- : 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] active(and(X1,X2)) -> and(active(X1),X2)
[5] active(plus(X1,X2)) -> plus(active(X1),X2)
[6] active(plus(X1,X2)) -> plus(X1,active(X2))
[7] active(s(X)) -> s(active(X))
[8] and(mark(X1),X2) -> mark(and(X1,X2))
[9] plus(mark(X1),X2) -> mark(plus(X1,X2))
[10] plus(X1,mark(X2)) -> mark(plus(X1,X2))
[11] s(mark(X)) -> mark(s(X))
[12] proper(and(X1,X2)) -> and(proper(X1),proper(X2))
[13] proper(tt) -> ok(tt)
[14] proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
[15] proper(0) -> ok(0)
[16] proper(s(X)) -> s(proper(X))
[17] and(ok(X1),ok(X2)) -> ok(and(X1,X2))
[18] plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
[19] s(ok(X)) -> ok(s(X))
[20] top(mark(X)) -> top(proper(X))
[21] top(ok(X)) -> top(active(X))


Sub problem: 
guided: 

DP termination of:
<Marked_active(plus(N,s(M))) , Marked_s(plus(N,M))>
<Marked_active(plus(N,s(M))) , Marked_plus(N,M)>
<Marked_active(and(X1,X2)) , Marked_and(active(X1),X2)>
<Marked_active(and(X1,X2)) , Marked_active(X1)>
<Marked_active(plus(X1,X2)) , Marked_plus(active(X1),X2)>
<Marked_active(plus(X1,X2)) , Marked_active(X1)>
<Marked_active(plus(X1,X2)) , Marked_plus(X1,active(X2))>
<Marked_active(plus(X1,X2)) , Marked_active(X2)>
<Marked_active(s(X)) , Marked_s(active(X))>
<Marked_active(s(X)) , Marked_active(X)>
<Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
<Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
<Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)>
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_proper(and(X1,X2)) , Marked_and(proper(X1),proper(X2))>
<Marked_proper(and(X1,X2)) , Marked_proper(X1)>
<Marked_proper(and(X1,X2)) , Marked_proper(X2)>
<Marked_proper(plus(X1,X2)) , Marked_plus(proper(X1),proper(X2))>
<Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
<Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
<Marked_proper(s(X)) , Marked_s(proper(X))>
<Marked_proper(s(X)) , Marked_proper(X)>
<Marked_and(ok(X1),ok(X2)) , Marked_and(X1,X2)>
<Marked_plus(ok(X1),ok(X2)) , Marked_plus(X1,X2)>
<Marked_s(ok(X)) , Marked_s(X)>
<Marked_top(mark(X)) , Marked_top(proper(X))>
<Marked_top(mark(X)) , Marked_proper(X)>
<Marked_top(ok(X)) , Marked_top(active(X))>
<Marked_top(ok(X)) , Marked_active(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 6 components:

{  <Marked_top(ok(X)) , Marked_top(active(X))> 
      --> <Marked_top(ok(X)) , Marked_top(active(X))>
  <Marked_top(ok(X)) , Marked_top(active(X))> 
     --> <Marked_top(mark(X)) , Marked_top(proper(X))>
  <Marked_top(mark(X)) , Marked_top(proper(X))> 
     --> <Marked_top(ok(X)) , Marked_top(active(X))>
  <Marked_top(mark(X)) , Marked_top(proper(X))> 
     --> <Marked_top(mark(X)) , Marked_top(proper(X))>
}

{  <Marked_proper(s(X)) , Marked_proper(X)> 
      --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(s(X)) , Marked_proper(X)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(plus(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X2)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(s(X)) , Marked_proper(X)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X2)>
  <Marked_proper(and(X1,X2)) , Marked_proper(X1)> 
     --> <Marked_proper(and(X1,X2)) , Marked_proper(X1)>
}

{  <Marked_active(s(X)) , Marked_active(X)> 
      --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X2)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X1)>
  <Marked_active(s(X)) , Marked_active(X)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(plus(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(plus(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X2)>
  <Marked_active(plus(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X1)>
  <Marked_active(plus(X1,X2)) , Marked_active(X2)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(plus(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(plus(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X2)>
  <Marked_active(plus(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X1)>
  <Marked_active(plus(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(s(X)) , Marked_active(X)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X2)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(plus(X1,X2)) , Marked_active(X1)>
  <Marked_active(and(X1,X2)) , Marked_active(X1)> 
     --> <Marked_active(and(X1,X2)) , Marked_active(X1)>
}

