MAYBE Problem: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Proof: DP Processor: DPs: 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(),V2)) -> isNatKind#(V2) active#(U31(tt(),V2)) -> U32#(isNatKind(V2)) active#(U31(tt(),V2)) -> mark#(U32(isNatKind(V2))) active#(U32(tt())) -> mark#(tt()) active#(U41(tt())) -> mark#(tt()) active#(U51(tt(),N)) -> isNatKind#(N) active#(U51(tt(),N)) -> U52#(isNatKind(N),N) active#(U51(tt(),N)) -> mark#(U52(isNatKind(N),N)) active#(U52(tt(),N)) -> mark#(N) active#(U61(tt(),M,N)) -> isNatKind#(M) active#(U61(tt(),M,N)) -> U62#(isNatKind(M),M,N) active#(U61(tt(),M,N)) -> mark#(U62(isNatKind(M),M,N)) active#(U62(tt(),M,N)) -> isNat#(N) active#(U62(tt(),M,N)) -> U63#(isNat(N),M,N) active#(U62(tt(),M,N)) -> mark#(U63(isNat(N),M,N)) active#(U63(tt(),M,N)) -> isNatKind#(N) active#(U63(tt(),M,N)) -> U64#(isNatKind(N),M,N) active#(U63(tt(),M,N)) -> mark#(U64(isNatKind(N),M,N)) active#(U64(tt(),M,N)) -> plus#(N,M) active#(U64(tt(),M,N)) -> s#(plus(N,M)) active#(U64(tt(),M,N)) -> mark#(s(plus(N,M))) 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#(isNatKind(0())) -> mark#(tt()) active#(isNatKind(plus(V1,V2))) -> isNatKind#(V1) active#(isNatKind(plus(V1,V2))) -> U31#(isNatKind(V1),V2) active#(isNatKind(plus(V1,V2))) -> mark#(U31(isNatKind(V1),V2)) active#(isNatKind(s(V1))) -> isNatKind#(V1) active#(isNatKind(s(V1))) -> U41#(isNatKind(V1)) active#(isNatKind(s(V1))) -> mark#(U41(isNatKind(V1))) active#(plus(N,0())) -> isNat#(N) active#(plus(N,0())) -> U51#(isNat(N),N) active#(plus(N,0())) -> mark#(U51(isNat(N),N)) active#(plus(N,s(M))) -> isNat#(M) active#(plus(N,s(M))) -> U61#(isNat(M),M,N) active#(plus(N,s(M))) -> mark#(U61(isNat(M),M,N)) 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#(tt()) -> active#(tt()) 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#(isNatKind(X)) -> active#(isNatKind(X)) 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#(isNat(X)) -> active#(isNat(X)) 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)) -> mark#(X1) mark#(U31(X1,X2)) -> U31#(mark(X1),X2) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> U32#(mark(X)) mark#(U32(X)) -> active#(U32(mark(X))) mark#(U41(X)) -> mark#(X) mark#(U41(X)) -> U41#(mark(X)) mark#(U41(X)) -> active#(U41(mark(X))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> U51#(mark(X1),X2) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> U52#(mark(X1),X2) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) mark#(U61(X1,X2,X3)) -> mark#(X1) mark#(U61(X1,X2,X3)) -> U61#(mark(X1),X2,X3) mark#(U61(X1,X2,X3)) -> active#(U61(mark(X1),X2,X3)) mark#(U62(X1,X2,X3)) -> mark#(X1) mark#(U62(X1,X2,X3)) -> U62#(mark(X1),X2,X3) mark#(U62(X1,X2,X3)) -> active#(U62(mark(X1),X2,X3)) mark#(U63(X1,X2,X3)) -> mark#(X1) mark#(U63(X1,X2,X3)) -> U63#(mark(X1),X2,X3) mark#(U63(X1,X2,X3)) -> active#(U63(mark(X1),X2,X3)) mark#(U64(X1,X2,X3)) -> mark#(X1) mark#(U64(X1,X2,X3)) -> U64#(mark(X1),X2,X3) mark#(U64(X1,X2,X3)) -> active#(U64(mark(X1),X2,X3)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(mark(X))) 