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

TRS termination of:
[1] eq(0,0) -> true
[2] eq(0,s(x)) -> false
[3] eq(s(x),0) -> false
[4] eq(s(x),s(y)) -> eq(x,y)
[5] le(0,y) -> true
[6] le(s(x),0) -> false
[7] le(s(x),s(y)) -> le(x,y)
[8] app(nil,y) -> y
[9] app(add(n,x),y) -> add(n,app(x,y))
[10] min(add(n,nil)) -> n
[11] min(add(n,add(m,x))) -> if_min(le(n,m),add(n,add(m,x)))
[12] if_min(true,add(n,add(m,x))) -> min(add(n,x))
[13] if_min(false,add(n,add(m,x))) -> min(add(m,x))
[14] head(add(n,x)) -> n
[15] tail(add(n,x)) -> x
[16] tail(nil) -> nil
[17] null(nil) -> true
[18] null(add(n,x)) -> false
[19] rm(n,nil) -> nil
[20] rm(n,add(m,x)) -> if_rm(eq(n,m),n,add(m,x))
[21] if_rm(true,n,add(m,x)) -> rm(n,x)
[22] if_rm(false,n,add(m,x)) -> add(m,rm(n,x))
[23] minsort(x) -> mins(x,nil,nil)
[24] mins(x,y,z) -> if(null(x),x,y,z)
[25] if(true,x,y,z) -> z
[26] if(false,x,y,z) -> if2(eq(head(x),min(x)),x,y,z)
[27] if2(true,x,y,z) ->
 mins(app(rm(head(x),tail(x)),y),nil,app(z,add(head(x),nil)))
[28] if2(false,x,y,z) -> mins(tail(x),add(head(x),y),z)


Sub problem: 
guided: 

DP termination of:
<Marked_eq(s(x),s(y)) , Marked_eq(x,y)>
<Marked_le(s(x),s(y)) , Marked_le(x,y)>
<Marked_app(add(n,x),y) , Marked_app(x,y)>
<Marked_min(add(n,add(m,x))) , Marked_if_min(le(n,m),add(n,add(m,x)))>
<Marked_min(add(n,add(m,x))) , Marked_le(n,m)>
<Marked_if_min(true,add(n,add(m,x))) , Marked_min(add(n,x))>
<Marked_if_min(false,add(n,add(m,x))) , Marked_min(add(m,x))>
<Marked_rm(n,add(m,x)) , Marked_if_rm(eq(n,m),n,add(m,x))>
<Marked_rm(n,add(m,x)) , Marked_eq(n,m)>
<Marked_if_rm(true,n,add(m,x)) , Marked_rm(n,x)>
<Marked_if_rm(false,n,add(m,x)) , Marked_rm(n,x)>
<Marked_minsort(x) , Marked_mins(x,nil,nil)>
<Marked_mins(x,y,z) , Marked_if(null(x),x,y,z)>
<Marked_mins(x,y,z) , Marked_null(x)>
<Marked_if(false,x,y,z) , Marked_if2(eq(head(x),min(x)),x,y,z)>
<Marked_if(false,x,y,z) , Marked_eq(head(x),min(x))>
<Marked_if(false,x,y,z) , Marked_head(x)>
<Marked_if(false,x,y,z) , Marked_min(x)>
<Marked_if2(true,x,y,z) , Marked_mins(app(rm(head(x),tail(x)),y),nil,
                           app(z,add(head(x),nil)))>
<Marked_if2(true,x,y,z) , Marked_app(rm(head(x),tail(x)),y)>
<Marked_if2(true,x,y,z) , Marked_rm(head(x),tail(x))>
<Marked_if2(true,x,y,z) , Marked_head(x)>
<Marked_if2(true,x,y,z) , Marked_tail(x)>
<Marked_if2(true,x,y,z) , Marked_app(z,add(head(x),nil))>
<Marked_if2(true,x,y,z) , Marked_head(x)>
<Marked_if2(false,x,y,z) , Marked_mins(tail(x),add(head(x),y),z)>
<Marked_if2(false,x,y,z) , Marked_tail(x)>
<Marked_if2(false,x,y,z) , Marked_head(x)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 6 components:

{  <Marked_if2(false,x,y,z) , Marked_mins(tail(x),add(head(x),y),z)> 
      --> <Marked_mins(x,y,z) , Marked_if(null(x),x,y,z)>
  <Marked_if2(true,x,y,z) , Marked_mins(app(rm(head(x),tail(x)),y),nil,
                             app(z,add(head(x),nil)))> 
     --> <Marked_mins(x,y,z) , Marked_if(null(x),x,y,z)>
  <Marked_if(false,x,y,z) , Marked_if2(eq(head(x),min(x)),x,y,z)> 
     --> <Marked_if2(false,x,y,z) , Marked_mins(tail(x),add(head(x),y),z)>
  <Marked_if(false,x,y,z) , Marked_if2(eq(head(x),min(x)),x,y,z)> 
     --> <Marked_if2(true,x,y,z) , Marked_mins(app(rm(head(x),tail(x)),y),
                                    nil,app(z,add(head(x),nil)))>
  <Marked_mins(x,y,z) , Marked_if(null(x),x,y,z)> 
     --> <Marked_if(false,x,y,z) , Marked_if2(eq(head(x),min(x)),x,y,z)>
}

