YES
af/ONE-SORTED/503.trs
Input rules:
   [ f(a,a,b,b) -> f(c,c,c,c),
     a -> b,
     a -> c,
     b -> a,
     b -> c ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ f(a,a,b,b) -> f(c,c,c,c),
     a -> b,
     a -> c,
     b -> a,
     b -> c ]
Constructor pattern: [f(?x_1,?x_2,?x_3,?x_4),c]
Defined pattern: [b,a]
Constructor subsystem:
   [ ]
Modified Constructor subsystem:
   [ ]
candidate for b:
   [ b -> a ]
   [ b -> c ]
candidate for a:
   [ a -> b ]
   [ a -> c ]
Find a quasi-ordering ...
order successfully found
Precedence:
 f : Mul;
 b : Mul,  a : Mul;
 c : Mul;
Rules:
   [ b -> c,
     a -> c ]
Conjectures:
   [ f(a,a,b,b) = f(c,c,c,c),
     a = b,
     b = a ]
STEP 0
ES:
   [ f(a,a,b,b) = f(c,c,c,c),
     a = b,
     b = a ]
HS:
   [ ]
ES0:
   [ f(c,c,c,c) = f(c,c,c,c),
     c = c,
     c = c ]
HS0:
   [ ]
ES1:
   [ ]
HS1:
   [ ]
: Success(GCR)
(3 msec.)
0.02