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#(0()) -> active#(0()) 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) isNatKind#(mark(X)) -> isNatKind#(X) isNatKind#(active(X)) -> isNatKind#(X) 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) isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) 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) -> U31#(X1,X2) U31#(X1,mark(X2)) -> U31#(X1,X2) U31#(active(X1),X2) -> U31#(X1,X2) U31#(X1,active(X2)) -> U31#(X1,X2) U32#(mark(X)) -> U32#(X) U32#(active(X)) -> U32#(X) U41#(mark(X)) -> U41#(X) U41#(active(X)) -> U41#(X) U51#(mark(X1),X2) -> U51#(X1,X2) U51#(X1,mark(X2)) -> U51#(X1,X2) U51#(active(X1),X2) -> U51#(X1,X2) U51#(X1,active(X2)) -> U51#(X1,X2) U52#(mark(X1),X2) -> U52#(X1,X2) U52#(X1,mark(X2)) -> U52#(X1,X2) U52#(active(X1),X2) -> U52#(X1,X2) U52#(X1,active(X2)) -> U52#(X1,X2) U61#(mark(X1),X2,X3) -> U61#(X1,X2,X3) U61#(X1,mark(X2),X3) -> U61#(X1,X2,X3) U61#(X1,X2,mark(X3)) -> U61#(X1,X2,X3) U61#(active(X1),X2,X3) -> U61#(X1,X2,X3) U61#(X1,active(X2),X3) -> U61#(X1,X2,X3) U61#(X1,X2,active(X3)) -> U61#(X1,X2,X3) U62#(mark(X1),X2,X3) -> U62#(X1,X2,X3) U62#(X1,mark(X2),X3) -> U62#(X1,X2,X3) U62#(X1,X2,mark(X3)) -> U62#(X1,X2,X3) U62#(active(X1),X2,X3) -> U62#(X1,X2,X3) U62#(X1,active(X2),X3) -> U62#(X1,X2,X3) U62#(X1,X2,active(X3)) -> U62#(X1,X2,X3) U63#(mark(X1),X2,X3) -> U63#(X1,X2,X3) U63#(X1,mark(X2),X3) -> U63#(X1,X2,X3) U63#(X1,X2,mark(X3)) -> U63#(X1,X2,X3) U63#(active(X1),X2,X3) -> U63#(X1,X2,X3) U63#(X1,active(X2),X3) -> U63#(X1,X2,X3) U63#(X1,X2,active(X3)) -> U63#(X1,X2,X3) U64#(mark(X1),X2,X3) -> U64#(X1,X2,X3) U64#(X1,mark(X2),X3) -> U64#(X1,X2,X3) U64#(X1,X2,mark(X3)) -> U64#(X1,X2,X3) U64#(active(X1),X2,X3) -> U64#(X1,X2,X3) U64#(X1,active(X2),X3) -> U64#(X1,X2,X3) U64#(X1,X2,active(X3)) -> U64#(X1,X2,X3) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) 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) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) TDG Processor: DPs: 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(),V2)) -> isNatKind#(V2) active#(U31(tt(),V2)) -> U32#(isNatKind(V2)) active#(U31(tt(),V2)) -> mark#(U32(isNatKind(V2))) active#(U32(tt())) -> mark#(tt()) active#(U41(tt())) -> mark#(tt()) active#(U51(tt(),N)) -> isNatKind#(N) active#(U51(tt(),N)) -> U52#(isNatKind(N),N) active#(U51(tt(),N)) -> mark#(U52(isNatKind(N),N)) active#(U52(tt(),N)) -> mark#(N) active#(U61(tt(),M,N)) -> isNatKind#(M) active#(U61(tt(),M,N)) -> U62#(isNatKind(M),M,N) active#(U61(tt(),M,N)) -> mark#(U62(isNatKind(M),M,N)) active#(U62(tt(),M,N)) -> isNat#(N) active#(U62(tt(),M,N)) -> U63#(isNat(N),M,N) active#(U62(tt(),M,N)) -> mark#(U63(isNat(N),M,N)) active#(U63(tt(),M,N)) -> isNatKind#(N) active#(U63(tt(),M,N)) -> U64#(isNatKind(N),M,N) active#(U63(tt(),M,N)) -> mark#(U64(isNatKind(N),M,N)) active#(U64(tt(),M,N)) -> plus#(N,M) active#(U64(tt(),M,N)) -> s#(plus(N,M)) active#(U64(tt(),M,N)) -> mark#(s(plus(N,M))) 