- : 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] +(1(x),1(y)) -> 0(+(+(x,y),1(#)))
[8] +(+(x,y),z) -> +(x,+(y,z))
[9] -(#,x) -> #
[10] -(x,#) -> x
[11] -(0(x),0(y)) -> 0(-(x,y))
[12] -(0(x),1(y)) -> 1(-(-(x,y),1(#)))
[13] -(1(x),0(y)) -> 1(-(x,y))
[14] -(1(x),1(y)) -> 0(-(x,y))
[15] not(true) -> false
[16] not(false) -> true
[17] if(true,x,y) -> x
[18] if(false,x,y) -> y
[19] eq(#,#) -> true
[20] eq(#,1(y)) -> false
[21] eq(1(x),#) -> false
[22] eq(#,0(y)) -> eq(#,y)
[23] eq(0(x),#) -> eq(x,#)
[24] eq(1(x),1(y)) -> eq(x,y)
[25] eq(0(x),1(y)) -> false
[26] eq(1(x),0(y)) -> false
[27] eq(0(x),0(y)) -> eq(x,y)
[28] ge(0(x),0(y)) -> ge(x,y)
[29] ge(0(x),1(y)) -> not(ge(y,x))
[30] ge(1(x),0(y)) -> ge(x,y)
[31] ge(1(x),1(y)) -> ge(x,y)
[32] ge(x,#) -> true
[33] ge(#,0(x)) -> ge(#,x)
[34] ge(#,1(x)) -> false
[35] log(x) -> -(log'(x),1(#))
[36] log'(#) -> #
[37] log'(1(x)) -> +(log'(x),1(#))
[38] log'(0(x)) -> if(ge(x,1(#)),+(log'(x),1(#)),#)
[39]  *(#,x) -> #
[40]  *(0(x),y) -> 0( *(x,y))
[41]  *(1(x),y) -> +(0( *(x,y)),y)
[42]  *( *(x,y),z) ->  *(x, *(y,z))
[43]  *(x,+(y,z)) -> +( *(x,y), *(x,z))
[44] app(nil,l) -> l
[45] app(cons(x,l1),l2) -> cons(x,app(l1,l2))
[46] sum(nil) -> 0(#)
[47] sum(cons(x,l)) -> +(x,sum(l))
[48] sum(app(l1,l2)) -> +(sum(l1),sum(l2))
[49] prod(nil) -> 1(#)
[50] prod(cons(x,l)) ->  *(x,prod(l))
[51] prod(app(l1,l2)) ->  *(prod(l1),prod(l2))
[52] mem(x,nil) -> false
[53] mem(x,cons(y,l)) -> if(eq(x,y),true,mem(x,l))
[54] inter(x,nil) -> nil
[55] inter(nil,x) -> nil
[56] inter(app(l1,l2),l3) -> app(inter(l1,l3),inter(l2,l3))
[57] inter(l1,app(l2,l3)) -> app(inter(l1,l2),inter(l1,l3))
[58] inter(cons(x,l1),l2) -> ifinter(mem(x,l2),x,l1,l2)
[59] inter(l1,cons(x,l2)) -> ifinter(mem(x,l1),x,l2,l1)
[60] ifinter(true,x,l1,l2) -> cons(x,inter(l1,l2))
[61] ifinter(false,x,l1,l2) -> inter(l1,l2)