{  <Marked_and(ok(X1),ok(X2)) , Marked_and(X1,X2)> 
      --> <Marked_and(ok(X1),ok(X2)) , Marked_and(X1,X2)>
  <Marked_and(ok(X1),ok(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(ok(X1),ok(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(ok(X1),ok(X2)) , Marked_plus(X1,X2)> 
      --> <Marked_plus(ok(X1),ok(X2)) , Marked_plus(X1,X2)>
  <Marked_plus(ok(X1),ok(X2)) , Marked_plus(X1,X2)> 
     --> <Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)>
  <Marked_plus(ok(X1),ok(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(ok(X1),ok(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(ok(X1),ok(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(ok(X)) , Marked_s(X)> --> <Marked_s(ok(X)) , Marked_s(X)>
  <Marked_s(ok(X)) , Marked_s(X)> --> <Marked_s(mark(X)) , Marked_s(X)>
  <Marked_s(mark(X)) , Marked_s(X)> --> <Marked_s(ok(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:
{
  active(and(tt,X)) >= mark(X) ;
  active(and(X1,X2)) >= and(active(X1),X2) ;
  active(plus(N,0)) >= mark(N) ;
  active(plus(N,s(M))) >= mark(s(plus(N,M))) ;
  active(plus(X1,X2)) >= plus(active(X1),X2) ;
  active(plus(X1,X2)) >= plus(X1,active(X2)) ;
  active(s(X)) >= s(active(X)) ;
  and(mark(X1),X2) >= mark(and(X1,X2)) ;
  and(ok(X1),ok(X2)) >= ok(and(X1,X2)) ;
  plus(mark(X1),X2) >= mark(plus(X1,X2)) ;
  plus(ok(X1),ok(X2)) >= ok(plus(X1,X2)) ;
  plus(X1,mark(X2)) >= mark(plus(X1,X2)) ;
  s(mark(X)) >= mark(s(X)) ;
  s(ok(X)) >= ok(s(X)) ;
  proper(and(X1,X2)) >= and(proper(X1),proper(X2)) ;
  proper(tt) >= ok(tt) ;
  proper(plus(X1,X2)) >= plus(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(s(X)) >= s(proper(X)) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_top(mark(X)) >= Marked_top(proper(X)) ;
  Marked_top(ok(X)) >= Marked_top(active(X)) ;
 }
 + Disjunctions:{ 
{
  Marked_top(mark(X)) > Marked_top(proper(X)) ;
 }
{
  Marked_top(ok(X)) > Marked_top(active(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: active(and(tt,X)) >= mark(X)
constraint: active(and(X1,X2)) >= and(active(X1),X2)
constraint: active(plus(N,0)) >= mark(N)
constraint: active(plus(N,s(M))) >= mark(s(plus(N,M)))
constraint: active(plus(X1,X2)) >= plus(active(X1),X2)
constraint: active(plus(X1,X2)) >= plus(X1,active(X2))
constraint: active(s(X)) >= s(active(X))
constraint: and(mark(X1),X2) >= mark(and(X1,X2))
constraint: and(ok(X1),ok(X2)) >= ok(and(X1,X2))
constraint: plus(mark(X1),X2) >= mark(plus(X1,X2))
constraint: plus(ok(X1),ok(X2)) >= ok(plus(X1,X2))
constraint: plus(X1,mark(X2)) >= mark(plus(X1,X2))
constraint: s(mark(X)) >= mark(s(X))
constraint: s(ok(X)) >= ok(s(X))
constraint: proper(and(X1,X2)) >= and(proper(X1),proper(X2))
constraint: proper(tt) >= ok(tt)
constraint: proper(plus(X1,X2)) >= plus(proper(X1),proper(X2))
constraint: proper(0) >= ok(0)
constraint: proper(s(X)) >= s(proper(X))
constraint: top(mark(X)) >= top(proper(X))
constraint: top(ok(X)) >= top(active(X))
constraint: Marked_top(mark(X)) >= Marked_top(proper(X))
constraint: Marked_top(ok(X)) >= Marked_top(active(X))
APPLY CRITERIA (Subterm criterion)

ST: Marked_proper -> 1

APPLY CRITERIA (Subterm criterion)

