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

TRS termination of:
[1] a__and(tt,X) -> mark(X)
[2] a__plus(N,0) -> mark(N)
[3] a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M)))
[4] mark(and(X1,X2)) -> a__and(mark(X1),X2)
[5] mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
[6] mark(tt) -> tt
[7] mark(0) -> 0
[8] mark(s(X)) -> s(mark(X))
[9] a__and(X1,X2) -> and(X1,X2)
[10] a__plus(X1,X2) -> plus(X1,X2)


Sub problem: 
guided: 

DP termination of:
<Marked_a__and(tt,X) , Marked_mark(X)>
<Marked_a__plus(N,0) , Marked_mark(N)>
<Marked_a__plus(N,s(M)) , Marked_a__plus(mark(N),mark(M))>
<Marked_a__plus(N,s(M)) , Marked_mark(N)>
<Marked_a__plus(N,s(M)) , Marked_mark(M)>
<Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(plus(X1,X2)) , Marked_a__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_mark(X)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_mark(s(X)) , Marked_mark(X)> 
      --> <Marked_mark(s(X)) , Marked_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_a__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_a__and(mark(X1),X2)>
  <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(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_a__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_a__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(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_a__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_a__and(mark(X1),X2)>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,s(M)) , Marked_mark(M)>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,s(M)) , Marked_mark(N)>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,s(M)) , Marked_a__plus(mark(N),mark(M))>
  <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))> 
     --> <Marked_a__plus(N,0) , Marked_mark(N)>
  <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(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_a__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_a__and(mark(X1),X2)>
  <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)> 
     --> <Marked_a__and(tt,X) , Marked_mark(X)>
  <Marked_a__plus(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__plus(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__plus(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__plus(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__plus(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__plus(N,s(M)) , Marked_mark(M)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__plus(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__plus(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__plus(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__plus(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__plus(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__plus(N,s(M)) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__plus(N,s(M)) , Marked_a__plus(mark(N),mark(M))> 
     --> <Marked_a__plus(N,s(M)) , Marked_mark(M)>
  <Marked_a__plus(N,s(M)) , Marked_a__plus(mark(N),mark(M))> 
     --> <Marked_a__plus(N,s(M)) , Marked_mark(N)>
  <Marked_a__plus(N,s(M)) , Marked_a__plus(mark(N),mark(M))> 
     --> <Marked_a__plus(N,s(M)) , Marked_a__plus(mark(N),mark(M))>
  <Marked_a__plus(N,s(M)) , Marked_a__plus(mark(N),mark(M))> 
     --> <Marked_a__plus(N,0) , Marked_mark(N)>
  <Marked_a__plus(N,0) , Marked_mark(N)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__plus(N,0) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__plus(N,0) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__plus(N,0) , Marked_mark(N)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__plus(N,0) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__plus(N,0) , Marked_mark(N)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X2)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_mark(X1)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(plus(X1,X2)) , Marked_a__plus(mark(X1),mark(X2))>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <Marked_a__and(tt,X) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(tt) >= tt ;
  mark(0) >= 0 ;
  mark(s(X)) >= s(mark(X)) ;
  mark(and(X1,X2)) >= a__and(mark(X1),X2) ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  a__and(tt,X) >= mark(X) ;
  a__and(X1,X2) >= and(X1,X2) ;
  a__plus(N,0) >= mark(N) ;
  a__plus(N,s(M)) >= s(a__plus(mark(N),mark(M))) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  Marked_a__plus(N,0) >= Marked_mark(N) ;
  Marked_a__plus(N,s(M)) >= Marked_a__plus(mark(N),mark(M)) ;
  Marked_a__plus(N,s(M)) >= Marked_mark(N) ;
  Marked_a__plus(N,s(M)) >= Marked_mark(M) ;
  Marked_a__and(tt,X) >= Marked_mark(X) ;
  Marked_mark(s(X)) >= Marked_mark(X) ;
  Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2) ;
  Marked_mark(and(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2)) ;
  Marked_mark(plus(X1,X2)) >= Marked_mark(X1) ;
  Marked_mark(plus(X1,X2)) >= Marked_mark(X2) ;
 }
 + Disjunctions:{ 
{
  Marked_a__plus(N,0) > Marked_mark(N) ;
 }
{
  Marked_a__plus(N,s(M)) > Marked_a__plus(mark(N),mark(M)) ;
 }
{
  Marked_a__plus(N,s(M)) > Marked_mark(N) ;
 }
{
  Marked_a__plus(N,s(M)) > Marked_mark(M) ;
 }
{
  Marked_a__and(tt,X) > Marked_mark(X) ;
 }
{
  Marked_mark(s(X)) > Marked_mark(X) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_a__and(mark(X1),X2) ;
 }
{
  Marked_mark(and(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(plus(X1,X2)) > Marked_a__plus(mark(X1),mark(X2)) ;
 }
{
  Marked_mark(plus(X1,X2)) > Marked_mark(X1) ;
 }
{
  Marked_mark(plus(X1,X2)) > Marked_mark(X2) ;
 }
 } 
=== 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(tt) >= tt
constraint: mark(0) >= 0
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2)
constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2))
constraint: a__and(tt,X) >= mark(X)
constraint: a__and(X1,X2) >= and(X1,X2)
constraint: a__plus(N,0) >= mark(N)
constraint: a__plus(N,s(M)) >= s(a__plus(mark(N),mark(M)))
constraint: a__plus(X1,X2) >= plus(X1,X2)
constraint: Marked_a__plus(N,0) >= Marked_mark(N)
constraint: Marked_a__plus(N,s(M)) >= Marked_a__plus(mark(N),mark(M))
constraint: Marked_a__plus(N,s(M)) >= Marked_mark(N)
constraint: Marked_a__plus(N,s(M)) >= Marked_mark(M)
constraint: Marked_a__and(tt,X) >= Marked_mark(X)
constraint: Marked_mark(s(X)) >= Marked_mark(X)
constraint: Marked_mark(and(X1,X2)) >= Marked_a__and(mark(X1),X2)
constraint: Marked_mark(and(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(plus(X1,X2)) >= Marked_a__plus(mark(X1),mark(X2))
constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X1)
constraint: Marked_mark(plus(X1,X2)) >= Marked_mark(X2)
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_a__plus(N,s(M)) , Marked_a__plus(mark(N),mark(M))> 
      --> <Marked_a__plus(N,s(M)) , Marked_a__plus(mark(N),mark(M))>
}