{  <Marked_if_rm(false,n,add(m,x)) , Marked_rm(n,x)> 
      --> <Marked_rm(n,add(m,x)) , Marked_if_rm(eq(n,m),n,add(m,x))>
  <Marked_if_rm(true,n,add(m,x)) , Marked_rm(n,x)> 
     --> <Marked_rm(n,add(m,x)) , Marked_if_rm(eq(n,m),n,add(m,x))>
  <Marked_rm(n,add(m,x)) , Marked_if_rm(eq(n,m),n,add(m,x))> 
     --> <Marked_if_rm(false,n,add(m,x)) , Marked_rm(n,x)>
  <Marked_rm(n,add(m,x)) , Marked_if_rm(eq(n,m),n,add(m,x))> 
     --> <Marked_if_rm(true,n,add(m,x)) , Marked_rm(n,x)>
}

{  <Marked_app(add(n,x),y) , Marked_app(x,y)> 
      --> <Marked_app(add(n,x),y) , Marked_app(x,y)>
}

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

{  <Marked_if_min(false,add(n,add(m,x))) , Marked_min(add(m,x))> 
      --> <Marked_min(add(n,add(m,x))) , Marked_if_min(le(n,m),add(n,add(m,x)))>
  <Marked_if_min(true,add(n,add(m,x))) , Marked_min(add(n,x))> 
     --> <Marked_min(add(n,add(m,x))) , Marked_if_min(le(n,m),add(n,add(m,x)))>
  <Marked_min(add(n,add(m,x))) , Marked_if_min(le(n,m),add(n,add(m,x)))> 
     --> <Marked_if_min(false,add(n,add(m,x))) , Marked_min(add(m,x))>
  <Marked_min(add(n,add(m,x))) , Marked_if_min(le(n,m),add(n,add(m,x)))> 
     --> <Marked_if_min(true,add(n,add(m,x))) , Marked_min(add(n,x))>
}

{  <Marked_le(s(x),s(y)) , Marked_le(x,y)> 
      --> <Marked_le(s(x),s(y)) , Marked_le(x,y)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  eq(0,0) >= true ;
  eq(0,s(x)) >= false ;
  eq(s(x),0) >= false ;
  eq(s(x),s(y)) >= eq(x,y) ;
  le(0,y) >= true ;
  le(s(x),0) >= false ;
  le(s(x),s(y)) >= le(x,y) ;
  app(nil,y) >= y ;
  app(add(n,x),y) >= add(n,app(x,y)) ;
  min(add(n,nil)) >= n ;
  min(add(n,add(m,x))) >= if_min(le(n,m),add(n,add(m,x))) ;
  if_min(true,add(n,add(m,x))) >= min(add(n,x)) ;
  if_min(false,add(n,add(m,x))) >= min(add(m,x)) ;
  head(add(n,x)) >= n ;
  tail(nil) >= nil ;
  tail(add(n,x)) >= x ;
  null(nil) >= true ;
  null(add(n,x)) >= false ;
  rm(n,nil) >= nil ;
  rm(n,add(m,x)) >= if_rm(eq(n,m),n,add(m,x)) ;
  if_rm(true,n,add(m,x)) >= rm(n,x) ;
  if_rm(false,n,add(m,x)) >= add(m,rm(n,x)) ;
  mins(x,y,z) >= if(null(x),x,y,z) ;
  minsort(x) >= mins(x,nil,nil) ;
  if(true,x,y,z) >= z ;
  if(false,x,y,z) >= if2(eq(head(x),min(x)),x,y,z) ;
  if2(true,x,y,z) >= mins(app(rm(head(x),tail(x)),y),nil,
                      app(z,add(head(x),nil))) ;
  if2(false,x,y,z) >= mins(tail(x),add(head(x),y),z) ;
  Marked_if2(true,x,y,z) >= Marked_mins(app(rm(head(x),tail(x)),y),nil,
                             app(z,add(head(x),nil))) ;
  Marked_if2(false,x,y,z) >= Marked_mins(tail(x),add(head(x),y),z) ;
  Marked_mins(x,y,z) >= Marked_if(null(x),x,y,z) ;
  Marked_if(false,x,y,z) >= Marked_if2(eq(head(x),min(x)),x,y,z) ;
 }
 + Disjunctions:{ 
{
  Marked_if2(true,x,y,z) > Marked_mins(app(rm(head(x),tail(x)),y),nil,
                            app(z,add(head(x),nil))) ;
 }
{
  Marked_if2(false,x,y,z) > Marked_mins(tail(x),add(head(x),y),z) ;
 }
{
  Marked_mins(x,y,z) > Marked_if(null(x),x,y,z) ;
 }
{
  Marked_if(false,x,y,z) > Marked_if2(eq(head(x),min(x)),x,y,z) ;
 }
 } 
=== 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 timeout reached
=== STOPING TIMER virtual ===
Time out 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 72.918787 seconds (real time)
Cime Exit Status: 0