MAYBE MAYBE TRS: { mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3)), mark(isNatKind(X)) -> active(isNatKind(X)), mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)), mark(tt()) -> active(tt()), 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(U22(X1, X2)) -> active(U22(mark(X1), X2)), mark(U21(X1, X2)) -> active(U21(mark(X1), X2)), mark(U23(X)) -> active(U23(mark(X))), mark(U32(X)) -> active(U32(mark(X))), mark(U31(X1, X2)) -> active(U31(mark(X1), X2)), mark(U41(X)) -> active(U41(mark(X))), mark(U52(X1, X2)) -> active(U52(mark(X1), X2)), mark(U51(X1, X2)) -> active(U51(mark(X1), X2)), mark(U62(X1, X2, X3)) -> active(U62(mark(X1), X2, X3)), mark(U61(X1, X2, X3)) -> active(U61(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()), U12(X1, X2, mark(X3)) -> U12(X1, X2, X3), U12(X1, X2, active(X3)) -> U12(X1, X2, X3), U12(X1, mark(X2), X3) -> U12(X1, X2, X3), U12(X1, active(X2), X3) -> U12(X1, X2, X3), U12(mark(X1), X2, X3) -> U12(X1, X2, X3), U12(active(X1), X2, X3) -> U12(X1, X2, X3), isNatKind(mark(X)) -> isNatKind(X), isNatKind(active(X)) -> isNatKind(X), active(U12(tt(), V1, V2)) -> mark(U13(isNatKind(V2), V1, V2)), active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))), active(isNatKind(plus(V1, V2))) -> mark(U31(isNatKind(V1), V2)), active(isNatKind(0())) -> mark(tt()), active(U11(tt(), V1, V2)) -> mark(U12(isNatKind(V1), 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(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)), active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2)), active(isNat(0())) -> mark(tt()), active(U16(tt())) -> mark(tt()), active(U22(tt(), V1)) -> mark(U23(isNat(V1))), active(U21(tt(), V1)) -> mark(U22(isNatKind(V1), V1)), active(U23(tt())) -> mark(tt()), active(U32(tt())) -> mark(tt()), active(U31(tt(), V2)) -> mark(U32(isNatKind(V2))), active(U41(tt())) -> mark(tt()), active(U52(tt(), N)) -> mark(N), active(U51(tt(), N)) -> mark(U52(isNatKind(N), N)), active(U62(tt(), M, N)) -> mark(U63(isNat(N), M, N)), active(U61(tt(), M, N)) -> mark(U62(isNatKind(M), M, N)), active(U63(tt(), M, N)) -> mark(U64(isNatKind(N), M, N)), active(U64(tt(), M, N)) -> mark(s(plus(N, M))), active(plus(N, s(M))) -> mark(U61(isNat(M), M, N)), active(plus(N, 0())) -> mark(U51(isNat(N), N)), U11(X1, X2, mark(X3)) -> U11(X1, X2, X3), U11(X1, X2, active(X3)) -> U11(X1, X2, X3), U11(X1, mark(X2), X3) -> U11(X1, X2, X3), U11(X1, active(X2), X3) -> U11(X1, X2, X3), U11(mark(X1), X2, X3) -> U11(X1, X2, X3), U11(active(X1), X2, X3) -> U11(X1, X2, X3), U13(X1, X2, mark(X3)) -> U13(X1, X2, X3), U13(X1, X2, active(X3)) -> U13(X1, X2, X3), U13(X1, mark(X2), X3) -> U13(X1, X2, X3), U13(X1, active(X2), X3) -> U13(X1, X2, X3), U13(mark(X1), X2, X3) -> U13(X1, X2, X3), U13(active(X1), X2, X3) -> U13(X1, X2, X3), U14(X1, X2, mark(X3)) -> U14(X1, X2, X3), U14(X1, X2, active(X3)) -> U14(X1, X2, X3), U14(X1, mark(X2), X3) -> U14(X1, X2, X3), U14(X1, active(X2), X3) -> U14(X1, X2, X3), U14(mark(X1), X2, X3) -> U14(X1, X2, X3), U14(active(X1), X2, X3) -> U14(X1, X2, X3), U15(X1, mark(X2)) -> U15(X1, X2), U15(X1, active(X2)) -> U15(X1, X2), U15(mark(X1), X2) -> U15(X1, X2), U15(active(X1), X2) -> U15(X1, X2), isNat(mark(X)) -> isNat(X), isNat(active(X)) -> isNat(X), U16(mark(X)) -> U16(X), U16(active(X)) -> U16(X), U22(X1, mark(X2)) -> U22(X1, X2), U22(X1, active(X2)) -> U22(X1, X2), U22(mark(X1), X2) -> U22(X1, X2), U22(active(X1), X2) -> U22(X1, X2), U21(X1, mark(X2)) -> U21(X1, X2), U21(X1, active(X2)) -> U21(X1, X2), U21(mark(X1), X2) -> U21(X1, X2), U21(active(X1), X2) -> U21(X1, X2), U23(mark(X)) -> U23(X), U23(active(X)) -> U23(X), U32(mark(X)) -> U32(X), U32(active(X)) -> U32(X), U31(X1, mark(X2)) -> U31(X1, X2), U31(X1, active(X2)) -> U31(X1, X2), U31(mark(X1), X2) -> U31(X1, X2), U31(active(X1), X2) -> U31(X1, X2), U41(mark(X)) -> U41(X), U41(active(X)) -> U41(X), U52(X1, mark(X2)) -> U52(X1, X2), U52(X1, active(X2)) -> U52(X1, X2), U52(mark(X1), X2) -> U52(X1, X2), U52(active(X1), X2) -> U52(X1, X2), U51(X1, mark(X2)) -> U51(X1, X2), U51(X1, active(X2)) -> U51(X1, X2), U51(mark(X1), X2) -> U51(X1, X2), U51(active(X1), X2) -> U51(X1, X2), U62(X1, X2, mark(X3)) -> U62(X1, X2, X3), U62(X1, X2, active(X3)) -> U62(X1, X2, X3), U62(X1, mark(X2), X3) -> U62(X1, X2, X3), U62(X1, active(X2), X3) -> U62(X1, X2, X3), U62(mark(X1), X2, X3) -> U62(X1, X2, X3), U62(active(X1), X2, X3) -> U62(X1, X2, X3), U61(X1, X2, mark(X3)) -> U61(X1, X2, X3), U61(X1, X2, active(X3)) -> U61(X1, X2, X3), U61(X1, mark(X2), X3) -> U61(X1, X2, X3), U61(X1, active(X2), X3) -> U61(X1, X2, X3), U61(mark(X1), X2, X3) -> U61(X1, X2, X3), U61(active(X1), X2, X3) -> U61(X1, X2, X3), U63(X1, X2, mark(X3)) -> U63(X1, X2, X3), U63(X1, X2, active(X3)) -> U63(X1, X2, X3), U63(X1, mark(X2), X3) -> U63(X1, X2, X3), U63(X1, active(X2), X3) -> U63(X1, X2, X3), U63(mark(X1), X2, X3) -> U63(X1, X2, X3), U63(active(X1), X2, X3) -> U63(X1, X2, X3), U64(X1, X2, mark(X3)) -> U64(X1, X2, X3), U64(X1, X2, active(X3)) -> U64(X1, X2, X3), U64(X1, mark(X2), X3) -> U64(X1, X2, X3), U64(X1, active(X2), X3) -> U64(X1, X2, X3), U64(mark(X1), X2, X3) -> U64(X1, X2, X3), U64(active(X1), X2, X3) -> U64(X1, X2, X3), s(mark(X)) -> s(X), s(active(X)) -> s(X), plus(X1, mark(X2)) -> plus(X1, X2), plus(X1, active(X2)) -> plus(X1, X2), plus(mark(X1), X2) -> plus(X1, X2), plus(active(X1), X2) -> plus(X1, X2) } DUP: We consider a duplicating system. Trs: { mark(U12(X1, X2, X3)) -> active(U12(mark(X1), X2, X3)), mark(isNatKind(X)) -> active(isNatKind(X)), mark(U11(X1, X2, X3)) -> active(U11(mark(X1), X2, X3)), mark(tt()) -> active(tt()), 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(U22(X1, X2)) -> active(U22(mark(X1), X2)), mark(U21(X1, X2)) -> active(U21(mark(X1), X2)), mark(U23(X)) -> active(U23(mark(X))), mark(U32(X)) -> active(U32(mark(X))), mark(U31(X1, X2)) -> active(U31(mark(X1), X2)), mark(U41(X)) -> active(U41(mark(X))), mark(U52(X1, X2)) -> active(U52(mark(X1), X2)), mark(U51(X1, X2)) -> active(U51(mark(X1), X2)), mark(U62(X1, X2, X3)) -> active(U62(mark(X1), X2, X3)), mark(U61(X1, X2, X3)) -> active(U61(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()), U12(X1, X2, mark(X3)) -> U12(X1, X2, X3), U12(X1, X2, active(X3)) -> U12(X1, X2, X3), U12(X1, mark(X2), X3) -> U12(X1, X2, X3), U12(X1, active(X2), X3) -> U12(X1, X2, X3), U12(mark(X1), X2, X3) -> U12(X1, X2, X3), U12(active(X1), X2, X3) -> U12(X1, X2, X3), isNatKind(mark(X)) -> isNatKind(X), isNatKind(active(X)) -> isNatKind(X), active(U12(tt(), V1, V2)) -> mark(U13(isNatKind(V2), V1, V2)), active(isNatKind(s(V1))) -> mark(U41(isNatKind(V1))), active(isNatKind(plus(V1, V2))) -> mark(U31(isNatKind(V1), V2)), active(isNatKind(0())) -> mark(tt()), active(U11(tt(), V1, V2)) -> mark(U12(isNatKind(V1), 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(isNat(s(V1))) -> mark(U21(isNatKind(V1), V1)), active(isNat(plus(V1, V2))) -> mark(U11(isNatKind(V1), V1, V2)), active(isNat(0())) -> mark(tt()), active(U16(tt())) -> mark(tt()), active(U22(tt(), V1)) -> mark(U23(isNat(V1))), active(U21(tt(), V1)) -> mark(U22(isNatKind(V1), V1)), active(U23(tt())) -> mark(tt()), active(U32(tt())) -> mark(tt()), active(U31(tt(), V2)) -> mark(U32(isNatKind(V2))), active(U41(tt())) -> mark(tt()), active(U52(tt(), N)) -> mark(N), active(U51(tt(), N)) -> mark(U52(isNatKind(N), N)), active(U62(tt(), M, N)) -> mark(U63(isNat(N), M, N)), active(U61(tt(), M, N)) -> mark(U62(isNatKind(M), M, N)), active(U63(tt(), M, N)) -> mark(U64(isNatKind(N), M, N)), active(U64(tt(), M, N)) -> mark(s(plus(N, M))), active(plus(N, s(M))) -> mark(U61(isNat(M), M, N)), active(plus(N, 0())) -> mark(U51(isNat(N), N)), U11(X1, X2, mark(X3)) -> U11(X1, X2, X3), U11(X1, X2, active(X3)) -> U11(X1, X2, X3), U11(X1, mark(X2), X3) -> U11(X1, X2, X3), U11(X1, active(X2), X3) -> U11(X1, X2, X3), U11(mark(X1), X2, X3) -> U11(X1, X2, X3), U11(active(X1), X2, X3) -> U11(X1, X2, X3), U13(X1, X2, mark(X3)) -> U13(X1, X2, X3), U13(X1, X2, active(X3)) -> U13(X1, X2, X3), U13(X1, mark(X2), X3) -> U13(X1, X2, X3), U13(X1, active(X2), X3) -> U13(X1, X2, X3), U13(mark(X1), X2, X3) -> U13(X1, X2, X3), U13(active(X1), X2, X3) -> U13(X1, X2, X3), U14(X1, X2, mark(X3)) -> U14(X1, X2, X3), U14(X1, X2, active(X3)) -> U14(X1, X2, X3), U14(X1, mark(X2), X3) -> U14(X1, X2, X3), U14(X1, active(X2), X3) -> U14(X1, X2, X3), U14(mark(X1), X2, X3) -> U14(X1, X2, X3), U14(active(X1), X2, X3) -> U14(X1, X2, X3), U15(X1, mark(X2)) -> U15(X1, X2), U15(X1, active(X2)) -> U15(X1, X2), U15(mark(X1), X2) -> U15(X1, X2), U15(active(X1), X2) -> U15(X1, X2), isNat(mark(X)) -> isNat(X), isNat(active(X)) -> isNat(X), U16(mark(X)) -> U16(X), U16(active(X)) -> U16(X), U22(X1, mark(X2)) -> U22(X1, X2), U22(X1, active(X2)) -> U22(X1, X2), U22(mark(X1), X2) -> U22(X1, X2), U22(active(X1), X2) -> U22(X1, X2), U21(X1, mark(X2)) -> U21(X1, X2), U21(X1, active(X2)) -> U21(X1, X2), U21(mark(X1), X2) -> U21(X1, X2), U21(active(X1), X2) -> U21(X1, X2), U23(mark(X)) -> U23(X), U23(active(X)) -> U23(X), U32(mark(X)) -> U32(X), U32(active(X)) -> U32(X), U31(X1, mark(X2)) -> U31(X1, X2), U31(X1, active(X2)) -> U31(X1, X2), U31(mark(X1), X2) -> U31(X1, X2), U31(active(X1), X2) -> U31(X1, X2), U41(mark(X)) -> U41(X), U41(active(X)) -> U41(X), U52(X1, mark(X2)) -> U52(X1, X2), U52(X1, active(X2)) -> U52(X1, X2), U52(mark(X1), X2) -> U52(X1, X2), U52(active(X1), X2) -> U52(X1, X2), U51(X1, mark(X2)) -> U51(X1, X2), U51(X1, active(X2)) -> U51(X1, X2), U51(mark(X1), X2) -> U51(X1, X2), U51(active(X1), X2) -> U51(X1, X2), U62(X1, X2, mark(X3)) -> U62(X1, X2, X3), U62(X1, X2, active(X3)) -> U62(X1, X2, X3), U62(X1, mark(X2), X3) -> U62(X1, X2, X3), U62(X1, active(X2), X3) -> U62(X1, X2, X3), U62(mark(X1), X2, X3) -> U62(X1, X2, X3), U62(active(X1), X2, X3) -> U62(X1, X2, X3), U61(X1, X2, mark(X3)) -> U61(X1, X2, X3), U61(X1, X2, active(X3)) -> U61(X1, X2, X3), U61(X1, mark(X2), X3) -> U61(X1, X2, X3), U61(X1, active(X2), X3) -> U61(X1, X2, X3), U61(mark(X1), X2, X3) -> U61(X1, X2, X3), U61(active(X1), X2, X3) -> U61(X1, X2, X3), U63(X1, X2, mark(X3)) -> U63(X1, X2, X3), U63(X1, X2, active(X3)) -> U63(X1, X2, X3), U63(X1, mark(X2), X3) -> U63(X1, X2, X3), U63(X1, active(X2), X3) -> U63(X1, X2, X3), U63(mark(X1), X2, X3) -> U63(X1, X2, X3), U63(active(X1), X2, X3) -> U63(X1, X2, X3), U64(X1, X2, mark(X3)) -> U64(X1, X2, X3), U64(X1, X2, active(X3)) -> U64(X1, X2, X3), U64(X1, mark(X2), X3) -> U64(X1, X2, X3), U64(X1, active(X2), X3) -> U64(X1, X2, X3), U64(mark(X1), X2, X3) -> U64(X1, X2, X3), U64(active(X1), X2, X3) -> U64(X1, X2, X3), s(mark(X)) -> s(X), s(active(X)) -> s(X), plus(X1, mark(X2)) -> plus(X1, X2), plus(X1, active(X2)) -> plus(X1, X2), plus(mark(X1), X2) -> plus(X1, X2), plus(active(X1), X2) -> plus(X1, X2) } Fail