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#(isNatKind(0())) -> mark#(tt()) active#(isNatKind(plus(V1,V2))) -> isNatKind#(V1) active#(isNatKind(plus(V1,V2))) -> U31#(isNatKind(V1),V2) active#(isNatKind(plus(V1,V2))) -> mark#(U31(isNatKind(V1),V2)) active#(isNatKind(s(V1))) -> isNatKind#(V1) active#(isNatKind(s(V1))) -> U41#(isNatKind(V1)) active#(isNatKind(s(V1))) -> mark#(U41(isNatKind(V1))) active#(plus(N,0())) -> isNat#(N) active#(plus(N,0())) -> U51#(isNat(N),N) active#(plus(N,0())) -> mark#(U51(isNat(N),N)) active#(plus(N,s(M))) -> isNat#(M) active#(plus(N,s(M))) -> U61#(isNat(M),M,N) active#(plus(N,s(M))) -> mark#(U61(isNat(M),M,N)) 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#(tt()) -> active#(tt()) 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#(isNatKind(X)) -> active#(isNatKind(X)) 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#(isNat(X)) -> active#(isNat(X)) 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)) -> mark#(X1) mark#(U31(X1,X2)) -> U31#(mark(X1),X2) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> U32#(mark(X)) mark#(U32(X)) -> active#(U32(mark(X))) mark#(U41(X)) -> mark#(X) mark#(U41(X)) -> U41#(mark(X)) mark#(U41(X)) -> active#(U41(mark(X))) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> U51#(mark(X1),X2) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> U52#(mark(X1),X2) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) mark#(U61(X1,X2,X3)) -> mark#(X1) mark#(U61(X1,X2,X3)) -> U61#(mark(X1),X2,X3) mark#(U61(X1,X2,X3)) -> active#(U61(mark(X1),X2,X3)) mark#(U62(X1,X2,X3)) -> mark#(X1) mark#(U62(X1,X2,X3)) -> U62#(mark(X1),X2,X3) mark#(U62(X1,X2,X3)) -> active#(U62(mark(X1),X2,X3)) mark#(U63(X1,X2,X3)) -> mark#(X1) mark#(U63(X1,X2,X3)) -> U63#(mark(X1),X2,X3) mark#(U63(X1,X2,X3)) -> active#(U63(mark(X1),X2,X3)) mark#(U64(X1,X2,X3)) -> mark#(X1) mark#(U64(X1,X2,X3)) -> U64#(mark(X1),X2,X3) mark#(U64(X1,X2,X3)) -> active#(U64(mark(X1),X2,X3)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(mark(X))) 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#(0()) -> active#(0()) 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) isNatKind#(mark(X)) -> isNatKind#(X) isNatKind#(active(X)) -> isNatKind#(X) 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) isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) 