- : unit = ()
h : heuristic = <heuristic>
- : unit = ()
APPLY CRITERIA (Marked dependency pairs)

TRS termination of:
[1] 0(#) -> #
[2] +(#,x) -> x
[3] +(x,#) -> x
[4] +(0(x),0(y)) -> 0(+(x,y))
[5] +(0(x),1(y)) -> 1(+(x,y))
[6] +(1(x),0(y)) -> 1(+(x,y))
[7] +(0(x),j(y)) -> j(+(x,y))
[8] +(j(x),0(y)) -> j(+(x,y))
[9] +(1(x),1(y)) -> j(+(+(x,y),1(#)))
[10] +(j(x),j(y)) -> 1(+(+(x,y),j(#)))
[11] +(1(x),j(y)) -> 0(+(x,y))
[12] +(j(x),1(y)) -> 0(+(x,y))
[13] +(+(x,y),z) -> +(x,+(y,z))
[14] opp(#) -> #
[15] opp(0(x)) -> 0(opp(x))
[16] opp(1(x)) -> j(opp(x))
[17] opp(j(x)) -> 1(opp(x))
[18] -(x,y) -> +(x,opp(y))
[19]  *(#,x) -> #
[20]  *(0(x),y) -> 0( *(x,y))
[21]  *(1(x),y) -> +(0( *(x,y)),y)
[22]  *(j(x),y) -> -(0( *(x,y)),y)
[23]  *( *(x,y),z) ->  *(x, *(y,z))
[24]  *(+(x,y),z) -> +( *(x,z), *(y,z))
[25]  *(x,+(y,z)) -> +( *(x,y), *(x,z))


Sub problem: 
guided: 

DP termination of:
<Marked_+(0(x),0(y)) , Marked_0(+(x,y))>
<Marked_+(0(x),0(y)) , Marked_+(x,y)>
<Marked_+(0(x),1(y)) , Marked_+(x,y)>
<Marked_+(1(x),0(y)) , Marked_+(x,y)>
<Marked_+(0(x),j(y)) , Marked_+(x,y)>
<Marked_+(j(x),0(y)) , Marked_+(x,y)>
<Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
<Marked_+(1(x),1(y)) , Marked_+(x,y)>
<Marked_+(j(x),j(y)) , Marked_+(+(x,y),j(#))>
<Marked_+(j(x),j(y)) , Marked_+(x,y)>
<Marked_+(1(x),j(y)) , Marked_0(+(x,y))>
<Marked_+(1(x),j(y)) , Marked_+(x,y)>
<Marked_+(j(x),1(y)) , Marked_0(+(x,y))>
<Marked_+(j(x),1(y)) , Marked_+(x,y)>
<Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
<Marked_+(+(x,y),z) , Marked_+(y,z)>
<Marked_opp(0(x)) , Marked_0(opp(x))>
<Marked_opp(0(x)) , Marked_opp(x)>
<Marked_opp(1(x)) , Marked_opp(x)>
<Marked_opp(j(x)) , Marked_opp(x)>
<Marked_-(x,y) , Marked_+(x,opp(y))>
<Marked_-(x,y) , Marked_opp(y)>
<Marked_*(0(x),y) , Marked_0( *(x,y))>
<Marked_*(0(x),y) , Marked_*(x,y)>
<Marked_*(1(x),y) , Marked_+(0( *(x,y)),y)>
<Marked_*(1(x),y) , Marked_0( *(x,y))>
<Marked_*(1(x),y) , Marked_*(x,y)>
<Marked_*(j(x),y) , Marked_-(0( *(x,y)),y)>
<Marked_*(j(x),y) , Marked_0( *(x,y))>
<Marked_*(j(x),y) , Marked_*(x,y)>
<Marked_*( *(x,y),z) , Marked_*(x, *(y,z))>
<Marked_*( *(x,y),z) , Marked_*(y,z)>
<Marked_*(+(x,y),z) , Marked_+( *(x,z), *(y,z))>
<Marked_*(+(x,y),z) , Marked_*(x,z)>
<Marked_*(+(x,y),z) , Marked_*(y,z)>
<Marked_*(x,+(y,z)) , Marked_+( *(x,y), *(x,z))>
<Marked_*(x,+(y,z)) , Marked_*(x,y)>
<Marked_*(x,+(y,z)) , Marked_*(x,z)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 3 components:

{  <Marked_*(x,+(y,z)) , Marked_*(x,z)> 
      --> <Marked_*(x,+(y,z)) , Marked_*(x,z)>
  <Marked_*(x,+(y,z)) , Marked_*(x,z)> --> <Marked_*(x,+(y,z)) , Marked_*(x,y)>
  <Marked_*(x,+(y,z)) , Marked_*(x,z)> --> <Marked_*(+(x,y),z) , Marked_*(y,z)>
  <Marked_*(x,+(y,z)) , Marked_*(x,z)> --> <Marked_*(+(x,y),z) , Marked_*(x,z)>
  <Marked_*(x,+(y,z)) , Marked_*(x,z)> 
     --> <Marked_*( *(x,y),z) , Marked_*(y,z)>
  <Marked_*(x,+(y,z)) , Marked_*(x,z)> 
     --> <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))>
  <Marked_*(x,+(y,z)) , Marked_*(x,z)> --> <Marked_*(j(x),y) , Marked_*(x,y)>
  <Marked_*(x,+(y,z)) , Marked_*(x,z)> --> <Marked_*(1(x),y) , Marked_*(x,y)>
  <Marked_*(x,+(y,z)) , Marked_*(x,z)> --> <Marked_*(0(x),y) , Marked_*(x,y)>
  <Marked_*(x,+(y,z)) , Marked_*(x,y)> --> <Marked_*(x,+(y,z)) , Marked_*(x,z)>
  <Marked_*(x,+(y,z)) , Marked_*(x,y)> --> <Marked_*(x,+(y,z)) , Marked_*(x,y)>
  <Marked_*(x,+(y,z)) , Marked_*(x,y)> --> <Marked_*(+(x,y),z) , Marked_*(y,z)>
  <Marked_*(x,+(y,z)) , Marked_*(x,y)> --> <Marked_*(+(x,y),z) , Marked_*(x,z)>
