- : unit = ()
- : 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] or(true,y) -> true
[6] or(false,y) -> y
[7] and(true,y) -> y
[8] and(false,y) -> false
[9] size(empty) -> 0
[10] size(edge(x,y,i)) -> s(size(i))
[11] le(0,y) -> true
[12] le(s(x),0) -> false
[13] le(s(x),s(y)) -> le(x,y)
[14] reachable(x,y,i) -> reach(x,y,0,i,i)
[15] reach(x,y,c,i,j) -> if1(eq(x,y),x,y,c,i,j)
[16] if1(true,x,y,c,i,j) -> true
[17] if1(false,x,y,c,i,j) -> if2(le(c,size(j)),x,y,c,i,j)
[18] if2(false,x,y,c,i,j) -> false
[19] if2(true,x,y,c,empty,j) -> false
[20] if2(true,x,y,c,edge(u,v,i),j) ->
 or(if2(true,x,y,c,i,j),and(eq(x,u),reach(v,y,s(c),j,j)))


Sub problem: 
guided: 

DP termination of:
<Marked_eq(s(x),s(y)) , Marked_eq(x,y)>
<Marked_size(edge(x,y,i)) , Marked_size(i)>
<Marked_le(s(x),s(y)) , Marked_le(x,y)>
<Marked_reachable(x,y,i) , Marked_reach(x,y,0,i,i)>
<Marked_reach(x,y,c,i,j) , Marked_if1(eq(x,y),x,y,c,i,j)>
<Marked_reach(x,y,c,i,j) , Marked_eq(x,y)>
<Marked_if1(false,x,y,c,i,j) , Marked_if2(le(c,size(j)),x,y,c,i,j)>
<Marked_if1(false,x,y,c,i,j) , Marked_le(c,size(j))>
<Marked_if1(false,x,y,c,i,j) , Marked_size(j)>
<Marked_if2(true,x,y,c,edge(u,v,i),j) , Marked_or(if2(true,x,y,c,i,j),
                                         and(eq(x,u),reach(v,y,s(c),j,j)))>
<Marked_if2(true,x,y,c,edge(u,v,i),j) , Marked_if2(true,x,y,c,i,j)>
<Marked_if2(true,x,y,c,edge(u,v,i),j) , Marked_and(eq(x,u),reach(v,y,s(c),j,j))>
<Marked_if2(true,x,y,c,edge(u,v,i),j) , Marked_eq(x,u)>
<Marked_if2(true,x,y,c,edge(u,v,i),j) , Marked_reach(v,y,s(c),j,j)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

{  <Marked_if2(true,x,y,c,edge(u,v,i),j) , Marked_reach(v,y,s(c),j,j)> 
      --> <Marked_reach(x,y,c,i,j) , Marked_if1(eq(x,y),x,y,c,i,j)>
  <Marked_if2(true,x,y,c,edge(u,v,i),j) , Marked_if2(true,x,y,c,i,j)> 
     --> <Marked_if2(true,x,y,c,edge(u,v,i),j) , Marked_reach(v,y,s(c),j,j)>
  <Marked_if2(true,x,y,c,edge(u,v,i),j) , Marked_if2(true,x,y,c,i,j)> 
     --> <Marked_if2(true,x,y,c,edge(u,v,i),j) , Marked_if2(true,x,y,c,i,j)>
  <Marked_if1(false,x,y,c,i,j) , Marked_if2(le(c,size(j)),x,y,c,i,j)> 
     --> <Marked_if2(true,x,y,c,edge(u,v,i),j) , Marked_reach(v,y,s(c),j,j)>
  <Marked_if1(false,x,y,c,i,j) , Marked_if2(le(c,size(j)),x,y,c,i,j)> 
     --> <Marked_if2(true,x,y,c,edge(u,v,i),j) , Marked_if2(true,x,y,c,i,j)>
  <Marked_reach(x,y,c,i,j) , Marked_if1(eq(x,y),x,y,c,i,j)> 
     --> <Marked_if1(false,x,y,c,i,j) , Marked_if2(le(c,size(j)),x,y,c,i,j)>
}

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

{  <Marked_size(edge(x,y,i)) , Marked_size(i)> 
      --> <Marked_size(edge(x,y,i)) , Marked_size(i)>
}