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) -> U31#(X1,X2) U31#(X1,mark(X2)) -> U31#(X1,X2) U31#(active(X1),X2) -> U31#(X1,X2) U31#(X1,active(X2)) -> U31#(X1,X2) U32#(mark(X)) -> U32#(X) U32#(active(X)) -> U32#(X) U41#(mark(X)) -> U41#(X) U41#(active(X)) -> U41#(X) U51#(mark(X1),X2) -> U51#(X1,X2) U51#(X1,mark(X2)) -> U51#(X1,X2) U51#(active(X1),X2) -> U51#(X1,X2) U51#(X1,active(X2)) -> U51#(X1,X2) U52#(mark(X1),X2) -> U52#(X1,X2) U52#(X1,mark(X2)) -> U52#(X1,X2) U52#(active(X1),X2) -> U52#(X1,X2) U52#(X1,active(X2)) -> U52#(X1,X2) U61#(mark(X1),X2,X3) -> U61#(X1,X2,X3) U61#(X1,mark(X2),X3) -> U61#(X1,X2,X3) U61#(X1,X2,mark(X3)) -> U61#(X1,X2,X3) U61#(active(X1),X2,X3) -> U61#(X1,X2,X3) U61#(X1,active(X2),X3) -> U61#(X1,X2,X3) U61#(X1,X2,active(X3)) -> U61#(X1,X2,X3) U62#(mark(X1),X2,X3) -> U62#(X1,X2,X3) U62#(X1,mark(X2),X3) -> U62#(X1,X2,X3) U62#(X1,X2,mark(X3)) -> U62#(X1,X2,X3) U62#(active(X1),X2,X3) -> U62#(X1,X2,X3) U62#(X1,active(X2),X3) -> U62#(X1,X2,X3) U62#(X1,X2,active(X3)) -> U62#(X1,X2,X3) U63#(mark(X1),X2,X3) -> U63#(X1,X2,X3) U63#(X1,mark(X2),X3) -> U63#(X1,X2,X3) U63#(X1,X2,mark(X3)) -> U63#(X1,X2,X3) U63#(active(X1),X2,X3) -> U63#(X1,X2,X3) U63#(X1,active(X2),X3) -> U63#(X1,X2,X3) U63#(X1,X2,active(X3)) -> U63#(X1,X2,X3) U64#(mark(X1),X2,X3) -> U64#(X1,X2,X3) U64#(X1,mark(X2),X3) -> U64#(X1,X2,X3) U64#(X1,X2,mark(X3)) -> U64#(X1,X2,X3) U64#(active(X1),X2,X3) -> U64#(X1,X2,X3) U64#(X1,active(X2),X3) -> U64#(X1,X2,X3) U64#(X1,X2,active(X3)) -> U64#(X1,X2,X3) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) 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) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) graph: ... SCC Processor: #sccs: 23 #rules: 161 #arcs: 5227/47961 DPs: mark#(0()) -> active#(0()) active#(U11(tt(),V1,V2)) -> mark#(U12(isNatKind(V1),V1,V2)) mark#(U11(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2,X3)) -> active#(U11(mark(X1),X2,X3)) active#(U12(tt(),V1,V2)) -> mark#(U13(isNatKind(V2),V1,V2)) mark#(tt()) -> active#(tt()) active#(U13(tt(),V1,V2)) -> mark#(U14(isNatKind(V2),V1,V2)) mark#(U12(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#(isNatKind(X)) -> active#(isNatKind(X)) active#(U15(tt(),V2)) -> mark#(U16(isNat(V2))) mark#(U13(X1,X2,X3)) -> mark#(X1) mark#(U13(X1,X2,X3)) -> active#(U13(mark(X1),X2,X3)) active#(U16(tt())) -> mark#(tt()) mark#(U14(X1,X2,X3)) -> mark#(X1) mark#(U14(X1,X2,X3)) -> active#(U14(mark(X1),X2,X3)) active#(U21(tt(),V1)) -> mark#(U22(isNatKind(V1),V1)) mark#(U15(X1,X2)) -> mark#(X1) mark#(U15(X1,X2)) -> active#(U15(mark(X1),X2)) active#(U22(tt(),V1)) -> mark#(U23(isNat(V1))) mark#(isNat(X)) -> active#(isNat(X)) active#(U23(tt())) -> mark#(tt()) mark#(U16(X)) -> mark#(X) mark#(U16(X)) -> active#(U16(mark(X))) active#(U31(tt(),V2)) -> mark#(U32(isNatKind(V2))) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> active#(U21(mark(X1),X2)) active#(U32(tt())) -> mark#(tt()) mark#(U22(X1,X2)) -> mark#(X1) mark#(U22(X1,X2)) -> active#(U22(mark(X1),X2)) active#(U41(tt())) -> mark#(tt()) mark#(U23(X)) -> mark#(X) mark#(U23(X)) -> active#(U23(mark(X))) active#(U51(tt(),N)) -> mark#(U52(isNatKind(N),N)) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> active#(U31(mark(X1),X2)) active#(U52(tt(),N)) -> mark#(N) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> active#(U32(mark(X))) active#(U61(tt