  <Marked_*(x,+(y,z)) , Marked_*(x,y)> 
     --> <Marked_*( *(x,y),z) , Marked_*(y,z)>
  <Marked_*(x,+(y,z)) , Marked_*(x,y)> 
     --> <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))>
  <Marked_*(x,+(y,z)) , Marked_*(x,y)> --> <Marked_*(j(x),y) , Marked_*(x,y)>
  <Marked_*(x,+(y,z)) , Marked_*(x,y)> --> <Marked_*(1(x),y) , Marked_*(x,y)>
  <Marked_*(x,+(y,z)) , Marked_*(x,y)> --> <Marked_*(0(x),y) , Marked_*(x,y)>
  <Marked_*(+(x,y),z) , Marked_*(y,z)> --> <Marked_*(x,+(y,z)) , Marked_*(x,z)>
  <Marked_*(+(x,y),z) , Marked_*(y,z)> --> <Marked_*(x,+(y,z)) , Marked_*(x,y)>
  <Marked_*(+(x,y),z) , Marked_*(y,z)> --> <Marked_*(+(x,y),z) , Marked_*(y,z)>
  <Marked_*(+(x,y),z) , Marked_*(y,z)> --> <Marked_*(+(x,y),z) , Marked_*(x,z)>
  <Marked_*(+(x,y),z) , Marked_*(y,z)> 
     --> <Marked_*( *(x,y),z) , Marked_*(y,z)>
  <Marked_*(+(x,y),z) , Marked_*(y,z)> 
     --> <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))>
  <Marked_*(+(x,y),z) , Marked_*(y,z)> --> <Marked_*(j(x),y) , Marked_*(x,y)>
  <Marked_*(+(x,y),z) , Marked_*(y,z)> --> <Marked_*(1(x),y) , Marked_*(x,y)>
  <Marked_*(+(x,y),z) , Marked_*(y,z)> --> <Marked_*(0(x),y) , Marked_*(x,y)>
  <Marked_*(+(x,y),z) , Marked_*(x,z)> --> <Marked_*(x,+(y,z)) , Marked_*(x,z)>
  <Marked_*(+(x,y),z) , Marked_*(x,z)> --> <Marked_*(x,+(y,z)) , Marked_*(x,y)>
  <Marked_*(+(x,y),z) , Marked_*(x,z)> --> <Marked_*(+(x,y),z) , Marked_*(y,z)>
  <Marked_*(+(x,y),z) , Marked_*(x,z)> --> <Marked_*(+(x,y),z) , Marked_*(x,z)>
  <Marked_*(+(x,y),z) , Marked_*(x,z)> 
     --> <Marked_*( *(x,y),z) , Marked_*(y,z)>
  <Marked_*(+(x,y),z) , Marked_*(x,z)> 
     --> <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))>
  <Marked_*(+(x,y),z) , Marked_*(x,z)> --> <Marked_*(j(x),y) , Marked_*(x,y)>
  <Marked_*(+(x,y),z) , Marked_*(x,z)> --> <Marked_*(1(x),y) , Marked_*(x,y)>
  <Marked_*(+(x,y),z) , Marked_*(x,z)> --> <Marked_*(0(x),y) , Marked_*(x,y)>
  <Marked_*( *(x,y),z) , Marked_*(y,z)> 
     --> <Marked_*(x,+(y,z)) , Marked_*(x,z)>
  <Marked_*( *(x,y),z) , Marked_*(y,z)> 
     --> <Marked_*(x,+(y,z)) , Marked_*(x,y)>
  <Marked_*( *(x,y),z) , Marked_*(y,z)> 
     --> <Marked_*(+(x,y),z) , Marked_*(y,z)>
  <Marked_*( *(x,y),z) , Marked_*(y,z)> 
     --> <Marked_*(+(x,y),z) , Marked_*(x,z)>
  <Marked_*( *(x,y),z) , Marked_*(y,z)> 
     --> <Marked_*( *(x,y),z) , Marked_*(y,z)>
  <Marked_*( *(x,y),z) , Marked_*(y,z)> 
     --> <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))>
  <Marked_*( *(x,y),z) , Marked_*(y,z)> --> <Marked_*(j(x),y) , Marked_*(x,y)>
  <Marked_*( *(x,y),z) , Marked_*(y,z)> --> <Marked_*(1(x),y) , Marked_*(x,y)>
  <Marked_*( *(x,y),z) , Marked_*(y,z)> --> <Marked_*(0(x),y) , Marked_*(x,y)>
  <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))> 
     --> <Marked_*(x,+(y,z)) , Marked_*(x,z)>
  <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))> 
     --> <Marked_*(x,+(y,z)) , Marked_*(x,y)>
  <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))> 
     --> <Marked_*(+(x,y),z) , Marked_*(y,z)>
  <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))> 
     --> <Marked_*(+(x,y),z) , Marked_*(x,z)>
  <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))> 
     --> <Marked_*( *(x,y),z) , Marked_*(y,z)>
  <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))> 
     --> <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))>
  <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))> 
     --> <Marked_*(j(x),y) , Marked_*(x,y)>
  <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))> 
