YES
af/ONE-SORTED/40.trs
Input rules:
   [ f(a) -> b,
     f(a) -> f(c),
     a -> d,
     f(d) -> b,
     f(c) -> b,
     d -> c ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ f(a) -> b,
     f(a) -> f(c),
     a -> d,
     f(d) -> b,
     f(c) -> b,
     d -> c ]
Constructor pattern: [f(?x_1),b,c]
Defined pattern: [d,a]
Constructor subsystem:
   [ f(c) -> b ]
Modified Constructor subsystem:
   [ f(c) -> b ]
candidate for d:
   [ d -> c ]
candidate for a:
   [ a -> d ]
Find a quasi-ordering ...
order successfully found
Precedence:
 a : Mul;
 d : Mul;
 f : Mul;
 c : Mul,  b : Mul;
Rules:
   [ d -> c,
     a -> d,
     f(c) -> b ]
Check confluence of constructor subsystem...
Check Termination...
Terminating, WCR: CR
Conjectures:
   [ f(a) = b,
     f(a) = f(c),
     f(d) = b ]
STEP 0
ES:
   [ f(a) = b,
     f(a) = f(c),
     f(d) = b ]
HS:
   [ ]
ES0:
   [ b = b,
     b = b,
     b = b ]
HS0:
   [ ]
ES1:
   [ ]
HS1:
   [ ]
: Success(GCR)
(2 msec.)
0.02