{  <Marked_eq(s(x),s(y)) , Marked_eq(x,y)> 
      --> <Marked_eq(s(x),s(y)) , Marked_eq(x,y)>
}
APPLY CRITERIA (Subterm criterion)
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) ;
  or(true,y) >= true ;
  or(false,y) >= y ;
  and(true,y) >= y ;
  and(false,y) >= false ;
  size(empty) >= 0 ;
  size(edge(x,y,i)) >= s(size(i)) ;
  le(0,y) >= true ;
  le(s(x),0) >= false ;
  le(s(x),s(y)) >= le(x,y) ;
  reach(x,y,c,i,j) >= if1(eq(x,y),x,y,c,i,j) ;
  reachable(x,y,i) >= reach(x,y,0,i,i) ;
  if1(true,x,y,c,i,j) >= true ;
  if1(false,x,y,c,i,j) >= if2(le(c,size(j)),x,y,c,i,j) ;
  if2(true,x,y,c,empty,j) >= false ;
  if2(true,x,y,c,edge(u,v,i),j) >= or(if2(true,x,y,c,i,j),
                                    and(eq(x,u),reach(v,y,s(c),j,j))) ;
  if2(false,x,y,c,i,j) >= false ;
  Marked_if2(true,x,y,c,edge(u,v,i),j) >= Marked_if2(true,x,y,c,i,j) ;
  Marked_if2(true,x,y,c,edge(u,v,i),j) >= Marked_reach(v,y,s(c),j,j) ;
  Marked_reach(x,y,c,i,j) >= Marked_if1(eq(x,y),x,y,c,i,j) ;
  Marked_if1(false,x,y,c,i,j) >= Marked_if2(le(c,size(j)),x,y,c,i,j) ;
 }
 + Disjunctions:{ 
{
  Marked_if2(true,x,y,c,edge(u,v,i),j) > Marked_if2(true,x,y,c,i,j) ;
 }
{
  Marked_if2(true,x,y,c,edge(u,v,i),j) > Marked_reach(v,y,s(c),j,j) ;
 }
{
  Marked_reach(x,y,c,i,j) > Marked_if1(eq(x,y),x,y,c,i,j) ;
 }
{
  Marked_if1(false,x,y,c,i,j) > Marked_if2(le(c,size(j)),x,y,c,i,j) ;
 }
 } 
=== 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
=== 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:
{
  eq(0,0) >= true ;
  eq(0,s(x)) >= false ;
  eq(s(x),0) >= false ;
  eq(s(x),s(y)) >= eq(x,y) ;
  or(true,y) >= true ;
  or(false,y) >= y ;
  and(true,y) >= y ;
  and(false,y) >= false ;
  size(empty) >= 0 ;
  size(edge(x,y,i)) >= s(size(i)) ;
  le(0,y) >= true ;
  le(s(x),0) >= false ;
  le(s(x),s(y)) >= le(x,y) ;
  reach(x,y,c,i,j) >= if1(eq(x,y),x,y,c,i,j) ;
  reachable(x,y,i) >= reach(x,y,0,i,i) ;
  if1(true,x,y,c,i,j) >= true ;
  if1(false,x,y,c,i,j) >= if2(le(c,size(j)),x,y,c,i,j) ;
  if2(true,x,y,c,empty,j) >= false ;
  if2(true,x,y,c,edge(u,v,i),j) >= or(if2(true,x,y,c,i,j),
                                    and(eq(x,u),reach(v,y,s(c),j,j))) ;
  if2(false,x,y,c,i,j) >= false ;
  Marked_if2(true,x,y,c,edge(u,v,i),j) > Marked_if2(true,x,y,c,i,j) ;
  Marked_if2(true,x,y,c,edge(u,v,i),j) >= Marked_reach(v,y,s(c),j,j) ;
  Marked_reach(x,y,c,i,j) >= Marked_if1(eq(x,y),x,y,c,i,j) ;
  Marked_if1(false,x,y,c,i,j) > Marked_if2(le(c,size(j)),x,y,c,i,j) ;
 }

APPLY CRITERIA (SOLVE_ORD)
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) ;
  or(true,y) >= true ;
  or(false,y) >= y ;
  and(true,y) >= y ;
  and(false,y) >= false ;
  size(empty) >= 0 ;
  size(edge(x,y,i)) >= s(size(i)) ;
  le(0,y) >= true ;
  le(s(x),0) >= false ;
  le(s(x),s(y)) >= le(x,y) ;
  reach(x,y,c,i,j) >= if1(eq(x,y),x,y,c,i,j) ;
  reachable(x,y,i) >= reach(x,y,0,i,i) ;
  if1(true,x,y,c,i,j) >= true ;
  if1(false,x,y,c,i,j) >= if2(le(c,size(j)),x,y,c,i,j) ;
  if2(true,x,y,c,empty,j) >= false ;
  if2(true,x,y,c,edge(u,v,i),j) >= or(if2(true,x,y,c,i,j),
                                    and(eq(x,u),reach(v,y,s(c),j,j))) ;
  if2(false,x,y,c,i,j) >= false ;
  Marked_if2(true,x,y,c,edge(u,v,i),j) > Marked_if2(true,x,y,c,i,j) ;
  Marked_if2(true,x,y,c,edge(u,v,i),j) >= Marked_reach(v,y,s(c),j,j) ;
  Marked_reach(x,y,c,i,j) >= Marked_if1(eq(x,y),x,y,c,i,j) ;
  Marked_if1(false,x,y,c,i,j) > Marked_if2(le(c,size(j)),x,y,c,i,j) ;
 }
 + 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 ===
Time out for these parameters.
=== 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 83.097667 seconds (real time)
Cime Exit Status: 0