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

TRS termination of:
[1] eq(0,0) -> true
[2] eq(0,s(m)) -> false
[3] eq(s(n),0) -> false
[4] eq(s(n),s(m)) -> eq(n,m)
[5] le(0,m) -> true
[6] le(s(n),0) -> false
[7] le(s(n),s(m)) -> le(n,m)
[8] min(cons(0,nil)) -> 0
[9] min(cons(s(n),nil)) -> s(n)
[10] min(cons(n,cons(m,x))) -> if_min(le(n,m),cons(n,cons(m,x)))
[11] if_min(true,cons(n,cons(m,x))) -> min(cons(n,x))
[12] if_min(false,cons(n,cons(m,x))) -> min(cons(m,x))
[13] replace(n,m,nil) -> nil
[14] replace(n,m,cons(k,x)) -> if_replace(eq(n,k),n,m,cons(k,x))
[15] if_replace(true,n,m,cons(k,x)) -> cons(m,x)
[16] if_replace(false,n,m,cons(k,x)) -> cons(k,replace(n,m,x))
[17] sort(nil) -> nil
[18] sort(cons(n,x)) -> cons(min(cons(n,x)),sort(replace(min(cons(n,x)),n,x)))


Sub problem: 
guided: 

DP termination of:
<Marked_eq(s(n),s(m)) , Marked_eq(n,m)>
<Marked_le(s(n),s(m)) , Marked_le(n,m)>
<Marked_min(cons(n,cons(m,x))) , Marked_if_min(le(n,m),cons(n,cons(m,x)))>
<Marked_min(cons(n,cons(m,x))) , Marked_le(n,m)>
<Marked_if_min(true,cons(n,cons(m,x))) , Marked_min(cons(n,x))>
<Marked_if_min(false,cons(n,cons(m,x))) , Marked_min(cons(m,x))>
<Marked_replace(n,m,cons(k,x)) , Marked_if_replace(eq(n,k),n,m,cons(k,x))>
<Marked_replace(n,m,cons(k,x)) , Marked_eq(n,k)>
<Marked_if_replace(false,n,m,cons(k,x)) , Marked_replace(n,m,x)>
<Marked_sort(cons(n,x)) , Marked_min(cons(n,x))>
<Marked_sort(cons(n,x)) , Marked_sort(replace(min(cons(n,x)),n,x))>
<Marked_sort(cons(n,x)) , Marked_replace(min(cons(n,x)),n,x)>
<Marked_sort(cons(n,x)) , Marked_min(cons(n,x))>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 5 components:

{  <Marked_sort(cons(n,x)) , Marked_sort(replace(min(cons(n,x)),n,x))> 
      --> <Marked_sort(cons(n,x)) , Marked_sort(replace(min(cons(n,x)),n,x))>
}

{  <Marked_if_replace(false,n,m,cons(k,x)) , Marked_replace(n,m,x)> 
      --> <Marked_replace(n,m,cons(k,x)) , Marked_if_replace(eq(n,k),
                                            n,m,cons(k,x))>
  <Marked_replace(n,m,cons(k,x)) , Marked_if_replace(eq(n,k),n,m,cons(k,x))> 
     --> <Marked_if_replace(false,n,m,cons(k,x)) , Marked_replace(n,m,x)>
}

{  <Marked_eq(s(n),s(m)) , Marked_eq(n,m)> 
      --> <Marked_eq(s(n),s(m)) , Marked_eq(n,m)>
}

