How to concatenate strings in inline assembly

Question

Im trying to concatenate two given strings using inline assembly in C using the gcc compiler and intel syntax. I have been successfull to print the first string but not the second and I can't figure out why. Here is my code:

#include <stdio.h>

void my_strcat(char *str1, const char *str2) {
    __asm__ volatile (
            "mov %[str1], %%rax\n\t"    // Move str1 pointer to rax register
            "mov %[str2], %%rbx\n\t"    // Move str2 pointer to rbx register
            "1:\n\t"                     // Loop label
            "cmpb $0, (%%rax)\n\t"       // Compare the value at rax with 0
            "jne 2f\n\t"                  // Jump to 2 if not equal (i.e., not end of str1)
            "lodsb\n\t"                  // Load a byte from str2 to al and increment str2 pointer
            "stosb\n\t"                  // Store a byte from al to str1 and increment str1 pointer
            "testb %%al, %%al\n\t"       // Test if al is 0
            "jne 1b\n\t"                  // Jump to 1 if not equal (i.e., not end of str2)
            "2:\n\t"                      // Loop label
            "dec %%rax\n\t"              // Decrement rax to undo the null terminator
            "movb $0, (%%rax)\n\t"       // Null terminate the concatenated string
            : [str1] "+r" (str1), [str2] "+r" (str2)   // Input/output operands
    :                                      // No input-only operands
    : "rax", "rbx", "memory"                // Clobbered registers and memory
    );
}

int main() {
    char str1[20] = "Hello";
    char str2[20] = " world!";
    my_strcat(str1, str2);
    printf("Concatenated string: %s\n", str1);
    return 0;
}

Any help would be appreciated !