NO Problem 1: (VAR v_NonEmpty:S M:S N:S) (RULES U11(tt) -> U12(isNatKind) U12(tt) -> U13(isNatKind) U13(tt) -> U14(isNatKind) U14(tt) -> U15(isNat) U15(tt) -> U16(isNat) U16(tt) -> tt U21(tt) -> U22(isNatKind) U22(tt) -> U23(isNat) U23(tt) -> tt U31(tt) -> U32(isNatKind) U32(tt) -> tt U41(tt) -> tt U51(tt) -> U52(isNatKind) U52(tt) -> N:S U61(tt) -> U62(isNatKind) U62(tt) -> U63(isNat) U63(tt) -> U64(isNatKind) U64(tt) -> s(plus(N:S,M:S)) isNat -> U11(isNatKind) isNat -> U21(isNatKind) isNat -> tt isNatKind -> U31(isNatKind) isNatKind -> U41(isNatKind) isNatKind -> tt plus(N:S,0) -> U51(isNat) plus(N:S,s(M:S)) -> U61(isNat) ) Problem 1: Extra Variables Processor: -> Rules: U11(tt) -> U12(isNatKind) U12(tt) -> U13(isNatKind) U13(tt) -> U14(isNatKind) U14(tt) -> U15(isNat) U15(tt) -> U16(isNat) U16(tt) -> tt U21(tt) -> U22(isNatKind) U22(tt) -> U23(isNat) U23(tt) -> tt U31(tt) -> U32(isNatKind) U32(tt) -> tt U41(tt) -> tt U51(tt) -> U52(isNatKind) U52(tt) -> N:S U61(tt) -> U62(isNatKind) U62(tt) -> U63(isNat) U63(tt) -> U64(isNatKind) U64(tt) -> s(plus(N:S,M:S)) isNat -> U11(isNatKind) isNat -> U21(isNatKind) isNat -> tt isNatKind -> U31(isNatKind) isNatKind -> U41(isNatKind) isNatKind -> tt plus(N:S,0) -> U51(isNat) plus(N:S,s(M:S)) -> U61(isNat) -> The system has extra variables. The problem is infinite.