YES
(ignored inputs)COMMENT the following rules are removed from the original TRS * ( + ( y , x ) , z ) -> + ( * ( x , z ) , * ( y , z ) )
Rewrite Rules:
   [ *(+(?x,?y),?z) -> +(*(?x,?z),*(?y,?z)),
     +(?x,?y) -> +(?y,?x) ]
Apply Direct Methods...
Inner CPs:
   [ *(+(?y_1,?x_1),?z) = +(*(?x_1,?z),*(?y_1,?z)) ]
Outer CPs:
   [  ]
not Overlay, check Termination...
unknown/not Terminating
unknown Knuth & Bendix
Left-Linear, not Right-Linear
unknown Development Closed
unknown Weakly-Non-Overlapping & Non-Collapsing & Shallow
inner CP cond (upside-parallel)
innter CP Cond (outside)
unknown Upside-Parallel-Closed/Outside-Closed
(inner) Parallel CPs:
   [ *(+(?y_2,?x_2),?z) = +(*(?x_2,?z),*(?y_2,?z)) {?x_2,?y_2} ]
unknown Toyama (Parallel CPs)
Simultaneous CPs:
   [ *(+(?y,?x),?z) = +(*(?x,?z),*(?y,?z)),
     +(*(?x,?z_2),*(?y,?z_2)) = *(+(?y,?x),?z_2) ]
Okui (Simultaneous CPs)
Direct Methods: CR

Combined result: CR
/tmp/file1wdPtG.trs: Success(CR)
(0 msec.)