)),activate(N)) and#(tt(),X) -> activate#(X) isNat#(n__plus(V1,V2)) -> activate#(V2) isNat#(n__plus(V1,V2)) -> activate#(V1) isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) isNat#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNat#(n__plus(V1,V2)) -> U11#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) isNat#(n__s(V1)) -> activate#(V1) isNat#(n__s(V1)) -> isNatKind#(activate(V1)) isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) isNat#(n__x(V1,V2)) -> activate#(V2) isNat#(n__x(V1,V2)) -> activate#(V1) isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) isNat#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNat#(n__x(V1,V2)) -> U31#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) isNatKind#(n__plus(V1,V2)) -> activate#(V2) isNatKind#(n__plus(V1,V2)) -> activate#(V1) isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) isNatKind#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNatKind#(n__s(V1)) -> activate#(V1) isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) isNatKind#(n__x(V1,V2)) -> activate#(V2) isNatKind#(n__x(V1,V2)) -> activate#(V1) isNatKind#(n__x(V1,V2)) -> isNatKind#(activate(V1)) isNatKind#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) plus#(N,0()) -> isNat#(N) plus#(N,0()) -> and#(isNat(N),n__isNatKind(N)) plus#(N,0()) -> U41#(and(isNat(N),n__isNatKind(N)),N) plus#(N,s(M)) -> isNat#(N) plus#(N,s(M)) -> isNat#(M) plus#(N,s(M)) -> and#(isNat(M),n__isNatKind(M)) plus#(N,s(M)) -> and#(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))) plus#(N,s(M)) -> U51#(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) x#(N,0()) -> isNat#(N) x#(N,0()) -> and#(isNat(N),n__isNatKind(N)) x#(N,0()) -> U61#(and(isNat(N),n__isNatKind(N))) x#(N,s(M)) -> isNat#(N) x#(N,s(M)) -> isNat#(M) x#(N,s(M)) -> and#(isNat(M),n__isNatKind(M)) x#(N,s(M)) -> and#(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))) x#(N,s(M)) -> U71#(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) activate#(n__0()) -> 0#() activate#(n__plus(X1,X2)) -> plus#(X1,X2) activate#(n__isNatKind(X)) -> isNatKind#(X) activate#(n__s(X)) -> s#(X) activate#(n__x(X1,X2)) -> x#(X1,X2) activate#(n__and(X1,X2)) -> and#(X1,X2) TRS: U11(tt(),V1,V2) -> U12(isNat(activate(V1)),activate(V2)) U12(tt(),V2) -> U13(isNat(activate(V2))) U13(tt()) -> tt() U21(tt(),V1) -> U22(isNat(activate(V1))) U22(tt()) -> tt() U31(tt(),V1,V2) -> U32(isNat(activate(V1)),activate(V2)) U32(tt(),V2) -> U33(isNat(activate(V2))) U33(tt()) -> tt() U41(tt(),N) -> activate(N) U51(tt(),M,N) -> s(plus(activate(N),activate(M))) U61(tt()) -> 0() U71(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N)) and(tt(),X) -> activate(X) isNat(n__0()) -> tt() isNat(n__plus(V1,V2)) -> U11(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNat(n__x(V1,V2)) -> U31(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) isNatKind(n__0()) -> tt() isNatKind(n__plus(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNatKind(n__s(V1)) -> isNatKind(activate(V1)) isNatKind(n__x(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatKind(activate(V2))) plus(N,0()) -> U41(and(isNat(N),n__isNatKind(N)),N) plus(N,s(M)) -> U51(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) x(N,0()) -> U61(and(isNat(N),n__isNatKind(N))) x(N,s(M)) -> U71(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) 0() -> n__0() plus(X1,X2) -> n__plus(X1,X2) isNatKind(X) -> n__isNatKind(X) s(X) -> n__s(X) x(X1,X2) -> n__x(X1,X2) and(X1,X2) -> n__and(X1,X2) activate(n__0()) -> 0() activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__isNatKind(X)) -> isNatKind(X) activate(n__s(X)) -> s(X) activate(n__x(X1,X2)) -> x(X1,X2) activate(n__and(X1,X2)) -> and(X1,X2) activate(X) -> X TDG Processor: DPs: U11#(tt(),V1,V2) -> activate#(V2) U11#(tt(),V1,V2) -> activate#(V1) U11#(tt(),V1,V2) -> isNat#(activate(V1)) U11#(tt(),V1,V2) -> U12#(isNat(activate(V1)),activate(V2)) U12#(tt(),V2) -> activate#(V2) U12#(tt(),V2) -> isNat#(activate(V2)) U12#(tt(),V2) -> U13#(isNat(activate(V2))) U21#(tt(),V1) -> activate#(V1) U21#(tt(),V1) -> isNat#(activate(V1)) U21#(tt(),V1) -> U22#(isNat(activate(V1))) U31#(tt(),V1,V2) -> activate#(V2) U31#(tt(),V1,V2) -> activate#(V1) U31#(tt(),V1,V2) -> isNat#(activate(V1)) U31#(tt(),V1,V2) -> U32#(isNat(activate(V1)),activate(V2)) U32#(tt(),V2) -> activate#(V2) U32#(tt(),V2) -> isNat#(activate(V2)) U32#(tt(),V2) -> U33#(isNat(activate(V2))) U41#(tt(),N) -> activate#(N) U51#(tt(),M,N) -> activate#(M) U51#(tt(),M,N) -> activate#(N) U51#(tt(),M,N) -> plus#(activate(N),activate(M)) U51#(tt(),M,N) -> s#(plus(activate(N),activate(M))) U61#(tt()) -> 0#() U71#(tt(),M,N) -> activate#(M) U71#(tt(),M,N) -> activate#(N) U71#(tt(),M,N) -> x#(activate(N),activate(M)) U71#(tt(),M,N) -> plus#(x(activate(N),activate(M)),activate(N)) and#(tt(),X) -> activate#(X) isNat#(n__plus(V1,V2)) -> activate#(V2) isNat#(n__plus(V1,V2)) -> activate#(V1) isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) isNat#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNat#(n__plus(V1,V2)) -> U11#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) isNat#(n__s(V1)) -> activate#(V1) isNat#(n__s(V1)) -> isNatKind#(activate(V1)) isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) isNat#(n__x(V1,V2)) -> activate#(V2) isNat#(n__x(V1,V2)) -> activate#(V1) isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) isNat#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNat#(n__x(V1,V2)) -> U31#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) isNatKind#(n__plus(V1,V2)) -> activate#(V2) isNatKind#(n__plus(V1,V2)) -> activate#(V1) isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) isNatKind#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNatKind#(n__s(V1)) -> activate#(V1) isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) isNatKind#(n__x(V1,V2)) -> activate#(V2) isNatKind#(n__x(V1,V2)) -> activate#(V1) isNatKind#(n__x(V1,V2)) -> isNatKind#(activate(V1)) isNatKind#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) plus#(N,0()) -> isNat#(N) plus#(N,0()) -> and#(isNat(N),n__isNatKind(N)) plus#(N,0()) -> U41#(and(isNat(N),n__isNatKind(N)),N) plus#(N,s(M)) -> isNat#(N) plus#(N,s(M)) -> isNat#(M) plus#(N,s(M)) -> and#(isNat(M),n__isNatKind(M)) plus#(N,s(M)) -> and#(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))) plus#(N,s(M)) -> U51#(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) x#(N,0()) -> isNat#(N) x#(N,0()) -> and#(isNat(N),n__isNatKind(N)) x#(N,0()) -> U61#(and(isNat(N),n__isNatKind(N))) x#(N,s(M)) -> isNat#(N) x#(N,s(M)) -> isNat#(M) x#(N,s(M)) -> and#(isNat(M),n__isNatKind(M)) x#(N,s(M)) -> and#(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))) x#(N,s(M)) -> U71#(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) activate#(n__0()) -> 