MAYBE
Rewrite Rules:
   [ a(f(?x),?y) -> f(a(f(?y),?x)),
     a(b(?x),?y) -> a(?x,b(?x)),
     a(g(?x),?x) -> g(b(g(?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...
   [ a(f(?x),?y) -> f(a(f(?y),?x)),
     a(b(?x),?y) -> a(?x,b(?x)),
     a(g(?x),?x) -> g(b(g(?x))) ]
Sort Assignment:
 a : 15*15=>15
 b : 15=>15
 f : 15=>15
 g : 15=>15
maximal types: {15}
Persistent Decomposition failed: Can't judge

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

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


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