Task: Zeckendorf arithmetic
Go: package main

import (
    "fmt"
    "strings"
)

var (
    dig  = [3]string{"00", "01", "10"}
    dig1 = [3]string{"", "1", "10"}
)

type Zeckendorf struct{ dVal, dLen int }

func NewZeck(x string) *Zeckendorf {
    z := new(Zeckendorf)
    if x == "" {
        x = "0"
    }
    q := 1
    i := len(x) - 1
    z.dLen = i / 2
    for ; i >= 0; i-- {
        z.dVal += int(x[i]-'0') * q
        q *= 2
    }
    return z
}

func (z *Zeckendorf) a(i int) {
    for ; ; i++ {
        if z.dLen < i {
            z.dLen = i
        }
        j := (z.dVal >> uint(i*2)) & 3
        switch j {
        case 0, 1:
            return
        case 2:
            if ((z.dVal >> (uint(i+1) * 2)) & 1) != 1 {
                return
            }
            z.dVal += 1 << uint(i*2+1)
            return
        case 3:
            z.dVal &= ^(3 << uint(i*2))
            z.b((i + 1) * 2)
        }
    }
}

func (z *Zeckendorf) b(pos int) {
    if pos == 0 {
        z.Inc()
        return
    }
    if ((z.dVal >> uint(pos)) & 1) == 0 {
        z.dVal += 1 << uint(pos)
        z.a(pos / 2)
        if pos > 1 {
            z.a(pos/2 - 1)
        }
    } else {
        z.dVal &= ^(1 << uint(pos))
        z.b(pos + 1)
        temp := 1
        if pos > 1 {
            temp = 2
        }
        z.b(pos - temp)
    }
}

func (z *Zeckendorf) c(pos int) {
    if ((z.dVal >> uint(pos)) & 1) == 1 {
        z.dVal &= ^(1 << uint(pos))
        return
    }
    z.c(pos + 1)
    if pos > 0 {
        z.b(pos - 1)
    } else {
        z.Inc()
    }
}

func (z *Zeckendorf) Inc() {
    z.dVal++
    z.a(0)
}

func (z1 *Zeckendorf) PlusAssign(z2 *Zeckendorf) {
    for gn := 0; gn < (z2.dLen+1)*2; gn++ {
        if ((z2.dVal >> uint(gn)) & 1) == 1 {
            z1.b(gn)
        }
    }
}

func (z1 *Zeckendorf) MinusAssign(z2 *Zeckendorf) {
    for gn := 0; gn < (z2.dLen+1)*2; gn++ {
        if ((z2.dVal >> uint(gn)) & 1) == 1 {
            z1.c(gn)
        }
    }

    for z1.dLen > 0 && ((z1.dVal>>uint(z1.dLen*2))&3) == 0 {
        z1.dLen--
    }
}

func (z1 *Zeckendorf) TimesAssign(z2 *Zeckendorf) {
    na := z2.Copy()
    nb := z2.Copy()
    nr := new(Zeckendorf)
    for i := 0; i <= (z1.dLen+1)*2; i++ {
        if ((z1.dVal >> uint(i)) & 1) > 0 {
            nr.PlusAssign(nb)
        }
        nt := nb.Copy()
        nb.PlusAssign(na)
        na = nt.Copy()
    }
    z1.dVal = nr.dVal
    z1.dLen = nr.dLen
}

func (z *Zeckendorf) Copy() *Zeckendorf {
    return &Zeckendorf{z.dVal, z.dLen}
}

func (z1 *Zeckendorf) Compare(z2 *Zeckendorf) int {
    switch {
    case z1.dVal < z2.dVal:
        return -1
    case z1.dVal > z2.dVal:
        return 1
    default:
        return 0
    }
}

func (z *Zeckendorf) String() string {
    if z.dVal == 0 {
        return "0"
    }
    var sb strings.Builder
    sb.WriteString(dig1[(z.dVal>>uint(z.dLen*2))&3])
    for i := z.dLen - 1; i >= 0; i-- {
        sb.WriteString(dig[(z.dVal>>uint(i*2))&3])
    }
    return sb.String()
}

func main() {
    fmt.Println("Addition:")
    g := NewZeck("10")
    g.PlusAssign(NewZeck("10"))
    fmt.Println(g)
    g.PlusAssign(NewZeck("10"))
    fmt.Println(g)
    g.PlusAssign(NewZeck("1001"))
    fmt.Println(g)
    g.PlusAssign(NewZeck("1000"))
    fmt.Println(g)
    g.PlusAssign(NewZeck("10101"))
    fmt.Println(g)

    fmt.Println("\nSubtraction:")
    g = NewZeck("1000")
    g.MinusAssign(NewZeck("101"))
    fmt.Println(g)
    g = NewZeck("10101010")
    g.MinusAssign(NewZeck("1010101"))
    fmt.Println(g)

    fmt.Println("\nMultiplication:")
    g = NewZeck("1001")
    g.TimesAssign(NewZeck("101"))
    fmt.Println(g)
    g = NewZeck("101010")
    g.PlusAssign(NewZeck("101"))
    fmt.Println(g)
}