0#() activate#(n__plus(X1,X2)) -> plus#(X1,X2) activate#(n__isNatKind(X)) -> isNatKind#(X) activate#(n__s(X)) -> s#(X) activate#(n__x(X1,X2)) -> x#(X1,X2) activate#(n__and(X1,X2)) -> and#(X1,X2) TRS: U11(tt(),V1,V2) -> U12(isNat(activate(V1)),activate(V2)) U12(tt(),V2) -> U13(isNat(activate(V2))) U13(tt()) -> tt() U21(tt(),V1) -> U22(isNat(activate(V1))) U22(tt()) -> tt() U31(tt(),V1,V2) -> U32(isNat(activate(V1)),activate(V2)) U32(tt(),V2) -> U33(isNat(activate(V2))) U33(tt()) -> tt() U41(tt(),N) -> activate(N) U51(tt(),M,N) -> s(plus(activate(N),activate(M))) U61(tt()) -> 0() U71(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N)) and(tt(),X) -> activate(X) isNat(n__0()) -> tt() isNat(n__plus(V1,V2)) -> U11(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNat(n__x(V1,V2)) -> U31(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) isNatKind(n__0()) -> tt() isNatKind(n__plus(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNatKind(n__s(V1)) -> isNatKind(activate(V1)) isNatKind(n__x(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatKind(activate(V2))) plus(N,0()) -> U41(and(isNat(N),n__isNatKind(N)),N) plus(N,s(M)) -> U51(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) x(N,0()) -> U61(and(isNat(N),n__isNatKind(N))) x(N,s(M)) -> U71(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) 0() -> n__0() plus(X1,X2) -> n__plus(X1,X2) isNatKind(X) -> n__isNatKind(X) s(X) -> n__s(X) x(X1,X2) -> n__x(X1,X2) and(X1,X2) -> n__and(X1,X2) activate(n__0()) -> 0() activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__isNatKind(X)) -> isNatKind(X) activate(n__s(X)) -> s(X) activate(n__x(X1,X2)) -> x(X1,X2) activate(n__and(X1,X2)) -> and(X1,X2) activate(X) -> X graph: isNatKind#(n__x(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNatKind#(n__x(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> isNatKind#(activate(V1)) isNatKind#(n__x(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> activate#(V1) isNatKind#(n__x(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> activate#(V2) isNatKind#(n__x(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) isNatKind#(n__x(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__s(V1)) -> activate#(V1) isNatKind#(n__x(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNatKind#(n__x(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) isNatKind#(n__x(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> activate#(V1) isNatKind#(n__x(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> activate#(V2) isNatKind#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) -> and#(tt(),X) -> activate#(X) isNatKind#(n__x(V1,V2)) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isNatKind#(n__x(V1,V2)) -> activate#(V2) -> activate#(n__x(X1,X2)) -> x#(X1,X2) isNatKind#(n__x(V1,V2)) -> activate#(V2) -> activate#(n__s(X)) -> s#(X) isNatKind#(n__x(V1,V2)) -> activate#(V2) -> activate#(n__isNatKind(X)) -> isNatKind#(X) isNatKind#(n__x(V1,V2)) -> activate#(V2) -> activate#(n__plus(X1,X2)) -> plus#(X1,X2) isNatKind#(n__x(V1,V2)) -> activate#(V2) -> activate#(n__0()) -> 0#() isNatKind#(n__x(V1,V2)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isNatKind#(n__x(V1,V2)) -> activate#(V1) -> activate#(n__x(X1,X2)) -> x#(X1,X2) isNatKind#(n__x(V1,V2)) -> activate#(V1) -> activate#(n__s(X)) -> s#(X) isNatKind#(n__x(V1,V2)) -> activate#(V1) -> activate#(n__isNatKind(X)) -> isNatKind#(X) isNatKind#(n__x(V1,V2)) -> activate#(V1) -> activate#(n__plus(X1,X2)) -> plus#(X1,X2) isNatKind#(n__x(V1,V2)) -> activate#(V1) -> activate#(n__0()) -> 0#() isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> isNatKind#(activate(V1)) isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> activate#(V1) isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> activate#(V2) isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__s(V1)) -> activate#(V1) isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> activate#(V1) isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> activate#(V2) isNatKind#(n__s(V1)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isNatKind#(n__s(V1)) -> activate#(V1) -> activate#(n__x(X1,X2)) -> x#(X1,X2) isNatKind#(n__s(V1)) -> activate#(V1) -> activate#(n__s(X)) -> s#(X) isNatKind#(n__s(V1)) -> activate#(V1) -> activate#(n__isNatKind(X)) -> isNatKind#(X) isNatKind#(n__s(V1)) -> activate#(V1) -> activate#(n__plus(X1,X2)) -> plus#(X1,X2) isNatKind#(n__s(V1)) -> activate#(V1) -> activate#(n__0()) -> 0#() isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> isNatKind#(activate(V1)) isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> activate#(V1) isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> activate#(V2) isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__s(V1)) -> activate#(V1) isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> activate#(V1) isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> activate#(V2) isNatKind#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) -> and#(tt(),X) -> activate#(X) isNatKind#(n__plus(V1,V2)) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isNatKind#(n__plus(V1,V2)) -> activate#(V2) -> activate#(n__x(X1,X2)) -> x#(X1,X2) isNatKind#(n__plus(V1,V2)) -> activate#(V2) -> activate#(n__s(X)) -> s#(X) isNatKind#(n__plus(V1,V2)) -> activate#(V2) -> activate#(n__isNatKind(X)) -> isNatKind#(X) isNatKind#(n__plus(V1,V2)) -> activate#(V2) -> activate#(n__plus(X1,X2)) -> plus#(X1,X2) isNatKind#(n__plus(V1,V2)) -> activate#(V2) -> activate#(n__0()) -> 