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

{  <Marked_le(s(n),s(m)) , Marked_le(n,m)> 
      --> <Marked_le(s(n),s(m)) , Marked_le(n,m)>
}
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  eq(0,0) >= true ;
  eq(0,s(m)) >= false ;
  eq(s(n),0) >= false ;
  eq(s(n),s(m)) >= eq(n,m) ;
  le(0,m) >= true ;
  le(s(n),0) >= false ;
  le(s(n),s(m)) >= le(n,m) ;
  min(cons(0,nil)) >= 0 ;
  min(cons(s(n),nil)) >= s(n) ;
  min(cons(n,cons(m,x))) >= if_min(le(n,m),cons(n,cons(m,x))) ;
  if_min(true,cons(n,cons(m,x))) >= min(cons(n,x)) ;
  if_min(false,cons(n,cons(m,x))) >= min(cons(m,x)) ;
  replace(n,m,cons(k,x)) >= if_replace(eq(n,k),n,m,cons(k,x)) ;
  replace(n,m,nil) >= nil ;
  if_replace(true,n,m,cons(k,x)) >= cons(m,x) ;
  if_replace(false,n,m,cons(k,x)) >= cons(k,replace(n,m,x)) ;
  sort(cons(n,x)) >= cons(min(cons(n,x)),sort(replace(min(cons(n,x)),n,x))) ;
  sort(nil) >= nil ;
  Marked_sort(cons(n,x)) >= Marked_sort(replace(min(cons(n,x)),n,x)) ;
 }
 + Disjunctions:{ 
{
  Marked_sort(cons(n,x)) > Marked_sort(replace(min(cons(n,x)),n,x)) ;
 }
 } 
=== 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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: eq(0,0) >= true
constraint: eq(0,s(m)) >= false
constraint: eq(s(n),0) >= false
constraint: eq(s(n),s(m)) >= eq(n,m)
constraint: le(0,m) >= true
constraint: le(s(n),0) >= false
constraint: le(s(n),s(m)) >= le(n,m)
constraint: min(cons(0,nil)) >= 0
constraint: min(cons(s(n),nil)) >= s(n)
constraint: min(cons(n,cons(m,x))) >= if_min(le(n,m),cons(n,cons(m,x)))
constraint: if_min(true,cons(n,cons(m,x))) >= min(cons(n,x))
constraint: if_min(false,cons(n,cons(m,x))) >= min(cons(m,x))
constraint: replace(n,m,cons(k,x)) >= if_replace(eq(n,k),n,m,cons(k,x))
constraint: replace(n,m,nil) >= nil
constraint: if_replace(true,n,m,cons(k,x)) >= cons(m,x)
constraint: if_replace(false,n,m,cons(k,x)) >= cons(k,replace(n,m,x))
constraint: sort(cons(n,x)) >= cons(min(cons(n,x)),
                                sort(replace(min(cons(n,x)),n,x)))
constraint: sort(nil) >= nil
constraint: Marked_sort(cons(n,x)) >= Marked_sort(replace(min(cons(n,x)),n,x))
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  eq(0,0) >= true ;
  eq(0,s(m)) >= false ;
  eq(s(n),0) >= false ;
  eq(s(n),s(m)) >= eq(n,m) ;
  le(0,m) >= true ;
  le(s(n),0) >= false ;
  le(s(n),s(m)) >= le(n,m) ;
  min(cons(0,nil)) >= 0 ;
  min(cons(s(n),nil)) >= s(n) ;
  min(cons(n,cons(m,x))) >= if_min(le(n,m),cons(n,cons(m,x))) ;
  if_min(true,cons(n,cons(m,x))) >= min(cons(n,x)) ;
  if_min(false,cons(n,cons(m,x))) >= min(cons(m,x)) ;
  replace(n,m,cons(k,x)) >= if_replace(eq(n,k),n,m,cons(k,x)) ;
  replace(n,m,nil) >= nil ;
  if_replace(true,n,m,cons(k,x)) >= cons(m,x) ;
  if_replace(false,n,m,cons(k,x)) >= cons(k,replace(n,m,x)) ;
  sort(cons(n,x)) >= cons(min(cons(n,x)),sort(replace(min(cons(n,x)),n,x))) ;
  sort(nil) >= nil ;
  Marked_replace(n,m,cons(k,x)) >= Marked_if_replace(eq(n,k),n,m,cons(k,x)) ;
  Marked_if_replace(false,n,m,cons(k,x)) >= Marked_replace(n,m,x) ;
 }
 + Disjunctions:{ 
{
  Marked_replace(n,m,cons(k,x)) > Marked_if_replace(eq(n,k),n,m,cons(k,x)) ;
 }
{
  Marked_if_replace(false,n,m,cons(k,x)) > Marked_replace(n,m,x) ;
 }
 } 
=== 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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: eq(0,0) >= true
constraint: eq(0,s(m)) >= false
constraint: eq(s(n),0) >= false
constraint: eq(s(n),s(m)) >= eq(n,m)
constraint: le(0,m) >= true
constraint: le(s(n),0) >= false
constraint: le(s(n),s(m)) >= le(n,m)
constraint: min(cons(0,nil)) >= 0
constraint: min(cons(s(n),nil)) >= s(n)
constraint: min(cons(n,cons(m,x))) >= if_min(le(n,m),cons(n,cons(m,x)))
constraint: if_min(true,cons(n,cons(m,x))) >= min(cons(n,x))
constraint: if_min(false,cons(n,cons(m,x))) >= min(cons(m,x))
constraint: replace(n,m,cons(k,x)) >= if_replace(eq(n,k),n,m,cons(k,x))
constraint: replace(n,m,nil) >= nil
constraint: if_replace(true,n,m,cons(k,x)) >= cons(m,x)
constraint: if_replace(false,n,m,cons(k,x)) >= cons(k,replace(n,m,x))
constraint: sort(cons(n,x)) >= cons(min(cons(n,x)),
                                sort(replace(min(cons(n,x)),n,x)))
constraint: sort(nil) >= nil
constraint: Marked_replace(n,m,cons(k,x)) >= Marked_if_replace(eq(n,k),
                                              n,m,cons(k,x))
constraint: Marked_if_replace(false,n,m,cons(k,x)) >= Marked_replace(n,m,x)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  eq(0,0) >= true ;
  eq(0,s(m)) >= false ;
  eq(s(n),0) >= false ;
  eq(s(n),s(m)) >= eq(n,m) ;
  le(0,m) >= true ;
  le(s(n),0) >= false ;
  le(s(n),s(m)) >= le(n,m) ;
  min(cons(0,nil)) >= 0 ;
  min(cons(s(n),nil)) >= s(n) ;
  min(cons(n,cons(m,x))) >= if_min(le(n,m),cons(n,cons(m,x))) ;
  if_min(true,cons(n,cons(m,x))) >= min(cons(n,x)) ;
  if_min(false,cons(n,cons(m,x))) >= min(cons(m,x)) ;
  replace(n,m,cons(k,x)) >= if_replace(eq(n,k),n,m,cons(k,x)) ;
  replace(n,m,nil) >= nil ;
  if_replace(true,n,m,cons(k,x)) >= cons(m,x) ;
  if_replace(false,n,m,cons(k,x)) >= cons(k,replace(n,m,x)) ;
  sort(cons(n,x)) >= cons(min(cons(n,x)),sort(replace(min(cons(n,x)),n,x))) ;
  sort(nil) >= nil ;
  Marked_eq(s(n),s(m)) >= Marked_eq(n,m) ;
 }
 + Disjunctions:{ 
{
  Marked_eq(s(n),s(m)) > Marked_eq(n,m) ;
 }
 } 
=== 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 timeout reached
=== 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 54.761699 seconds (real time)
Cime Exit Status: 0