Java: import java.util.List;

public class Zeckendorf implements Comparable<Zeckendorf> {
    private static List<String> dig = List.of("00", "01", "10");
    private static List<String> dig1 = List.of("", "1", "10");

    private String x;
    private int dVal = 0;
    private int dLen = 0;

    public Zeckendorf() {
        this("0");
    }

    public Zeckendorf(String x) {
        this.x = x;

        int q = 1;
        int i = x.length() - 1;
        dLen = i / 2;
        while (i >= 0) {
            dVal += (x.charAt(i) - '0') * q;
            q *= 2;
            i--;
        }
    }

    private void a(int n) {
        int i = n;
        while (true) {
            if (dLen < i) dLen = i;
            int j = (dVal >> (i * 2)) & 3;
            switch (j) {
                case 0:
                case 1:
                    return;
                case 2:
                    if (((dVal >> ((i + 1) * 2)) & 1) != 1) return;
                    dVal += 1 << (i * 2 + 1);
                    return;
                case 3:
                    int temp = 3 << (i * 2);
                    temp ^= -1;
                    dVal = dVal & temp;
                    b((i + 1) * 2);
                    break;
            }
            i++;
        }
    }

    private void b(int pos) {
        if (pos == 0) {
            Zeckendorf thiz = this;
            thiz.inc();
            return;
        }
        if (((dVal >> pos) & 1) == 0) {
            dVal += 1 << pos;
            a(pos / 2);
            if (pos > 1) a(pos / 2 - 1);
        } else {
            int temp = 1 << pos;
            temp ^= -1;
            dVal = dVal & temp;
            b(pos + 1);
            b(pos - (pos > 1 ? 2 : 1));
        }
    }

    private void c(int pos) {
        if (((dVal >> pos) & 1) == 1) {
            int temp = 1 << pos;
            temp ^= -1;
            dVal = dVal & temp;
            return;
        }
        c(pos + 1);
        if (pos > 0) {
            b(pos - 1);
        } else {
            Zeckendorf thiz = this;
            thiz.inc();
        }
    }

    public Zeckendorf inc() {
        dVal++;
        a(0);
        return this;
    }

    public void plusAssign(Zeckendorf other) {
        for (int gn = 0; gn < (other.dLen + 1) * 2; gn++) {
            if (((other.dVal >> gn) & 1) == 1) {
                b(gn);
            }
        }
    }

    public void minusAssign(Zeckendorf other) {
        for (int gn = 0; gn < (other.dLen + 1) * 2; gn++) {
            if (((other.dVal >> gn) & 1) == 1) {
                c(gn);
            }
        }
        while ((((dVal >> dLen * 2) & 3) == 0) || (dLen == 0)) {
            dLen--;
        }
    }

    public void timesAssign(Zeckendorf other) {
        Zeckendorf na = other.copy();
        Zeckendorf nb = other.copy();
        Zeckendorf nt;
        Zeckendorf nr = new Zeckendorf();
        for (int i = 0; i < (dLen + 1) * 2; i++) {
            if (((dVal >> i) & 1) > 0) {
                nr.plusAssign(nb);
            }
            nt = nb.copy();
            nb.plusAssign(na);
            na = nt.copy();
        }
        dVal = nr.dVal;
        dLen = nr.dLen;
    }

    private Zeckendorf copy() {
        Zeckendorf z = new Zeckendorf();
        z.dVal = dVal;
        z.dLen = dLen;
        return z;
    }

    @Override
    public int compareTo(Zeckendorf other) {
        return ((Integer) dVal).compareTo(other.dVal);
    }

    @Override
    public String toString() {
        if (dVal == 0) {
            return "0";
        }

        int idx = (dVal >> (dLen * 2)) & 3;
        StringBuilder stringBuilder = new StringBuilder(dig1.get(idx));
        for (int i = dLen - 1; i >= 0; i--) {
            idx = (dVal >> (i * 2)) & 3;
            stringBuilder.append(dig.get(idx));
        }
        return stringBuilder.toString();
    }

    public static void main(String[] args) {
        System.out.println("Addition:");
        Zeckendorf g = new Zeckendorf("10");
        g.plusAssign(new Zeckendorf("10"));
        System.out.println(g);
        g.plusAssign(new Zeckendorf("10"));
        System.out.println(g);
        g.plusAssign(new Zeckendorf("1001"));
        System.out.println(g);
        g.plusAssign(new Zeckendorf("1000"));
        System.out.println(g);
        g.plusAssign(new Zeckendorf("10101"));
        System.out.println(g);

        System.out.println("\nSubtraction:");
        g = new Zeckendorf("1000");
        g.minusAssign(new Zeckendorf("101"));
        System.out.println(g);
        g = new Zeckendorf("10101010");
        g.minusAssign(new Zeckendorf("1010101"));
        System.out.println(g);

        System.out.println("\nMultiplication:");
        g = new Zeckendorf("1001");
        g.timesAssign(new Zeckendorf("101"));
        System.out.println(g);
        g = new Zeckendorf("101010");
        g.plusAssign(new Zeckendorf("101"));
        System.out.println(g);
    }
}