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_+(1(x),1(y)) , Marked_0(+(+(x,y),1(#)))>
<Marked_+(1(x),1(y)) , Marked_+(+(x,y),1(#))>
<Marked_+(1(x),1(y)) , Marked_+(x,y)>
<Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
<Marked_+(+(x,y),z) , Marked_+(y,z)>
<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),1(#))>
<Marked_-(0(x),1(y)) , Marked_-(x,y)>
<Marked_-(1(x),0(y)) , Marked_-(x,y)>
<Marked_-(1(x),1(y)) , Marked_0(-(x,y))>
<Marked_-(1(x),1(y)) , Marked_-(x,y)>
<Marked_eq(#,0(y)) , Marked_eq(#,y)>
<Marked_eq(0(x),#) , Marked_eq(x,#)>
<Marked_eq(1(x),1(y)) , Marked_eq(x,y)>
<Marked_eq(0(x),0(y)) , Marked_eq(x,y)>
<Marked_ge(0(x),0(y)) , Marked_ge(x,y)>
<Marked_ge(0(x),1(y)) , Marked_not(ge(y,x))>
<Marked_ge(0(x),1(y)) , Marked_ge(y,x)>
<Marked_ge(1(x),0(y)) , Marked_ge(x,y)>
<Marked_ge(1(x),1(y)) , Marked_ge(x,y)>
<Marked_ge(#,0(x)) , Marked_ge(#,x)>
<Marked_log(x) , Marked_-(log'(x),1(#))>
<Marked_log(x) , Marked_log'(x)>
<Marked_log'(1(x)) , Marked_+(log'(x),1(#))>
<Marked_log'(1(x)) , Marked_log'(x)>
<Marked_log'(0(x)) , Marked_if(ge(x,1(#)),+(log'(x),1(#)),#)>
<Marked_log'(0(x)) , Marked_ge(x,1(#))>
<Marked_log'(0(x)) , Marked_+(log'(x),1(#))>
<Marked_log'(0(x)) , Marked_log'(x)>
<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_*( *(x,y),z) , Marked_*(x, *(y,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)>
<Marked_app(cons(x,l1),l2) , Marked_app(l1,l2)>
<Marked_sum(nil) , Marked_0(#)>
<Marked_sum(cons(x,l)) , Marked_+(x,sum(l))>
<Marked_sum(cons(x,l)) , Marked_sum(l)>
<Marked_sum(app(l1,l2)) , Marked_+(sum(l1),sum(l2))>
<Marked_sum(app(l1,l2)) , Marked_sum(l1)>
<Marked_sum(app(l1,l2)) , Marked_sum(l2)>
<Marked_prod(cons(x,l)) , Marked_*(x,prod(l))>
<Marked_prod(cons(x,l)) , Marked_prod(l)>
<Marked_prod(app(l1,l2)) , Marked_*(prod(l1),prod(l2))>
<Marked_prod(app(l1,l2)) , Marked_prod(l1)>
<Marked_prod(app(l1,l2)) , Marked_prod(l2)>
<Marked_mem(x,cons(y,l)) , Marked_if(eq(x,y),true,mem(x,l))>
<Marked_mem(x,cons(y,l)) , Marked_eq(x,y)>
<Marked_mem(x,cons(y,l)) , Marked_mem(x,l)>
<Marked_inter(app(l1,l2),l3) , Marked_app(inter(l1,l3),inter(l2,l3))>
<Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)>
<Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)>
<Marked_inter(l1,app(l2,l3)) , Marked_app(inter(l1,l2),inter(l1,l3))>
<Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)>
<Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)>
<Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)>
<Marked_inter(cons(x,l1),l2) , Marked_mem(x,l2)>
<Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)>
<Marked_inter(l1,cons(x,l2)) , Marked_mem(x,l1)>
<Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)>
<Marked_ifinter(false,x,l1,l2) , Marked_inter(l1,l2)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 14 components:

{  <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),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),1(y)) , Marked_-(-(x,y),1(#))>
  <Marked_-(1(x),1(y)) , Marked_-(x,y)> 
     --> <Marked_-(0(x),0(y)) , Marked_-(x,y)>
  <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),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),1(y)) , Marked_-(-(x,y),1(#))>
  <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_-(1(x),1(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),1(y)) , Marked_-(-(x,y),1(#))>
  <Marked_-(0(x),1(y)) , Marked_-(x,y)> 
     --> <Marked_-(0(x),0(y)) , Marked_-(x,y)>
  <Marked_-(0(x),1(y)) , Marked_-(-(x,y),1(#))> 
     --> <Marked_-(1(x),1(y)) , Marked_-(x,y)>
  <Marked_-(0(x),1(y)) , Marked_-(-(x,y),1(#))> 
     --> <Marked_-(0(x),1(y)) , Marked_-(x,y)>
  <Marked_-(0(x),1(y)) , Marked_-(-(x,y),1(#))> 
     --> <Marked_-(0(x),1(y)) , Marked_-(-(x,y),1(#))>
  <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),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),1(y)) , Marked_-(-(x,y),1(#))>
  <Marked_-(0(x),0(y)) , Marked_-(x,y)> 
     --> <Marked_-(0(x),0(y)) , Marked_-(x,y)>
}

{  <Marked_log'(0(x)) , Marked_log'(x)> 
      --> <Marked_log'(0(x)) , Marked_log'(x)>
  <Marked_log'(0(x)) , Marked_log'(x)> --> <Marked_log'(1(x)) , Marked_log'(x)>
  <Marked_log'(1(x)) , Marked_log'(x)> --> <Marked_log'(0(x)) , Marked_log'(x)>
  <Marked_log'(1(x)) , Marked_log'(x)> --> <Marked_log'(1(x)) , Marked_log'(x)>
}

