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

TRS termination of:
[1] plus(s(X),plus(Y,Z)) -> plus(X,plus(s(s(Y)),Z))
[2] plus(s(X1),plus(X2,plus(X3,X4))) -> plus(X1,plus(X3,plus(X2,X4)))


Sub problem: 
guided: 

DP termination of:
<Marked_plus(s(X),plus(Y,Z)) , Marked_plus(X,plus(s(s(Y)),Z))>
<Marked_plus(s(X),plus(Y,Z)) , Marked_plus(s(s(Y)),Z)>
<Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X1,plus(X3,plus(X2,X4)))>
<Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X3,plus(X2,X4))>
<Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X2,X4)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X2,X4)> 
      --> <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X2,X4)>
  <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X2,X4)> 
     --> <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X3,plus(X2,X4))>
  <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X2,X4)> 
     --> <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X1,
                                                     plus(X3,plus(X2,X4)))>
  <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X2,X4)> 
     --> <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(s(s(Y)),Z)>
  <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X2,X4)> 
     --> <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(X,plus(s(s(Y)),Z))>
  <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X3,plus(X2,X4))> 
     --> <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X2,X4)>
  <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X3,plus(X2,X4))> 
     --> <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X3,plus(X2,X4))>
  <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X3,plus(X2,X4))> 
     --> <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X1,
                                                     plus(X3,plus(X2,X4)))>
  <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X3,plus(X2,X4))> 
     --> <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(s(s(Y)),Z)>
  <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X3,plus(X2,X4))> 
     --> <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(X,plus(s(s(Y)),Z))>
  <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X1,
                                              plus(X3,plus(X2,X4)))> 
     --> <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X2,X4)>
  <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X1,
                                              plus(X3,plus(X2,X4)))> 
     --> <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X3,plus(X2,X4))>
  <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X1,
                                              plus(X3,plus(X2,X4)))> 
     --> <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X1,
                                                     plus(X3,plus(X2,X4)))>
  <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X1,
                                              plus(X3,plus(X2,X4)))> 
     --> <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(s(s(Y)),Z)>
  <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X1,
                                              plus(X3,plus(X2,X4)))> 
     --> <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(X,plus(s(s(Y)),Z))>
  <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(s(s(Y)),Z)> 
     --> <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X2,X4)>
  <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(s(s(Y)),Z)> 
     --> <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X3,plus(X2,X4))>
  <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(s(s(Y)),Z)> 
     --> <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X1,
                                                     plus(X3,plus(X2,X4)))>
  <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(s(s(Y)),Z)> 
     --> <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(s(s(Y)),Z)>
  <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(s(s(Y)),Z)> 
     --> <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(X,plus(s(s(Y)),Z))>
  <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(X,plus(s(s(Y)),Z))> 
     --> <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X2,X4)>
  <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(X,plus(s(s(Y)),Z))> 
     --> <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X3,plus(X2,X4))>
  <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(X,plus(s(s(Y)),Z))> 
     --> <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X1,
                                                     plus(X3,plus(X2,X4)))>
  <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(X,plus(s(s(Y)),Z))> 
     --> <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(s(s(Y)),Z)>
