MAYBE Problem: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Proof: DP Processor: DPs: active#(U101(tt(),M,N)) -> isNatKind#(M) active#(U101(tt(),M,N)) -> U102#(isNatKind(M),M,N) active#(U101(tt(),M,N)) -> mark#(U102(isNatKind(M),M,N)) active#(U102(tt(),M,N)) -> isNat#(N) active#(U102(tt(),M,N)) -> U103#(isNat(N),M,N) active#(U102(tt(),M,N)) -> mark#(U103(isNat(N),M,N)) active#(U103(tt(),M,N)) -> isNatKind#(N) active#(U103(tt(),M,N)) -> U104#(isNatKind(N),M,N) active#(U103(tt(),M,N)) -> mark#(U104(isNatKind(N),M,N)) active#(U104(tt(),M,N)) -> x#(N,M) active#(U104(tt(),M,N)) -> plus#(x(N,M),N) active#(U104(tt(),M,N)) -> mark#(plus(x(N,M),N)) active#(U11(tt(),V1,V2)) -> isNatKind#(V1) active#(U11(tt(),V1,V2)) -> U12#(isNatKind(V1),V1,V2) active#(U11(tt(),V1,V2)) -> mark#(U12(isNatKind(V1),V1,V2)) active#(U12(tt(),V1,V2)) -> isNatKind#(V2) active#(U12(tt(),V1,V2)) -> U13#(isNatKind(V2),V1,V2) active#(U12(tt(),V1,V2)) -> mark#(U13(isNatKind(V2),V1,V2)) active#(U13(tt(),V1,V2)) -> isNatKind#(V2) active#(U13(tt(),V1,V2)) -> U14#(isNatKind(V2),V1,V2) active#(U13(tt(),V1,V2)) -> mark#(U14(isNatKind(V2),V1,V2)) active#(U14(tt(),V1,V2)) -> isNat#(V1) active#(U14(tt(),V1,V2)) -> U15#(isNat(V1),V2) active#(U14(tt(),V1,V2)) -> mark#(U15(isNat(V1),V2)) active#(U15(tt(),V2)) -> isNat#(V2) active#(U15(tt(),V2)) -> U16#(isNat(V2)) active#(U15(tt(),V2)) -> mark#(U16(isNat(V2))) active#(U16(tt())) -> mark#(tt()) active#(U21(tt(),V1)) -> isNatKind#(V1) active#(U21(tt(),V1)) -> U22#(isNatKind(V1),V1) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> isNat#(V1) active#(U22(tt(),V1)) -> U23#(isNat(V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) active#(U23(tt())) -> mark#(tt()) active#(U31(tt(),V1,V2)) -> isNatKind#(V1) active#(U31(tt(),V1,V2)) -> U32#(isNatKind(V1),V1,V2) active#(U31(tt(),V1,V2)) -> mark#(U32(isNatKind(V1),V1,V2)) active#(U32(tt(),V1,V2)) -> isNatKind#(V2) active#(U32(tt(),V1,V2)) -> U33#(isNatKind(V2),V1,V2) active#(U32(tt(),V1,V2)) -> mark#(U33(isNatKind(V2),V1,V2)) active#(U33(tt(),V1,V2)) -> isNatKind#(V2) active#(U33(tt(),V1,V2)) -> U34#(isNatKind(V2),V1,V2) active#(U33(tt(),V1,V2)) -> mark#(U34(isNatKind(V2),V1,V2)) active#(U34(tt(),V1,V2)) -> isNat#(V1) active#(U34(tt(),V1,V2)) -> U35#(isNat(V1),V2) active#(U34(tt(),V1,V2)) -> mark#(U35(isNat(V1),V2)) active#(U35(tt(),V2)) -> isNat#(V2) active#(U35(tt(),V2)) -> U36#(isNat(V2)) active#(U35(tt(),V2)) -> mark#(U36(isNat(V2))) active#(U36(tt())) -> mark#(tt()) active#(U41(tt(),V2)) -> isNatKind#(V2) active#(U41(tt(),V2)) -> U42#(isNatKind(V2)) active#(U41(tt(),V2)) -> mark#(U42(isNatKind(V2))) active#(U42(tt())) -> mark#(tt()) active#(U51(tt())) -> mark#(tt()) active#(U61(tt(),V2)) -> isNatKind#(V2) active#(U61(tt(),V2)) -> U62#(isNatKind(V2)) active#(U61(tt(),V2)) -> mark#(U62(isNatKind(V2))) active#(U62(tt())) -> mark#(tt()) active#(U71(tt(),N)) -> isNatKind#(N) active#(U71(tt(),N)) -> U72#(isNatKind(N),N) active#(U71(tt(),N)) -> mark#(U72(isNatKind(N),N)) active#(U72(tt(),N)) -> mark#(N) active#(U81(tt(),M,N)) -> isNatKind#(M) active#(U81(tt(),M,N)) -> U82#(isNatKind(M),M,N) active#(U81(tt(),M,N)) -> mark#(U82(isNatKind(M),M,N)) active#(U82(tt(),M,N)) -> isNat#(N) active#(U82(tt(),M,N)) -> U83#(isNat(N),M,N) active#(U82(tt(),M,N)) -> mark#(U83(isNat(N),M,N)) active#(U83(tt(),M,N)) -> isNatKind#(N) active#(U83(tt(),M,N)) -> U84#(isNatKind(N),M,N) active#(U83(tt(),M,N)) -> mark#(U84(isNatKind(N),M,N)) active#(U84(tt(),M,N)) -> plus#(N,M) active#(U84(tt(),M,N)) -> s#(plus(N,M)) active#(U84(tt(),M,N)) -> mark#(s(plus(N,M))) active#(U91(tt(),N)) -> isNatKind#(N) active#(U91(tt(),N)) -> U92#(isNatKind(N)) active#(U91(tt(),N)) -> mark#(U92(isNatKind(N))) active#(U92(tt())) -> mark#(0()) active#(isNat(0())) -> mark#(tt()) active#(isNat(plus(V1,V2))) -> isNatKind#(V1) active#(isNat(plus(V1,V2))) -> U11#(isNatKind(V1),V1,V2) active#(isNat(plus(V1,V2))) -> mark#(U11(isNatKind(V1),V1,V2)) active#(isNat(s(V1))) -> isNatKind#(V1) active#(isNat(s(V1))) -> U21#(isNatKind(V1),V1) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) active#(isNat(x(V1,V2))) -> isNatKind#(V1) active#(isNat(x(V1,V2))) -> U31#(isNatKind(V1),V1,V2) active#(isNat(x(V1,V2))) -> mark#(U31(isNatKind(V1),V1,V2)) active#(isNatKind(0())) -> mark#(tt()) active#(isNatKind(plus(V1,V2))) -> isNatKind#(V1) active#(isNatKind(plus(V1,V2))) -> U41#(isNatKind(V1),V2) active#(isNatKind(plus(V1,V2))) -> mark#(U41(isNatKind(V1),V2)) active#(isNatKind(s(V1))) -> isNatKind#(V1) active#(isNatKind(s(V1))) -> U51#(isNatKind(V1)) active#(isNatKind(s(V1))) -> mark#(U51(isNatKind(V1))) active#(isNatKind(x(V1,V2))) -> isNatKind#(V1) active#(isNatKind(x(V1,V2))) -> U61#(isNatKind(V1),V2) active#(isNatKind(x(V1,V2))) -> mark#(U61(isNatKind(V1),V2)) active#(plus(N,0())) -> isNat#(N) active#(plus(N,0())) -> U71#(isNat(N),N) active#(plus(N,0())) -> mark#(U71(isNat(N),N)) active#(plus(N,s(M))) -> isNat#(M) active#(plus(N,s(M))) -> U81#(isNat(M),M,N) active#(plus(N,s(M))) -> mark#(U81(isNat(M),M,N)) active#(x(N,0())) -> isNat#(N) active#(x(N,0())) -> U91#(isNat(N),N) active#(x(N,0())) -> mark#(U91(isNat(N),N)) active#(x(N,s(M))) -> isNat#(M) active#(x(N,s(M))) -> U101#(isNat(M),M,N) active#(x(N,s(M))) -> mark#(U101(isNat(M),M,N)) mark#(U101(X1,X2,X3)) -> mark#(X1) mark#(U101(X1,X2,X3)) -> U101#(mark(X1),X2,X3) mark#(U101(X1,X2,X3)) -> active#(U101(mark(X1),X2,X3)) mark#(tt()) -> active#(tt()) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U102(X1,X2,X3)) -> U102#(mark(X1),X2,X3) mark#(U102(X1,X2,X3)) -> active#(U102(mark(X1),X2,X3)) mark#(isNatKind(X)) -> active#(isNatKind(X)) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(U103(X1,X2,X3)) -> U103#(mark(X1),X2,X3) mark#(U103(X1,X2,X3)) -> active#(U103(mark(X1),X2,X3)) mark#(isNat(X)) -> active#(isNat(X)) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(U104(X1,X2,X3)) -> U104#(mark(X1),X2,X3) mark#(U104(X1,X2,X3)) -> active#(U104(mark(X1),X2,X3)) mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(x(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> x#(mark(X1),mark(X2)) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> U11#(mark(X1),X2,X3) mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> U12#(mark(X1),X2,X3) mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) mark#(U13(X1,X2,X3)) -> mark#(X1) mark#(U13(X1,X2,X3)) -> U13#(mark(X1),X2,X3) mark#(U13(X1,X2,X3)) -> active#(U13(mark(X1),X2,X3)) mark#(U14(X1,X2,X3)) -> mark#(X1) mark#(U14(X1,X2,X3)) -> U14#(mark(X1),X2,X3) mark#(U14(X1,X2,X3)) -> active#(U14(mark(X1),X2,X3