0#() isNatKind#(n__plus(V1,V2)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isNatKind#(n__plus(V1,V2)) -> activate#(V1) -> activate#(n__x(X1,X2)) -> x#(X1,X2) isNatKind#(n__plus(V1,V2)) -> activate#(V1) -> activate#(n__s(X)) -> s#(X) isNatKind#(n__plus(V1,V2)) -> activate#(V1) -> activate#(n__isNatKind(X)) -> isNatKind#(X) isNatKind#(n__plus(V1,V2)) -> activate#(V1) -> activate#(n__plus(X1,X2)) -> plus#(X1,X2) isNatKind#(n__plus(V1,V2)) -> activate#(V1) -> activate#(n__0()) -> 0#() and#(tt(),X) -> activate#(X) -> activate#(n__and(X1,X2)) -> and#(X1,X2) and#(tt(),X) -> activate#(X) -> activate#(n__x(X1,X2)) -> x#(X1,X2) and#(tt(),X) -> activate#(X) -> activate#(n__s(X)) -> s#(X) and#(tt(),X) -> activate#(X) -> activate#(n__isNatKind(X)) -> isNatKind#(X) and#(tt(),X) -> activate#(X) -> activate#(n__plus(X1,X2)) -> plus#(X1,X2) and#(tt(),X) -> activate#(X) -> activate#(n__0()) -> 0#() x#(N,0()) -> and#(isNat(N),n__isNatKind(N)) -> and#(tt(),X) -> activate#(X) x#(N,0()) -> U61#(and(isNat(N),n__isNatKind(N))) -> U61#(tt()) -> 0#() x#(N,0()) -> isNat#(N) -> isNat#(n__x(V1,V2)) -> U31#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) x#(N,0()) -> isNat#(N) -> isNat#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) x#(N,0()) -> isNat#(N) -> isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) x#(N,0()) -> isNat#(N) -> isNat#(n__x(V1,V2)) -> activate#(V1) x#(N,0()) -> isNat#(N) -> isNat#(n__x(V1,V2)) -> activate#(V2) x#(N,0()) -> isNat#(N) -> isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) x#(N,0()) -> isNat#(N) -> isNat#(n__s(V1)) -> isNatKind#(activate(V1)) x#(N,0()) -> isNat#(N) -> isNat#(n__s(V1)) -> activate#(V1) x#(N,0()) -> isNat#(N) -> isNat#(n__plus(V1,V2)) -> U11#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) x#(N,0()) -> isNat#(N) -> isNat#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) x#(N,0()) -> isNat#(N) -> isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) x#(N,0()) -> isNat#(N) -> isNat#(n__plus(V1,V2)) -> activate#(V1) x#(N,0()) -> isNat#(N) -> isNat#(n__plus(V1,V2)) -> activate#(V2) x#(N,s(M)) -> and#(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))) -> and#(tt(),X) -> activate#(X) x#(N,s(M)) -> and#(isNat(M),n__isNatKind(M)) -> and#(tt(),X) -> activate#(X) x#(N,s(M)) -> U71#(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) -> U71#(tt(),M,N) -> plus#(x(activate(N),activate(M)),activate(N)) x#(N,s(M)) -> U71#(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) -> U71#(tt(),M,N) -> x#(activate(N),activate(M)) x#(N,s(M)) -> U71#(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) -> U71#(tt(),M,N) -> activate#(N) x#(N,s(M)) -> U71#(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) -> U71#(tt(),M,N) -> activate#(M) x#(N,s(M)) -> isNat#(N) -> isNat#(n__x(V1,V2)) -> U31#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) x#(N,s(M)) -> isNat#(N) -> isNat#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) x#(N,s(M)) -> isNat#(N) -> isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) x#(N,s(M)) -> isNat#(N) -> isNat#(n__x(V1,V2)) -> activate#(V1) x#(N,s(M)) -> isNat#(N) -> isNat#(n__x(V1,V2)) -> activate#(V2) x#(N,s(M)) -> isNat#(N) -> isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) x#(N,s(M)) -> isNat#(N) -> isNat#(n__s(V1)) -> isNatKind#(activate(V1)) x#(N,s(M)) -> isNat#(N) -> isNat#(n__s(V1)) -> activate#(V1) x#(N,s(M)) -> isNat#(N) -> isNat#(n__plus(V1,V2)) -> U11#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) x#(N,s(M)) -> isNat#(N) -> isNat#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) x#(N,s(M)) -> isNat#(N) -> isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) x#(N,s(M)) -> isNat#(N) -> isNat#(n__plus(V1,V2)) -> activate#(V1) x#(N,s(M)) -> isNat#(N) -> isNat#(n__plus(V1,V2)) -> activate#(V2) x#(N,s(M)) -> isNat#(M) -> isNat#(n__x(V1,V2)) -> U31#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) x#(N,s(M)) -> isNat#(M) -> isNat#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) x#(N,s(M)) -> isNat#(M) -> isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) x#(N,s(M)) -> isNat#(M) -> isNat#(n__x(V1,V2)) -> activate#(V1) x#(N,s(M)) -> isNat#(M) -> isNat#(n__x(V1,V2)) -> activate#(V2) x#(N,s(M)) -> isNat#(M) -> isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) x#(N,s(M)) -> isNat#(M) -> isNat#(n__s(V1)) -> isNatKind#(activate(V1)) x#(N,s(M)) -> isNat#(M) -> isNat#(n__s(V1)) -> activate#(V1) x#(N,s(M)) -> isNat#(M) -> isNat#(n__plus(V1,V2)) -> U11#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) x#(N,s(M)) -> isNat#(M) -> isNat#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) x#(N,s(M)) -> isNat#(M) -> isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) x#(N,s(M)) -> isNat#(M) -> isNat#(n__plus(V1,V2)) -> activate#(V1) x#(N,s(M)) -> isNat#(M) -> isNat#(n__plus(V1,V2)) -> activate#(V2) U71#(tt(),M,N) -> x#(activate(N),activate(M)) -> x#(N,s(M)) -> U71#(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) U71#(tt(),M,N) -> x#(activate(N),activate(M)) -> x#(N,s(M)) -> and#(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))) U71#(tt(),M,N) -> x#(activate(N),activate(M)) -> x#(N,s(M)) -> and#(isNat(M),n__isNatKind(M)) U71#(tt(),M,N) -> x#(activate(N),activate(M)) -> x#(N,s(M)) -> isNat#(M) U71#(tt(),M,N) -> x#(activate(N),activate(M)) -> x#(N,s(M)) -> isNat#(N) U71#(tt(),M,N) -> x#(activate(N),activate(M)) -> x#(N,0()) -> U61#(and(isNat(N),n__isNatKind(N))) U71#(tt(),M,N) -> x#(activate(N),activate(M)) -> x#(N,0()) -> and