NO
af/ONE-SORTED/683.trs
Input rules:
   [ f(h(b,a)) -> a,
     f(f(f(c))) -> c,
     b -> c,
     c -> c,
     a -> a ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ f(h(b,a)) -> a,
     f(f(f(c))) -> c,
     b -> c,
     c -> c,
     a -> a ]
Constructor pattern: [h(?x_1,?x_2)]
Defined pattern: [c,a,b,f(?x_1)]
Constructor subsystem:
   [ ]
Modified Constructor subsystem:
   [ ]
No orientable rules for c. Add rules, and retry...
failed to construct defining rules
Retry with a different D/C-partition.
Constructor pattern: [h(?x_1,?x_2),c]
Defined pattern: [a,b,f(?x_1)]
Constructor subsystem:
   [ c -> c ]
c -> c
{}
   [  ]
Modified Constructor subsystem:
   [ ]
No orientable rules for a. Add rules, and retry...
failed to construct defining rules
Retry with a different D/C-partition.
Constructor pattern: [h(?x_1,?x_2),c,a]
Defined pattern: [b,f(?x_1)]
Constructor subsystem:
   [ c -> c,
     a -> a ]
a -> a
{}
   [  ]
c -> c
{}
   [  ]
Modified Constructor subsystem:
   [ ]
candidate for b:
   [ b -> c ]
No orientable rules for f(?x_1). Add rules, and retry...
failed to construct defining rules
Retry with a different D/C-partition.
Constructor pattern: [h(?x_1,?x_2),c,a,f(?x_1)]
Defined pattern: [b]
Constructor subsystem:
   [ f(f(f(c))) -> c,
     c -> c,
     a -> a ]
a -> a
{}
   [  ]
c -> c
{}
   [  ]
Modified Constructor subsystem:
   [ f(f(f(c))) -> c ]
candidate for b:
   [ b -> c ]
Find a quasi-ordering ...
order successfully found
Precedence:
 b : Mul;
 h : Mul;
 f : Mul;
 c : Mul;
 a : Mul;
Rules:
   [ b -> c,
     f(f(f(c))) -> c ]
Check confluence of constructor subsystem...
Check Termination...
Terminating, WCR: CR
Conjectures:
   [ f(h(b,a)) = a ]
STEP 0
ES:
   [ f(h(b,a)) = a ]
HS:
   [ ]
ES0:
   [ f(h(c,a)) = a ]
HS0:
   [ ]
ES1:
   [ f(h(c,a)) = a ]
HS1:
   [ ]
No equation to expand
check Non-Ground-Confluence...
ground constructor terms for instantiation: {}
ground terms for instantiation: {b:o}
obtain 10 rules by 3 steps unfolding
obtain 8 candidates for checking non-joinability
check by TCAP-Approximation (failure)
check by Ordering(rpo), check by Tree-Automata Approximation (success)
Witness for Non-Confluence: <f(h(c,a)) <- f(h(b,f(h(b,a)))) -> a>
: Success(not GCR)
(25 msec.)
0.05