(),M,N)) -> mark#(U62(isNatKind(M),M,N)) mark#(U41(X)) -> mark#(X) mark#(U41(X)) -> active#(U41(mark(X))) active#(U62(tt(),M,N)) -> mark#(U63(isNat(N),M,N)) mark#(U51(X1,X2)) -> mark#(X1) mark#(U51(X1,X2)) -> active#(U51(mark(X1),X2)) active#(U63(tt(),M,N)) -> mark#(U64(isNatKind(N),M,N)) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> active#(U52(mark(X1),X2)) active#(U64(tt(),M,N)) -> mark#(s(plus(N,M))) mark#(U61(X1,X2,X3)) -> mark#(X1) mark#(U61(X1,X2,X3)) -> active#(U61(mark(X1),X2,X3)) active#(isNat(0())) -> mark#(tt()) mark#(U62(X1,X2,X3)) -> mark#(X1) mark#(U62(X1,X2,X3)) -> active#(U62(mark(X1),X2,X3)) active#(isNat(plus(V1,V2))) -> mark#(U11(isNatKind(V1),V1,V2)) mark#(U63(X1,X2,X3)) -> mark#(X1) mark#(U63(X1,X2,X3)) -> active#(U63(mark(X1),X2,X3)) active#(isNat(s(V1))) -> mark#(U21(isNatKind(V1),V1)) mark#(U64(X1,X2,X3)) -> mark#(X1) mark#(U64(X1,X2,X3)) -> active#(U64(mark(X1),X2,X3)) active#(isNatKind(0())) -> mark#(tt()) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) active#(isNatKind(plus(V1,V2))) -> mark#(U31(isNatKind(V1),V2)) mark#(plus(X1,X2)) -> mark#(X2) mark#(plus(X1,X2)) -> mark#(X1) mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2))) active#(isNatKind(s(V1))) -> mark#(U41(isNatKind(V1))) active#(plus(N,0())) -> mark#(U51(isNat(N),N)) active#(plus(N,s(M))) -> mark#(U61(isNat(M),M,N)) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Open DPs: 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) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Open DPs: isNatKind#(mark(X)) -> isNatKind#(X) isNatKind#(active(X)) -> isNatKind#(X) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Open DPs: 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) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Open DPs: 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) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Open DPs: isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Open DPs: 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) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Open DPs: U16#(mark(X)) -> U16#(X) U16#(active(X)) -> U16#(X) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Open DPs: 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) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Open DPs: U23#(mark(X)) -> U23#(X) U23#(active(X)) -> U23#(X) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Open DPs: U32#(mark(X)) -> U32#(X) U32#(active(X)) -> U32#(X) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Open DPs: U52#(mark(X1),X2) -> U52#(X1,X2) U52#(X1,mark(X2)) -> U52#(X1,X2) U52#(active(X1),X2) -> U52#(X1,X2) U52#(X1,active(X2)) -> U52#(X1,X2) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Open DPs: U62#(mark(X1),X2,X3) -> U62#(X1,X2,X3) U62#(X1,mark(X2),X3) -> U62#(X1,X2,X3) U62#(X1,X2,mark(X3)) -> U62#(X1,X2,X3) U62#(active(X1),X2,X3) -> U62#(X1,X2,X3) U62#(X1,active(X2),X3) -> U62#(X1,X2,X3) U62#(X1,X2,active(X3)) -> U62#(X1,X2,X3) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Open