#(isNat(N),n__isNatKind(N)) U71#(tt(),M,N) -> x#(activate(N),activate(M)) -> x#(N,0()) -> isNat#(N) U71#(tt(),M,N) -> plus#(x(activate(N),activate(M)),activate(N)) -> plus#(N,s(M)) -> U51#(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) U71#(tt(),M,N) -> plus#(x(activate(N),activate(M)),activate(N)) -> plus#(N,s(M)) -> and#(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))) U71#(tt(),M,N) -> plus#(x(activate(N),activate(M)),activate(N)) -> plus#(N,s(M)) -> and#(isNat(M),n__isNatKind(M)) U71#(tt(),M,N) -> plus#(x(activate(N),activate(M)),activate(N)) -> plus#(N,s(M)) -> isNat#(M) U71#(tt(),M,N) -> plus#(x(activate(N),activate(M)),activate(N)) -> plus#(N,s(M)) -> isNat#(N) U71#(tt(),M,N) -> plus#(x(activate(N),activate(M)),activate(N)) -> plus#(N,0()) -> U41#(and(isNat(N),n__isNatKind(N)),N) U71#(tt(),M,N) -> plus#(x(activate(N),activate(M)),activate(N)) -> plus#(N,0()) -> and#(isNat(N),n__isNatKind(N)) U71#(tt(),M,N) -> plus#(x(activate(N),activate(M)),activate(N)) -> plus#(N,0()) -> isNat#(N) U71#(tt(),M,N) -> activate#(N) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U71#(tt(),M,N) -> activate#(N) -> activate#(n__x(X1,X2)) -> x#(X1,X2) U71#(tt(),M,N) -> activate#(N) -> activate#(n__s(X)) -> s#(X) U71#(tt(),M,N) -> activate#(N) -> activate#(n__isNatKind(X)) -> isNatKind#(X) U71#(tt(),M,N) -> activate#(N) -> activate#(n__plus(X1,X2)) -> plus#(X1,X2) U71#(tt(),M,N) -> activate#(N) -> activate#(n__0()) -> 0#() U71#(tt(),M,N) -> activate#(M) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U71#(tt(),M,N) -> activate#(M) -> activate#(n__x(X1,X2)) -> x#(X1,X2) U71#(tt(),M,N) -> activate#(M) -> activate#(n__s(X)) -> s#(X) U71#(tt(),M,N) -> activate#(M) -> activate#(n__isNatKind(X)) -> isNatKind#(X) U71#(tt(),M,N) -> activate#(M) -> activate#(n__plus(X1,X2)) -> plus#(X1,X2) U71#(tt(),M,N) -> activate#(M) -> activate#(n__0()) -> 0#() plus#(N,0()) -> and#(isNat(N),n__isNatKind(N)) -> and#(tt(),X) -> activate#(X) plus#(N,0()) -> U41#(and(isNat(N),n__isNatKind(N)),N) -> U41#(tt(),N) -> activate#(N) plus#(N,0()) -> isNat#(N) -> isNat#(n__x(V1,V2)) -> U31#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) plus#(N,0()) -> isNat#(N) -> isNat#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) plus#(N,0()) -> isNat#(N) -> isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) plus#(N,0()) -> isNat#(N) -> isNat#(n__x(V1,V2)) -> activate#(V1) plus#(N,0()) -> isNat#(N) -> isNat#(n__x(V1,V2)) -> activate#(V2) plus#(N,0()) -> isNat#(N) -> isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) plus#(N,0()) -> isNat#(N) -> isNat#(n__s(V1)) -> isNatKind#(activate(V1)) plus#(N,0()) -> isNat#(N) -> isNat#(n__s(V1)) -> activate#(V1) plus#(N,0()) -> isNat#(N) -> isNat#(n__plus(V1,V2)) -> U11#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) plus#(N,0()) -> isNat#(N) -> isNat#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) plus#(N,0()) -> isNat#(N) -> isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) plus#(N,0()) -> isNat#(N) -> isNat#(n__plus(V1,V2)) -> activate#(V1) plus#(N,0()) -> isNat#(N) -> isNat#(n__plus(V1,V2)) -> activate#(V2) plus#(N,s(M)) -> and#(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))) -> and#(tt(),X) -> activate#(X) plus#(N,s(M)) -> and#(isNat(M),n__isNatKind(M)) -> and#(tt(),X) -> activate#(X) plus#(N,s(M)) -> U51#(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) -> U51#(tt(),M,N) -> s#(plus(activate(N),activate(M))) plus#(N,s(M)) -> U51#(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) -> U51#(tt(),M,N) -> plus#(activate(N),activate(M)) plus#(N,s(M)) -> U51#(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) -> U51#(tt(),M,N) -> activate#(N) plus#(N,s(M)) -> U51#(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) -> U51#(tt(),M,N) -> activate#(M) plus#(N,s(M)) -> isNat#(N) -> isNat#(n__x(V1,V2)) -> U31#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) plus#(N,s(M)) -> isNat#(N) -> isNat#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) plus#(N,s(M)) -> isNat#(N) -> isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) plus#(N,s(M)) -> isNat#(N) -> isNat#(n__x(V1,V2)) -> activate#(V1) plus#(N,s(M)) -> isNat#(N) -> isNat#(n__x(V1,V2)) -> activate#(V2) plus#(N,s(M)) -> isNat#(N) -> isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) plus#(N,s(M)) -> isNat#(N) -> isNat#(n__s(V1)) -> isNatKind#(activate(V1)) plus#(N,s(M)) -> isNat#(N) -> isNat#(n__s(V1)) -> activate#(V1) plus#(N,s(M)) -> isNat#(N) -> isNat#(n__plus(V1,V2)) -> U11#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) plus#(N,s(M)) -> isNat#(N) -> isNat#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) plus#(N,s(M)) -> isNat#(N) -> isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) plus#(N,s(M)) -> isNat#(N) -> isNat#(n__plus(V1,V2)) -> activate#(V1) plus#(N,s(M)) -> isNat#(N) -> isNat#(n__plus(V1,V2)) -> activate#(V2) plus#(N,s(M)) -> isNat#(M) -> isNat#(n__x(V1,V2)) -> U31#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) plus#(N,s(M)) -> isNat#(M) -> isNat#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) plus#(N,s(M)) -> isNat#(M) -> isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) plus#(N,s(M)) -> isNat#(M) -> isNat#(n__x(V1,V2)) -> activate#(V1) plus#(N,s(M)) -> isNat#(M) -> isNat#(n__x(V1,V2)) -> activate#(V2) plus#(N,s(M)) -> isNat#(M) -> isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) plus#(N,s(M)) -> isNat#(M) -> isNat#(n__s(V1)) -> isNatKind#(activate(V1)) plus#(N,s(M)) -> isNat#(M) -> isNat#(n__s(V1)) -> activate#(V1) plus#(N,s(M)) -> isNat#(M) -> isNat#(n__plus(V1,V2)) -> U11#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) plus#(N,s(M)) -> isNat#(M) -> isNat#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) plus#(N,s(M)) -> isNat#(M) -> isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) plus#(N,s(M)) -> isNat#(M) -> isNat#(n__plus(V1,V2)) -> activate#(V1) plus#(N,s(M)) -> isNat#(M) -> isNat#(n__plus(V1,V2)) -> activate#(V2) U51#(tt(),M,N) -> plus#(activate(N),activate(M)) -> plus#(N,s(M)) -> U51#(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) U51#(tt(),M,N) -> plus#(activate(N),activate(M)) -> plus#(N,s(M)) -> and#(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))) U51#(tt(),M,N) -> plus#(activate(N),activate(M)) -> plus#(N,s(M)) -> and#(isNat(M),n__isNatKind(M)) U51#(tt(),M,N) -> plus#(activate(N),activate(M)) -> plus#(N,s(M)) -> isNat#(M) U51#(tt(),M,N) -> plus#(activate(N),activate(M)) -> plus#(N,s(M)) -> isNat#(N) U51#(tt(),M,N) -> plus#(activate(N),activate(M)) -> plus#(N,0()) -> U41#(and(isNat(N),n__isNatKind(N)),N) U51#(tt(),M,N) -> plus#(activate(N),activate(M)) -> plus#(N,0()) -> and#(isNat(N),n__isNatKind(N)) U51#(tt(),M,N) -> plus#(activate(N),activate(M)) -> plus#(N,0()) -> isNat#(N) U51#(tt(),M,N) -> activate#(N) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U51#(tt(),M,N) -> activate#(N) -> activate#(n__x(X1,X2)) -> x#(X1,X2) U51#(tt(),M,N) -> activate#(N) -> activate#(n__s(X)) -> s#(X) U51#(tt(),M,N) -> activate#(N) -> activate#(n__isNatKind(X)) -> isNatKind#(X) U51#(tt(),M,N) -> activate#(N) -> activate#(n__plus(X1,X2)) -> plus#(X1,X2) U51#(tt(),M,N) -> activate#(N) -> activate#(n__0()) -> 0#() U51#(tt(),M,N) -> activate#(M) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U51#(tt(),M,N) -> activate#(M) -> activate#(n__x(X1,X2)) -> x#(X1,X2) U51#(tt(),M,N) -> activate#(M) -> activate#(n__s(X)) -> s#(X) U51#(tt(),M,N) -> activate#(M) -> activate#(n__isNatKind(X)) -> isNatKind#(X) U51#(tt(),M,N) -> activate#(M) -> activate#(n__plus(X1,X2)) -> plus#(X1,X2) U51#(tt(),M,N) -> activate#(M) -> activate#(n__0()) -> 0#() U41#(tt(),N) -> activate#(N) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U41#(tt(),N) -> activate#(N) -> activate#(n__x(X1,X2)) -> x#(X1,X2) U41#(tt(),N) -> activate#(N) -> activate#(n__s(X)) -> s#(X) U41#(tt(),N) -> activate#(N) -> activate#(n__isNatKind(X)) -> isNatKind#(X) U41#(tt(),N) -> activate#(N) -> activate#(n__plus(X1,X2)) -> plus#(X1,X2) U41#(tt(),N) -> activate#(N) -> activate#(n__0()) -> 0#() U32#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__x(V1,V2)) -> U31#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) U32#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) U32#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) U32#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__x(V1,V2)) -> activate#(V1) U32#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__x(V1,V2)) -> activate#(V2) U32#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) U32#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__s(V1)) -> isNatKind#(activate(V1)) U32#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__s(V1)) -> activate#(V1) U32#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__plus(V1,V2)) -> U11#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) U32#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) U32#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) U32#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__plus(V1,V2)) -> activate#(V1) U32#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__plus(V1,V2)) -> activate#(V2) U32#(tt(),V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U32#(tt(),V2) -> activate#(V2) -> activate#(n__x(X1,X2)) -> x#(X1,X2) U32#(tt(),V2) -> activate#(V2) -> activate#(n__s(X)) -> s#(X) U32#(tt(),V2) -> activate#(V2) -> activate#(n__isNatKind(X)) -> isNatKind#(X) U32#(tt(),V2) -> activate#(V2) -> activate#(n__plus(X1,X2)) -> plus#(X1,X2) U32#(tt(),V2) -> activate#(V2) -> activate#(n__0()) -> 0#() U31#(tt(),V1,V2) -> U32#(isNat(activate(V1)),activate(V2)) -> U32#(tt(),V2) -> U33#(isNat(activate(V2))) U31#(tt(),V1,V2) -> U32#(isNat(activate(V1)),activate(V2)) -> U32#(tt(),V2) -> isNat#(activate(V2)) U31#(tt(),V1,V2) -> U32#(isNat(activate(V1)),activate(V2)) -> U32#(tt(),V2) -> activate#(V2) U31#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__x(V1,V2)) -> U31#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) U31#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) U31#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) U31#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__x(V1,V2)) -> activate#(V1) U31#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__x(V1,V2)) -> activate#(V2) U31#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) U31#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__s(V1)) -> isNatKind#(activate(V1)) U31#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__s(V1)) -> activate#(V1) U31#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__plus(V1,V2)) -> U11#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) U31#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) U31#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) U31#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__plus(V1,V2)) -> activate#(V1) U31#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__plus(V1,V2)) -> activate#(V2) U31#(tt(),V1,V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U31#(tt(),V1,V2) -> activate#(V2) -> activate#(n__x(X1,X2)) -> x#(X1,X2) U31#(tt(),V1,V2) -> activate#(V2) -> activate#(n__s(X)) -> s#(X) U31#(tt(),V1,V2) -> activate#(V2) -> activate#(n__isNatKind(X)) -> isNatKind#(X) U31#(tt(),V1,V2) -> activate#(V2) -> activate#(n__plus(X1,X2)) -> plus#(X1,X2) U31#(tt(),V1,V2) -> activate#(V2) -> activate#(n__0()) -> 0#() U31#(tt(),V1,V2) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U31#(tt(),V1,V2) -> activate#(V1) -> activate#(n__x(X1,X2)) -> x#(X1,X2) U31#(tt(),V1,V2) -> activate#(V1) -> activate#(n__s(X)) -> s#(X) U31#(tt(),V1,V2) -> activate#(V1) -> activate#(n__isNatKind(X)) -> isNatKind#(X) U31#(tt(),V1,V2) -> activate#(V1) -> activate#(n__plus(X1,X2)) -> plus#(X1,X2) U31#(tt(),V1,V2) -> activate#(V1) -> activate#(n__0()) -> 