     --> <Marked_*(1(x),y) , Marked_*(x,y)>
  <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))> 
     --> <Marked_*(0(x),y) , Marked_*(x,y)>
  <Marked_*(j(x),y) , Marked_*(x,y)> --> <Marked_*(x,+(y,z)) , Marked_*(x,z)>
  <Marked_*(j(x),y) , Marked_*(x,y)> --> <Marked_*(x,+(y,z)) , Marked_*(x,y)>
  <Marked_*(j(x),y) , Marked_*(x,y)> --> <Marked_*(+(x,y),z) , Marked_*(y,z)>
  <Marked_*(j(x),y) , Marked_*(x,y)> --> <Marked_*(+(x,y),z) , Marked_*(x,z)>
  <Marked_*(j(x),y) , Marked_*(x,y)> --> <Marked_*( *(x,y),z) , Marked_*(y,z)>
  <Marked_*(j(x),y) , Marked_*(x,y)> 
     --> <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))>
  <Marked_*(j(x),y) , Marked_*(x,y)> --> <Marked_*(j(x),y) , Marked_*(x,y)>
  <Marked_*(j(x),y) , Marked_*(x,y)> --> <Marked_*(1(x),y) , Marked_*(x,y)>
  <Marked_*(j(x),y) , Marked_*(x,y)> --> <Marked_*(0(x),y) , Marked_*(x,y)>
  <Marked_*(1(x),y) , Marked_*(x,y)> --> <Marked_*(x,+(y,z)) , Marked_*(x,z)>
  <Marked_*(1(x),y) , Marked_*(x,y)> --> <Marked_*(x,+(y,z)) , Marked_*(x,y)>
  <Marked_*(1(x),y) , Marked_*(x,y)> --> <Marked_*(+(x,y),z) , Marked_*(y,z)>
  <Marked_*(1(x),y) , Marked_*(x,y)> --> <Marked_*(+(x,y),z) , Marked_*(x,z)>
  <Marked_*(1(x),y) , Marked_*(x,y)> --> <Marked_*( *(x,y),z) , Marked_*(y,z)>
  <Marked_*(1(x),y) , Marked_*(x,y)> 
     --> <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))>
  <Marked_*(1(x),y) , Marked_*(x,y)> --> <Marked_*(j(x),y) , Marked_*(x,y)>
  <Marked_*(1(x),y) , Marked_*(x,y)> --> <Marked_*(1(x),y) , Marked_*(x,y)>
  <Marked_*(1(x),y) , Marked_*(x,y)> --> <Marked_*(0(x),y) , Marked_*(x,y)>
  <Marked_*(0(x),y) , Marked_*(x,y)> --> <Marked_*(x,+(y,z)) , Marked_*(x,z)>
  <Marked_*(0(x),y) , Marked_*(x,y)> --> <Marked_*(x,+(y,z)) , Marked_*(x,y)>
  <Marked_*(0(x),y) , Marked_*(x,y)> --> <Marked_*(+(x,y),z) , Marked_*(y,z)>
  <Marked_*(0(x),y) , Marked_*(x,y)> --> <Marked_*(+(x,y),z) , Marked_*(x,z)>
  <Marked_*(0(x),y) , Marked_*(x,y)> --> <Marked_*( *(x,y),z) , Marked_*(y,z)>
  <Marked_*(0(x),y) , Marked_*(x,y)> 
     --> <Marked_*( *(x,y),z) , Marked_*(x, *(y,z))>
  <Marked_*(0(x),y) , Marked_*(x,y)> --> <Marked_*(j(x),y) , Marked_*(x,y)>
  <Marked_*(0(x),y) , Marked_*(x,y)> --> <Marked_*(1(x),y) , Marked_*(x,y)>
  <Marked_*(0(x),y) , Marked_*(x,y)> --> <Marked_*(0(x),y) , Marked_*(x,y)>
}

{  <Marked_opp(j(x)) , Marked_opp(x)> --> <Marked_opp(j(x)) , Marked_opp(x)>
  <Marked_opp(j(x)) , Marked_opp(x)> --> <Marked_opp(1(x)) , Marked_opp(x)>
  <Marked_opp(j(x)) , Marked_opp(x)> --> <Marked_opp(0(x)) , Marked_opp(x)>
  <Marked_opp(1(x)) , Marked_opp(x)> --> <Marked_opp(j(x)) , Marked_opp(x)>
  <Marked_opp(1(x)) , Marked_opp(x)> --> <Marked_opp(1(x)) , Marked_opp(x)>
  <Marked_opp(1(x)) , Marked_opp(x)> --> <Marked_opp(0(x)) , Marked_opp(x)>
  <Marked_opp(0(x)) , Marked_opp(x)> --> <Marked_opp(j(x)) , Marked_opp(x)>
  <Marked_opp(0(x)) , Marked_opp(x)> --> <Marked_opp(1(x)) , Marked_opp(x)>
  <Marked_opp(0(x)) , Marked_opp(x)> --> <Marked_opp(0(x)) , Marked_opp(x)>
}

{  <Marked_+(+(x,y),z) , Marked_+(y,z)> 
      --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(+(x,y),z) , Marked_+(y,z)> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(+(x,y),z) , Marked_+(y,z)> 
     --> <Marked_+(j(x),1(y)) , Marked_+(x,y)>
  <Marked_+(+(x,y),z) , Marked_+(y,z)> 
     --> <Marked_+(1(x),j(y)) , Marked_+(x,y)>
  <Marked_+(+(x,y),z) , Marked_+(y,z)> 
     --> <Marked_+(j(x),j(y)) , Marked_+(x,y)>
  <Marked_+(+(x,y),z) , Marked_+(y,z)> 
     --> <Marked_+(j(x),j(y)) , Marked_+(+(x,y),j(#))>