ST: Marked_active -> 1

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_top(ok(X)) , Marked_top(active(X))> 
      --> <Marked_top(ok(X)) , Marked_top(active(X))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  active(and(tt,X)) >= mark(X) ;
  active(and(X1,X2)) >= and(active(X1),X2) ;
  active(plus(N,0)) >= mark(N) ;
  active(plus(N,s(M))) >= mark(s(plus(N,M))) ;
  active(plus(X1,X2)) >= plus(active(X1),X2) ;
  active(plus(X1,X2)) >= plus(X1,active(X2)) ;
  active(s(X)) >= s(active(X)) ;
  and(mark(X1),X2) >= mark(and(X1,X2)) ;
  and(ok(X1),ok(X2)) >= ok(and(X1,X2)) ;
  plus(mark(X1),X2) >= mark(plus(X1,X2)) ;
  plus(ok(X1),ok(X2)) >= ok(plus(X1,X2)) ;
  plus(X1,mark(X2)) >= mark(plus(X1,X2)) ;
  s(mark(X)) >= mark(s(X)) ;
  s(ok(X)) >= ok(s(X)) ;
  proper(and(X1,X2)) >= and(proper(X1),proper(X2)) ;
  proper(tt) >= ok(tt) ;
  proper(plus(X1,X2)) >= plus(proper(X1),proper(X2)) ;
  proper(0) >= ok(0) ;
  proper(s(X)) >= s(proper(X)) ;
  top(mark(X)) >= top(proper(X)) ;
  top(ok(X)) >= top(active(X)) ;
  Marked_top(ok(X)) >= Marked_top(active(X)) ;
 }
 + Disjunctions:{ 
{
  Marked_top(ok(X)) > Marked_top(active(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: active(and(tt,X)) >= mark(X)
constraint: active(and(X1,X2)) >= and(active(X1),X2)
constraint: active(plus(N,0)) >= mark(N)
constraint: active(plus(N,s(M))) >= mark(s(plus(N,M)))
constraint: active(plus(X1,X2)) >= plus(active(X1),X2)
constraint: active(plus(X1,X2)) >= plus(X1,active(X2))
constraint: active(s(X)) >= s(active(X))
constraint: and(mark(X1),X2) >= mark(and(X1,X2))
constraint: and(ok(X1),ok(X2)) >= ok(and(X1,X2))
constraint: plus(mark(X1),X2) >= mark(plus(X1,X2))
constraint: plus(ok(X1),ok(X2)) >= ok(plus(X1,X2))
constraint: plus(X1,mark(X2)) >= mark(plus(X1,X2))
constraint: s(mark(X)) >= mark(s(X))
constraint: s(ok(X)) >= ok(s(X))
constraint: proper(and(X1,X2)) >= and(proper(X1),proper(X2))
constraint: proper(tt) >= ok(tt)
constraint: proper(plus(X1,X2)) >= plus(proper(X1),proper(X2))
constraint: proper(0) >= ok(0)
constraint: proper(s(X)) >= s(proper(X))
constraint: top(mark(X)) >= top(proper(X))
constraint: top(ok(X)) >= top(active(X))
constraint: Marked_top(ok(X)) >= Marked_top(active(X))
APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
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)>
}
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)>
}
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] active(and(X1,X2)) -> and(active(X1),X2)
[5] active(plus(X1,X2)) -> plus(active(X1),X2)
[6] active(plus(X1,X2)) -> plus(X1,active(X2))
[7] active(s(X)) -> s(active(X))
[8] and(mark(X1),X2) -> mark(and(X1,X2))
[9] plus(mark(X1),X2) -> mark(plus(X1,X2))
[10] plus(X1,mark(X2)) -> mark(plus(X1,X2))
[11] s(mark(X)) -> mark(s(X))
[12] proper(and(X1,X2)) -> and(proper(X1),proper(X2))
[13] proper(tt) -> ok(tt)
[14] proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
[15] proper(0) -> ok(0)
[16] proper(s(X)) -> s(proper(X))
[17] and(ok(X1),ok(X2)) -> ok(and(X1,X2))
[18] plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
[19] s(ok(X)) -> ok(s(X))
[20] top(mark(X)) -> top(proper(X))
[21] top(ok(X)) -> top(active(X))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_active(plus(N,s(M))) , Marked_s(plus(N,M))>
<Marked_active(plus(N,s(M))) , Marked_plus(N,M)>
<Marked_active(and(X1,X2)) , Marked_and(active(X1),X2)>
<Marked_active(and(X1,X2)) , Marked_active(X1)>
<Marked_active(plus(X1,X2)) , Marked_plus(active(X1),X2)>
<Marked_active(plus(X1,X2)) , Marked_active(X1)>
<Marked_active(plus(X1,X2)) , Marked_plus(X1,active(X2))>
<Marked_active(plus(X1,X2)) , Marked_active(X2)>
<Marked_active(s(X)) , Marked_s(active(X))>
<Marked_active(s(X)) , Marked_active(X)>
<Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
<Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
<Marked_plus(X1,mark(X2)) , Marked_plus(X1,X2)>
<Marked_s(mark(X)) , Marked_s(X)>
<Marked_proper(and(X1,X2)) , Marked_and(proper(X1),proper(X2))>
<Marked_proper(and(X1,X2)) , Marked_proper(X1)>
<Marked_proper(and(X1,X2)) , Marked_proper(X2)>
<Marked_proper(plus(X1,X2)) , Marked_plus(proper(X1),proper(X2))>
<Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
<Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
<Marked_proper(s(X)) , Marked_s(proper(X))>
<Marked_proper(s(X)) , Marked_proper(X)>
<Marked_and(ok(X1),ok(X2)) , Marked_and(X1,X2)>
<Marked_plus(ok(X1),ok(X2)) , Marked_plus(X1,X2)>
<Marked_s(ok(X)) , Marked_s(X)>
<Marked_top(mark(X)) , Marked_top(proper(X))>
<Marked_top(mark(X)) , Marked_proper(X)>
<Marked_top(ok(X)) , Marked_top(active(X))>
<Marked_top(ok(X)) , Marked_active(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_top(mark(X)) , Marked_top(proper(X))>
<Marked_top(ok(X)) , Marked_top(active(X))>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 1*X0 + 1; 
 [ ok ] (X0) = 1*X0; 
 [ plus ] (X0,X1) = 2*X1 + 2*X0; 
 [ and ] (X0,X1) = 1*X1 + 1*X0 + 1; 
 [ Marked_top ] (X0) = 1*X0; 
 [ s ] (X0) = 1*X0 + 2; 
 [ active ] (X0) = 1*X0; 
 [ top ] (X0) = 0; 
 [ 0 ] () = 1; 
 [ tt ] () = 0; 
 [ proper ] (X0) = 1*X0; 
 removing <Marked_top(mark(X)),Marked_top(proper(X))>
 [ {
      