0#() U21#(tt(),V1) -> isNat#(activate(V1)) -> isNat#(n__x(V1,V2)) -> U31#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) U21#(tt(),V1) -> isNat#(activate(V1)) -> isNat#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) U21#(tt(),V1) -> isNat#(activate(V1)) -> isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) U21#(tt(),V1) -> isNat#(activate(V1)) -> isNat#(n__x(V1,V2)) -> activate#(V1) U21#(tt(),V1) -> isNat#(activate(V1)) -> isNat#(n__x(V1,V2)) -> activate#(V2) U21#(tt(),V1) -> isNat#(activate(V1)) -> isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) U21#(tt(),V1) -> isNat#(activate(V1)) -> isNat#(n__s(V1)) -> isNatKind#(activate(V1)) U21#(tt(),V1) -> isNat#(activate(V1)) -> isNat#(n__s(V1)) -> activate#(V1) U21#(tt(),V1) -> isNat#(activate(V1)) -> isNat#(n__plus(V1,V2)) -> U11#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) U21#(tt(),V1) -> isNat#(activate(V1)) -> isNat#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) U21#(tt(),V1) -> isNat#(activate(V1)) -> isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) U21#(tt(),V1) -> isNat#(activate(V1)) -> isNat#(n__plus(V1,V2)) -> activate#(V1) U21#(tt(),V1) -> isNat#(activate(V1)) -> isNat#(n__plus(V1,V2)) -> activate#(V2) U21#(tt(),V1) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U21#(tt(),V1) -> activate#(V1) -> activate#(n__x(X1,X2)) -> x#(X1,X2) U21#(tt(),V1) -> activate#(V1) -> activate#(n__s(X)) -> s#(X) U21#(tt(),V1) -> activate#(V1) -> activate#(n__isNatKind(X)) -> isNatKind#(X) U21#(tt(),V1) -> activate#(V1) -> activate#(n__plus(X1,X2)) -> plus#(X1,X2) U21#(tt(),V1) -> activate#(V1) -> activate#(n__0()) -> 0#() U12#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__x(V1,V2)) -> U31#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) U12#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) U12#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) U12#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__x(V1,V2)) -> activate#(V1) U12#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__x(V1,V2)) -> activate#(V2) U12#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) U12#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__s(V1)) -> isNatKind#(activate(V1)) U12#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__s(V1)) -> activate#(V1) U12#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__plus(V1,V2)) -> U11#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) U12#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) U12#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) U12#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__plus(V1,V2)) -> activate#(V1) U12#(tt(),V2) -> isNat#(activate(V2)) -> isNat#(n__plus(V1,V2)) -> activate#(V2) U12#(tt(),V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U12#(tt(),V2) -> activate#(V2) -> activate#(n__x(X1,X2)) -> x#(X1,X2) U12#(tt(),V2) -> activate#(V2) -> activate#(n__s(X)) -> s#(X) U12#(tt(),V2) -> activate#(V2) -> activate#(n__isNatKind(X)) -> isNatKind#(X) U12#(tt(),V2) -> activate#(V2) -> activate#(n__plus(X1,X2)) -> plus#(X1,X2) U12#(tt(),V2) -> activate#(V2) -> activate#(n__0()) -> 0#() isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> isNatKind#(activate(V1)) isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> activate#(V1) isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> activate#(V2) isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__s(V1)) -> activate#(V1) isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> activate#(V1) isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> activate#(V2) isNat#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) -> and#(tt(),X) -> activate#(X) isNat#(n__x(V1,V2)) -> U31#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) -> U31#(tt(),V1,V2) -> U32#(isNat(activate(V1)),activate(V2)) isNat#(n__x(V1,V2)) -> U31#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) -> U31#(tt(),V1,V2) -> isNat#(activate(V1)) isNat#(n__x(V1,V2)) -> U31#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) -> U31#(tt(),V1,V2) -> activate#(V1) isNat#(n__x(V1,V2)) -> U31#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) -> U31#(tt(),V1,V2) -> activate#(V2) isNat#(n__x(V1,V2)) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isNat#(n__x(V1,V2)) -> activate#(V2) -> activate#(n__x(X1,X2)) -> x#(X1,X2) isNat#(n__x(V1,V2)) -> activate#(V2) -> activate#(n__s(X)) -> s#(X) isNat#(n__x(V1,V2)) -> activate#(V2) -> activate#(n__isNatKind(X)) -> isNatKind#(X) isNat#(n__x(V1,V2)) -> activate#(V2) -> activate#(n__plus(X1,X2)) -> plus#(X1,X2) isNat#(n__x(V1,V2)) -> activate#(V2) -> activate#(n__0()) -> 0#() isNat#(n__x(V1,V2)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isNat#(n__x(V1,V2)) -> activate#(V1) -> activate#(n__x(X1,X2)) -> x#(X1,X2) isNat#(n__x(V1,V2)) -> activate#(V1) -> activate#(n__s(X)) -> s#(X) isNat#(n__x(V1,V2)) -> activate#(V1) -> activate#(n__isNatKind(X)) -> isNatKind#(X) isNat#(n__x(V1,V2)) -> activate#(V1) -> activate#(n__plus(X1,X2)) -> plus#(X1,X2) isNat#(n__x(V1,V2)) -> activate#(V1) -> activate#(n__0()) -> 0#() isNat#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNat#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> isNatKind#(activate(V1)) isNat#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> activate#(V1) isNat#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> activate#(V2) isNat#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) isNat#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__s(V1)) -> activate#(V1) isNat#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNat#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) isNat#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> activate#(V1) isNat#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> activate#(V2) isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) -> U21#(tt(),V1) -> U22#(isNat(activate(V1))) isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) -> U21#(tt(),V1) -> isNat#(activate(V1)) isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) -> U21#(tt(),V1) -> activate#(V1) isNat#(n__s(V1)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isNat#(n__s(V1)) -> activate#(V1) -> activate#(n__x(X1,X2)) -> x#(X1,X2) isNat#(n__s(V1)) -> activate#(V1) -> activate#(n__s(X)) -> s#(X) isNat#(n__s(V1)) -> activate#(V1) -> activate#(n__isNatKind(X)) -> isNatKind#(X) isNat#(n__s(V1)) -> activate#(V1) -> activate#(n__plus(X1,X2)) -> plus#(X1,X2) isNat#(n__s(V1)) -> activate#(V1) -> activate#(n__0()) -> 