DPs: U63#(mark(X1),X2,X3) -> U63#(X1,X2,X3) U63#(X1,mark(X2),X3) -> U63#(X1,X2,X3) U63#(X1,X2,mark(X3)) -> U63#(X1,X2,X3) U63#(active(X1),X2,X3) -> U63#(X1,X2,X3) U63#(X1,active(X2),X3) -> U63#(X1,X2,X3) U63#(X1,X2,active(X3)) -> U63#(X1,X2,X3) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Open DPs: U64#(mark(X1),X2,X3) -> U64#(X1,X2,X3) U64#(X1,mark(X2),X3) -> U64#(X1,X2,X3) U64#(X1,X2,mark(X3)) -> U64#(X1,X2,X3) U64#(active(X1),X2,X3) -> U64#(X1,X2,X3) U64#(X1,active(X2),X3) -> U64#(X1,X2,X3) U64#(X1,X2,active(X3)) -> U64#(X1,X2,X3) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Open DPs: 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) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Open DPs: s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Open DPs: 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) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Open DPs: 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) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Open DPs: U31#(mark(X1),X2) -> U31#(X1,X2) U31#(X1,mark(X2)) -> U31#(X1,X2) U31#(active(X1),X2) -> U31#(X1,X2) U31#(X1,active(X2)) -> U31#(X1,X2) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Open DPs: U41#(mark(X)) -> U41#(X) U41#(active(X)) -> U41#(X) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Open DPs: U51#(mark(X1),X2) -> U51#(X1,X2) U51#(X1,mark(X2)) -> U51#(X1,X2) U51#(active(X1),X2) -> U51#(X1,X2) U51#(X1,active(X2)) -> U51#(X1,X2) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Open DPs: U61#(mark(X1),X2,X3) -> U61#(X1,X2,X3) U61#(X1,mark(X2),X3) -> U61#(X1,X2,X3) U61#(X1,X2,mark(X3)) -> U61#(X1,X2,X3) U61#(active(X1),X2,X3) -> U61#(X1,X2,X3) U61#(X1,active(X2),X3) -> U61#(X1,X2,X3) U61#(X1,X2,active(X3)) -> U61#(X1,X2,X3) TRS: active(U11(tt(),V1,V2)) -> mark(U12(isNatKind(V1),V1,V2)) active(U12(tt(),V1,V2)) -> mark(U13(isNatKind(V2),V1,V2)) active(U13(tt(),V1,V2)) -> mark(U14(isNatKind(V2),V1,V2)) active(U14(tt(),V1,V2)) -> mark(U15(isNat(V1),V2)) active(U15(tt(),V2)) -> mark(U16(isNat(V2))) active(U16(tt())) -> mark(tt()) active(U21(tt(),V1)) -> mark(U22(isNatKind(V1),V1)) active(U22(tt(),V1)) -> mark(U23(isNat(V1))) active(U23(tt())) -> mark(tt()) active(U31(tt(),V2)) -> mark(U32(isNatKind(V2))) active(U32(tt())) -> mark(tt()) active(U41(tt())) -> mark(tt()) active(U51(tt(),N)) -> mark(U52(isNatKind(N),N)) active(U52(tt(),N)) -> mark(N) active(U61(tt(),M,N)) -> mark(U62(isNatKind(M),M,N)) active(U62(tt(),M,N)) -> mark(U63(isNat(N),M,N)) active(U63(tt(),M,N)) -> mark(U64(isNatKind(N),M,N)) active(U64(tt(),M,N)) -> mark(s(plus(N,M))) active(isNat(0())) -> mark(tt()) active(isNat(plus(V1,V2))) -> mark(U11(isNatKind(V1),V1,V2)) active(isNat(s(V1))) -> mark(U21(isNatKind(V1),V1)) active(isNatKind(0())) -> mark(tt()) active(isNatKind(plus(V1,V2))) -> mark(U31(isNatKind(V1),V2)) active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))) active(plus(N,0())) -> mark(U51(isNat(N),N)) active(plus(N,s(M))) -> mark(U61(isNat(M),M,N)) mark(U11(X1,X2,X3)) -> active(U11(mark(X1),X2,X3)) mark(tt()) -> active(tt()) mark(U12(X1,X2,X3)) -> active(U12(mark(X1),X2,X3)) mark(isNatKind(X)) -> active(isNatKind(X)) 