YES
(ignored inputs)COMMENT the following rules are removed from the original TRS c ( ) -> a ( ) c ( ) -> b ( )
Rewrite Rules:
   [ a -> b,
     b -> a,
     a -> d ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [ b = d ]
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:
   [ d = b,
     b = d ]
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 <d, b> by Rules <2, 0> preceded by []
 joinable by a reduction of rules <[], [([],1),([],2)]>
Satisfiable by 1>2,3; ; 1>2,3
Diagram Decreasing
Direct Methods: CR

Combined result: CR
/tmp/filegdeSrl.trs: Success(CR)
(13 msec.)