0#() isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> isNatKind#(activate(V1)) isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> activate#(V1) isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__x(V1,V2)) -> activate#(V2) isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__s(V1)) -> activate#(V1) isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> activate#(V1) isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__plus(V1,V2)) -> activate#(V2) isNat#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) -> and#(tt(),X) -> activate#(X) isNat#(n__plus(V1,V2)) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isNat#(n__plus(V1,V2)) -> activate#(V2) -> activate#(n__x(X1,X2)) -> x#(X1,X2) isNat#(n__plus(V1,V2)) -> activate#(V2) -> activate#(n__s(X)) -> s#(X) isNat#(n__plus(V1,V2)) -> activate#(V2) -> activate#(n__isNatKind(X)) -> isNatKind#(X) isNat#(n__plus(V1,V2)) -> activate#(V2) -> activate#(n__plus(X1,X2)) -> plus#(X1,X2) isNat#(n__plus(V1,V2)) -> activate#(V2) -> activate#(n__0()) -> 0#() isNat#(n__plus(V1,V2)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(X1,X2) isNat#(n__plus(V1,V2)) -> activate#(V1) -> activate#(n__x(X1,X2)) -> x#(X1,X2) isNat#(n__plus(V1,V2)) -> activate#(V1) -> activate#(n__s(X)) -> s#(X) isNat#(n__plus(V1,V2)) -> activate#(V1) -> activate#(n__isNatKind(X)) -> isNatKind#(X) isNat#(n__plus(V1,V2)) -> activate#(V1) -> activate#(n__plus(X1,X2)) -> plus#(X1,X2) isNat#(n__plus(V1,V2)) -> activate#(V1) -> activate#(n__0()) -> 0#() isNat#(n__plus(V1,V2)) -> U11#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) -> U11#(tt(),V1,V2) -> U12#(isNat(activate(V1)),activate(V2)) isNat#(n__plus(V1,V2)) -> U11#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) -> U11#(tt(),V1,V2) -> isNat#(activate(V1)) isNat#(n__plus(V1,V2)) -> U11#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) -> U11#(tt(),V1,V2) -> activate#(V1) isNat#(n__plus(V1,V2)) -> U11#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) -> U11#(tt(),V1,V2) -> activate#(V2) activate#(n__and(X1,X2)) -> and#(X1,X2) -> and#(tt(),X) -> activate#(X) activate#(n__x(X1,X2)) -> x#(X1,X2) -> x#(N,s(M)) -> U71#(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) activate#(n__x(X1,X2)) -> x#(X1,X2) -> x#(N,s(M)) -> and#(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))) activate#(n__x(X1,X2)) -> x#(X1,X2) -> x#(N,s(M)) -> and#(isNat(M),n__isNatKind(M)) activate#(n__x(X1,X2)) -> x#(X1,X2) -> x#(N,s(M)) -> isNat#(M) activate#(n__x(X1,X2)) -> x#(X1,X2) -> x#(N,s(M)) -> isNat#(N) activate#(n__x(X1,X2)) -> x#(X1,X2) -> x#(N,0()) -> U61#(and(isNat(N),n__isNatKind(N))) activate#(n__x(X1,X2)) -> x#(X1,X2) -> x#(N,0()) -> and#(isNat(N),n__isNatKind(N)) activate#(n__x(X1,X2)) -> x#(X1,X2) -> x#(N,0()) -> isNat#(N) activate#(n__isNatKind(X)) -> isNatKind#(X) -> isNatKind#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) activate#(n__isNatKind(X)) -> isNatKind#(X) -> isNatKind#(n__x(V1,V2)) -> isNatKind#(activate(V1)) activate#(n__isNatKind(X)) -> isNatKind#(X) -> isNatKind#(n__x(V1,V2)) -> activate#(V1) activate#(n__isNatKind(X)) -> isNatKind#(X) -> isNatKind#(n__x(V1,V2)) -> activate#(V2) activate#(n__isNatKind(X)) -> isNatKind#(X) -> isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) activate#(n__isNatKind(X)) -> isNatKind#(X) -> isNatKind#(n__s(V1)) -> activate#(V1) activate#(n__isNatKind(X)) -> isNatKind#(X) -> isNatKind#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) activate#(n__isNatKind(X)) -> isNatKind#(X) -> isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) activate#(n__isNatKind(X)) -> isNatKind#(X) -> isNatKind#(n__plus(V1,V2)) -> activate#(V1) activate#(n__isNatKind(X)) -> isNatKind#(X) -> isNatKind#(n__plus(V1,V2)) -> activate#(V2) activate#(n__plus(X1,X2)) -> plus#(X1,X2) -> plus#(N,s(M)) -> U51#(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) activate#(n__plus(X1,X2)) -> plus#(X1,X2) -> plus#(N,s(M)) -> and#(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))) activate#(n__plus(X1,X2)) -> plus#(X1,X2) -> plus#(N,s(M)) -> and#(isNat(M),n__isNatKind(M)) activate#(n__plus(X1,X2)) -> plus#(X1,X2) -> plus#(N,s(M)) -> isNat#(M) activate#(n__plus(X1,X2)) -> plus#(X1,X2) -> plus#(N,s(M)) -> isNat#(N) activate#(n__plus(X1,X2)) -> plus#(X1,X2) -> plus#(N,0()) -> U41#(and(isNat(N),n__isNatKind(N)),N) activate#(n__plus(X1,X2)) -> plus#(X1,X2) -> plus#(N,0()) -> and#(isNat(N),n__isNatKind(N)) activate#(n__plus(X1,X2)) -> plus#(X1,X2) -> plus#(N,0()) -> isNat#(N) U11#(tt(),V1,V2) -> U12#(isNat(activate(V1)),activate(V2)) -> U12#(tt(),V2) -> U13#(isNat(activate(V2))) U11#(tt(),V1,V2) -> U12#(isNat(activate(V1)),activate(V2)) -> U12#(tt(),V2) -> isNat#(activate(V2)) U11#(tt(),V1,V2) -> U12#(isNat(activate(V1)),activate(V2)) -> U12#(tt(),V2) -> activate#(V2) U11#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__x(V1,V2)) -> U31#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) U11#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) U11#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) U11#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__x(V1,V2)) -> activate#(V1) U11#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__x(V1,V2)) -> activate#(V2) U11#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) U11#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__s(V1)) -> isNatKind#(activate(V1)) U11#