YES
Rewrite Rules:
   [ H(I(?x)) -> K(J(?x)),
     J(?x) -> K(J(?x)),
     I(?x) -> I(J(?x)),
     J(?x) -> J(K(J(?x))) ]
Apply Direct Methods...
Inner CPs:
   [ H(I(J(?x_2))) = K(J(?x_2)) ]
Outer CPs:
   [ K(J(?x_1)) = J(K(J(?x_1))) ]
not Overlay, check Termination...
unknown/not Terminating
unknown Knuth & Bendix
Linear
unknown Development Closed
unknown Strongly Closed
unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow
unknown Upside-Parallel-Closed/Outside-Closed
(inner) Parallel CPs: (not computed)
unknown Toyama (Parallel CPs)
Simultaneous CPs:
   [ H(I(J(?x))) = K(J(?x)),
     J(K(J(?x))) = K(J(?x)),
     K(J(?x)) = H(I(J(?x))),
     K(J(?x)) = J(K(J(?x))) ]
Okui (Simultaneous CPs)
Direct Methods: CR

Final result: CR
100.trs: Success(CR)
(5 msec.)