NO
af/ONE-SORTED/735.trs
Input rules:
   [ a -> a,
     a -> b,
     f(a,a) -> f(b,f(f(a,b),a)) ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ a -> a,
     a -> b,
     f(a,a) -> f(b,f(f(a,b),a)) ]
Constructor pattern: [b,f(?x_1,?x_2)]
Defined pattern: [a]
Constructor subsystem:
   [ ]
Modified Constructor subsystem:
   [ ]
candidate for a:
   [ a -> b ]
Find a quasi-ordering ...
order successfully found
Precedence:
 a : Mul;
 b : Mul;
 f : Mul;
Rules:
   [ a -> b ]
Conjectures:
   [ f(a,a) = f(b,f(f(a,b),a)),
     a = a ]
STEP 0
ES:
   [ f(a,a) = f(b,f(f(a,b),a)),
     a = a ]
HS:
   [ ]
ES0:
   [ f(b,b) = f(b,f(f(b,b),b)),
     b = b ]
HS0:
   [ ]
ES1:
   [ f(b,b) = f(b,f(f(b,b),b)) ]
HS1:
   [ ]
No equation to expand
check Non-Ground-Confluence...
ground constructor terms for instantiation: {b,f(b,b)}
ground terms for instantiation: {b:o,f(b,b):o}
obtain 6 rules by 3 steps unfolding
obtain 29 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <f(b,f(f(a,b),a)) <- f(a,a) -> f(a,b)>
: Success(not GCR)
(4 msec.)
0.02