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

TRS termination of:
[1] le(0,y) -> true
[2] le(s(x),0) -> false
[3] le(s(x),s(y)) -> le(x,y)
[4] eq(0,0) -> true
[5] eq(0,s(y)) -> false
[6] eq(s(x),0) -> false
[7] eq(s(x),s(y)) -> eq(x,y)
[8] if1(true,x,y,xs) -> min(x,xs)
[9] if1(false,x,y,xs) -> min(y,xs)
[10] if2(true,x,y,xs) -> xs
[11] if2(false,x,y,xs) -> cons(y,del(x,xs))
[12] minsort(nil) -> nil
[13] minsort(cons(x,y)) -> cons(min(x,y),minsort(del(min(x,y),cons(x,y))))
[14] min(x,nil) -> x
[15] min(x,cons(y,z)) -> if1(le(x,y),x,y,z)
[16] del(x,nil) -> nil
[17] del(x,cons(y,z)) -> if2(eq(x,y),x,y,z)


Sub problem: 
guided: 

DP termination of:
<Marked_le(s(x),s(y)) , Marked_le(x,y)>
<Marked_eq(s(x),s(y)) , Marked_eq(x,y)>
<Marked_if1(true,x,y,xs) , Marked_min(x,xs)>
<Marked_if1(false,x,y,xs) , Marked_min(y,xs)>
<Marked_if2(false,x,y,xs) , Marked_del(x,xs)>
<Marked_minsort(cons(x,y)) , Marked_min(x,y)>
<Marked_minsort(cons(x,y)) , Marked_minsort(del(min(x,y),cons(x,y)))>
<Marked_minsort(cons(x,y)) , Marked_del(min(x,y),cons(x,y))>
<Marked_minsort(cons(x,y)) , Marked_min(x,y)>
<Marked_min(x,cons(y,z)) , Marked_if1(le(x,y),x,y,z)>
<Marked_min(x,cons(y,z)) , Marked_le(x,y)>
<Marked_del(x,cons(y,z)) , Marked_if2(eq(x,y),x,y,z)>
<Marked_del(x,cons(y,z)) , Marked_eq(x,y)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 5 components:

{  <Marked_minsort(cons(x,y)) , Marked_minsort(del(min(x,y),cons(x,y)))> 
      --> <Marked_minsort(cons(x,y)) , Marked_minsort(del(min(x,y),cons(x,y)))>
}

{  <Marked_min(x,cons(y,z)) , Marked_if1(le(x,y),x,y,z)> 
      --> <Marked_if1(false,x,y,xs) , Marked_min(y,xs)>
  <Marked_min(x,cons(y,z)) , Marked_if1(le(x,y),x,y,z)> 
     --> <Marked_if1(true,x,y,xs) , Marked_min(x,xs)>
  <Marked_if1(false,x,y,xs) , Marked_min(y,xs)> 
     --> <Marked_min(x,cons(y,z)) , Marked_if1(le(x,y),x,y,z)>
  <Marked_if1(true,x,y,xs) , Marked_min(x,xs)> 
     --> <Marked_min(x,cons(y,z)) , Marked_if1(le(x,y),x,y,z)>
}

{  <Marked_le(s(x),s(y)) , Marked_le(x,y)> 
      --> <Marked_le(s(x),s(y)) , Marked_le(x,y)>
}

{  <Marked_del(x,cons(y,z)) , Marked_if2(eq(x,y),x,y,z)> 
      --> <Marked_if2(false,x,y,xs) , Marked_del(x,xs)>
  <Marked_if2(false,x,y,xs) , Marked_del(x,xs)> 
     --> <Marked_del(x,cons(y,z)) , Marked_if2(eq(x,y),x,y,z)>
}

{  <Marked_eq(s(x),s(y)) , Marked_eq(x,y)> 
      --> <Marked_eq(s(x),s(y)) , Marked_eq(x,y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  le(0,y) >= true ;
  le(s(x),0) >= false ;
  le(s(x),s(y)) >= le(x,y) ;
  eq(0,0) >= true ;
  eq(0,s(y)) >= false ;
  eq(s(x),0) >= false ;
  eq(s(x),s(y)) >= eq(x,y) ;
  min(x,cons(y,z)) >= if1(le(x,y),x,y,z) ;
  min(x,nil) >= x ;
  if1(true,x,y,xs) >= min(x,xs) ;
  if1(false,x,y,xs) >= min(y,xs) ;
  if2(true,x,y,xs) >= xs ;
  if2(false,x,y,xs) >= cons(y,del(x,xs)) ;
  del(x,cons(y,z)) >= if2(eq(x,y),x,y,z) ;
  del(x,nil) >= nil ;
  minsort(cons(x,y)) >= cons(min(x,y),minsort(del(min(x,y),cons(x,y)))) ;
  minsort(nil) >= nil ;
  Marked_minsort(cons(x,y)) >= Marked_minsort(del(min(x,y),cons(x,y))) ;
 }
 + Disjunctions:{ 
{
  Marked_minsort(cons(x,y)) > Marked_minsort(del(min(x,y),cons(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 : 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 19.910081 seconds (real time)
Cime Exit Status: 0