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

TRS termination of:
[1] +(x,0) -> x
[2] +(minus(x),x) -> 0
[3] minus(0) -> 0
[4] minus(minus(x)) -> x
[5] minus(+(x,y)) -> +(minus(y),minus(x))
[6]  *(x,1) -> x
[7]  *(x,0) -> 0
[8]  *(x,+(y,z)) -> +( *(x,y), *(x,z))
[9]  *(x,minus(y)) -> minus( *(x,y))


Sub problem: 
guided: 

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

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

ST: Marked_* -> 2

APPLY CRITERIA (Subterm criterion)

ST: Marked_minus -> 1

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

Cime worked for 0.009049 seconds (real time)
Cime Exit Status: 0