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

TRS termination of:
[1] active(and(tt,X)) -> mark(X)
[2] active(plus(N,0)) -> mark(N)
[3] active(plus(N,s(M))) -> mark(s(plus(N,M)))
[4] mark(and(X1,X2)) -> active(and(mark(X1),X2))
[5] mark(tt) -> active(tt)
[6] mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
[7] mark(0) -> active(0)
[8] mark(s(X)) -> active(s(mark(X)))
[9] and(mark(X1),X2) -> and(X1,X2)
[10] and(X1,mark(X2)) -> and(X1,X2)
[11] and(active(X1),X2) -> and(X1,X2)
[12] and(X1,active(X2)) -> and(X1,X2)
[13] plus(mark(X1),X2) -> plus(X1,X2)
[14] plus(X1,mark(X2)) -> plus(X1,X2)
[15] plus(active(X1),X2) -> plus(X1,X2)
[16] plus(X1,active(X2)) -> plus(X1,X2)
[17] s(mark(X)) -> s(X)
[18] s(active(X)) -> s(X)


Sub problem: 
guided: 

DP termination of:
<Marked_active(and(tt,X)) , Marked_mark(X)>
<Marked_active(plus(N,0)) , Marked_mark(N)>
<Marked_active(plus(N,s(M))) , Marked_mark(s(plus(N,M)))>
<Marked_active(plus(N,s(M))) , Marked_s(plus(N,M))>
<Marked_active(plus(N,s(M))) , Marked_plus(N,M)>
<Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
<Marked_mark(and(X1,X2)) , Marked_and(mark(X1),X2)>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(tt) , Marked_active(tt)>
<Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
<Marked_mark(plus(X1,X2)) , Marked_plus(mark(X1),mark(X2))>
<Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
<Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
<Marked_mark(0) , Marked_active(0)>
<Marked_mark(s(X)) , Marked_active(s(mark(X)))>
<Marked_mark(s(X)) , Marked_s(mark(X))>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
<Marked_and(X1,mark(X2)) , Marked_and(X1,X2)>
<Marked_and(active(X1),X2) , Marked_and(X1,X2)>
<Marked_and(X1,active(X2)) , Marked_and(X1,X2)>
<Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
<Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)>
<Marked_plus(active(X1),X2) , Marked_plus(X1,X2)>
<Marked_plus(X1,active(X2)) , Marked_plus(X1,X2)>
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_s(active(X)) , Marked_s(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 4 components:

{  <Marked_mark(s(X)) , Marked_mark(X)> 
      --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(s(X)) , Marked_active(s(mark(X)))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(s(X)) , Marked_active(s(mark(X)))> 
     --> <Marked_active(plus(N,0)) , Marked_mark(N)>
  <Marked_mark(s(X)) , Marked_active(s(mark(X)))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X2)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(plus(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(plus(N,0)) , Marked_mark(N)>
  <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(plus(N,s(M))) , Marked_mark(s(plus(N,M)))>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(plus(N,0)) , Marked_mark(N)>
  <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))> 
     --> <Marked_active(and(tt,X)) , Marked_mark(X)>
  <Marked_active(plus(N,s(M))) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(plus(N,s(M))) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_active(plus(N,s(M))) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(plus(N,s(M))) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(plus(N,s(M))) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,s(M))) , Marked_mark(s(plus(N,M)))> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(plus(N,0)) , Marked_mark(N)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(plus(N,0)) , Marked_mark(N)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_active(plus(N,0)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(plus(N,0)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,0)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(plus(N,0)) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(plus(N,0)) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_active(s(mark(X)))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_active(and(tt,X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
}

