MAYBE
Rewrite Rules:
   [ f(?x,?x) -> h(?x,?x),
     c -> h(c,g(c)),
     h(g3(?x),g1(g2(?x))) -> f(?x,h(?x,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...
   [ f(?x,?x) -> h(?x,?x),
     c -> h(c,g(c)),
     h(g3(?x),g1(g2(?x))) -> f(?x,h(?x,g(?x))) ]
Sort Assignment:
 c : =>18
 f : 18*18=>18
 g : 18=>18
 h : 18*18=>18
 g1 : 12=>18
 g2 : 18=>12
 g3 : 18=>18
maximal types: {12,18}
Persistent Decomposition failed: Can't judge

Try Layer Preserving Decomposition for...
   [ f(?x,?x) -> h(?x,?x),
     c -> h(c,g(c)),
     h(g3(?x),g1(g2(?x))) -> f(?x,h(?x,g(?x))) ]
Layer Preserving Decomposition failed: Can't judge

Try Commutative Decomposition for...
   [ f(?x,?x) -> h(?x,?x),
     c -> h(c,g(c)),
     h(g3(?x),g1(g2(?x))) -> f(?x,h(?x,g(?x))) ]
Commutative Decomposition failed: Can't judge
No further decomposition possible


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