  <Marked_+(+(x,y),z) , Marked_+(y,z)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(x,y)>
  <Marked_+(+(x,y),z) , Marked_+(y,z)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
  <Marked_+(+(x,y),z) , Marked_+(y,z)> 
     --> <Marked_+(j(x),0(y)) , Marked_+(x,y)>
  <Marked_+(+(x,y),z) , Marked_+(y,z)> 
     --> <Marked_+(0(x),j(y)) , Marked_+(x,y)>
  <Marked_+(+(x,y),z) , Marked_+(y,z)> 
     --> <Marked_+(1(x),0(y)) , Marked_+(x,y)>
  <Marked_+(+(x,y),z) , Marked_+(y,z)> 
     --> <Marked_+(0(x),1(y)) , Marked_+(x,y)>
  <Marked_+(+(x,y),z) , Marked_+(y,z)> 
     --> <Marked_+(0(x),0(y)) , Marked_+(x,y)>
  <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))> 
     --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))> 
     --> <Marked_+(j(x),1(y)) , Marked_+(x,y)>
  <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))> 
     --> <Marked_+(1(x),j(y)) , Marked_+(x,y)>
  <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))> 
     --> <Marked_+(j(x),j(y)) , Marked_+(x,y)>
  <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))> 
     --> <Marked_+(j(x),j(y)) , Marked_+(+(x,y),j(#))>
  <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))> 
     --> <Marked_+(1(x),1(y)) , Marked_+(x,y)>
  <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))> 
     --> <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
  <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))> 
     --> <Marked_+(j(x),0(y)) , Marked_+(x,y)>
  <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))> 
     --> <Marked_+(0(x),j(y)) , Marked_+(x,y)>
  <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))> 
     --> <Marked_+(1(x),0(y)) , Marked_+(x,y)>
  <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))> 
     --> <Marked_+(0(x),1(y)) , Marked_+(x,y)>
  <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))> 
     --> <Marked_+(0(x),0(y)) , Marked_+(x,y)>
  <Marked_+(j(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(j(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(j(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),1(y)) , Marked_+(x,y)>
  <Marked_+(j(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),j(y)) , Marked_+(x,y)>
  <Marked_+(j(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),j(y)) , Marked_+(x,y)>
  <Marked_+(j(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),j(y)) , Marked_+(+(x,y),j(#))>
  <Marked_+(j(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(x,y)>
  <Marked_+(j(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
  <Marked_+(j(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),0(y)) , Marked_+(x,y)>
  <Marked_+(j(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),j(y)) , Marked_+(x,y)>
  <Marked_+(j(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),0(y)) , Marked_+(x,y)>
  <Marked_+(j(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),1(y)) , Marked_+(x,y)>
  <Marked_+(j(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),0(y)) , Marked_+(x,y)>
  <Marked_+(1(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(1(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(1(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),1(y)) , Marked_+(x,y)>
  <Marked_+(1(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),j(y)) , Marked_+(x,y)>
  <Marked_+(1(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),j(y)) , Marked_+(x,y)>
  <Marked_+(1(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),j(y)) , Marked_+(+(x,y),j(#))>
  <Marked_+(1(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(x,y)>