{  <Marked_and(X1,active(X2)) , Marked_and(X1,X2)> 
      --> <Marked_and(X1,active(X2)) , Marked_and(X1,X2)>
  <Marked_and(X1,active(X2)) , Marked_and(X1,X2)> 
     --> <Marked_and(active(X1),X2) , Marked_and(X1,X2)>
  <Marked_and(X1,active(X2)) , Marked_and(X1,X2)> 
     --> <Marked_and(X1,mark(X2)) , Marked_and(X1,X2)>
  <Marked_and(X1,active(X2)) , Marked_and(X1,X2)> 
     --> <Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
  <Marked_and(active(X1),X2) , Marked_and(X1,X2)> 
     --> <Marked_and(X1,active(X2)) , Marked_and(X1,X2)>
  <Marked_and(active(X1),X2) , Marked_and(X1,X2)> 
     --> <Marked_and(active(X1),X2) , Marked_and(X1,X2)>
  <Marked_and(active(X1),X2) , Marked_and(X1,X2)> 
     --> <Marked_and(X1,mark(X2)) , Marked_and(X1,X2)>
  <Marked_and(active(X1),X2) , Marked_and(X1,X2)> 
     --> <Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
  <Marked_and(X1,mark(X2)) , Marked_and(X1,X2)> 
     --> <Marked_and(X1,active(X2)) , Marked_and(X1,X2)>
  <Marked_and(X1,mark(X2)) , Marked_and(X1,X2)> 
     --> <Marked_and(active(X1),X2) , Marked_and(X1,X2)>
  <Marked_and(X1,mark(X2)) , Marked_and(X1,X2)> 
     --> <Marked_and(X1,mark(X2)) , Marked_and(X1,X2)>
  <Marked_and(X1,mark(X2)) , Marked_and(X1,X2)> 
     --> <Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
  <Marked_and(mark(X1),X2) , Marked_and(X1,X2)> 
     --> <Marked_and(X1,active(X2)) , Marked_and(X1,X2)>
  <Marked_and(mark(X1),X2) , Marked_and(X1,X2)> 
     --> <Marked_and(active(X1),X2) , Marked_and(X1,X2)>
  <Marked_and(mark(X1),X2) , Marked_and(X1,X2)> 
     --> <Marked_and(X1,mark(X2)) , Marked_and(X1,X2)>
  <Marked_and(mark(X1),X2) , Marked_and(X1,X2)> 
     --> <Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
}

{  <Marked_plus(X1,active(X2)) , Marked_plus(X1,X2)> 
      --> <Marked_plus(X1,active(X2)) , Marked_plus(X1,X2)>
  <Marked_plus(X1,active(X2)) , Marked_plus(X1,X2)> 
     --> <Marked_plus(active(X1),X2) , Marked_plus(X1,X2)>
  <Marked_plus(X1,active(X2)) , Marked_plus(X1,X2)> 
     --> <Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)>
  <Marked_plus(X1,active(X2)) , Marked_plus(X1,X2)> 
     --> <Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
  <Marked_plus(active(X1),X2) , Marked_plus(X1,X2)> 
     --> <Marked_plus(X1,active(X2)) , Marked_plus(X1,X2)>
  <Marked_plus(active(X1),X2) , Marked_plus(X1,X2)> 
     --> <Marked_plus(active(X1),X2) , Marked_plus(X1,X2)>
  <Marked_plus(active(X1),X2) , Marked_plus(X1,X2)> 
     --> <Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)>
  <Marked_plus(active(X1),X2) , Marked_plus(X1,X2)> 
     --> <Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
  <Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)> 
     --> <Marked_plus(X1,active(X2)) , Marked_plus(X1,X2)>
  <Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)> 
     --> <Marked_plus(active(X1),X2) , Marked_plus(X1,X2)>
  <Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)> 
     --> <Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)>
  <Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)> 
     --> <Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
  <Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)> 
     --> <Marked_plus(X1,active(X2)) , Marked_plus(X1,X2)>
  <Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)> 
     --> <Marked_plus(active(X1),X2) , Marked_plus(X1,X2)>
  <Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)> 
     --> <Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)>
  <Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)> 
     --> <Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
}