)) mark#(U15(X1,X2)) -> mark#(X1) mark#(U15(X1,X2)) -> U15#(mark(X1),X2) mark#(U15(X1,X2)) -> active#(U15(mark(X1),X2)) mark#(U16(X)) -> mark#(X) mark#(U16(X)) -> U16#(mark(X)) mark#(U16(X)) -> active#(U16(mark(X))) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> U21#(mark(X1),X2) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> U22#(mark(X1),X2) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> U23#(mark(X)) mark#(U23(X)) -> active#(U23(mark(X))) mark#(U31(X1,X2,X3)) -> mark#(X1) mark#(U31(X1,X2,X3)) -> U31#(mark(X1),X2,X3) mark#(U31(X1,X2,X3)) -> active#(U31(mark(X1),X2,X3)) mark#(U32(X1,X2,X3)) -> mark#(X1) mark#(U32(X1,X2,X3)) -> U32#(mark(X1),X2,X3) mark#(U32(X1,X2,X3)) -> active#(U32(mark(X1),X2,X3)) mark#(U33(X1,X2,X3)) -> mark#(X1) mark#(U33(X1,X2,X3)) -> U33#(mark(X1),X2,X3) mark#(U33(X1,X2,X3)) -> active#(U33(mark(X1),X2,X3)) mark#(U34(X1,X2,X3)) -> mark#(X1) mark#(U34(X1,X2,X3)) -> U34#(mark(X1),X2,X3) mark#(U34(X1,X2,X3)) -> active#(U34(mark(X1),X2,X3)) mark#(U35(X1,X2)) -> mark#(X1) mark#(U35(X1,X2)) -> U35#(mark(X1),X2) mark#(U35(X1,X2)) -> active#(U35(mark(X1),X2)) mark#(U36(X)) -> mark#(X) mark#(U36(X)) -> U36#(mark(X)) mark#(U36(X)) -> active#(U36(mark(X))) mark#(U41(X1,X2)) -> mark#(X1) mark#(U41(X1,X2)) -> U41#(mark(X1),X2) mark#(U41(X1,X2)) -> active#(U41(mark(X1),X2)) mark#(U42(X)) -> mark#(X) mark#(U42(X)) -> U42#(mark(X)) mark#(U42(X)) -> active#(U42(mark(X))) mark#(U51(X)) -> mark#(X) mark#(U51(X)) -> U51#(mark(X)) mark#(U51(X)) -> active#(U51(mark(X))) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> U61#(mark(X1),X2) mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2)) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> U62#(mark(X)) mark#(U62(X)) -> active#(U62(mark(X))) mark#(U71(X1,X2)) -> mark#(X1) mark#(U71(X1,X2)) -> U71#(mark(X1),X2) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) mark#(U72(X1,X2)) -> mark#(X1) mark#(U72(X1,X2)) -> U72#(mark(X1),X2) mark#(U72(X1,X2)) -> active#(U72(mark(X1),X2)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> U81#(mark(X1),X2,X3) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> U82#(mark(X1),X2,X3) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> U83#(mark(X1),X2,X3) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> U84#(mark(X1),X2,X3) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(mark(X))) mark#(U91(X1,X2)) -> mark#(X1) mark#(U91(X1,X2)) -> U91#(mark(X1),X2) mark#(U91(X1,X2)) -> active#(U91(mark(X1),X2)) mark#(U92(X)) -> mark#(X) mark#(U92(X)) -> U92#(mark(X)) mark#(U92(X)) -> active#(U92(mark(X))) mark#(0()) -> active#(0()) U101#(mark(X1),X2,X3) -> U101#(X1,X2,X3) U101#(X1,mark(X2),X3) -> U101#(X1,X2,X3) U101#(X1,X2,mark(X3)) -> U101#(X1,X2,X3) U101#(active(X1),X2,X3) -> U101#(X1,X2,X3) U101#(X1,active(X2),X3) -> U101#(X1,X2,X3) U101#(X1,X2,active(X3)) -> U101#(X1,X2,X3) U102#(mark(X1),X2,X3) -> U102#(X1,X2,X3) U102#(X1,mark(X2),X3) -> U102#(X1,X2,X3) U102#(X1,X2,mark(X3)) -> U102#(X1,X2,X3) U102#(active(X1),X2,X3) -> U102#(X1,X2,X3) U102#(X1,active(X2),X3) -> U102#(X1,X2,X3) U102#(X1,X2,active(X3)) -> U102#(X1,X2,X3) isNatKind#(mark(X)) -> isNatKind#(X) isNatKind#(active(X)) -> isNatKind#(X) U103#(mark(X1),X2,X3) -> U103#(X1,X2,X3) U103#(X1,mark(X2),X3) -> U103#(X1,X2,X3) U103#(X1,X2,mark(X3)) -> U103#(X1,X2,X3) U103#(active(X1),X2,X3) -> U103#(X1,X2,X3) U103#(X1,active(X2),X3) -> U103#(X1,X2,X3) U103#(X1,X2,active(X3)) -> U103#(X1,X2,X3) isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) U104#(mark(X1),X2,X3) -> U104#(X1,X2,X3) U104#(X1,mark(X2),X3) -> U104#(X1,X2,X3) U104#(X1,X2,mark(X3)) -> U104#(X1,X2,X3) U104#(active(X1),X2,X3) -> U104#(X1,X2,X3) U104#(X1,active(X2),X3) -> U104#(X1,X2,X3) U104#(X1,X2,active(X3)) -> U104#(X1,X2,X3) plus#(mark(X1),X2) -> plus#(X1,X2) plus#(X1,mark(X2)) -> plus#(X1,X2) plus#(active(X1),X2) -> plus#(X1,X2) plus#(X1,active(X2)) -> plus#(X1,X2) x#(mark(X1),X2) -> x#(X1,X2) x#(X1,mark(X2)) -> x#(X1,X2) x#(active(X1),X2) -> x#(X1,X2) x#(X1,active(X2)) -> x#(X1,X2) U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3) U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3) U11#(active(X1),X2,X3) -> U11#(X1,X2,X3) U11#(X1,active(X2),X3) -> U11#(X1,X2,X3) U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3) U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3) U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3) U12#(active(X1),X2,X3) -> U12#(X1,X2,X3) U12#(X1,active(X2),X3) -> U12#(X1,X2,X3) U12#(X1,X2,active(X3)) -> U12#(X1,X2,X3) U13#(mark(X1),X2,X3) -> U13#(X1,X2,X3) U13#(X1,mark(X2),X3) -> U13#(X1,X2,X3) U13#(X1,X2,mark(X3)) -> U13#(X1,X2,X3) U13#(active(X1),X2,X3) -> U13#(X1,X2,X3) U13#(X1,active(X2),X3) -> U13#(X1,X2,X3) U13#(X1,X2,active(X3)) -> U13#(X1,X2,X3) U14#(mark(X1),X2,X3) -> U14#(X1,X2,X3) U14#(X1,mark(X2),X3) -> U14#(X1,X2,X3) U14#(X1,X2,mark(X3)) -> U14#(X1,X2,X3) U14#(active(X1),X2,X3) -> U14#(X1,X2,X3) U14#(X1,active(X2),X3) -> U14#(X1,X2,X3) U14#(X1,X2,active(X3)) -> U14#(X1,X2,X3) U15#(mark(X1),X2) -> U15#(X1,X2) U15#(X1,mark(X2)) -> U15#(X1,X2) U15#(active(X1),X2) -> U15#(X1,X2) U15#(X1,active(X2)) -> U15#(X1,X2) U16#(mark(X)) -> U16#(X) U16#(active(X)) -> U16#(X) U21#(mark(X1),X2) -> U21#(X1,X2) U21#(X1,mark(X2)) -> U21#(X1,X2) U21#(active(X1),X2) -> U21#(X1,X2) U21#(X1,active(X2)) -> U21#(X1,X2) U22#(mark(X1),X2) -> U22#(X1,X2) U22#(X1,mark(X2)) -> U22#(X1,X2) U22#(active(X1),X2) -> U22#(X1,X2) U22#(X1,active(X2)) -> U22#(X1,X2) U23#(mark(X)) -> U23#(X) U23#(active(X)) -> U23#(X) U31#(mark(X1),X2,X3) -> U31#(X1,X2,X3) U31#(X1,mark(X2),X3) -> U31#(X1,X2,X3) U31#(X1,X2,mark(X3)) -> U31#(X1,X2,X3) U31#(active(X1),X2,X3) -> U31#(X1,X2,X3) U31#(X1,active(X2),X3) -> U31#(X1,X2,X3) U31#(X1,X2,active(X3)) -> U31#(X1,X2,X3) U32#(mark(X1),X2,X3) -> U32#(X1,X2,X3) U32#(X1,mark(X2),X3) -> U32#(X1,X2,X3) U32#(X1,X2,mark(X3)) -> U32#(X1,X2,X3) U32#(active(X1),X2,X3) -> U32#(X1,X2,X3) U32#(X1,active(X2),X3) -> U32#(X1,X2,X3) U32#(X1,X2,active(X3)) -> U32#(X1,X2,X3) U33#(mark(X1),X2,X3) -> U33#(X1,X2,X3) U33#(X1,mark(X2),X3) -> U33#(X1,X2,X3) U33#(X1,X2,mark(X3)) -> U33#(X1,X2,X3) U33#(active(X1),X2,X3) -> U33#(X1,X2,X3) U33#(X1,active(X2),X3) -> U33#(X1,X2,X3) U33#(X1,X2,active(X3)) -> U33#(X1,X2,X3) U34#(mark(X1),X2,X3) -> U34#(X1,X2,X3) U34#(X1,mark(X2),X3) -> U34#(X1,X2,X3) U34#(X1,X2,mark(X3)) -> U34#(X1,X2,X3) U34#(active(X1),X2,X3) -> U34#(X1,X2,X3) U34#(X1,active(X2),X3) -> U34#(X1,X2,X3) U34#(X1,X2,active(X3)) -> U34#(X1,X2,X3) U35#(mark(X1),X2) -> U35#(X1,X2) U35#(X1,mark(X2)) -> U35#(X1,X2) U35#(active