  <Marked_+(1(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
  <Marked_+(1(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),0(y)) , Marked_+(x,y)>
  <Marked_+(1(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),j(y)) , Marked_+(x,y)>
  <Marked_+(1(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),0(y)) , Marked_+(x,y)>
  <Marked_+(1(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),1(y)) , Marked_+(x,y)>
  <Marked_+(1(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),0(y)) , Marked_+(x,y)>
  <Marked_+(j(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(j(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(j(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),1(y)) , Marked_+(x,y)>
  <Marked_+(j(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),j(y)) , Marked_+(x,y)>
  <Marked_+(j(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),j(y)) , Marked_+(x,y)>
  <Marked_+(j(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),j(y)) , Marked_+(+(x,y),j(#))>
  <Marked_+(j(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(x,y)>
  <Marked_+(j(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
  <Marked_+(j(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),0(y)) , Marked_+(x,y)>
  <Marked_+(j(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),j(y)) , Marked_+(x,y)>
  <Marked_+(j(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),0(y)) , Marked_+(x,y)>
  <Marked_+(j(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),1(y)) , Marked_+(x,y)>
  <Marked_+(j(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),0(y)) , Marked_+(x,y)>
  <Marked_+(j(x),j(y)) , Marked_+(+(x,y),j(#))> 
     --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(j(x),j(y)) , Marked_+(+(x,y),j(#))> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(j(x),j(y)) , Marked_+(+(x,y),j(#))> 
     --> <Marked_+(1(x),j(y)) , Marked_+(x,y)>
  <Marked_+(j(x),j(y)) , Marked_+(+(x,y),j(#))> 
     --> <Marked_+(j(x),j(y)) , Marked_+(x,y)>
  <Marked_+(j(x),j(y)) , Marked_+(+(x,y),j(#))> 
     --> <Marked_+(j(x),j(y)) , Marked_+(+(x,y),j(#))>
  <Marked_+(j(x),j(y)) , Marked_+(+(x,y),j(#))> 
     --> <Marked_+(0(x),j(y)) , Marked_+(x,y)>
  <Marked_+(1(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(1(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(1(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),1(y)) , Marked_+(x,y)>
  <Marked_+(1(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),j(y)) , Marked_+(x,y)>
  <Marked_+(1(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),j(y)) , Marked_+(x,y)>
  <Marked_+(1(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),j(y)) , Marked_+(+(x,y),j(#))>
  <Marked_+(1(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(x,y)>
  <Marked_+(1(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
  <Marked_+(1(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),0(y)) , Marked_+(x,y)>
  <Marked_+(1(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),j(y)) , Marked_+(x,y)>
  <Marked_+(1(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),0(y)) , Marked_+(x,y)>
  <Marked_+(1(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),1(y)) , Marked_+(x,y)>
  <Marked_+(1(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),0(y)) , Marked_+(x,y)>
  <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))> 
     --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))> 
     --> <Marked_+(j(x),1(y)) , Marked_+(x,y)>
  <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))> 