     DP termination of:
     <Marked_top(ok(X)) , Marked_top(active(X))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_top(ok(X)) , Marked_top(active(X))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ mark ] (X0) = 1*X0 + 0; 
 [ ok ] (X0) = 2 + 2*X0 + 0; 
 [ plus ] (X0,X1) = 2 + 2*X0 + 1*X1 + 0; 
 [ and ] (X0,X1) = 1*X1 + 0; 
 [ Marked_top ] (X0) = 3*X0 + 0; 
 [ s ] (X0) = 1 + 2*X0 + 0; 
 [ active ] (X0) = 2*X0 + 0; 
 [ top ] (X0) = 0; 
 [ 0 ] () = 0; 
 [ tt ] () = 2 + 0; 
 [ proper ] (X0) = 2 + 3*X0 + 0; 
 ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_proper(and(X1,X2)) , Marked_proper(X1)>
<Marked_proper(and(X1,X2)) , Marked_proper(X2)>
<Marked_proper(plus(X1,X2)) , Marked_proper(X1)>
<Marked_proper(plus(X1,X2)) , Marked_proper(X2)>
<Marked_proper(s(X)) , Marked_proper(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_active(and(X1,X2)) , Marked_active(X1)>
<Marked_active(plus(X1,X2)) , Marked_active(X1)>
<Marked_active(plus(X1,X2)) , Marked_active(X2)>
<Marked_active(s(X)) , Marked_active(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
{
 
DP termination of:
<Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
<Marked_and(ok(X1),ok(X2)) , Marked_and(X1,X2)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_and(mark(X1),X2) , Marked_and(X1,X2)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <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(ok(X1),ok(X2)) , Marked_plus(X1,X2)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_plus(mark(X1),X2) , Marked_plus(X1,X2)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <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(ok(X)) , Marked_s(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.192979 seconds (real time)
Cime Exit Status: 0