(X1),X2) -> U35#(X1,X2) U35#(X1,active(X2)) -> U35#(X1,X2) U36#(mark(X)) -> U36#(X) U36#(active(X)) -> U36#(X) U41#(mark(X1),X2) -> U41#(X1,X2) U41#(X1,mark(X2)) -> U41#(X1,X2) U41#(active(X1),X2) -> U41#(X1,X2) U41#(X1,active(X2)) -> U41#(X1,X2) U42#(mark(X)) -> U42#(X) U42#(active(X)) -> U42#(X) U51#(mark(X)) -> U51#(X) U51#(active(X)) -> U51#(X) U61#(mark(X1),X2) -> U61#(X1,X2) U61#(X1,mark(X2)) -> U61#(X1,X2) U61#(active(X1),X2) -> U61#(X1,X2) U61#(X1,active(X2)) -> U61#(X1,X2) U62#(mark(X)) -> U62#(X) U62#(active(X)) -> U62#(X) U71#(mark(X1),X2) -> U71#(X1,X2) U71#(X1,mark(X2)) -> U71#(X1,X2) U71#(active(X1),X2) -> U71#(X1,X2) U71#(X1,active(X2)) -> U71#(X1,X2) U72#(mark(X1),X2) -> U72#(X1,X2) U72#(X1,mark(X2)) -> U72#(X1,X2) U72#(active(X1),X2) -> U72#(X1,X2) U72#(X1,active(X2)) -> U72#(X1,X2) U81#(mark(X1),X2,X3) -> U81#(X1,X2,X3) U81#(X1,mark(X2),X3) -> U81#(X1,X2,X3) U81#(X1,X2,mark(X3)) -> U81#(X1,X2,X3) U81#(active(X1),X2,X3) -> U81#(X1,X2,X3) U81#(X1,active(X2),X3) -> U81#(X1,X2,X3) U81#(X1,X2,active(X3)) -> U81#(X1,X2,X3) U82#(mark(X1),X2,X3) -> U82#(X1,X2,X3) U82#(X1,mark(X2),X3) -> U82#(X1,X2,X3) U82#(X1,X2,mark(X3)) -> U82#(X1,X2,X3) U82#(active(X1),X2,X3) -> U82#(X1,X2,X3) U82#(X1,active(X2),X3) -> U82#(X1,X2,X3) U82#(X1,X2,active(X3)) -> U82#(X1,X2,X3) U83#(mark(X1),X2,X3) -> U83#(X1,X2,X3) U83#(X1,mark(X2),X3) -> U83#(X1,X2,X3) U83#(X1,X2,mark(X3)) -> U83#(X1,X2,X3) U83#(active(X1),X2,X3) -> U83#(X1,X2,X3) U83#(X1,active(X2),X3) -> U83#(X1,X2,X3) U83#(X1,X2,active(X3)) -> U83#(X1,X2,X3) U84#(mark(X1),X2,X3) -> U84#(X1,X2,X3) U84#(X1,mark(X2),X3) -> U84#(X1,X2,X3) U84#(X1,X2,mark(X3)) -> U84#(X1,X2,X3) U84#(active(X1),X2,X3) -> U84#(X1,X2,X3) U84#(X1,active(X2),X3) -> U84#(X1,X2,X3) U84#(X1,X2,active(X3)) -> U84#(X1,X2,X3) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) U91#(mark(X1),X2) -> U91#(X1,X2) U91#(X1,mark(X2)) -> U91#(X1,X2) U91#(active(X1),X2) -> U91#(X1,X2) U91#(X1,active(X2)) -> U91#(X1,X2) U92#(mark(X)) -> U92#(X) U92#(active(X)) -> U92#(X) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) EDG Processor: DPs: active#(U101(tt(),M,N)) -> isNatKind#(M) active#(U101(tt(),M,N)) -> U102#(isNatKind(M),M,N) active#(U101(tt(),M,N)) -> mark#(U102(isNatKind(M),M,N)) active#(U102(tt(),M,N)) -> isNat#(N) active#(U102(tt(),M,N)) -> U103#(isNat(N),M,N) active#(U102(tt(),M,N)) -> mark#(U103(isNat(N),M,N)) active#(U103(tt(),M,N)) -> isNatKind#(N) active#(U103(tt(),M,N)) -> U104#(isNatKind(N),M,N) active#(U103(tt(),M,N)) -> mark#(U104(isNatKind(N),M,N)) active#(U104(tt(),M,N)) -> x#(N,M) active#(U104(tt(),M,N)) -> plus#(x(N,M),N) active#(U104(tt(),M,N)) -> mark#(plus(x(N,M),N)) active#(U11(tt(),V1,V2)) -> isNatKind#(V1) active#(U11(tt(),V1,V2)) -> U12#(isNatKind(V1),V1,V2) active#(U11(tt(),V1,V2)) -> mark#(U12(isNatKind(V1),V1,V2)) active#(U12(tt(),V1,V2)) -> isNatKind#(V2) active#(U12(tt(),V1,V2)) -> U13#(isNatKind(V2),V1,V2) active#(U12(tt(),V1,V2)) -> mark#(U13(isNatKind(V2),V1,V2)) active#(U13(tt(),V1,V2)) -> isNatKind#(V2) active#(U13(tt(),V1,V2)) -> U14#(isNatKind(V2),V1,V2) active#(U13(tt(),V1,V2)) -> mark#(U14(isNatKind(V2),V1,V2)) active#(U14(tt(),V1,V2)) -> isNat#(V1) active#(U14(tt(),V1,V2)) -> U15#(isNat(V1),V2) active#(U14(tt(),V1,V2)) -> mark#(U15(isNat(V1),V2)) active#(U15(tt(),V2)) -> isNat#(V2) active#(U15(tt(),V2)) -> U16#(isNat(V2)) active#(U15(tt(),V2)) -> mark#(U16(isNat(V2))) active#(U16(tt())) -> mark#(tt()) active#(U21(tt(),V1)) -> isNatKind#(V1) active#(U21(tt(),V1)) -> U22#(isNatKind(V1),V1) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) active#(U22(tt(),V1)) -> isNat#(V1) active#(U22(tt(),V1)) -> U23#(isNat(V1)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) active#(U23(tt())) -> mark#(tt()) active#(U31(tt(),V1,V2)) -> isNatKind#(V1) active#(U31(tt(),V1,V2)) -> U32#(isNatKind(V1),V1,V2) active#(U31(tt(),V1,V2)) -> mark#(U32(isNatKind(V1),V1,V2)) active#(U32(tt(),V1,V2)) -> isNatKind#(V2) active#(U32(tt(),V1,V2)) -> U33#(isNatKind(V2),V1,V2) active#(U32(tt(),V1,V2)) -> mark#(U33(isNatKind(V2),V1,V2)) active#(U33(tt(),V1,V2)) -> isNatKind#(V2) active#(U33(tt(),V1,V2)) -> U34#(isNatKind(V2),V1,V2) active#(U33(tt(),V1,V2)) -> mark#(U34(isNatKind(V2),V1,V2)) active#(U34(tt(),V1,V2)) -> isNat#(V1) active#(U34(tt(),V1,V2)) -> U35#(isNat(V1),V2) active#(U34(tt(),V1,V2)) -> mark#(U35(isNat(V1),V2)) active#(U35(tt(),V2)) -> isNat#(V2) active#(U35(tt(),V2)) -> U36#(isNat(V2)) active#(U35(tt(),V2)) -> mark#(U36(isNat(V2))) active#(U36(tt())) -> mark#(tt()) active#(U41(tt(),V2)) -> isNatKind#(V2) active#(U41(tt(),V2)) -> U42#(isNatKind(V2)) active#(U41(tt(),V2)) -> mark#(U42(isNatKind(V2))) active#(U42(tt())) -> mark#(tt()) active#(U51(tt())) -> mark#(tt()) active#(U61(tt(),V2)) -> isNatKind#(V2) active#(U61(tt(),V2)) -> U62#(isNatKind(V2)) active#(U61(tt(),V2)) -> mark#(U62(isNatKind(V2))) active#(U62(tt())) -> mark#(tt()) active#(U71(tt(),N)) -> isNatKind#(N) active#(U71(tt(),N)) -> U72#(isNatKind(N),N) active#(U71(tt(),N)) -> mark#(U72(isNatKind(N),N)) active#(U72(tt(),N)) -> mark#(N) active#(U81(tt(),M,N)) -> isNatKind#(M) active#(U81(tt(),M,N)) -> U82#(isNatKind(M),M,N) active#(U81(tt(),M,N)) -> mark#(U82(isNatKind(M),M,N)) active#(U82(tt(),M,N)) -> isNat#(N) active#(U82(tt(),M,N)) -> U83#(isNat(N),M,N) active#(U82(tt(),M,N)) -> mark#(U83(isNat(N),M,N)) active#(U83(tt(),M,N)) -> isNatKind#(N) active#(U83(tt(),M,N)) -> U84#(isNatKind(N),M,N) active#(U83(tt(),M,N)) -> mark#(U84(isNatKind(N),M,N)) active#(U84(tt(),M,N)) -> plus#(N,M) active#(U84(tt(),M,N)) -> s#(plus(N,M)) active#(U84(tt(),M,N)) -> mark#(s(plus(N,M))) active#(U91(tt(),N)) -> isNatKind#(N) active#(U91(tt(),N)) -> U92#(isNatKind(N)) active#(U91(tt(),N)) -> mark#(U92(isNatKind(N))) active#(U92(tt())) -> mark#(0()) active#(isNat(0())) -> mark#(tt()) active#(isNat(plus(V1,V2))) -> isNatKind#(V1) active#(isNat(plus(V1,V2))) -> U11#(isNatKind(V1),V1,V2) active#(isNat(plus(V1,V2))) -> mark#(U11(isNatKind(V1),V1,V2)) active#(isNat(s(V1))) -> isNatKind#(V1) active#(isNat(s(V1))) -> U21#(isNatKind(V1),V1) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) active#(isNat(x(V1,V2))) -> isNatKind#(V1) active#(isNat(x(V1,V2))) -> U31#(isNatKind(V1),V1,V2) active#(isNat(x(V1,V2))) -> mark#(U31(isNatKind(V1),V1,V2)) active#(isNatKind(0())) -> mark#(tt()) active#(isNatKind(plus(V1,V2))) -> isNatKind#(V1) active#(isNatKind(plus(V1,V2))) -> U41#(isNatKind(V1),V2) active#(isNatKind(plus(V1,V2))) -> mark#(U41(isNatKind(V1),V2)) active#(isNatKind(s(V1))) -> isNatKind#(V1) active#(isNatKind(s(V1))) -> U51#(isNatKind(V1)) active#(isNatKind(s(V1))) -> mark#(U51(isNatKind(V1))) active#(isNatKind(x(V1,V2))) -> isNatKind#(V1) active#(isNatKind(x(V1,V2))) -> U61#(isNatKind(V1),V2) active#(isNatKind(x(V1,V2))) -> mark#(U61(isNatKind(V1),V2)) active#(plus(N,0())) -> isNat#(N) active#(plus(N,0())) -> U71#(isNat(N),N) active#(plus(N,0())) -> mark#(U71(isNat(N),N)) active#(plus(N,s(M))) -> isNat#(M) active#(plus(N,s(M))) -> U81#(isNat(M),M,N) active#(plus(N,s(M))) -> mark#(U81(isNat(M),M,N)) active#(x(N,0())) -> isNat#(N) active#(x(N,0())) -> U91#(isNat(N),N) active#(x(N,0())) -> mark#(U91(isNat(N),N)) active#(x(N,s(M))) -> isNat#(M) active#(x(N,s(M))) -> U101#(isNat(M),M,N) active#(x(N,s(M))) -> mark#(U101(isNat(M),M,N)) mark#(U101(X1,X2,X3)) -> mark#(X1) mark#(U101(X1,X2,X3)) -> U101#(mark(X1),X2,X3) mark#(U101(X1,X2,X3)) -> active#(U101(mark(X1),X2,X3)) mark#(tt()) -> active#(tt()) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U102(X1,X2,X3)) -> U102#(mark(X1),X2,X3) mark#(U102(X1,X2,X3)) -> active#(U102(mark(X1),X2,X3)) mark#(isNatKind(X)) -> active#(isNatKind(X)) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(U103(X1,X2,X3)) -> U103#(mark(X1),X2,X3) mark#(U103(X1,X2,X3)) -> active#(U103(mark(X1),X2,X3)) mark#(isNat(X)) -> active#(isNat(X)) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(U104(X1,X2,X3)) -> U104#(mark(X1),X2,X3) mark#(U104(X1,X2,X3)) -> active#(U104(mark(X1),X2,X3)) mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2)) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) mark#(x(X1,X2)) -> mark#(X2) mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> x#(mark(X1),mark(X2)) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> U11#(mark(X1),X2,X3) mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> U12#(mark(X1),X2,X3) mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) mark#(U13(X1,X2,X3)) -> mark#(X1) mark#(U13(X1,X2,X3)) -> U13#(mark(X1),X2,X3) mark#(U13(X1,X2,X3)) -> active#(U13(mark(X1),X2,X3)) mark#(U14(X1,X2,X3)) -> mark#(X1) mark#(U14(X1,X2,X3)) -> U14#(mark(X1),X2,X3) mark#(U14(X1,X2,X3)) -> active#(U14(mark(X1),X2,X3)) mark#(U15(X1,X2)) -> mark#(X1) mark#(U15(X1,X2)) -> U15#(mark(X1),X2) mark#(U15(X1,X2)) -> active#(U15(mark(X1),X2)) mark#(U16(X)) -> mark#(X) mark#(U16(X)) -> U16#(mark(X)) mark#(U16(X)) -> active#(U16(mark(X))) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> U21#(mark(X1),X2) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> U22#(mark(X1),X2) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> U23#(mark(X)) mark#(U23(X)) -> active#(U23(mark(X))) mark#(U31(X1,X2,X3)) -> mark#(X1) mark#(U31(X1,X2,X3)) -> U31#(mark(X1),X2,X3) mark#(U31(X1,X2,X3)) -> active#(U31(mark(X1),X2,X3)) mark#(U32(X1,X2,X3)) -> mark#(X1) mark#(U32(X1,X2,X3)) -> U32#(mark(X1),X2,X3) mark#(U32(X1,X2,X3)) -> active#(U32(mark(X1),X2,X3)) mark#(U33(X1,X2,X3)) -> mark#(X1) mark#(U33(X1,X2,X3)) -> U33#(mark(X1),X2,X3) mark#(U33(X1,X2,X3)) -> active#(U33(mark(X1),X2,X3)) mark#(U34(X1,X2,X3)) -> mark#(X1) mark#(U34(X1,X2,X3)) -> U34#(mark(X1),X2,X3) mark#(U34(X1,X2,X3)) -> active#(U34(mark(X1),X2,X3)) mark#(U35(X1,X2)) -> mark#(X1) mark#(U35(X1,X2)) -> U35#(mark(X1),X2) mark#(U35(X1,X2)) -> active#(U35(mark(X1),X2)) mark#(U36(X)) -> mark#(X) mark#(U36(X)) -> U36#(mark(X)) mark#(U36(X)) -> active#(U36(mark(X))) mark#(U41(X1,X2)) -> mark#(X1) mark#(U41(X1,X2)) -> U41#(mark(X1),X2) mark#(U41(X1,X2)) -> active#(U41(mark(X1),X2)) mark#(U42(X)) -> mark#(X) mark#(U42(X)) -> U42#(mark(X)) mark#(U42(X)) -> active#(U42(mark(X))) mark#(U51(X)) -> mark#(X) mark#(U51(X)) -> U51#(mark(X)) mark#(U51(X)) -> active#(U51(mark(X))) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> U61#(mark(X1),X2) mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2)) mark#(U62(X)) -> mark#(X) mark#(U62(X)) -> U62#(mark(X)) mark#(U62(X)) -> active#(U62(mark(X))) mark#(U71(X1,X2)) -> mark#(X1) mark#(U71(X1,X2)) -> U71#(mark(X1),X2) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) mark#(U72(X1,X2)) -> mark#(X1) mark#(U72(X1,X2)) -> U72#(mark(X1),X2) mark#(U72(X1,X2)) -> active#(U72(mark(X1),X2)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> U81#(mark(X1),X2,X3) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> U82#(mark(X1),X2,X3) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> U83#(mark(X1),X2,X3) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U84(X1,X2,X3)) -> U84#(mark(X1),X2,X3) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(mark(X))) mark#(U91(X1,X2)) -> mark#(X1) mark#(U91(X1,X2)) -> U91#(mark(X1),X2) mark#(U91(X1,X2)) -> active#(U91(mark(X1),X2)) mark#(U92(X)) -> mark#(X) mark#(U92(X)) -> U92#(mark(X)) mark#(U92(X)) -> active#(U92(mark(X))) mark#(0()) -> active#(0()) U101#(mark(X1),X2,X3) -> U101#(X1,X2,X3) U101#(X1,mark(X2),X3) -> U101#(X1,X2,X3) U101#(X1,X2,mark(X3)) -> U101#(X1,X2,X3) U101#(active(X1),X2,X3) -> U101#(X1,X2,X3) U101#(X1,active(X2),X3) -> U101#(X1,X2,X3) U101#(X1,X2,active(X3)) -> U101#(X1,X2,X3) U102#(mark(X1),X2,X3) -> U102#(X1,X2,X3) U102#(X1,mark(X2),X3) -> U102#(X1,X2,X3) U102#(X1,X2,mark(X3)) -> U102#(X1,X2,X3) U102#(active(X1),X2,X3) -> U102#(X1,X2,X3) U102#(X1,active(X2),X3) -> U102#(X1,X2,X3) U102#(X1,X2,active(X3)) -> U102#(X1,X2,X3) isNatKind#(mark(X)) -> isNatKind#(X) isNatKind#(active(X)) -> isNatKind#(X) U103#(mark(X1),X2,X3) -> U103#(X1,X2,X3) U103#(X1,mark(X2),X3) -> U103#(X1,X2,X3) U103#(X1,X2,mark(X3)) -> U103#(X1,X2,X3) U103#(active(X1),X2,X3) -> U103#(X1,X2,X3) U103#(X1,active(X2),X3) -> U103#(X1,X2,X3) U103#(X1,X2,active(X3)) -> U103#(X1,X2,X3) isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) U104#(mark(X1),X2,X3) -> U104#(X1,X2,X3) U104#(X1,mark(X2),X3) -> U104#(X1,X2,X3) U104#(X1,X2,mark(X3)) -> U104#(X1,X2,X3) U104#(active(X1),X2,X3) -> U104#(X1,X2,X3) U104#(X1,active(X2),X3) -> U104#(X1,X2,X3) U104#(X1,X2,active(X3)) -> U104#(X1,X2,X3) plus#(mark(X1),X2) -> plus#(X1,X2) plus#(X1,mark(X2)) -> plus#(X1,X2) plus#(active(X1),X2) -> plus#(X1,X2) plus#(X1,active(X2)) -> plus#(X1,X2) x#(mark(X1),X2) -> x#(X1,X2) x#(X1,mark(X2)) -> x#(X1,X2) x#(active(X1),X2) -> x#(X1,X2) x#(X1,active(X2)) -> x#(X1,X2) U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3) U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3) U11#(active(X1),X2,X3) -> U11#(X1,X2,X3) U11#(X1,active(X2),X3) -> U11#(X1,X2,X3) U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3) U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3) U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3) U12#(active(X1),X2,X3) -> U12#(X1,X2,X3) U12#(X1,active(X2),X3) -> U12#(X1,X2,X3) U12#(X1,X2,active(X3)) -> U12#(X1,X2,X3) U13#(mark(X1),X2,X3) -> U13#(X1,X2,X3) U13#(X1,mark(X2),X3) -> U13#(X1,X2,X3) U13#(X1,X2,mark(X3)) -> U13#(X1,X2,X3) U13#(active(X1),X2,X3) -> U13#(X1,X2,X3) U13#(X1,active(X2),X3) -> U13#(X1,X2,X3) U13#(X1,X2,active(X3)) -> U13#(X1,X2,X3) U14#(mark(X1),X2,X3) -> U14#(X1,X2,X3) U14#(X1,mark(X2),X3) -> U14#(X1,X2,X3) U14#(X1,X2,mark(X3)) -> U14#(X1,X2,X3) U14#(active(X1),X2,X3) -> U14#(X1,X2,X3) U14#(X1,active(X2),X3) -> U14#(X1,X2,X3) U14#(X1,X2,active(X3)) -> U14#(X1,X2,X3) U15#(mark(X1),X2) -> U15#(X1,X2) U15#(X1,mark(X2)) -> U15#(X1,X2) U15#(active(X1),X2) -> U15#(X1,X2) U15#(X1,active(X2)) -> U15#(X1,X2) U16#(mark(X)) -> U16#(X) U16#(active(X)) -> U16#(X) U21#(mark(X1),X2) -> U21#(X1,X2) U21#(X1,mark(X2)) -> U21#(X1,X2) U21#(active(X1),X2) -> U21#(X1,X2) U21#(X1,active(X2)) -> U21#(X1,X2) U22#(mark(X1),X2) -> U22#(X1,X2) U22#(X1,mark(X2)) -> U22#(X1,X2) U22#(active(X1),X2) -> U22#(X1,X2) U22#(X1,active(X2)) -> U22#(X1,X2) U23#(mark(X)) -> U23#(X) U23#(active(X)) -> U23#(X) U31#(mark(X1),X2,X3) -> U31#(X1,X2,X3) U31#(X1,mark(X2),X3) -> U31#(X1,X2,X3) U31#(X1,X2,mark(X3)) -> U31#(X1,X2,X3) U31#(active(X1),X2,X3) -> U31#(X1,X2,X3) U31#(X1,active(X2),X3) -> U31#(X1,X2,X3) U31#(X1,X2,active(X3)) -> U31#(X1,X2,X3) U32#(mark(X1),X2,X3) -> U32#(X1,X2,X3) U32#(X1,mark(X2),X3) -> U32#(X1,X2,X3) U32#(X1,X2,mark(X3)) -> U32#(X1,X2,X3) U32#(active(X1),X2,X3) -> U32#(X1,X2,X3) U32#(X1,active(X2),X3) -> U32#(X1,X2,X3) U32#(X1,X2,active(X3)) -> U32#(X1,X2,X3) U33#(mark(X1),X2,X3) -> U33#(X1,X2,X3) U33#(X1,mark(X2),X3) -> U33#(X1,X2,X3) U33#(X1,X2,mark(X3)) -> U33#(X1,X2,X3) U33#(active(X1),X2,X3) -> U33#(X1,X2,X3) U33#(X1,active(X2),X3) -> U33#(X1,X2,X3) U33#(X1,X2,active(X3)) -> U33#(X1,X2,X3) U34#(mark(X1),X2,X3) -> U34#(X1,X2,X3) U34#(X1,mark(X2),X3) -> U34#(X1,X2,X3) U34#(X1,X2,mark(X3)) -> U34#(X1,X2,X3) U34#(active(X1),X2,X3) -> U34#(X1,X2,X3) U34#(X1,active(X2),X3) -> U34#(X1,X2,X3) U34#(X1,X2,active(X3)) -> U34#(X1,X2,X3) U35#(mark(X1),X2) -> U35#(X1,X2) U35#(X1,mark(X2)) -> U35#(X1,X2) U35#(active(X1),X2) -> U35#(X1,X2) U35#(X1,active(X2)) -> U35#(X1,X2) U36#(mark(X)) -> U36#(X) U36#(active(X)) -> U36#(X) U41#(mark(X1),X2) -> U41#(X1,X2) U41#(X1,mark(X2)) -> U41#(X1,X2) U41#(active(X1),X2) -> U41#(X1,X2) U41#(X1,active(X2)) -> U41#(X1,X2) U42#(mark(X)) -> U42#(X) U42#(active(X)) -> U42#(X) U51#(mark(X)) -> U51#(X) U51#(active(X)) -> U51#(X) U61#(mark(X1),X2) -> U61#(X1,X2) U61#(X1,mark(X2)) -> U61#(X1,X2) U61#(active(X1),X2) -> U61#(X1,X2) U61#(X1,active(X2)) -> U61#(X1,X2) U62#(mark(X)) -> U62#(X) U62#(active(X)) -> U62#(X) U71#(mark(X1),X2) -> U71#(X1,X2) U71#(X1,mark(X2)) -> U71#(X1,X2) U71#(active(X1),X2) -> U71#(X1,X2) U71#(X1,active(X2)) -> U71#(X1,X2) U72#(mark(X1),X2) -> U72#(X1,X2) U72#(X1,mark(X2)) -> U72#(X1,X2) U72#(active(X1),X2) -> U72#(X1,X2) U72#(X1,active(X2)) -> U72#(X1,X2) U81#(mark(X1),X2,X3) -> U81#(X1,X2,X3) U81#(X1,mark(X2),X3) -> U81#(X1,X2,X3) U81#(X1,X2,mark(X3)) -> U81#(X1,X2,X3) U81#(active(X1),X2,X3) -> U81#(X1,X2,X3) U81#(X1,active(X2),X3) -> U81#(X1,X2,X3) U81#(X1,X2,active(X3)) -> U81#(X1,X2,X3) U82#(mark(X1),X2,X3) -> U82#(X1,X2,X3) U82#(X1,mark(X2),X3) -> U82#(X1,X2,X3) U82#(X1,X2,mark(X3)) -> U82#(X1,X2,X3) U82#(active(X1),X2,X3) -> U82#(X1,X2,X3) U82#(X1,active(X2),X3) -> U82#(X1,X2,X3) U82#(X1,X2,active(X3)) -> U82#(X1,X2,X3) U83#(mark(X1),X2,X3) -> U83#(X1,X2,X3) U83#(X1,mark(X2),X3) -> U83#(X1,X2,X3) U83#(X1,X2,mark(X3)) -> U83#(X1,X2,X3) U83#(active(X1),X2,X3) -> U83#(X1,X2,X3) U83#(X1,active(X2),X3) -> U83#(X1,X2,X3) U83#(X1,X2,active(X3)) -> U83#(X1,X2,X3) U84#(mark(X1),X2,X3) -> U84#(X1,X2,X3) U84#(X1,mark(X2),X3) -> U84#(X1,X2,X3) U84#(X1,X2,mark(X3)) -> U84#(X1,X2,X3) U84#(active(X1),X2,X3) -> U84#(X1,X2,X3) U84#(X1,active(X2),X3) -> U84#(X1,X2,X3) U84#(X1,X2,active(X3)) -> U84#(X1,X2,X3) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) U91#(mark(X1),X2) -> U91#(X1,X2) U91#(X1,mark(X2)) -> U91#(X1,X2) U91#(active(X1),X2) -> U91#(X1,X2) U91#(X1,active(X2)) -> U91#(X1,X2) U92#(mark(X)) -> U92#(X) U92#(active(X)) -> U92#(X) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) graph: ... SCC Processor: #sccs: 38 #rules: 269 #arcs: 13249/146689 DPs: mark#(U92(X)) -> mark#(X) mark#(U92(X)) -> active#(U92(mark(X))) active#(x(N,s(M))) -> mark#(U101(isNat(M),M,N)) mark#(U91(X1,X2)) -> active#(U91(mark(X1),X2)) active#(x(N,0())) -> mark#(U91(isNat(N),N)) mark#(U91(X1,X2)) -> mark#(X1) mark#(s(X)) -> active#(s(mark(X))) active#(plus(N,s(M))) -> mark#(U81(isNat(M),M,N)) mark#(s(X)) -> mark#(X) mark#(U84(X1,X2,X3)) -> active#(U84(mark(X1),X2,X3)) active#(plus(N,0())) -> mark#(U71(isNat(N),N)) mark#(U84(X1,X2,X3)) -> mark#(X1) mark#(U83(X1,X2,X3)) -> active#(U83(mark(X1),X2,X3)) active#(isNatKind(x(V1,V2))) -> mark#(U61(isNatKind(V1),V2)) mark#(U83(X1,X2,X3)) -> mark#(X1) mark#(U82(X1,X2,X3)) -> active#(U82(mark(X1),X2,X3)) active#(isNatKind(s(V1))) -> mark#(U51(isNatKind(V1))) mark#(U82(X1,X2,X3)) -> mark#(X1) mark#(U81(X1,X2,X3)) -> active#(U81(mark(X1),X2,X3)) active#(isNatKind(plus(V1,V2))) -> mark#(U41(isNatKind(V1),V2)) mark#(U81(X1,X2,X3)) -> mark#(X1) mark#(U72(X1,X2)) -> active#(U72(mark(X1),X2)) active#(isNat(x(V1,V2))) -> mark#(U31(isNatKind(V1),V1,V2)) mark#(U72(X1,X2)) -> mark#(X1) mark#(U71(X1,X2)) -> active#(U71(mark(X1),X2)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U71(X1,X2)) -> mark#(X1) mark#(U62(X)) -> active#(U62(mark(X))) active#(isNat(plus(V1,V2))) -> mark#(U11(isNatKind(V1),V1,V2)) mark#(U62(X)) -> mark#(X) mark#(U61(X1,X2)) -> active#(U61(mark(X1),X2)) active#(U91(tt(),N)) -> mark#(U92(isNatKind(N))) mark#(U61(X1,X2)) -> mark#(X1) mark#(U51(X)) -> active#(U51(mark(X))) active#(U84(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(U51(X)) -> mark#(X) mark#(U42(X)) -> active#(U42(mark(X))) active#(U83(tt(),M,N)) -> mark#(U84(isNatKind(N),M,N)) mark#(U42(X)) -> mark#(X) mark#(U41(X1,X2)) -> active#(U41(mark(X1),X2)) active#(U82(tt(),M,N)) -> mark#(U83(isNat(N),M,N)) mark#(U41(X1,X2)) -> mark#(X1) mark#(U36(X)) -> active#(U36(mark(X))) active#(U81(tt(),M,N)) -> mark#(U82(isNatKind(M),M,N)) mark#(U36(X)) -> mark#(X) mark#(U35(X1,X2)) -> active#(U35(mark(X1),X2)) active#(U72(tt(),N)) -> mark#(N) mark#(U35(X1,X2)) -> mark#(X1) mark#(U34(X1,X2,X3)) -> active#(U34(mark(X1),X2,X3)) active#(U71(tt(),N)) -> mark#(U72(isNatKind(N),N)) mark#(U34(X1,X2,X3)) -> mark#(X1) mark#(U33(X1,X2,X3)) -> active#(U33(mark(X1),X2,X3)) active#(U61(tt(),V2)) -> mark#(U62(isNatKind(V2))) mark#(U33(X1,X2,X3)) -> mark#(X1) mark#(U32(X1,X2,X3)) -> active#(U32(mark(X1),X2,X3)) active#(U41(tt(),V2)) -> mark#(U42(isNatKind(V2))) mark#(U32(X1,X2,X3)) -> mark#(X1) mark#(U31(X1,X2,X3)) -> active#(U31(mark(X1),X2,X3)) active#(U35(tt(),V2)) -> mark#(U36(isNat(V2))) mark#(U31(X1,X2,X3)) -> mark#(X1) mark#(U23(X)) -> active#(U23(mark(X))) active#(U34(tt(),V1,V2)) -> mark#(U35(isNat(V1),V2)) mark#(U23(X)) -> mark#(X) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U33(tt(),V1,V2)) -> mark#(U34(isNatKind(V2),V1,V2)) mark#(U22(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U32(tt(),V1,V2)) -> mark#(U33(isNatKind(V2),V1,V2)) mark#(U21(X1,X2)) -> mark#(X1) mark#(U16(X)) -> active#(U16(mark(X))) active#(U31(tt(),V1,V2)) -> mark#(U32(isNatKind(V1),V1,V2)) mark#(U16(X)) -> mark#(X) mark#(U15(X1,X2)) -> active#(U15(mark(X1),X2)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(U15(X1,X2)) -> mark#(X1) mark#(U14(X1,X2,X3)) -> active#(U14(mark(X1),X2,X3)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) mark#(U14(X1,X2,X3)) -> mark#(X1) mark#(U13(X1,X2,X3)) -> active#(U13(mark(X1),X2,X3)) active#(U15(tt(),V2)) -> mark#(U16(isNat(V2))) mark#(U13(X1,X2,X3)) -> mark#(X1) mark#(U12(X1,X2,X3)) -> active#(U12(mark(X1),X2,X3)) active#(U14(tt(),V1,V2)) -> mark#(U15(isNat(V1),V2)) mark#(U12(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) active#(U13(tt(),V1,V2)) -> mark#(U14(isNatKind(V2),V1,V2)) mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(x(X1,X2)) -> active#(x(mark(X1),mark(X2))) active#(U12(tt(),V1,V2)) -> mark#(U13(isNatKind(V2),V1,V2)) mark#(x(X1,X2)) -> mark#(X1) mark#(x(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(U11(tt(),V1,V2)) -> mark#(U12(isNatKind(V1),V1,V2)) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> mark#(X2) mark#(U104(X1,X2,X3)) -> active#(U104(mark(X1),X2,X3)) active#(U104(tt(),M,N)) -> mark#(plus(x(N,M),N)) mark#(U104(X1,X2,X3)) -> mark#(X1) mark#(isNat(X)) -> active#(isNat(X)) active#(U103(tt(),M,N)) -> mark#(U104(isNatKind(N),M,N)) mark#(U103(X1,X2,X3)) -> active#(U103(mark(X1),X2,X3)) active#(U102(tt(),M,N)) -> mark#(U103(isNat(N),M,N)) mark#(U103(X1,X2,X3)) -> mark#(X1) mark#(isNatKind(X)) -> active#(isNatKind(X)) active#(U101(tt(),M,N)) -> mark#(U102(isNatKind(M),M,N)) mark#(U102(X1,X2,X3)) -> active#(U102(mark(X1),X2,X3)) mark#(U102(X1,X2,X3)) -> mark#(X1) mark#(U101(X1,X2,X3)) -> active#(U101(mark(X1),X2,X3)) mark#(U101(X1,X2,X3)) -> mark#(X1) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U102#(X1,X2,active(X3)) -> U102#(X1,X2,X3) U102#(X1,active(X2),X3) -> U102#(X1,X2,X3) U102#(active(X1),X2,X3) -> U102#(X1,X2,X3) U102#(X1,X2,mark(X3)) -> U102#(X1,X2,X3) U102#(X1,mark(X2),X3) -> U102#(X1,X2,X3) U102#(mark(X1),X2,X3) -> U102#(X1,X2,X3) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: isNatKind#(active(X)) -> isNatKind#(X) isNatKind#(mark(X)) -> isNatKind#(X) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U103#(mark(X1),X2,X3) -> U103#(X1,X2,X3) U103#(X1,X2,active(X3)) -> U103#(X1,X2,X3) U103#(X1,active(X2),X3) -> U103#(X1,X2,X3) U103#(active(X1),X2,X3) -> U103#(X1,X2,X3) U103#(X1,X2,mark(X3)) -> U103#(X1,X2,X3) U103#(X1,mark(X2),X3) -> U103#(X1,X2,X3) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U104#(mark(X1),X2,X3) -> U104#(X1,X2,X3) U104#(X1,X2,active(X3)) -> U104#(X1,X2,X3) U104#(X1,active(X2),X3) -> U104#(X1,X2,X3) U104#(active(X1),X2,X3) -> U104#(X1,X2,X3) U104#(X1,X2,mark(X3)) -> U104#(X1,X2,X3) U104#(X1,mark(X2),X3) -> U104#(X1,X2,X3) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: x#(mark(X1),X2) -> x#(X1,X2) x#(X1,active(X2)) -> x#(X1,X2) x#(active(X1),X2) -> x#(X1,X2) x#(X1,mark(X2)) -> x#(X1,X2) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: plus#(mark(X1),X2) -> plus#(X1,X2) plus#(X1,active(X2)) -> plus#(X1,X2) plus#(active(X1),X2) -> plus#(X1,X2) plus#(X1,mark(X2)) -> plus#(X1,X2) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U12#(mark(X1),X2,X3) -> U12#(X1,X2,X3) U12#(X1,X2,active(X3)) -> U12#(X1,X2,X3) U12#(X1,active(X2),X3) -> U12#(X1,X2,X3) U12#(active(X1),X2,X3) -> U12#(X1,X2,X3) U12#(X1,X2,mark(X3)) -> U12#(X1,X2,X3) U12#(X1,mark(X2),X3) -> U12#(X1,X2,X3) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U13#(mark(X1),X2,X3) -> U13#(X1,X2,X3) U13#(X1,X2,active(X3)) -> U13#(X1,X2,X3) U13#(X1,active(X2),X3) -> U13#(X1,X2,X3) U13#(active(X1),X2,X3) -> U13#(X1,X2,X3) U13#(X1,X2,mark(X3)) -> U13#(X1,X2,X3) U13#(X1,mark(X2),X3) -> U13#(X1,X2,X3) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U14#(mark(X1),X2,X3) -> U14#(X1,X2,X3) U14#(X1,X2,active(X3)) -> U14#(X1,X2,X3) U14#(X1,active(X2),X3) -> U14#(X1,X2,X3) U14#(active(X1),X2,X3) -> U14#(X1,X2,X3) U14#(X1,X2,mark(X3)) -> U14#(X1,X2,X3) U14#(X1,mark(X2),X3) -> U14#(X1,X2,X3) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U15#(mark(X1),X2) -> U15#(X1,X2) U15#(X1,active(X2)) -> U15#(X1,X2) U15#(active(X1),X2) -> U15#(X1,X2) U15#(X1,mark(X2)) -> U15#(X1,X2) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U16#(mark(X)) -> U16#(X) U16#(active(X)) -> U16#(X) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U22#(mark(X1),X2) -> U22#(X1,X2) U22#(X1,active(X2)) -> U22#(X1,X2) U22#(active(X1),X2) -> U22#(X1,X2) U22#(X1,mark(X2)) -> U22#(X1,X2) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U23#(mark(X)) -> U23#(X) U23#(active(X)) -> U23#(X) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U32#(mark(X1),X2,X3) -> U32#(X1,X2,X3) U32#(X1,X2,active(X3)) -> U32#(X1,X2,X3) U32#(X1,active(X2),X3) -> U32#(X1,X2,X3) U32#(active(X1),X2,X3) -> U32#(X1,X2,X3) U32#(X1,X2,mark(X3)) -> U32#(X1,X2,X3) U32#(X1,mark(X2),X3) -> U32#(X1,X2,X3) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U33#(mark(X1),X2,X3) -> U33#(X1,X2,X3) U33#(X1,X2,active(X3)) -> U33#(X1,X2,X3) U33#(X1,active(X2),X3) -> U33#(X1,X2,X3) U33#(active(X1),X2,X3) -> U33#(X1,X2,X3) U33#(X1,X2,mark(X3)) -> U33#(X1,X2,X3) U33#(X1,mark(X2),X3) -> U33#(X1,X2,X3) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U34#(mark(X1),X2,X3) -> U34#(X1,X2,X3) U34#(X1,X2,active(X3)) -> U34#(X1,X2,X3) U34#(X1,active(X2),X3) -> U34#(X1,X2,X3) U34#(active(X1),X2,X3) -> U34#(X1,X2,X3) U34#(X1,X2,mark(X3)) -> U34#(X1,X2,X3) U34#(X1,mark(X2),X3) -> U34#(X1,X2,X3) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U35#(mark(X1),X2) -> U35#(X1,X2) U35#(X1,active(X2)) -> U35#(X1,X2) U35#(active(X1),X2) -> U35#(X1,X2) U35#(X1,mark(X2)) -> U35#(X1,X2) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U36#(mark(X)) -> U36#(X) U36#(active(X)) -> U36#(X) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U42#(mark(X)) -> U42#(X) U42#(active(X)) -> U42#(X) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U62#(mark(X)) -> U62#(X) U62#(active(X)) -> U62#(X) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U72#(mark(X1),X2) -> U72#(X1,X2) U72#(X1,active(X2)) -> U72#(X1,X2) U72#(active(X1),X2) -> U72#(X1,X2) U72#(X1,mark(X2)) -> U72#(X1,X2) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U82#(mark(X1),X2,X3) -> U82#(X1,X2,X3) U82#(X1,X2,active(X3)) -> U82#(X1,X2,X3) U82#(X1,active(X2),X3) -> U82#(X1,X2,X3) U82#(active(X1),X2,X3) -> U82#(X1,X2,X3) U82#(X1,X2,mark(X3)) -> U82#(X1,X2,X3) U82#(X1,mark(X2),X3) -> U82#(X1,X2,X3) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U83#(mark(X1),X2,X3) -> U83#(X1,X2,X3) U83#(X1,X2,active(X3)) -> U83#(X1,X2,X3) U83#(X1,active(X2),X3) -> U83#(X1,X2,X3) U83#(active(X1),X2,X3) -> U83#(X1,X2,X3) U83#(X1,X2,mark(X3)) -> U83#(X1,X2,X3) U83#(X1,mark(X2),X3) -> U83#(X1,X2,X3) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U84#(mark(X1),X2,X3) -> U84#(X1,X2,X3) U84#(X1,X2,active(X3)) -> U84#(X1,X2,X3) U84#(X1,active(X2),X3) -> U84#(X1,X2,X3) U84#(active(X1),X2,X3) -> U84#(X1,X2,X3) U84#(X1,X2,mark(X3)) -> U84#(X1,X2,X3) U84#(X1,mark(X2),X3) -> U84#(X1,X2,X3) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U92#(mark(X)) -> U92#(X) U92#(active(X)) -> U92#(X) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U11#(mark(X1),X2,X3) -> U11#(X1,X2,X3) U11#(X1,X2,active(X3)) -> U11#(X1,X2,X3) U11#(X1,active(X2),X3) -> U11#(X1,X2,X3) U11#(active(X1),X2,X3) -> U11#(X1,X2,X3) U11#(X1,X2,mark(X3)) -> U11#(X1,X2,X3) U11#(X1,mark(X2),X3) -> U11#(X1,X2,X3) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U21#(mark(X1),X2) -> U21#(X1,X2) U21#(X1,active(X2)) -> U21#(X1,X2) U21#(active(X1),X2) -> U21#(X1,X2) U21#(X1,mark(X2)) -> U21#(X1,X2) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U31#(mark(X1),X2,X3) -> U31#(X1,X2,X3) U31#(X1,X2,active(X3)) -> U31#(X1,X2,X3) U31#(X1,active(X2),X3) -> U31#(X1,X2,X3) U31#(active(X1),X2,X3) -> U31#(X1,X2,X3) U31#(X1,X2,mark(X3)) -> U31#(X1,X2,X3) U31#(X1,mark(X2),X3) -> U31#(X1,X2,X3) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U41#(mark(X1),X2) -> U41#(X1,X2) U41#(X1,active(X2)) -> U41#(X1,X2) U41#(active(X1),X2) -> U41#(X1,X2) U41#(X1,mark(X2)) -> U41#(X1,X2) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U51#(mark(X)) -> U51#(X) U51#(active(X)) -> U51#(X) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U61#(mark(X1),X2) -> U61#(X1,X2) U61#(X1,active(X2)) -> U61#(X1,X2) U61#(active(X1),X2) -> U61#(X1,X2) U61#(X1,mark(X2)) -> U61#(X1,X2) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U71#(mark(X1),X2) -> U71#(X1,X2) U71#(X1,active(X2)) -> U71#(X1,X2) U71#(active(X1),X2) -> U71#(X1,X2) U71#(X1,mark(X2)) -> U71#(X1,X2) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U81#(mark(X1),X2,X3) -> U81#(X1,X2,X3) U81#(X1,X2,active(X3)) -> U81#(X1,X2,X3) U81#(X1,active(X2),X3) -> U81#(X1,X2,X3) U81#(active(X1),X2,X3) -> U81#(X1,X2,X3) U81#(X1,X2,mark(X3)) -> U81#(X1,X2,X3) U81#(X1,mark(X2),X3) -> U81#(X1,X2,X3) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U91#(mark(X1),X2) -> U91#(X1,X2) U91#(X1,active(X2)) -> U91#(X1,X2) U91#(active(X1),X2) -> U91#(X1,X2) U91#(X1,mark(X2)) -> U91#(X1,X2) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open DPs: U101#(mark(X1),X2,X3) -> U101#(X1,X2,X3) U101#(X1,X2,active(X3)) -> U101#(X1,X2,X3) U101#(X1,active(X2),X3) -> U101#(X1,X2,X3) U101#(active(X1),X2,X3) -> U101#(X1,X2,X3) U101#(X1,X2,mark(X3)) -> U101#(X1,X2,X3) U101#(X1,mark(X2),X3) -> U101#(X1,X2,X3) TRS: active(U101(tt(),M,N)) -> mark(U102(isNatKind(M),M,N)) active(U102(tt(),M,N)) -> mark(U103(isNat(N),M,N)) active(U103(tt(),M,N)) -> mark(U104(isNatKind(N),M,N)) active(U104(tt(),M,N)) -> mark(plus(x(N,M),N)) 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(),V1,V2)) -> mark(U32(isNatKind(V1),V1,V2)) active(U32(tt(),V1,V2)) -> mark(U33(isNatKind(V2),V1,V2)) active(U33(tt(),V1,V2)) -> mark(U34(isNatKind(V2),V1,V2)) active(U34(tt(),V1,V2)) -> mark(U35(isNat(V1),V2)) active(U35(tt(),V2)) -> mark(U36(isNat(V2))) active(U36(tt())) -> mark(tt()) active(U41(tt(),V2)) -> mark(U42(isNatKind(V2))) active(U42(tt())) -> mark(tt()) active(U51(tt())) -> mark(tt()) active(U61(tt(),V2)) -> mark(U62(isNatKind(V2))) active(U62(tt())) -> mark(tt()) active(U71(tt(),N)) -> mark(U72(isNatKind(N),N)) active(U72(tt(),N)) -> mark(N) active(U81(tt(),M,N)) -> mark(U82(isNatKind(M),M,N)) active(U82(tt(),M,N)) -> mark(U83(isNat(N),M,N)) active(U83(tt(),M,N)) -> mark(U84(isNatKind(N),M,N)) active(U84(tt(),M,N)) -> mark(s(plus(N,M))) active(U91(tt(),N)) -> mark(U92(isNatKind(N))) active(U92(tt())) -> mark(0()) 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(isNat(x(V1,V2))) -> mark(U31(isNatKind(V1),V1,V2)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U41(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U51(isNatKind(V1))) active(isNatKind(x(V1,V2))) -> mark(U61(isNatKind(V1),V2)) active(plus(N,0())) -> mark(U71(isNat(N),N)) active(plus(N,s(M))) -> mark(U81(isNat(M),M,N)) active(x(N,0())) -> mark(U91(isNat(N),N)) active(x(N,s(M))) -> mark(U101(isNat(M),M,N)) mark(U101(X1,X2,X3)) -> active(U101(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U102(X1,X2,X3)) -> active(U102(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) mark(U103(X1,X2,X3)) -> active(U103(mark(X1),X2,X3)) mark(isNat(X)) -> active(isNat(X)) mark(U104(X1,X2,X3)) -> active(U104(mark(X1),X2,X3)) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(x(X1,X2)) -> active(x(mark(X1),mark(X2))) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(U13(X1,X2,X3)) -> active(U13(mark(X1),X2,X3)) mark(U14(X1,X2,X3)) -> active(U14(mark(X1),X2,X3)) mark(U15(X1,X2)) -> active(U15(mark(X1),X2)) mark(U16(X)) -> active(U16(mark(X))) mark(U21(X1,X2)) -> active(U21(mark(X1),X2)) mark(U22(X1,X2)) -> active(U22(mark(X1),X2)) mark(U23(X)) -> active(U23(mark(X))) mark(U31(X1,X2,X3)) -> active(U31(mark(X1),X2,X3)) mark(U32(X1,X2,X3)) -> active(U32(mark(X1),X2,X3)) mark(U33(X1,X2,X3)) -> active(U33(mark(X1),X2,X3)) mark(U34(X1,X2,X3)) -> active(U34(mark(X1),X2,X3)) mark(U35(X1,X2)) -> active(U35(mark(X1),X2)) mark(U36(X)) -> active(U36(mark(X))) mark(U41(X1,X2)) -> active(U41(mark(X1),X2)) mark(U42(X)) -> active(U42(mark(X))) mark(U51(X)) -> active(U51(mark(X))) mark(U61(X1,X2)) -> active(U61(mark(X1),X2)) mark(U62(X)) -> active(U62(mark(X))) mark(U71(X1,X2)) -> active(U71(mark(X1),X2)) mark(U72(X1,X2)) -> active(U72(mark(X1),X2)) mark