     --> <Marked_+(1(x),1(y)) , Marked_+(x,y)>
  <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))> 
     --> <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
  <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))> 
     --> <Marked_+(0(x),1(y)) , Marked_+(x,y)>
  <Marked_+(j(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(j(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(j(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),1(y)) , Marked_+(x,y)>
  <Marked_+(j(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),j(y)) , Marked_+(x,y)>
  <Marked_+(j(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),j(y)) , Marked_+(x,y)>
  <Marked_+(j(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),j(y)) , Marked_+(+(x,y),j(#))>
  <Marked_+(j(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(x,y)>
  <Marked_+(j(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
  <Marked_+(j(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),0(y)) , Marked_+(x,y)>
  <Marked_+(j(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),j(y)) , Marked_+(x,y)>
  <Marked_+(j(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),0(y)) , Marked_+(x,y)>
  <Marked_+(j(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),1(y)) , Marked_+(x,y)>
  <Marked_+(j(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),0(y)) , Marked_+(x,y)>
  <Marked_+(0(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(0(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(0(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),1(y)) , Marked_+(x,y)>
  <Marked_+(0(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),j(y)) , Marked_+(x,y)>
  <Marked_+(0(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),j(y)) , Marked_+(x,y)>
  <Marked_+(0(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),j(y)) , Marked_+(+(x,y),j(#))>
  <Marked_+(0(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(x,y)>
  <Marked_+(0(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
  <Marked_+(0(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),0(y)) , Marked_+(x,y)>
  <Marked_+(0(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),j(y)) , Marked_+(x,y)>
  <Marked_+(0(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),0(y)) , Marked_+(x,y)>
  <Marked_+(0(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),1(y)) , Marked_+(x,y)>
  <Marked_+(0(x),j(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),0(y)) , Marked_+(x,y)>
  <Marked_+(1(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(1(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(1(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),1(y)) , Marked_+(x,y)>
  <Marked_+(1(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),j(y)) , Marked_+(x,y)>
  <Marked_+(1(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),j(y)) , Marked_+(x,y)>
  <Marked_+(1(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),j(y)) , Marked_+(+(x,y),j(#))>
  <Marked_+(1(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(x,y)>
  <Marked_+(1(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
  <Marked_+(1(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),0(y)) , Marked_+(x,y)>
  <Marked_+(1(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),j(y)) , Marked_+(x,y)>
  <Marked_+(1(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),0(y)) , Marked_+(x,y)>
  <Marked_+(1(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),1(y)) , Marked_+(x,y)>
  <Marked_+(1(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),0(y)) , Marked_+(x,y)>