  <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(X,plus(s(s(Y)),Z))> 
     --> <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(X,plus(s(s(Y)),Z))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  plus(s(X),plus(Y,Z)) >= plus(X,plus(s(s(Y)),Z)) ;
  plus(s(X1),plus(X2,plus(X3,X4))) >= plus(X1,plus(X3,plus(X2,X4))) ;
  Marked_plus(s(X),plus(Y,Z)) >= Marked_plus(s(s(Y)),Z) ;
  Marked_plus(s(X),plus(Y,Z)) >= Marked_plus(X,plus(s(s(Y)),Z)) ;
  Marked_plus(s(X1),plus(X2,plus(X3,X4))) >= Marked_plus(X1,
                                              plus(X3,plus(X2,X4))) ;
  Marked_plus(s(X1),plus(X2,plus(X3,X4))) >= Marked_plus(X2,X4) ;
  Marked_plus(s(X1),plus(X2,plus(X3,X4))) >= Marked_plus(X3,plus(X2,X4)) ;
 }
 + Disjunctions:{ 
{
  Marked_plus(s(X),plus(Y,Z)) > Marked_plus(s(s(Y)),Z) ;
 }
{
  Marked_plus(s(X),plus(Y,Z)) > Marked_plus(X,plus(s(s(Y)),Z)) ;
 }
{
  Marked_plus(s(X1),plus(X2,plus(X3,X4))) > Marked_plus(X1,
                                             plus(X3,plus(X2,X4))) ;
 }
{
  Marked_plus(s(X1),plus(X2,plus(X3,X4))) > Marked_plus(X2,X4) ;
 }
{
  Marked_plus(s(X1),plus(X2,plus(X3,X4))) > Marked_plus(X3,plus(X2,X4)) ;
 }
 } 
=== 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: plus(s(X),plus(Y,Z)) >= plus(X,plus(s(s(Y)),Z))
constraint: plus(s(X1),plus(X2,plus(X3,X4))) >= plus(X1,plus(X3,plus(X2,X4)))
constraint: Marked_plus(s(X),plus(Y,Z)) >= Marked_plus(s(s(Y)),Z)
constraint: Marked_plus(s(X),plus(Y,Z)) >= Marked_plus(X,plus(s(s(Y)),Z))
constraint: Marked_plus(s(X1),plus(X2,plus(X3,X4))) >= Marked_plus(X1,
                                                        plus(X3,plus(X2,X4)))
constraint: Marked_plus(s(X1),plus(X2,plus(X3,X4))) >= Marked_plus(X2,X4)
constraint: Marked_plus(s(X1),plus(X2,plus(X3,X4))) >= Marked_plus(X3,
                                                        plus(X2,X4))
APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X1,
                                               plus(X3,plus(X2,X4)))> 
      --> <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X1,
                                                      plus(X3,plus(X2,X4)))>
  <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X1,
                                              plus(X3,plus(X2,X4)))> 
     --> <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(X,plus(s(s(Y)),Z))>
  <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(X,plus(s(s(Y)),Z))> 
     --> <Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X1,
                                                     plus(X3,plus(X2,X4)))>
  <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(X,plus(s(s(Y)),Z))> 
     --> <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(X,plus(s(s(Y)),Z))>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_plus -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] plus(s(X),plus(Y,Z)) -> plus(X,plus(s(s(Y)),Z))
[2] plus(s(X1),plus(X2,plus(X3,X4))) -> plus(X1,plus(X3,plus(X2,X4)))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(X,plus(s(s(Y)),Z))>
<Marked_plus(s(X),plus(Y,Z)) , Marked_plus(s(s(Y)),Z)>
<Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X1,plus(X3,plus(X2,X4)))>
<Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X3,plus(X2,X4))>
<Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X2,X4)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(X,plus(s(s(Y)),Z))>
<Marked_plus(s(X),plus(Y,Z)) , Marked_plus(s(s(Y)),Z)>
<Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X1,plus(X3,plus(X2,X4)))>
<Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X3,plus(X2,X4))>
<Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X2,X4)>
 ,
 CRITERION: CG using polynomial interpretation = 
 [ plus ] (X0,X1) = 2*X1 + 2; 
 [ Marked_plus ] (X0,X1) = 2*X1; 
 [ s ] (X0) = 0; 
 removing <Marked_plus(s(X),plus(Y,Z)),Marked_plus(s(s(Y)),Z)><Marked_plus(
                                                                s(X1),
                                                                plus(
                                                                 X2,
                                                                 plus(X3,X4))),
Marked_plus(X3,plus(X2,X4))><Marked_plus(s(X1),plus(X2,plus(X3,X4))),
Marked_plus(X2,X4)>
 [ {
      
     DP termination of:
     <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(X,plus(s(s(Y)),Z))>
<Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X1,plus(X3,plus(X2,X4)))>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_plus(s(X),plus(Y,Z)) , Marked_plus(X,plus(s(s(Y)),Z))>
<Marked_plus(s(X1),plus(X2,plus(X3,X4))) , Marked_plus(X1,plus(X3,plus(X2,X4)))>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
 ]} 
 ]} 

Cime worked for 0.059966 seconds (real time)
Cime Exit Status: 0