YES
(ignored inputs)COMMENT Example 3.2 of \cite{KS10} doi: http://dx.doi.org/10.1007/978-3-642-12251-4_20
Rewrite Rules:
   [ a -> b,
     a -> c,
     a -> e,
     b -> d,
     c -> a,
     d -> a,
     d -> e,
     g(?x) -> h(a),
     h(?x) -> e ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [ b = c,
     b = e,
     c = e,
     a = e ]
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:
   [ c = b,
     e = b,
     b = c,
     e = c,
     b = e,
     c = e,
     e = a,
     a = e ]
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 <c, b> by Rules <1, 0> preceded by []
 joinable by a reduction of rules <[([],4),([],0)], []>
 joinable by a reduction of rules <[([],4)], [([],3),([],5)]>
 joinable by a reduction of rules <[([],4),([],2)], [([],3),([],6)]>
Critical Pair <e, b> by Rules <2, 0> preceded by []
 joinable by a reduction of rules <[], [([],3),([],6)]>
Critical Pair <e, c> by Rules <2, 1> preceded by []
 joinable by a reduction of rules <[], [([],4),([],2)]>
Critical Pair <e, a> by Rules <6, 5> preceded by []
 joinable by a reduction of rules <[], [([],2)]>
Satisfiable by 1>6>2,3,5,7>4,8,9; g(0)h(0); 2>1>6>3,5,7>4,8,9
Diagram Decreasing
Direct Methods: CR

Final result: CR
111.trs: Success(CR)
(10 msec.)