{  <Marked_s(active(X)) , Marked_s(X)> --> <Marked_s(active(X)) , Marked_s(X)>
  <Marked_s(active(X)) , Marked_s(X)> --> <Marked_s(mark(X)) , Marked_s(X)>
  <Marked_s(mark(X)) , Marked_s(X)> --> <Marked_s(active(X)) , Marked_s(X)>
  <Marked_s(mark(X)) , Marked_s(X)> --> <Marked_s(mark(X)) , Marked_s(X)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(and(X1,X2)) >= active(and(mark(X1),X2)) ;
  mark(tt) >= active(tt) ;
  mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2))) ;
  mark(0) >= active(0) ;
  mark(s(X)) >= active(s(mark(X))) ;
  active(and(tt,X)) >= mark(X) ;
  active(plus(N,0)) >= mark(N) ;
  active(plus(N,s(M))) >= mark(s(plus(N,M))) ;
  and(mark(X1),X2) >= and(X1,X2) ;
  and(active(X1),X2) >= and(X1,X2) ;
  and(X1,mark(X2)) >= and(X1,X2) ;
  and(X1,active(X2)) >= and(X1,X2) ;
  plus(mark(X1),X2) >= plus(X1,X2) ;
  plus(active(X1),X2) >= plus(X1,X2) ;
  plus(X1,mark(X2)) >= plus(X1,X2) ;
  plus(X1,active(X2)) >= plus(X1,X2) ;
  s(mark(X)) >= s(X) ;
  s(active(X)) >= s(X) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2)) ;
  Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ;
  Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2))) ;
  Marked_mark(s(X)) >= Marked_mark(X) ;
  Marked_mark(s(X)) >= Marked_active(s(mark(X))) ;
  Marked_active(and(tt,X)) >= Marked_mark(X) ;
  Marked_active(plus(N,0)) >= Marked_mark(N) ;
  Marked_active(plus(N,s(M))) >= Marked_mark(s(plus(N,M))) ;
 }
 + Disjunctions:{ 
{
  Marked_mark(and(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_active(and(mark(X1),X2)) ;
 }
{
  Marked_mark(plus(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(plus(X1,X2)) > Marked_mark(X2) ;
 }
{
  Marked_mark(plus(X1,X2)) > Marked_active(plus(mark(X1),mark(X2))) ;
 }
{
  Marked_mark(s(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(s(X)) > Marked_active(s(mark(X))) ;
 }
{
  Marked_active(and(tt,X)) > Marked_mark(X) ;
 }
{
  Marked_active(plus(N,0)) > Marked_mark(N) ;
 }
{
  Marked_active(plus(N,s(M))) > Marked_mark(s(plus(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
Sat solver result read
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
constraint: mark(and(X1,X2)) >= active(and(mark(X1),X2))
constraint: mark(tt) >= active(tt)
constraint: mark(plus(X1,X2)) >= active(plus(mark(X1),mark(X2)))
constraint: mark(0) >= active(0)
constraint: mark(s(X)) >= active(s(mark(X)))
constraint: active(and(tt,X)) >= mark(X)
constraint: active(plus(N,0)) >= mark(N)
constraint: active(plus(N,s(M))) >= mark(s(plus(N,M)))
constraint: and(mark(X1),X2) >= and(X1,X2)
constraint: and(active(X1),X2) >= and(X1,X2)
constraint: and(X1,mark(X2)) >= and(X1,X2)
constraint: and(X1,active(X2)) >= and(X1,X2)
constraint: plus(mark(X1),X2) >= plus(X1,X2)
constraint: plus(active(X1),X2) >= plus(X1,X2)
constraint: plus(X1,mark(X2)) >= plus(X1,X2)
constraint: plus(X1,active(X2)) >= plus(X1,X2)
constraint: s(mark(X)) >= s(X)
constraint: s(active(X)) >= s(X)
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(and(X1,X2)) >= Marked_active(and(mark(X1),X2))
constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2)
constraint: Marked_mark(plus(X1,X2)) >= Marked_active(plus(mark(X1),mark(X2)))
constraint: Marked_mark(s(X)) >= Marked_mark(X)
constraint: Marked_mark(s(X)) >= Marked_active(s(mark(X)))
constraint: Marked_active(and(tt,X)) >= Marked_mark(X)
constraint: Marked_active(plus(N,0)) >= Marked_mark(N)
constraint: Marked_active(plus(N,s(M))) >= Marked_mark(s(plus(N,M)))
APPLY CRITERIA (Subterm criterion)

ST: Marked_and -> 2

APPLY CRITERIA (Subterm criterion)

ST: Marked_plus -> 2

APPLY CRITERIA (Subterm criterion)