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__s(V1)) -> activate#(V1) U11#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__plus(V1,V2)) -> U11#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) U11#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) U11#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) U11#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__plus(V1,V2)) -> activate#(V1) U11#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__plus(V1,V2)) -> activate#(V2) U11#(tt(),V1,V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U11#(tt(),V1,V2) -> activate#(V2) -> activate#(n__x(X1,X2)) -> x#(X1,X2) U11#(tt(),V1,V2) -> activate#(V2) -> activate#(n__s(X)) -> s#(X) U11#(tt(),V1,V2) -> activate#(V2) -> activate#(n__isNatKind(X)) -> isNatKind#(X) U11#(tt(),V1,V2) -> activate#(V2) -> activate#(n__plus(X1,X2)) -> plus#(X1,X2) U11#(tt(),V1,V2) -> activate#(V2) -> activate#(n__0()) -> 0#() U11#(tt(),V1,V2) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(X1,X2) U11#(tt(),V1,V2) -> activate#(V1) -> activate#(n__x(X1,X2)) -> x#(X1,X2) U11#(tt(),V1,V2) -> activate#(V1) -> activate#(n__s(X)) -> s#(X) U11#(tt(),V1,V2) -> activate#(V1) -> activate#(n__isNatKind(X)) -> isNatKind#(X) U11#(tt(),V1,V2) -> activate#(V1) -> activate#(n__plus(X1,X2)) -> plus#(X1,X2) U11#(tt(),V1,V2) -> activate#(V1) -> activate#(n__0()) -> 0#() SCC Processor: #sccs: 1 #rules: 65 #arcs: 429/5329 DPs: isNatKind#(n__x(V1,V2)) -> isNatKind#(activate(V1)) isNatKind#(n__plus(V1,V2)) -> activate#(V2) activate#(n__plus(X1,X2)) -> plus#(X1,X2) plus#(N,0()) -> isNat#(N) isNat#(n__plus(V1,V2)) -> activate#(V2) activate#(n__isNatKind(X)) -> isNatKind#(X) isNatKind#(n__plus(V1,V2)) -> activate#(V1) activate#(n__x(X1,X2)) -> x#(X1,X2) x#(N,0()) -> isNat#(N) isNat#(n__plus(V1,V2)) -> activate#(V1) activate#(n__and(X1,X2)) -> and#(X1,X2) and#(tt(),X) -> activate#(X) isNat#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) isNatKind#(n__plus(V1,V2)) -> isNatKind#(activate(V1)) isNatKind#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNatKind#(n__s(V1)) -> activate#(V1) isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) isNatKind#(n__x(V1,V2)) -> activate#(V2) isNatKind#(n__x(V1,V2)) -> activate#(V1) isNatKind#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNat#(n__plus(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNat#(n__plus(V1,V2)) -> U11#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) U11#(tt(),V1,V2) -> activate#(V2) U11#(tt(),V1,V2) -> activate#(V1) U11#(tt(),V1,V2) -> isNat#(activate(V1)) isNat#(n__s(V1)) -> activate#(V1) isNat#(n__s(V1)) -> isNatKind#(activate(V1)) isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) U21#(tt(),V1) -> activate#(V1) U21#(tt(),V1) -> isNat#(activate(V1)) isNat#(n__x(V1,V2)) -> activate#(V2) isNat#(n__x(V1,V2)) -> activate#(V1) isNat#(n__x(V1,V2)) -> isNatKind#(activate(V1)) isNat#(n__x(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNat#(n__x(V1,V2)) -> U31#(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) U31#(tt(),V1,V2) -> activate#(V2) U31#(tt(),V1,V2) -> activate#(V1) U31#(tt(),V1,V2) -> isNat#(activate(V1)) U31#(tt(),V1,V2) -> U32#(isNat(activate(V1)),activate(V2)) U32#(tt(),V2) -> activate#(V2) U32#(tt(),V2) -> isNat#(activate(V2)) U11#(tt(),V1,V2) -> U12#(isNat(activate(V1)),activate(V2)) U12#(tt(),V2) -> activate#(V2) U12#(tt(),V2) -> isNat#(activate(V2)) x#(N,0()) -> and#(isNat(N),n__isNatKind(N)) x#(N,s(M)) -> isNat#(N) x#(N,s(M)) -> isNat#(M) x#(N,s(M)) -> and#(isNat(M),n__isNatKind(M)) x#(N,s(M)) -> and#(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))) x#(N,s(M)) -> U71#(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) U71#(tt(),M,N) -> activate#(M) U71#(tt(),M,N) -> activate#(N) U71#(tt(),M,N) -> x#(activate(N),activate(M)) U71#(tt(),M,N) -> plus#(x(activate(N),activate(M)),activate(N)) plus#(N,0()) -> and#(isNat(N),n__isNatKind(N)) plus#(N,0()) -> U41#(and(isNat(N),n__isNatKind(N)),N) U41#(tt(),N) -> activate#(N) plus#(N,s(M)) -> isNat#(N) plus#(N,s(M)) -> isNat#(M) plus#(N,s(M)) -> and#(isNat(M),n__isNatKind(M)) plus#(N,s(M)) -> and#(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))) plus#(N,s(M)) -> U51#(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) U51#(tt(),M,N) -> activate#(M) U51#(tt(),M,N) -> activate#(N) U51#(tt(),M,N) -> plus#(activate(N),activate(M)) TRS: U11(tt(),V1,V2) -> U12(isNat(activate(V1)),activate(V2)) U12(tt(),V2) -> U13(isNat(activate(V2))) U13(tt()) -> tt() U21(tt(),V1) -> U22(isNat(activate(V1))) U22(tt()) -> tt() U31(tt(),V1,V2) -> U32(isNat(activate(V1)),activate(V2)) U32(tt(),V2) -> U33(isNat(activate(V2))) U33(tt()) -> tt() U41(tt(),N) -> activate(N) U51(tt(),M,N) -> s(plus(activate(N),activate(M))) U61(tt()) -> 0() U71(tt(),M,N) -> plus(x(activate(N),activate(M)),activate(N)) and(tt(),X) -> activate(X) isNat(n__0()) -> tt() isNat(n__plus(V1,V2)) -> U11(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNat(n__x(V1,V2)) -> U31(and(isNatKind(activate(V1)),n__isNatKind(activate(V2))),activate(V1),activate(V2)) isNatKind(n__0()) -> tt() isNatKind(n__plus(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNatKind(n__s(V1)) -> isNatKind(activate(V1)) isNatKind(n__x(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatKind(activate(V2))) plus(N,0()) -> U41(and(isNat(N),n__isNatKind(N)),N) plus(N,s(M)) -> U51(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) x(N,0()) -> U61(and(isNat(N),n__isNatKind(N))) x(N,s(M)) -> U71(and(and(isNat(M),n__isNatKind(M)),n__and(isNat(N),n__isNatKind(N))),M,N) 0() -> n__0() plus(X1,X2) -> n__plus(X1,X2) isNatKind(X) -> n__isNatKind(X) s(X) -> n__s(X) x(X1,X2) -> n__x(X1,X2) and(X1,X2) -> n__and(X1,X2) activate(n__0()) -> 0() activate(n__plus(X1,X2)) -> plus(X1,X2) activate(n__isNatKind(X)) -> isNatKind(X) activate(n__s(X)) -> s(X) activate(n__x(X1,X2)) -> x(X1,X2) activate(n__and(X1,X2)) -> and(X1,X2) activate(X) -> X Open