YES
(ignored inputs)COMMENT submitted by: Christina Kohl secret problem 2022 category: TRS
Rewrite Rules:
   [ f(g(?x)) -> h(?x,?x),
     g(a) -> b,
     f(?x) -> h(?x,?x),
     b -> a,
     h(?x,?y) -> h(g(?x),g(?y)),
     g(?x) -> ?x,
     a -> b ]
Apply Direct Methods...
Inner CPs:
   [ f(b) = h(a,a),
     f(?x_3) = h(?x_3,?x_3),
     g(b) = b ]
Outer CPs:
   [ h(?x,?x) = h(g(?x),g(?x)),
     b = a ]
Left-Linear, not Right-Linear
(inner) Parallel CPs:
   [ f(?x_4) = h(?x_4,?x_4) {?x_4},
     f(b) = h(a,a) {},
     g(b) = b {} ]
Toyama (Parallel CPs)
Direct Methods: CR

Combined result: CR
1654.trs: Success(CR)
(0 msec.)