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

TRS termination of:
[1] isEmpty(empty) -> true
[2] isEmpty(node(l,r)) -> false
[3] left(empty) -> empty
[4] left(node(l,r)) -> l
[5] right(empty) -> empty
[6] right(node(l,r)) -> r
[7] inc(0) -> s(0)
[8] inc(s(x)) -> s(inc(x))
[9] count(n,x) ->
 if(isEmpty(n),isEmpty(left(n)),right(n),
  node(left(left(n)),node(right(left(n)),right(n))),x,inc(x))
[10] if(true,b,n,m,x,y) -> x
[11] if(false,false,n,m,x,y) -> count(m,x)
[12] if(false,true,n,m,x,y) -> count(n,y)
[13] nrOfNodes(n) -> count(n,0)


Sub problem: 
guided: 

DP termination of:
<Marked_inc(s(x)) , Marked_inc(x)>
<Marked_count(n,x) , Marked_if(isEmpty(n),isEmpty(left(n)),right(n),
                      node(left(left(n)),node(right(left(n)),right(n))),
                      x,inc(x))>
<Marked_count(n,x) , Marked_isEmpty(n)>
<Marked_count(n,x) , Marked_isEmpty(left(n))>
<Marked_count(n,x) , Marked_left(n)>
<Marked_count(n,x) , Marked_right(n)>
<Marked_count(n,x) , Marked_left(left(n))>
<Marked_count(n,x) , Marked_left(n)>
<Marked_count(n,x) , Marked_right(left(n))>
<Marked_count(n,x) , Marked_left(n)>
<Marked_count(n,x) , Marked_right(n)>
<Marked_count(n,x) , Marked_inc(x)>
<Marked_if(false,false,n,m,x,y) , Marked_count(m,x)>
<Marked_if(false,true,n,m,x,y) , Marked_count(n,y)>
<Marked_nrOfNodes(n) , Marked_count(n,0)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_if(false,true,n,m,x,y) , Marked_count(n,y)> 
      --> <Marked_count(n,x) , Marked_if(isEmpty(n),isEmpty(left(n)),
                                right(n),
                                node(left(left(n)),
                                 node(right(left(n)),right(n))),x,inc(x))>
  <Marked_if(false,false,n,m,x,y) , Marked_count(m,x)> 
     --> <Marked_count(n,x) , Marked_if(isEmpty(n),isEmpty(left(n)),right(n),
                               node(left(left(n)),
                                node(right(left(n)),right(n))),x,inc(x))>
  <Marked_count(n,x) , Marked_if(isEmpty(n),isEmpty(left(n)),right(n),
                        node(left(left(n)),node(right(left(n)),right(n))),
                        x,inc(x))> 
     --> <Marked_if(false,true,n,m,x,y) , Marked_count(n,y)>
  <Marked_count(n,x) , Marked_if(isEmpty(n),isEmpty(left(n)),right(n),
                        node(left(left(n)),node(right(left(n)),right(n))),
                        x,inc(x))> 
     --> <Marked_if(false,false,n,m,x,y) , Marked_count(m,x)>
}

{  <Marked_inc(s(x)) , Marked_inc(x)> --> <Marked_inc(s(x)) , Marked_inc(x)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  isEmpty(empty) >= true ;
  isEmpty(node(l,r)) >= false ;
  left(empty) >= empty ;
  left(node(l,r)) >= l ;
  right(empty) >= empty ;
  right(node(l,r)) >= r ;
  inc(s(x)) >= s(inc(x)) ;
  inc(0) >= s(0) ;
  if(true,b,n,m,x,y) >= x ;
  if(false,true,n,m,x,y) >= count(n,y) ;
  if(false,false,n,m,x,y) >= count(m,x) ;
  count(n,x) >= if(isEmpty(n),isEmpty(left(n)),right(n),
                 node(left(left(n)),node(right(left(n)),right(n))),x,
                 inc(x)) ;
  nrOfNodes(n) >= count(n,0) ;
  Marked_count(n,x) >= Marked_if(isEmpty(n),isEmpty(left(n)),right(n),
                        node(left(left(n)),node(right(left(n)),right(n))),
                        x,inc(x)) ;
  Marked_if(false,true,n,m,x,y) >= Marked_count(n,y) ;
  Marked_if(false,false,n,m,x,y) >= Marked_count(m,x) ;
 }
 + Disjunctions:{ 
{
  Marked_count(n,x) > Marked_if(isEmpty(n),isEmpty(left(n)),right(n),
                       node(left(left(n)),node(right(left(n)),right(n))),
                       x,inc(x)) ;
 }
{
  Marked_if(false,true,n,m,x,y) > Marked_count(n,y) ;
 }
{
  Marked_if(false,false,n,m,x,y) > Marked_count(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
=== 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 : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
=== 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 (Simple graph)
Found the following constraints:
{
  isEmpty(empty) >= true ;
  isEmpty(node(l,r)) >= false ;
  left(empty) >= empty ;
  left(node(l,r)) >= l ;
  right(empty) >= empty ;
  right(node(l,r)) >= r ;
  inc(s(x)) >= s(inc(x)) ;
  inc(0) >= s(0) ;
  if(true,b,n,m,x,y) >= x ;
  if(false,true,n,m,x,y) >= count(n,y) ;
  if(false,false,n,m,x,y) >= count(m,x) ;
  count(n,x) >= if(isEmpty(n),isEmpty(left(n)),right(n),
                 node(left(left(n)),node(right(left(n)),right(n))),x,
                 inc(x)) ;
  nrOfNodes(n) >= count(n,0) ;
  Marked_count(n,x) > Marked_if(isEmpty(n),isEmpty(left(n)),right(n),
                       node(left(left(n)),node(right(left(n)),right(n))),
                       x,inc(x)) ;
  Marked_if(false,true,n,m,x,y) >= Marked_count(n,y) ;
  Marked_if(false,false,n,m,x,y) > Marked_count(m,x) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  isEmpty(empty) >= true ;
  isEmpty(node(l,r)) >= false ;
  left(empty) >= empty ;
  left(node(l,r)) >= l ;
  right(empty) >= empty ;
  right(node(l,r)) >= r ;
  inc(s(x)) >= s(inc(x)) ;
  inc(0) >= s(0) ;
  if(true,b,n,m,x,y) >= x ;
  if(false,true,n,m,x,y) >= count(n,y) ;
  if(false,false,n,m,x,y) >= count(m,x) ;
  count(n,x) >= if(isEmpty(n),isEmpty(left(n)),right(n),
                 node(left(left(n)),node(right(left(n)),right(n))),x,
                 inc(x)) ;
  nrOfNodes(n) >= count(n,0) ;
  Marked_count(n,x) > Marked_if(isEmpty(n),isEmpty(left(n)),right(n),
                       node(left(left(n)),node(right(left(n)),right(n))),
                       x,inc(x)) ;
  Marked_if(false,true,n,m,x,y) >= Marked_count(n,y) ;
  Marked_if(false,false,n,m,x,y) > Marked_count(m,x) ;
 }
 + Disjunctions:{ 
 } 
=== 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 ===
No solution found for these parameters.(60358 bt (59827) [4676])
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
=== 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 109.644444 seconds (real time)
Cime Exit Status: 0