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

TRS termination of:
[1] +(x,0) -> x
[2] +(x,i(x)) -> 0
[3] +(+(x,y),z) -> +(x,+(y,z))
[4]  *(x,+(y,z)) -> +( *(x,y), *(x,z))
[5]  *(+(x,y),z) -> +( *(x,z), *(y,z))


Sub problem: 
guided: 

DP termination of:
<Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
<Marked_+(+(x,y),z) , Marked_+(y,z)>
<Marked_*(x,+(y,z)) , Marked_+( *(x,y), *(x,z))>
<Marked_*(x,+(y,z)) , Marked_*(x,y)>
<Marked_*(x,+(y,z)) , Marked_*(x,z)>
<Marked_*(+(x,y),z) , Marked_+( *(x,z), *(y,z))>
<Marked_*(+(x,y),z) , Marked_*(x,z)>
<Marked_*(+(x,y),z) , Marked_*(y,z)>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_*(+(x,y),z) , Marked_*(y,z)> 
      --> <Marked_*(+(x,y),z) , Marked_*(y,z)>
  <Marked_*(+(x,y),z) , Marked_*(y,z)> --> <Marked_*(+(x,y),z) , Marked_*(x,z)>
  <Marked_*(+(x,y),z) , Marked_*(y,z)> --> <Marked_*(x,+(y,z)) , Marked_*(x,z)>
  <Marked_*(+(x,y),z) , Marked_*(y,z)> --> <Marked_*(x,+(y,z)) , Marked_*(x,y)>
  <Marked_*(+(x,y),z) , Marked_*(x,z)> --> <Marked_*(+(x,y),z) , Marked_*(y,z)>
  <Marked_*(+(x,y),z) , Marked_*(x,z)> --> <Marked_*(+(x,y),z) , Marked_*(x,z)>
  <Marked_*(+(x,y),z) , Marked_*(x,z)> --> <Marked_*(x,+(y,z)) , Marked_*(x,z)>
  <Marked_*(+(x,y),z) , Marked_*(x,z)> --> <Marked_*(x,+(y,z)) , Marked_*(x,y)>
  <Marked_*(x,+(y,z)) , Marked_*(x,z)> --> <Marked_*(+(x,y),z) , Marked_*(y,z)>
  <Marked_*(x,+(y,z)) , Marked_*(x,z)> --> <Marked_*(+(x,y),z) , Marked_*(x,z)>
  <Marked_*(x,+(y,z)) , Marked_*(x,z)> --> <Marked_*(x,+(y,z)) , Marked_*(x,z)>
  <Marked_*(x,+(y,z)) , Marked_*(x,z)> --> <Marked_*(x,+(y,z)) , Marked_*(x,y)>
  <Marked_*(x,+(y,z)) , Marked_*(x,y)> --> <Marked_*(+(x,y),z) , Marked_*(y,z)>
  <Marked_*(x,+(y,z)) , Marked_*(x,y)> --> <Marked_*(+(x,y),z) , Marked_*(x,z)>
  <Marked_*(x,+(y,z)) , Marked_*(x,y)> --> <Marked_*(x,+(y,z)) , Marked_*(x,z)>
  <Marked_*(x,+(y,z)) , Marked_*(x,y)> --> <Marked_*(x,+(y,z)) , Marked_*(x,y)>
}

{  <Marked_+(+(x,y),z) , Marked_+(y,z)> 
      --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(+(x,y),z) , Marked_+(y,z)> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
  <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))> 
     --> <Marked_+(+(x,y),z) , Marked_+(y,z)>
  <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))> 
     --> <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_* -> 2

APPLY CRITERIA (Subterm criterion)

ST: Marked_+ -> 1

APPLY CRITERIA (Graph splitting)
Found 1 components:

{  <Marked_*(+(x,y),z) , Marked_*(x,z)> 
      --> <Marked_*(+(x,y),z) , Marked_*(x,z)>
  <Marked_*(+(x,y),z) , Marked_*(x,z)> --> <Marked_*(+(x,y),z) , Marked_*(y,z)>
  <Marked_*(+(x,y),z) , Marked_*(y,z)> --> <Marked_*(+(x,y),z) , Marked_*(x,z)>
  <Marked_*(+(x,y),z) , Marked_*(y,z)> --> <Marked_*(+(x,y),z) , Marked_*(y,z)>
}
APPLY CRITERIA (Subterm criterion)

ST: Marked_* -> 1

APPLY CRITERIA (Graph splitting)
Found 0 components:
APPLY CRITERIA (Graph splitting)
Found 0 components:
SOLVED
{
 
TRS termination of:
[1] +(x,0) -> x
[2] +(x,i(x)) -> 0
[3] +(+(x,y),z) -> +(x,+(y,z))
[4]  *(x,+(y,z)) -> +( *(x,y), *(x,z))
[5]  *(+(x,y),z) -> +( *(x,z), *(y,z))
 ,
 CRITERION: MDP
 [ {
      
     DP termination of:
     <Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
<Marked_+(+(x,y),z) , Marked_+(y,z)>
<Marked_*(x,+(y,z)) , Marked_+( *(x,y), *(x,z))>
<Marked_*(x,+(y,z)) , Marked_*(x,y)>
<Marked_*(x,+(y,z)) , Marked_*(x,z)>
<Marked_*(+(x,y),z) , Marked_+( *(x,z), *(y,z))>
<Marked_*(+(x,y),z) , Marked_*(x,z)>
<Marked_*(+(x,y),z) , Marked_*(y,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_*(x,+(y,z)) , Marked_*(x,y)>
<Marked_*(x,+(y,z)) , Marked_*(x,z)>
<Marked_*(+(x,y),z) , Marked_*(x,z)>
<Marked_*(+(x,y),z) , Marked_*(y,z)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
     <Marked_*(+(x,y),z) , Marked_*(y,z)>
<Marked_*(+(x,y),z) , Marked_*(x,z)>
 ,
 CRITERION: SG
 [ {
      
     DP termination of:
     <Marked_*(+(x,y),z) , Marked_*(y,z)>
<Marked_*(+(x,y),z) , Marked_*(x,z)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 
{
 
DP termination of:
<Marked_+(+(x,y),z) , Marked_+(x,+(y,z))>
<Marked_+(+(x,y),z) , Marked_+(y,z)>
 ,
 CRITERION: ST
 [ {
      
     DP termination of:
      ,
      CRITERION: SG
      [  ]} 
      ]} 
 ]} 
 ]} 

Cime worked for 0.011989 seconds (real time)
Cime Exit Status: 0