(U81(X1,X2,X3)) -> active(U81(mark(X1),X2,X3)) mark(U82(X1,X2,X3)) -> active(U82(mark(X1),X2,X3)) mark(U83(X1,X2,X3)) -> active(U83(mark(X1),X2,X3)) mark(U84(X1,X2,X3)) -> active(U84(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(U91(X1,X2)) -> active(U91(mark(X1),X2)) mark(U92(X)) -> active(U92(mark(X))) mark(0()) -> active(0()) U101(mark(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,mark(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,mark(X3)) -> U101(X1,X2,X3) U101(active(X1),X2,X3) -> U101(X1,X2,X3) U101(X1,active(X2),X3) -> U101(X1,X2,X3) U101(X1,X2,active(X3)) -> U101(X1,X2,X3) U102(mark(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,mark(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,mark(X3)) -> U102(X1,X2,X3) U102(active(X1),X2,X3) -> U102(X1,X2,X3) U102(X1,active(X2),X3) -> U102(X1,X2,X3) U102(X1,X2,active(X3)) -> U102(X1,X2,X3) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) U103(mark(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,mark(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,mark(X3)) -> U103(X1,X2,X3) U103(active(X1),X2,X3) -> U103(X1,X2,X3) U103(X1,active(X2),X3) -> U103(X1,X2,X3) U103(X1,X2,active(X3)) -> U103(X1,X2,X3) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) U104(mark(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,mark(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,mark(X3)) -> U104(X1,X2,X3) U104(active(X1),X2,X3) -> U104(X1,X2,X3) U104(X1,active(X2),X3) -> U104(X1,X2,X3) U104(X1,X2,active(X3)) -> U104(X1,X2,X3) plus(mark(X1),X2) -> plus(X1,X2) plus(X1,mark(X2)) -> plus(X1,X2) plus(active(X1),X2) -> plus(X1,X2) plus(X1,active(X2)) -> plus(X1,X2) x(mark(X1),X2) -> x(X1,X2) x(X1,mark(X2)) -> x(X1,X2) x(active(X1),X2) -> x(X1,X2) x(X1,active(X2)) -> x(X1,X2) U11(mark(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,mark(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,mark(X3)) -> U11(X1,X2,X3) U11(active(X1),X2,X3) -> U11(X1,X2,X3) U11(X1,active(X2),X3) -> U11(X1,X2,X3) U11(X1,X2,active(X3)) -> U11(X1,X2,X3) U12(mark(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,mark(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,mark(X3)) -> U12(X1,X2,X3) U12(active(X1),X2,X3) -> U12(X1,X2,X3) U12(X1,active(X2),X3) -> U12(X1,X2,X3) U12(X1,X2,active(X3)) -> U12(X1,X2,X3) U13(mark(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,mark(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,mark(X3)) -> U13(X1,X2,X3) U13(active(X1),X2,X3) -> U13(X1,X2,X3) U13(X1,active(X2),X3) -> U13(X1,X2,X3) U13(X1,X2,active(X3)) -> U13(X1,X2,X3) U14(mark(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,mark(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,mark(X3)) -> U14(X1,X2,X3) U14(active(X1),X2,X3) -> U14(X1,X2,X3) U14(X1,active(X2),X3) -> U14(X1,X2,X3) U14(X1,X2,active(X3)) -> U14(X1,X2,X3) U15(mark(X1),X2) -> U15(X1,X2) U15(X1,mark(X2)) -> U15(X1,X2) U15(active(X1),X2) -> U15(X1,X2) U15(X1,active(X2)) -> U15(X1,X2) U16(mark(X)) -> U16(X) U16(active(X)) -> U16(X) U21(mark(X1),X2) -> U21(X1,X2) U21(X1,mark(X2)) -> U21(X1,X2) U21(active(X1),X2) -> U21(X1,X2) U21(X1,active(X2)) -> U21(X1,X2) U22(mark(X1),X2) -> U22(X1,X2) U22(X1,mark(X2)) -> U22(X1,X2) U22(active(X1),X2) -> U22(X1,X2) U22(X1,active(X2)) -> U22(X1,X2) U23(mark(X)) -> U23(X) U23(active(X)) -> U23(X) U31(mark(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,mark(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,mark(X3)) -> U31(X1,X2,X3) U31(active(X1),X2,X3) -> U31(X1,X2,X3) U31(X1,active(X2),X3) -> U31(X1,X2,X3) U31(X1,X2,active(X3)) -> U31(X1,X2,X3) U32(mark(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,mark(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,mark(X3)) -> U32(X1,X2,X3) U32(active(X1),X2,X3) -> U32(X1,X2,X3) U32(X1,active(X2),X3) -> U32(X1,X2,X3) U32(X1,X2,active(X3)) -> U32(X1,X2,X3) U33(mark(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,mark(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,mark(X3)) -> U33(X1,X2,X3) U33(active(X1),X2,X3) -> U33(X1,X2,X3) U33(X1,active(X2),X3) -> U33(X1,X2,X3) U33(X1,X2,active(X3)) -> U33(X1,X2,X3) U34(mark(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,mark(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,mark(X3)) -> U34(X1,X2,X3) U34(active(X1),X2,X3) -> U34(X1,X2,X3) U34(X1,active(X2),X3) -> U34(X1,X2,X3) U34(X1,X2,active(X3)) -> U34(X1,X2,X3) U35(mark(X1),X2) -> U35(X1,X2) U35(X1,mark(X2)) -> U35(X1,X2) U35(active(X1),X2) -> U35(X1,X2) U35(X1,active(X2)) -> U35(X1,X2) U36(mark(X)) -> U36(X) U36(active(X)) -> U36(X) U41(mark(X1),X2) -> U41(X1,X2) U41(X1,mark(X2)) -> U41(X1,X2) U41(active(X1),X2) -> U41(X1,X2) U41(X1,active(X2)) -> U41(X1,X2) U42(mark(X)) -> U42(X) U42(active(X)) -> U42(X) U51(mark(X)) -> U51(X) U51(active(X)) -> U51(X) U61(mark(X1),X2) -> U61(X1,X2) U61(X1,mark(X2)) -> U61(X1,X2) U61(active(X1),X2) -> U61(X1,X2) U61(X1,active(X2)) -> U61(X1,X2) U62(mark(X)) -> U62(X) U62(active(X)) -> U62(X) U71(mark(X1),X2) -> U71(X1,X2) U71(X1,mark(X2)) -> U71(X1,X2) U71(active(X1),X2) -> U71(X1,X2) U71(X1,active(X2)) -> U71(X1,X2) U72(mark(X1),X2) -> U72(X1,X2) U72(X1,mark(X2)) -> U72(X1,X2) U72(active(X1),X2) -> U72(X1,X2) U72(X1,active(X2)) -> U72(X1,X2) U81(mark(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,mark(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,mark(X3)) -> U81(X1,X2,X3) U81(active(X1),X2,X3) -> U81(X1,X2,X3) U81(X1,active(X2),X3) -> U81(X1,X2,X3) U81(X1,X2,active(X3)) -> U81(X1,X2,X3) U82(mark(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,mark(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,mark(X3)) -> U82(X1,X2,X3) U82(active(X1),X2,X3) -> U82(X1,X2,X3) U82(X1,active(X2),X3) -> U82(X1,X2,X3) U82(X1,X2,active(X3)) -> U82(X1,X2,X3) U83(mark(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,mark(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,mark(X3)) -> U83(X1,X2,X3) U83(active(X1),X2,X3) -> U83(X1,X2,X3) U83(X1,active(X2),X3) -> U83(X1,X2,X3) U83(X1,X2,active(X3)) -> U83(X1,X2,X3) U84(mark(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,mark(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,mark(X3)) -> U84(X1,X2,X3) U84(active(X1),X2,X3) -> U84(X1,X2,X3) U84(X1,active(X2),X3) -> U84(X1,X2,X3) U84(X1,X2,active(X3)) -> U84(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) U91(mark(X1),X2) -> U91(X1,X2) U91(X1,mark(X2)) -> U91(X1,X2) U91(active(X1),X2) -> U91(X1,X2) U91(X1,active(X2)) -> U91(X1,X2) U92(mark(X)) -> U92(X) U92(active(X)) -> U92(X) Open