{  <Marked_mark(s(X)) , Marked_mark(X)> 
      --> <Marked_mark(s(X)) , Marked_mark(X)>
  <Marked_mark(s(X)) , Marked_mark(X)> 
     --> <Marked_mark(and(X1,X2)) , Marked_mark(X1)>
  <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(and(X1,X2)) , Marked_mark(X1)>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  mark(tt) >= tt ;
  mark(0) >= 0 ;
  mark(s(X)) >= s(mark(X)) ;
  mark(and(X1,X2)) >= a__and(mark(X1),X2) ;
  mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2)) ;
  a__and(tt,X) >= mark(X) ;
  a__and(X1,X2) >= and(X1,X2) ;
  a__plus(N,0) >= mark(N) ;
  a__plus(N,s(M)) >= s(a__plus(mark(N),mark(M))) ;
  a__plus(X1,X2) >= plus(X1,X2) ;
  Marked_a__plus(N,s(M)) >= Marked_a__plus(mark(N),mark(M)) ;
 }
 + Disjunctions:{ 
{
  Marked_a__plus(N,s(M)) > Marked_a__plus(mark(N),mark(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(tt) >= tt
constraint: mark(0) >= 0
constraint: mark(s(X)) >= s(mark(X))
constraint: mark(and(X1,X2)) >= a__and(mark(X1),X2)
constraint: mark(plus(X1,X2)) >= a__plus(mark(X1),mark(X2))
constraint: a__and(tt,X) >= mark(X)
constraint: a__and(X1,X2) >= and(X1,X2)
constraint: a__plus(N,0) >= mark(N)
constraint: a__plus(N,s(M)) >= s(a__plus(mark(N),mark(M)))
constraint: a__plus(X1,X2) >= plus(X1,X2)
constraint: Marked_a__plus(N,s(M)) >= Marked_a__plus(mark(N),mark(M))
APPLY CRITERIA (Subterm criterion)

