YES
af/ONE-SORTED/74.trs
Input rules:
   [ a -> c,
     b -> c,
     f(a,b) -> d,
     f(?x:o,c) -> f(c,c),
     f(c,?x:o) -> f(c,c),
     d -> f(a,c),
     d -> f(c,b) ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ a -> c,
     b -> c,
     f(a,b) -> d,
     f(?x:o,c) -> f(c,c),
     f(c,?x:o) -> f(c,c),
     d -> f(a,c),
     d -> f(c,b) ]
Constructor pattern: [c,f(?x_1,?x_2)]
Defined pattern: [d,b,a]
Constructor subsystem:
   [ f(?x,c) -> f(c,c),
     f(c,?x) -> f(c,c) ]
f(c,?x) -> f(c,c)
{?x:=c}
   [ {?x:=f(?x_1,?x_2)} ]
f(?x,c) -> f(c,c)
{?x:=c}
   [ {?x:=f(?x_1,?x_2)} ]
Modified Constructor subsystem:
   [ f(f(?x_1,?x_2),c) -> f(c,c),
     f(c,f(?x_1,?x_2)) -> f(c,c) ]
candidate for d:
   [ d -> f(a,c) ]
   [ d -> f(c,b) ]
candidate for b:
   [ b -> c ]
candidate for a:
   [ a -> c ]
Find a quasi-ordering ...
order successfully found
Precedence:
 d : Mul,  b : Mul;
 a : Mul;
 f : Mul;
 c : Mul;
Rules:
   [ d -> f(a,c),
     b -> c,
     a -> c,
     f(f(?x_1,?x_2),c) -> f(c,c),
     f(c,f(?x_1,?x_2)) -> f(c,c) ]
Check confluence of constructor subsystem...
Check Termination...
Terminating, WCR: CR
Conjectures:
   [ f(a,b) = d,
     d = f(c,b) ]
STEP 0
ES:
   [ f(a,b) = d,
     d = f(c,b) ]
HS:
   [ ]
ES0:
   [ f(c,c) = f(c,c),
     f(c,c) = f(c,c) ]
HS0:
   [ ]
ES1:
   [ ]
HS1:
   [ ]
: Success(GCR)
(3 msec.)
0.02