as soon as the wave hits the bottom, increment is set to -1.
So the while loop will never end.

The increment was only for increasing/decreasing time.
Your x-value should be incremented by a fixed value.

And the check for  hitting the bottom/top should not be inside of you while-loop, it's enough to check once in draw().

1. float time = 0;
   float increment = .5;
   
   void setup() {
     size(550, 550);
     // smooth();
     background(100, 200, 50);
   }
   
   void draw() {
     background(#B72C2C);
     stroke(#F7EBEB);
   
     float x = 0;
     float y =  0;
   
     while (x< width) {
       stroke(255);
       y =  10 +10*sin(x/20 )*time;
       point(x, y );
       x = x + 0.1;
     }
   
     if (time >= (height-10)/10 || time <0) {
       increment  *= -1;
     }
   
     time = time + increment;
   
     println(y);
     println(time);
   }