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(isNat(X)) -> active(isNat(X)) 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)) -> active(U31(mark(X1),X2)) mark(U32(X)) -> active(U32(mark(X))) mark(U41(X)) -> active(U41(mark(X))) mark(U51(X1,X2)) -> active(U51(mark(X1),X2)) mark(U52(X1,X2)) -> active(U52(mark(X1),X2)) mark(U61(X1,X2,X3)) -> active(U61(mark(X1),X2,X3)) mark(U62(X1,X2,X3)) -> active(U62(mark(X1),X2,X3)) mark(U63(X1,X2,X3)) -> active(U63(mark(X1),X2,X3)) mark(U64(X1,X2,X3)) -> active(U64(mark(X1),X2,X3)) mark(s(X)) -> active(s(mark(X))) mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2))) mark(0()) -> active(0()) 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) isNatKind(mark(X)) -> isNatKind(X) isNatKind(active(X)) -> isNatKind(X) 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) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) 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) -> U31(X1,X2) U31(X1,mark(X2)) -> U31(X1,X2) U31(active(X1),X2) -> U31(X1,X2) U31(X1,active(X2)) -> U31(X1,X2) U32(mark(X)) -> U32(X) U32(active(X)) -> U32(X) U41(mark(X)) -> U41(X) U41(active(X)) -> U41(X) U51(mark(X1),X2) -> U51(X1,X2) U51(X1,mark(X2)) -> U51(X1,X2) U51(active(X1),X2) -> U51(X1,X2) U51(X1,active(X2)) -> U51(X1,X2) U52(mark(X1),X2) -> U52(X1,X2) U52(X1,mark(X2)) -> U52(X1,X2) U52(active(X1),X2) -> U52(X1,X2) U52(X1,active(X2)) -> U52(X1,X2) U61(mark(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,mark(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,mark(X3)) -> U61(X1,X2,X3) U61(active(X1),X2,X3) -> U61(X1,X2,X3) U61(X1,active(X2),X3) -> U61(X1,X2,X3) U61(X1,X2,active(X3)) -> U61(X1,X2,X3) U62(mark(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,mark(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,mark(X3)) -> U62(X1,X2,X3) U62(active(X1),X2,X3) -> U62(X1,X2,X3) U62(X1,active(X2),X3) -> U62(X1,X2,X3) U62(X1,X2,active(X3)) -> U62(X1,X2,X3) U63(mark(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,mark(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,mark(X3)) -> U63(X1,X2,X3) U63(active(X1),X2,X3) -> U63(X1,X2,X3) U63(X1,active(X2),X3) -> U63(X1,X2,X3) U63(X1,X2,active(X3)) -> U63(X1,X2,X3) U64(mark(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,mark(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,mark(X3)) -> U64(X1,X2,X3) U64(active(X1),X2,X3) -> U64(X1,X2,X3) U64(X1,active(X2),X3) -> U64(X1,X2,X3) U64(X1,X2,active(X3)) -> U64(X1,X2,X3) s(mark(X)) -> s(X) s(active(X)) -> s(X) 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) Open