NO
af/ONE-SORTED/696.trs
Input rules:
   [ h(a,c) -> b,
     c -> a,
     b -> f(b) ]
Sorts having no ground terms: 
Rules applicable to ground terms:
   [ h(a,c) -> b,
     c -> a,
     b -> f(b) ]
Constructor pattern: [h(?x_1,?x_2),a,f(?x_1)]
Defined pattern: [b,c]
Constructor subsystem:
   [ ]
Modified Constructor subsystem:
   [ ]
No orientable rules for b. Add rules, and retry...
failed to construct defining rules
Retry with a different D/C-partition.
Constructor pattern: [h(?x_1,?x_2),a,f(?x_1),b]
Defined pattern: [c]
Constructor subsystem:
   [ b -> f(b) ]
Modified Constructor subsystem:
   [ b -> f(b) ]
candidate for c:
   [ c -> a ]
Find a quasi-ordering ...
encodeSameNthStatus h/0, h/1
encodeSameNthStatus(sub) logArF:1, logArG:1
failed to find an ordering.
Try to supplement auxiliary rules.
{}{}{b}Supplemented Rules:
   [ ]
failed to supplement auxiliary rules
Retry with a different D/C-partition.
Constructor pattern: [h(?x_1,?x_2),a,f(?x_1),b,c]
Defined pattern: []
Constructor subsystem:
   [ h(a,c) -> b,
     c -> a,
     b -> f(b) ]
Modified Constructor subsystem:
   [ h(a,c) -> b,
     c -> a,
     b -> f(b) ]
Find a quasi-ordering ...
order successfully found
Precedence:
 f : Mul;
 b : Mul,  a : Mul;
 h : Mul;
 c : Mul;
Rules:
   [ h(a,c) -> b ]
Check confluence of constructor subsystem...
Check Termination...
Terminating, WCR: CR
Conjectures:
   [ c = a,
     b = f(b) ]
STEP 0
ES:
   [ c = a,
     b = f(b) ]
HS:
   [ ]
ES0:
   [ c = a,
     b = f(b) ]
HS0:
   [ ]
ES1:
   [ c = a,
     b = f(b) ]
HS1:
   [ ]
No equation to expand
check Non-Ground-Confluence...
ground constructor terms for instantiation: {a,h(a,a),f(a)}
ground terms for instantiation: {a:o,h(a,a):o,f(a):o}
obtain 10 rules by 3 steps unfolding
obtain 42 candidates for checking non-joinability
check by TCAP-Approximation (success)
Witness for Non-Confluence: <h(a,a) <- h(c,c) -> f(b)>
: Success(not GCR)
(10 msec.)
0.03