{  <Marked_ge(1(x),1(y)) , Marked_ge(x,y)> 
      --> <Marked_ge(1(x),1(y)) , Marked_ge(x,y)>
  <Marked_ge(1(x),1(y)) , Marked_ge(x,y)> 
     --> <Marked_ge(1(x),0(y)) , Marked_ge(x,y)>
  <Marked_ge(1(x),1(y)) , Marked_ge(x,y)> 
     --> <Marked_ge(0(x),1(y)) , Marked_ge(y,x)>
  <Marked_ge(1(x),1(y)) , Marked_ge(x,y)> 
     --> <Marked_ge(0(x),0(y)) , Marked_ge(x,y)>
  <Marked_ge(1(x),0(y)) , Marked_ge(x,y)> 
     --> <Marked_ge(1(x),1(y)) , Marked_ge(x,y)>
  <Marked_ge(1(x),0(y)) , Marked_ge(x,y)> 
     --> <Marked_ge(1(x),0(y)) , Marked_ge(x,y)>
  <Marked_ge(1(x),0(y)) , Marked_ge(x,y)> 
     --> <Marked_ge(0(x),1(y)) , Marked_ge(y,x)>
  <Marked_ge(1(x),0(y)) , Marked_ge(x,y)> 
     --> <Marked_ge(0(x),0(y)) , Marked_ge(x,y)>
  <Marked_ge(0(x),1(y)) , Marked_ge(y,x)> 
     --> <Marked_ge(1(x),1(y)) , Marked_ge(x,y)>
  <Marked_ge(0(x),1(y)) , Marked_ge(y,x)> 
     --> <Marked_ge(1(x),0(y)) , Marked_ge(x,y)>
  <Marked_ge(0(x),1(y)) , Marked_ge(y,x)> 
     --> <Marked_ge(0(x),1(y)) , Marked_ge(y,x)>
  <Marked_ge(0(x),1(y)) , Marked_ge(y,x)> 
     --> <Marked_ge(0(x),0(y)) , Marked_ge(x,y)>
  <Marked_ge(0(x),0(y)) , Marked_ge(x,y)> 
     --> <Marked_ge(1(x),1(y)) , Marked_ge(x,y)>
  <Marked_ge(0(x),0(y)) , Marked_ge(x,y)> 
     --> <Marked_ge(1(x),0(y)) , Marked_ge(x,y)>
  <Marked_ge(0(x),0(y)) , Marked_ge(x,y)> 
     --> <Marked_ge(0(x),1(y)) , Marked_ge(y,x)>
  <Marked_ge(0(x),0(y)) , Marked_ge(x,y)> 
     --> <Marked_ge(0(x),0(y)) , Marked_ge(x,y)>
}

{  <Marked_ge(#,0(x)) , Marked_ge(#,x)> 
      --> <Marked_ge(#,0(x)) , Marked_ge(#,x)>
}

{  <Marked_sum(app(l1,l2)) , Marked_sum(l2)> 
      --> <Marked_sum(app(l1,l2)) , Marked_sum(l2)>
  <Marked_sum(app(l1,l2)) , Marked_sum(l2)> 
     --> <Marked_sum(app(l1,l2)) , Marked_sum(l1)>
  <Marked_sum(app(l1,l2)) , Marked_sum(l2)> 
     --> <Marked_sum(cons(x,l)) , Marked_sum(l)>
  <Marked_sum(app(l1,l2)) , Marked_sum(l1)> 
     --> <Marked_sum(app(l1,l2)) , Marked_sum(l2)>
  <Marked_sum(app(l1,l2)) , Marked_sum(l1)> 
     --> <Marked_sum(app(l1,l2)) , Marked_sum(l1)>
  <Marked_sum(app(l1,l2)) , Marked_sum(l1)> 
     --> <Marked_sum(cons(x,l)) , Marked_sum(l)>
  <Marked_sum(cons(x,l)) , Marked_sum(l)> 
     --> <Marked_sum(app(l1,l2)) , Marked_sum(l2)>
  <Marked_sum(cons(x,l)) , Marked_sum(l)> 
     --> <Marked_sum(app(l1,l2)) , Marked_sum(l1)>
  <Marked_sum(cons(x,l)) , Marked_sum(l)> 
     --> <Marked_sum(cons(x,l)) , Marked_sum(l)>
}