  <Marked_+(0(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(0(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(0(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),1(y)) , Marked_+(x,y)>
  <Marked_+(0(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),j(y)) , Marked_+(x,y)>
  <Marked_+(0(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),j(y)) , Marked_+(x,y)>
  <Marked_+(0(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),j(y)) , Marked_+(+(x,y),j(#))>
  <Marked_+(0(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(x,y)>
  <Marked_+(0(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
  <Marked_+(0(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),0(y)) , Marked_+(x,y)>
  <Marked_+(0(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),j(y)) , Marked_+(x,y)>
  <Marked_+(0(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),0(y)) , Marked_+(x,y)>
  <Marked_+(0(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),1(y)) , Marked_+(x,y)>
  <Marked_+(0(x),1(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),0(y)) , Marked_+(x,y)>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),1(y)) , Marked_+(x,y)>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),j(y)) , Marked_+(x,y)>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),j(y)) , Marked_+(x,y)>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),j(y)) , Marked_+(+(x,y),j(#))>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(x,y)>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(j(x),0(y)) , Marked_+(x,y)>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),j(y)) , Marked_+(x,y)>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(1(x),0(y)) , Marked_+(x,y)>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),1(y)) , Marked_+(x,y)>
  <Marked_+(0(x),0(y)) , Marked_+(x,y)> 
     --> <Marked_+(0(x),0(y)) , Marked_+(x,y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  0(#) >= # ;
  +(#,x) >= x ;
  +(0(x),0(y)) >= 0(+(x,y)) ;
  +(0(x),1(y)) >= 1(+(x,y)) ;
  +(0(x),j(y)) >= j(+(x,y)) ;
  +(+(x,y),z) >= +(x,+(y,z)) ;
  +(1(x),0(y)) >= 1(+(x,y)) ;
  +(1(x),1(y)) >= j(+(+(x,y),1(#))) ;
  +(1(x),j(y)) >= 0(+(x,y)) ;
  +(j(x),0(y)) >= j(+(x,y)) ;
  +(j(x),1(y)) >= 0(+(x,y)) ;
  +(j(x),j(y)) >= 1(+(+(x,y),j(#))) ;
  +(x,#) >= x ;
  opp(#) >= # ;
  opp(0(x)) >= 0(opp(x)) ;
  opp(1(x)) >= j(opp(x)) ;
  opp(j(x)) >= 1(opp(x)) ;
  -(x,y) >= +(x,opp(y)) ;
   *(#,x) >= # ;
   *(0(x),y) >= 0( *(x,y)) ;
   *(+(x,y),z) >= +( *(x,z), *(y,z)) ;
   *(1(x),y) >= +(0( *(x,y)),y) ;
   *(j(x),y) >= -(0( *(x,y)),y) ;
   *( *(x,y),z) >=  *(x, *(y,z)) ;
   *(x,+(y,z)) >= +( *(x,y), *(x,z)) ;
  Marked_*(0(x),y) >= Marked_*(x,y) ;
  Marked_*(+(x,y),z) >= Marked_*(y,z) ;
  Marked_*(+(x,y),z) >= Marked_*(x,z) ;
  Marked_*(1(x),y) >= Marked_*(x,y) ;
  Marked_*(j(x),y) >= Marked_*(x,y) ;
  Marked_*( *(x,y),z) >= Marked_*(y,z) ;
  Marked_*( *(x,y),z) >= Marked_*(x, *(y,z)) ;
  Marked_*(x,+(y,z)) >= Marked_*(x,z) ;
  Marked_*(x,+(y,z)) >= Marked_*(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_*(0(x),y) > Marked_*(x,y) ;
 }
{
  Marked_*(+(x,y),z) > Marked_*(y,z) ;
 }
{
  Marked_*(+(x,y),z) > Marked_*(x,z) ;
 }
{
  Marked_*(1(x),y) > Marked_*(x,y) ;
 }
{
  Marked_*(j(x),y) > Marked_*(x,y) ;
 }
{
  Marked_*( *(x,y),z) > Marked_*(y,z) ;
 }
{
  Marked_*( *(x,y),z) > Marked_*(x, *(y,z)) ;
 }
{
  Marked_*(x,+(y,z)) > Marked_*(x,z) ;
 }
{
  Marked_*(x,+(y,z)) > Marked_*(x,y) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 1.977583 seconds (real time)
Cime Exit Status: 0