ST: Marked_mark -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] a__and(tt,X) -> mark(X)
[2] a__plus(N,0) -> mark(N)
[3] a__plus(N,s(M)) -> s(a__plus(mark(N),mark(M)))
[4] mark(and(X1,X2)) -> a__and(mark(X1),X2)
[5] mark(plus(X1,X2)) -> a__plus(mark(X1),mark(X2))
[6] mark(tt) -> tt
[7] mark(0) -> 0
[8] mark(s(X)) -> s(mark(X))
[9] a__and(X1,X2) -> and(X1,X2)
[10] a__plus(X1,X2) -> plus(X1,X2)
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_a__and(tt,X) , Marked_mark(X)>
<Marked_a__plus(N,0) , Marked_mark(N)>
<Marked_a__plus(N,s(M)) , Marked_a__plus(mark(N),mark(M))>
<Marked_a__plus(N,s(M)) , Marked_mark(N)>
<Marked_a__plus(N,s(M)) , Marked_mark(M)>
<Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(plus(X1,X2)) , Marked_a__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_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a__and(tt,X) , Marked_mark(X)>
<Marked_a__plus(N,0) , Marked_mark(N)>
<Marked_a__plus(N,s(M)) , Marked_a__plus(mark(N),mark(M))>
<Marked_a__plus(N,s(M)) , Marked_mark(N)>
<Marked_a__plus(N,s(M)) , Marked_mark(M)>
<Marked_mark(and(X1,X2)) , Marked_a__and(mark(X1),X2)>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(plus(X1,X2)) , Marked_a__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_mark(X)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ mark ] (X0) = 1*X0; 
 [ Marked_a__plus ] (X0,X1) = 1*X1 + 1*X0 + 2; 
 [ 0 ] () = 0; 
 [ tt ] () = 1; 
 [ Marked_mark ] (X0) = 1*X0 + 2; 
 [ and ] (X0,X1) = 3*X1 + 2*X0; 
 [ a__and ] (X0,X1) = 3*X1 + 2*X0; 
 [ Marked_a__and ] (X0,X1) = 3*X1 + 1*X0 + 1; 
 [ s ] (X0) = 1*X0; 
 [ a__plus ] (X0,X1) = 1*X1 + 1*X0 + 2; 
 [ plus ] (X0,X1) = 1*X1 + 1*X0 + 2; 
 removing <Marked_mark(and(X1,X2)),Marked_a__and(mark(X1),X2)><Marked_mark(
                                                                plus(
                                                                 X1,X2)),
Marked_a__plus(mark(X1),mark(X2))><Marked_mark(plus(X1,X2)),Marked_mark(X1)><
Marked_mark(plus(X1,X2)),Marked_mark(X2)>
 [ {
      
     DP termination of:
     <Marked_a__and(tt,X) , Marked_mark(X)>
<Marked_a__plus(N,0) , Marked_mark(N)>
<Marked_a__plus(N,s(M)) , Marked_a__plus(mark(N),mark(M))>
<Marked_a__plus(N,s(M)) , Marked_mark(N)>
<Marked_a__plus(N,s(M)) , Marked_mark(M)>
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_mark(X)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_a__plus(N,s(M)) , Marked_a__plus(mark(N),mark(M))>
 ,
 CRITERION: ORD
 [ 
     Solution found:
     polynomial interpretation = 
      [ mark ] (X0) = 1*X0 + 0; 
 [ Marked_a__plus ] (X0,X1) = 2*X1 + 0; 
 [ 0 ] () = 0; 
 [ tt ] () = 0; 
 [ and ] (X0,X1) = 3*X1 + 0; 
 [ a__and ] (X0,X1) = 3*X1 + 0; 
 [ s ] (X0) = 2 + 1*X0 + 0; 
 [ a__plus ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0; 
 [ plus ] (X0,X1) = 2 + 1*X0 + 1*X1 + 0; 
 ]} 
{
 
DP termination of:
<Marked_mark(and(X1,X2)) , Marked_mark(X1)>
<Marked_mark(s(X)) , Marked_mark(X)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.115740 seconds (real time)
Cime Exit Status: 0