YES
af/ONE-SORTED/505.trs
Input rules:
   [ a -> b,
     f(?x:o,a) -> b,
     f(b,b) -> b ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ a -> b,
     f(?x:o,a) -> b,
     f(b,b) -> b ]
Constructor pattern: [b]
Defined pattern: [f(?x_2,?x_3),a]
Constructor subsystem:
   [ ]
Modified Constructor subsystem:
   [ ]
candidate for f(?x_2,?x_3):
   [ f(b,b) -> b ]
candidate for a:
   [ a -> b ]
Find a quasi-ordering ...
order successfully found
Precedence:
 a : Mul;
 b : Mul;
 f : Mul;
Rules:
   [ f(b,b) -> b,
     a -> b ]
Conjectures:
   [ f(?x,a) = b ]
STEP 0
ES:
   [ f(?x,a) = b ]
HS:
   [ ]
ES0:
   [ f(?x,b) = b ]
HS0:
   [ ]
ES1:
   [ f(?x,b) = b ]
HS1:
   [ ]
Expand f(?x,b) = b
   [ b = b ]
ES2:
   [ b = b ]
HS2:
   [ f(?x,b) -> b ]
STEP 1
ES:
   [ b = b ]
HS:
   [ f(?x,b) -> b ]
ES0:
   [ b = b ]
HS0:
   [ f(?x,b) -> b ]
ES1:
   [ ]
HS1:
   [ f(?x,b) -> b ]
: Success(GCR)
(3 msec.)
0.01