YES
(ignored inputs)COMMENT the following rules are removed from the original TRS g ( x ) -> h ( a ( ) ) h ( x ) -> e ( )
Rewrite Rules:
   [ a -> c,
     c -> a,
     d -> a,
     b -> d,
     a -> b,
     a -> e,
     d -> e ]
Apply Direct Methods...
Inner CPs:
   [  ]
Outer CPs:
   [ c = b,
     c = e,
     a = e,
     b = 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:
   [ b = c,
     e = c,
     e = a,
     c = b,
     e = b,
     c = e,
     b = e,
     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 <b, c> by Rules <4, 0> preceded by []
 joinable by a reduction of rules <[([],3),([],2)], [([],1)]>
 joinable by a reduction of rules <[], [([],1),([],4)]>
 joinable by a reduction of rules <[([],3),([],6)], [([],1),([],5)]>
Critical Pair <e, c> by Rules <5, 0> preceded by []
 joinable by a reduction of rules <[], [([],1),([],5)]>
Critical Pair <e, a> by Rules <6, 2> preceded by []
 joinable by a reduction of rules <[], [([],5)]>
Critical Pair <e, b> by Rules <5, 4> preceded by []
 joinable by a reduction of rules <[], [([],3),([],6)]>
Satisfiable by 5>4,1>3>7,6>2; ; 4,1>5>3>6,7>2
Diagram Decreasing
Direct Methods: CR

Combined result: CR
/tmp/fileAcn0HY.trs: Success(CR)
(15 msec.)