NO
(ignored inputs)COMMENT Example 3.3.2 of \cite{Gra96thesis}
Rewrite Rules:
   [ f(b) -> a,
     f(b) -> f(c),
     f(c) -> f(b),
     f(c) -> d,
     b -> e,
     c -> e',
     f(e) -> a,
     f(e') -> d ]
Apply Direct Methods...
Inner CPs:
   [ f(e) = a,
     f(e) = f(c),
     f(e') = f(b),
     f(e') = d ]
Outer CPs:
   [ a = f(c),
     f(b) = d ]
not Overlay, check Termination...
unknown/not 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(c) = a,
     f(e) = a,
     a = f(c),
     f(e) = f(c),
     d = f(b),
     f(e') = f(b),
     f(b) = d,
     f(e') = d,
     a = f(e),
     f(c) = f(e),
     f(b) = f(e'),
     d = f(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 <f(e), a> by Rules <4, 0> preceded by [(f,1)]
 joinable by a reduction of rules <[([],6)], []>
Critical Pair <f(e), f(c)> by Rules <4, 1> preceded by [(f,1)]
 joinable by a reduction of rules <[], [([],2),([(f,1)],4)]>
 joinable by a reduction of rules <[([],6)], [([],2),([],0)]>
Critical Pair <f(e'), f(b)> by Rules <5, 2> preceded by [(f,1)]
 joinable by a reduction of rules <[], [([],1),([(f,1)],5)]>
 joinable by a reduction of rules <[([],7)], [([],1),([],3)]>
Critical Pair <f(e'), d> by Rules <5, 3> preceded by [(f,1)]
 joinable by a reduction of rules <[([],7)], []>
Critical Pair <f(c), a> by Rules <1, 0> preceded by []
 joinable by a reduction of rules <[([],2),([],0)], []>
Critical Pair <d, f(b)> by Rules <3, 2> preceded by []
 joinable by a reduction of rules <[], [([],1),([],3)]>
unknown Diagram Decreasing
check Non-Confluence...
obtain 18 rules by 3 steps unfolding
strenghten a and d
strenghten d and a
strenghten f(b) and a
strenghten f(b) and d
strenghten f(c) and a
strenghten f(c) and d
strenghten f(e) and a
strenghten f(e) and d
strenghten f(e') and a
strenghten f(e') and d
strenghten f(b) and f(c)
strenghten f(b) and f(e)
strenghten f(b) and f(e')
strenghten f(c) and f(b)
strenghten f(c) and f(e)
obtain 22 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <a, d>
Direct Methods: not CR

Final result: not CR
39.trs: Success(not CR)
(18 msec.)