ST: Marked_s -> 1

APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(and(X1,X2)) , Marked_mark(X1)> 
      --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_mark -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_and(mark(X1),X2) , Marked_and(X1,X2)> 
      --> <Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
  <Marked_and(mark(X1),X2) , Marked_and(X1,X2)> 
     --> <Marked_and(active(X1),X2) , Marked_and(X1,X2)>
  <Marked_and(active(X1),X2) , Marked_and(X1,X2)> 
     --> <Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
  <Marked_and(active(X1),X2) , Marked_and(X1,X2)> 
     --> <Marked_and(active(X1),X2) , Marked_and(X1,X2)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_and -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)> 
      --> <Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
  <Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)> 
     --> <Marked_plus(active(X1),X2) , Marked_plus(X1,X2)>
  <Marked_plus(active(X1),X2) , Marked_plus(X1,X2)> 
     --> <Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
  <Marked_plus(active(X1),X2) , Marked_plus(X1,X2)> 
     --> <Marked_plus(active(X1),X2) , Marked_plus(X1,X2)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_plus -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] active(and(tt,X)) -> mark(X)
[2] active(plus(N,0)) -> mark(N)
[3] active(plus(N,s(M))) -> mark(s(plus(N,M)))
[4] mark(and(X1,X2)) -> active(and(mark(X1),X2))
[5] mark(tt) -> active(tt)
[6] mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
[7] mark(0) -> active(0)
[8] mark(s(X)) -> active(s(mark(X)))
[9] and(mark(X1),X2) -> and(X1,X2)
[10] and(X1,mark(X2)) -> and(X1,X2)
[11] and(active(X1),X2) -> and(X1,X2)
[12] and(X1,active(X2)) -> and(X1,X2)
[13] plus(mark(X1),X2) -> plus(X1,X2)
[14] plus(X1,mark(X2)) -> plus(X1,X2)
[15] plus(active(X1),X2) -> plus(X1,X2)
[16] plus(X1,active(X2)) -> plus(X1,X2)
[17] s(mark(X)) -> s(X)
[18] s(active(X)) -> s(X)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_active(and(tt,X)) , Marked_mark(X)>
<Marked_active(plus(N,0)) , Marked_mark(N)>
<Marked_active(plus(N,s(M))) , Marked_mark(s(plus(N,M)))>
<Marked_active(plus(N,s(M))) , Marked_s(plus(N,M))>
<Marked_active(plus(N,s(M))) , Marked_plus(N,M)>
<Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
<Marked_mark(and(X1,X2)) , Marked_and(mark(X1),X2)>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(tt) , Marked_active(tt)>
<Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
<Marked_mark(plus(X1,X2)) , Marked_plus(mark(X1),mark(X2))>
<Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
<Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
<Marked_mark(0) , Marked_active(0)>
<Marked_mark(s(X)) , Marked_active(s(mark(X)))>
<Marked_mark(s(X)) , Marked_s(mark(X))>
<Marked_mark(s(X)) , Marked_mark(X)>
<Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
<Marked_and(X1,mark(X2)) , Marked_and(X1,X2)>
<Marked_and(active(X1),X2) , Marked_and(X1,X2)>
<Marked_and(X1,active(X2)) , Marked_and(X1,X2)>
<Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
<Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)>
<Marked_plus(active(X1),X2) , Marked_plus(X1,X2)>
<Marked_plus(X1,active(X2)) , Marked_plus(X1,X2)>
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_s(active(X)) , Marked_s(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_active(and(tt,X)) , Marked_mark(X)>
<Marked_active(plus(N,0)) , Marked_mark(N)>
<Marked_active(plus(N,s(M))) , Marked_mark(s(plus(N,M)))>
<Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
<Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
<Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
<Marked_mark(s(X)) , Marked_active(s(mark(X)))>
<Marked_mark(s(X)) , Marked_mark(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 1*X0; 
 [ plus ] (X0,X1) = 3*X1 + 2*X0 + 1; 
 [ and ] (X0,X1) = 2*X1 + 1*X0; 
 [ Marked_mark ] (X0) = 2*X0 + 2; 
 [ s ] (X0) = 1*X0 + 2; 
 [ active ] (X0) = 1*X0; 
 [ 0 ] () = 2; 
 [ tt ] () = 1; 
 [ Marked_active ] (X0) = 2*X0 + 2; 
 removing <Marked_active(and(tt,X)),Marked_mark(X)><Marked_active(plus(N,0)),
Marked_mark(N)><Marked_active(plus(N,s(M))),Marked_mark(s(plus(N,M)))><
Marked_mark(plus(X1,X2)),Marked_mark(X1)><Marked_mark(plus(X1,X2)),Marked_mark(
                                                                    X2)><
Marked_mark(s(X)),Marked_mark(X)>
 [ {
      
     DP termination of:
     <Marked_mark(and(X1,X2)) , Marked_active(and(mark(X1),X2))>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(plus(X1,X2)) , Marked_active(plus(mark(X1),mark(X2)))>
<Marked_mark(s(X)) , Marked_active(s(mark(X)))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
<Marked_and(X1,mark(X2)) , Marked_and(X1,X2)>
<Marked_and(active(X1),X2) , Marked_and(X1,X2)>
<Marked_and(X1,active(X2)) , Marked_and(X1,X2)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_and(active(X1),X2) , Marked_and(X1,X2)>
<Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_and(active(X1),X2) , Marked_and(X1,X2)>
<Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
<Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)>
<Marked_plus(active(X1),X2) , Marked_plus(X1,X2)>
<Marked_plus(X1,active(X2)) , Marked_plus(X1,X2)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_plus(active(X1),X2) , Marked_plus(X1,X2)>
<Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_plus(active(X1),X2) , Marked_plus(X1,X2)>
<Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_s(active(X)) , Marked_s(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.149659 seconds (real time)
Cime Exit Status: 0