{  <Marked_prod(app(l1,l2)) , Marked_prod(l2)> 
      --> <Marked_prod(app(l1,l2)) , Marked_prod(l2)>
  <Marked_prod(app(l1,l2)) , Marked_prod(l2)> 
     --> <Marked_prod(app(l1,l2)) , Marked_prod(l1)>
  <Marked_prod(app(l1,l2)) , Marked_prod(l2)> 
     --> <Marked_prod(cons(x,l)) , Marked_prod(l)>
  <Marked_prod(app(l1,l2)) , Marked_prod(l1)> 
     --> <Marked_prod(app(l1,l2)) , Marked_prod(l2)>
  <Marked_prod(app(l1,l2)) , Marked_prod(l1)> 
     --> <Marked_prod(app(l1,l2)) , Marked_prod(l1)>
  <Marked_prod(app(l1,l2)) , Marked_prod(l1)> 
     --> <Marked_prod(cons(x,l)) , Marked_prod(l)>
  <Marked_prod(cons(x,l)) , Marked_prod(l)> 
     --> <Marked_prod(app(l1,l2)) , Marked_prod(l2)>
  <Marked_prod(cons(x,l)) , Marked_prod(l)> 
     --> <Marked_prod(app(l1,l2)) , Marked_prod(l1)>
  <Marked_prod(cons(x,l)) , Marked_prod(l)> 
     --> <Marked_prod(cons(x,l)) , Marked_prod(l)>
}

{  <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, *(y,z))>
  <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, *(y,z))>
  <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, *(y,z))>
  <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, *(y,z))>
  <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_*(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, *(y,z))>
  <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, *(y,z))>
  <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_+(+(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_+(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_+(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_+(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_+(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_+(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_+(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_+(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_+(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_+(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_+(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_+(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_+(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_+(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_+(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_+(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)>
}

{  <Marked_ifinter(false,x,l1,l2) , Marked_inter(l1,l2)> 
      --> <Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)>
  <Marked_ifinter(false,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)>
  <Marked_ifinter(false,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)>
  <Marked_ifinter(false,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)>
  <Marked_ifinter(false,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)>
  <Marked_ifinter(false,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)>
  <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)>
  <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)>
  <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)>
  <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)>
  <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)>
  <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)>
  <Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)> 
     --> <Marked_ifinter(false,x,l1,l2) , Marked_inter(l1,l2)>
  <Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)> 
     --> <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)>
  <Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)> 
     --> <Marked_ifinter(false,x,l1,l2) , Marked_inter(l1,l2)>
  <Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)> 
     --> <Marked_ifinter(true,x,l1,l2) , Marked_inter(l1,l2)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)> 
     --> <Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)> 
     --> <Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)> 
     --> <Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)> 
     --> <Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)>
  <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)> 
     --> <Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)> 
     --> <Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)> 
     --> <Marked_inter(l1,cons(x,l2)) , Marked_ifinter(mem(x,l1),x,l2,l1)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)> 
     --> <Marked_inter(cons(x,l1),l2) , Marked_ifinter(mem(x,l2),x,l1,l2)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l3)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)> 
     --> <Marked_inter(l1,app(l2,l3)) , Marked_inter(l1,l2)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l2,l3)>
  <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)> 
     --> <Marked_inter(app(l1,l2),l3) , Marked_inter(l1,l3)>
}

{  <Marked_app(cons(x,l1),l2) , Marked_app(l1,l2)> 
      --> <Marked_app(cons(x,l1),l2) , Marked_app(l1,l2)>
}

{  <Marked_mem(x,cons(y,l)) , Marked_mem(x,l)> 
      --> <Marked_mem(x,cons(y,l)) , Marked_mem(x,l)>
}

{  <Marked_eq(0(x),0(y)) , Marked_eq(x,y)> 
      --> <Marked_eq(0(x),0(y)) , Marked_eq(x,y)>
  <Marked_eq(0(x),0(y)) , Marked_eq(x,y)> 
     --> <Marked_eq(1(x),1(y)) , Marked_eq(x,y)>
  <Marked_eq(1(x),1(y)) , Marked_eq(x,y)> 
     --> <Marked_eq(0(x),0(y)) , Marked_eq(x,y)>
  <Marked_eq(1(x),1(y)) , Marked_eq(x,y)> 
     --> <Marked_eq(1(x),1(y)) , Marked_eq(x,y)>
}

{  <Marked_eq(#,0(y)) , Marked_eq(#,y)> 
      --> <Marked_eq(#,0(y)) , Marked_eq(#,y)>
}

