MAYBE
Rewrite Rules:
   [ f(?x,?x) -> plus(plus(?x,?x),?x),
     plus(?x,?y) -> plus(?y,?x) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [  ]
Overlay, check Innermost Termination...
unknown Innermost Terminating
not Left-Linear, not Right-Linear
unknown Gomi&Oyamaguchi&Ohta
check Non-Confluence...Unknown
Direct Methods: Can't judge

Try Persistent Decomposition for...
   [ f(?x,?x) -> plus(plus(?x,?x),?x),
     plus(?x,?y) -> plus(?y,?x) ]
Sort Assignment:
 f : 10*10=>10
 plus : 10*10=>10
maximal types: {10}
Persistent Decomposition failed: Can't judge

Try Layer Preserving Decomposition for...
   [ f(?x,?x) -> plus(plus(?x,?x),?x),
     plus(?x,?y) -> plus(?y,?x) ]
Layer Preserving Decomposition failed: Can't judge

Try Commutative Decomposition for...
   [ f(?x,?x) -> plus(plus(?x,?x),?x),
     plus(?x,?y) -> plus(?y,?x) ]
Commutative Decomposition failed: Can't judge
No further decomposition possible


Final result: Can't judge
example9.trs: MAYBE (0 msec.)