MAYBE * Step 1: Failure MAYBE + Considered Problem: - Strict TRS: 0() -> n__0() 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(),N) -> activate(N) U41(tt(),M,N) -> s(plus(activate(N),activate(M))) activate(X) -> X activate(n__0()) -> 0() activate(n__and(X1,X2)) -> and(activate(X1),X2) activate(n__isNat(X)) -> isNat(X) activate(n__isNatKind(X)) -> isNatKind(X) activate(n__plus(X1,X2)) -> plus(activate(X1),activate(X2)) activate(n__s(X)) -> s(activate(X)) and(X1,X2) -> n__and(X1,X2) and(tt(),X) -> activate(X) isNat(X) -> n__isNat(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)) isNatKind(X) -> n__isNatKind(X) isNatKind(n__0()) -> tt() isNatKind(n__plus(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatKind(activate(V2))) isNatKind(n__s(V1)) -> isNatKind(activate(V1)) plus(N,0()) -> U31(and(isNat(N),n__isNatKind(N)),N) plus(N,s(M)) -> U41(and(and(isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N))),M,N) plus(X1,X2) -> n__plus(X1,X2) s(X) -> n__s(X) - Signature: {0/0,U11/3,U12/2,U13/1,U21/2,U22/1,U31/2,U41/3,activate/1,and/2,isNat/1,isNatKind/1,plus/2,s/1} / {n__0/0 ,n__and/2,n__isNat/1,n__isNatKind/1,n__plus/2,n__s/1,tt/0} - Obligation: innermost runtime complexity wrt. defined symbols {0,U11,U12,U13,U21,U22,U31,U41,activate,and,isNat ,isNatKind,plus,s} and constructors {n__0,n__and,n__isNat,n__isNatKind,n__plus,n__s,tt} + Applied Processor: NaturalMI {miDimension = 3, miDegree = 3, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} + Details: Incompatible MAYBE