Where are the null-terminated strings when converting from C to assembly?

I made two programs to output two strings, one in assembly and the other one in C. This is the program in assembly:

.section .data
string1:
.ascii "Hola\0"
string2:
.ascii "Adios\0"

.section .text
.globl _start
_start:

pushl $string1
call puts
addl $4, %esp

pushl $string2
call puts
addl $4, %esp

movl $1, %eax
movl $0, %ebx
int $0x80

I build the program with

as test.s -o test.o
ld -dynamic-linker /lib/ld-linux.so.2 -o test test.o -lc

And the output is as expected

Hola
Adios

This is the C program:

#include <stdio.h>
int main(void)
{
    puts("Hola");
    puts("Adios");
    return 0;
}

And I get the expected output, but when converting this C program to assembly with gcc -S (OS is Debian 32 bit) the output assembly source code does not include the null character in both strings, as you can see here:

    .file   "testc.c"
    .section    .rodata
.LC0:
    .string "Hola"
.LC1:
    .string "Adios"
    .text
    .globl  main
    .type   main, @function
main:
.LFB0:
    .cfi_startproc
    leal    4(%esp), %ecx
    .cfi_def_cfa 1, 0
    andl    $-16, %esp
    pushl   -4(%ecx)
    pushl   %ebp
    .cfi_escape 0x10,0x5,0x2,0x75,0
    movl    %esp, %ebp
    pushl   %ecx
    .cfi_escape 0xf,0x3,0x75,0x7c,0x6
    subl    $4, %esp
    subl    $12, %esp
    pushl   $.LC0
    call    puts
    addl    $16, %esp
    subl    $12, %esp
    pushl   $.LC1
    call    puts
    addl    $16, %esp
    movl    $0, %eax
    movl    -4(%ebp), %ecx
    .cfi_def_cfa 1, 0
    leave
    .cfi_restore 5
    leal    -4(%ecx), %esp
    .cfi_def_cfa 4, 4
    ret
    .cfi_endproc
.LFE0:
    .size   main, .-main
    .ident  "GCC: (Debian 4.9.2-10) 4.9.2"
    .section    .note.GNU-stack,"",@progbits

My two questions are:

1) Why the gcc generated assembly code does not append the null character at the end of both strings? I thought that C did this automatically.

2) If I skip the null characters in my hand made assembly code i get this output:

HolaAdios
Adios

I understand why I get the "HolaAdios" part at the first line, but why does the program end successfully after the "Adios" part if it is not null-terminated?