YES
(ignored inputs)COMMENT Example 1 of DOI:10.1007/s00200-004-0148-6
Rewrite Rules:
   [ f(f(a)) -> f(f(f(a))),
     f(f(a)) -> f(a) ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [ f(f(f(a))) = f(a) ]
Overlay, check Innermost Termination...
unknown Innermost 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:
   [ f(a) = f(f(f(a))),
     f(f(f(a))) = f(a) ]
unknown Okui (Simultaneous CPs)
unknown Strongly Depth-Preserving & Root-E-Closed/Non-E-Overlapping
unknown Strongly Weight-Preserving & Root-E-Closed/Non-E-Overlapping
check Locally Decreasing Diagrams by Rule Labelling...
Critical Pair <f(a), f(f(f(a)))> by Rules <1, 0> preceded by []
 joinable by a reduction of rules <[], [([(f,1)],1),([],1)]>
Satisfiable by 1,2; f(0); 1>2
Diagram Decreasing
Direct Methods: CR

Final result: CR
223.trs: Success(CR)
(2 msec.)