mdp

const int initY = 40;
const int initX = 80;

const int maxY = 580;
const int minX = 10;
const int maxX = 144;


formula Gate_1 = (((42<x & x<50) | (74<x & x<82))   & 164<y & y<172);
formula Gate_2 = (((72<x & x<80) | (104<x & x<112)) & 256<y & y<264);
formula Gate_3 = (((80<x & x<88) | (112<x & x<120)) & 349<y & y<357);
formula Gate_4 = (((54<x & x<62) | (88<x & x<96))   & 442<y & y<450);
formula Gate_5 = (((80<x & x<88) | (112<x & x<120)) & 530<y & y<538);


formula Tree_1 = ((x>=124 & x<=142) & (y>=190 & y<=200));
formula Tree_2 = ((x>=32 & x<=49)   & (y>=284 & y<=295));
formula Tree_3 = ((x>=30 & x<=49)   & (y>=317 & y<=327));
formula Tree_4 = ((x>=12 & x<=30)   & (y>=408 & y<=418));
formula Tree_5 = ((x>=129 & x<=146) & (y>=468 & y<=480));
formula Tree_6 = ((x>=140 & x<=152) & (y>=496 & y<=510));

formula Hit_Tree = Tree_1 | Tree_2 | Tree_3 | Tree_4 | Tree_5 | Tree_6;
formula Hit_Gate = Gate_1 | Gate_2 | Gate_3 | Gate_4 | Gate_5;


global move : [0..3];

module skier
  ski_position : [1..8] ;
  done : bool ;


  [left]  !Safe & !Unsafe & move=0 & ski_position>1 -> (ski_position'=ski_position-1) & (move'=1) & (done'=(Hit_Tree|Hit_Gate));
  [right] !Safe & !Unsafe & move=0 & ski_position<8 -> (ski_position'=ski_position+1) & (move'=1) & (done'=(Hit_Tree|Hit_Gate));
  [noop]  !Safe & !Unsafe & move=0 -> (move'=1) & (done'=(Hit_Tree|Hit_Gate));


  [done] Safe | Unsafe | done -> true;
endmodule

module updateY
  y : [initY..maxY] ;

  velocity: [0..16];
  standstill : [0..8] ;
  [update_y] move=1 & standstill>=5 -> (y'=y) & (move'=2);
  [update_y] move=1 & standstill<5  -> (y'=min(maxY,y+velocity)) & (move'=2);

  [update_y] move=2 & (ski_position=1 | ski_position = 8) & standstill>=5 -> (standstill'=min(8,standstill+1)) & (move'=3);
  [update_y] move=2 & (ski_position=1 | ski_position = 8) & standstill<5  -> (velocity'=max(0,velocity-4)) &(move'=3);
  [update_y] move=2 & (ski_position=2 | ski_position = 7) -> (velocity'=max(0 ,velocity-2)) & (standstill'=0) & (move'=3);
  [update_y] move=2 & (ski_position=3 | ski_position = 6) -> (velocity'=min(8,velocity+2)) & (standstill'=0) & (move'=3);
  [update_y] move=2 & (ski_position=4 | ski_position = 5) -> (velocity'=min(8,velocity+4)) & (standstill'=0) & (move'=3);
endmodule

module updateX
  x : [minX..maxX] ;

  [update_x]  move=3 & standstill>=8                                       -> (move'=0);
  [update_x]  move=3 & standstill<8 & (ski_position=4 | ski_position=5)    -> (move'=0);

  [update_x]  move=3 & standstill<8 & (ski_position=3)  -> 0.4: (x'=max(minX,x-0)) & (move'=0) + 0.6: (x'=max(minX,x-1)) & (move'=0);
  [update_x]  move=3 & standstill<8 & (ski_position=6)  -> 0.4: (x'=min(maxX,x+0)) & (move'=0) + 0.6: (x'=min(maxX,x+1)) & (move'=0);

  [update_x]  move=3 & standstill<8 & (ski_position=2)  -> 0.3: (x'=max(minX,x-0)) & (move'=0) + 0.7: (x'=max(minX,x-1)) & (move'=0);
  [update_x]  move=3 & standstill<8 & (ski_position=7)  -> 0.3: (x'=min(maxX,x+0)) & (move'=0) + 0.7: (x'=min(maxX,x+1)) & (move'=0);

  [update_x]  move=3 & standstill<8 & (ski_position=1)  -> 0.2: (x'=max(minX,x-0)) & (move'=0) + 0.8: (x'=max(minX,x-1)) & (move'=0);
  [update_x]  move=3 & standstill<8 & (ski_position=8)  -> 0.2: (x'=min(maxX,x+0)) & (move'=0) + 0.8: (x'=min(maxX,x+1)) & (move'=0);
endmodule

rewards
  [left]  !done & (Hit_Tree) : -100;
  [right] !done & (Hit_Tree) : -100;
  [noop]  !done & (Hit_Tree) : -100;
  [left]  !done & (Hit_Gate) : -100;
  [right] !done & (Hit_Gate) : -100;
  [noop]  !done & (Hit_Gate) : -100;
  [done]  Unsafe : -100;
endrewards