{  <Marked_eq(0(x),#) , Marked_eq(x,#)> 
      --> <Marked_eq(0(x),#) , Marked_eq(x,#)>
}
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)) ;
  +(+(x,y),z) >= +(x,+(y,z)) ;
  +(1(x),0(y)) >= 1(+(x,y)) ;
  +(1(x),1(y)) >= 0(+(+(x,y),1(#))) ;
  +(x,#) >= x ;
  -(#,x) >= # ;
  -(0(x),0(y)) >= 0(-(x,y)) ;
  -(0(x),1(y)) >= 1(-(-(x,y),1(#))) ;
  -(1(x),0(y)) >= 1(-(x,y)) ;
  -(1(x),1(y)) >= 0(-(x,y)) ;
  -(x,#) >= x ;
  not(false) >= true ;
  not(true) >= false ;
  if(false,x,y) >= y ;
  if(true,x,y) >= x ;
  eq(#,#) >= true ;
  eq(#,0(y)) >= eq(#,y) ;
  eq(#,1(y)) >= false ;
  eq(0(x),#) >= eq(x,#) ;
  eq(0(x),0(y)) >= eq(x,y) ;
  eq(0(x),1(y)) >= false ;
  eq(1(x),#) >= false ;
  eq(1(x),0(y)) >= false ;
  eq(1(x),1(y)) >= eq(x,y) ;
  ge(#,0(x)) >= ge(#,x) ;
  ge(#,1(x)) >= false ;
  ge(0(x),0(y)) >= ge(x,y) ;
  ge(0(x),1(y)) >= not(ge(y,x)) ;
  ge(1(x),0(y)) >= ge(x,y) ;
  ge(1(x),1(y)) >= ge(x,y) ;
  ge(x,#) >= true ;
  log'(#) >= # ;
  log'(0(x)) >= if(ge(x,1(#)),+(log'(x),1(#)),#) ;
  log'(1(x)) >= +(log'(x),1(#)) ;
  log(x) >= -(log'(x),1(#)) ;
   *(#,x) >= # ;
   *(0(x),y) >= 0( *(x,y)) ;
   *(1(x),y) >= +(0( *(x,y)),y) ;
   *( *(x,y),z) >=  *(x, *(y,z)) ;
   *(x,+(y,z)) >= +( *(x,y), *(x,z)) ;
  app(nil,l) >= l ;
  app(cons(x,l1),l2) >= cons(x,app(l1,l2)) ;
  sum(app(l1,l2)) >= +(sum(l1),sum(l2)) ;
  sum(nil) >= 0(#) ;
  sum(cons(x,l)) >= +(x,sum(l)) ;
  prod(app(l1,l2)) >=  *(prod(l1),prod(l2)) ;
  prod(nil) >= 1(#) ;
  prod(cons(x,l)) >=  *(x,prod(l)) ;
  mem(x,nil) >= false ;
  mem(x,cons(y,l)) >= if(eq(x,y),true,mem(x,l)) ;
  inter(app(l1,l2),l3) >= app(inter(l1,l3),inter(l2,l3)) ;
  inter(nil,x) >= nil ;
  inter(cons(x,l1),l2) >= ifinter(mem(x,l2),x,l1,l2) ;
  inter(l1,app(l2,l3)) >= app(inter(l1,l2),inter(l1,l3)) ;
  inter(l1,cons(x,l2)) >= ifinter(mem(x,l1),x,l2,l1) ;
  inter(x,nil) >= nil ;
  ifinter(false,x,l1,l2) >= inter(l1,l2) ;
  ifinter(true,x,l1,l2) >= cons(x,inter(l1,l2)) ;
  Marked_-(0(x),0(y)) >= Marked_-(x,y) ;
  Marked_-(0(x),1(y)) >= Marked_-(-(x,y),1(#)) ;
  Marked_-(0(x),1(y)) >= Marked_-(x,y) ;
  Marked_-(1(x),0(y)) >= Marked_-(x,y) ;
  Marked_-(1(x),1(y)) >= Marked_-(x,y) ;
 }
 + Disjunctions:{ 
{
  Marked_-(0(x),0(y)) > Marked_-(x,y) ;
 }
{
  Marked_-(0(x),1(y)) > Marked_-(-(x,y),1(#)) ;
 }
{
  Marked_-(0(x),1(y)) > Marked_-(x,y) ;
 }
{
  Marked_-(1(x),0(y)) > Marked_-(x,y) ;
 }
{
  Marked_-(1(x),1(y)) > 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 ===
Time out for these parameters.
=== 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 29.524011 seconds (real time)
Cime Exit Status: 0