YES

Problem 1: 

Infeasibility Problem:
[(VAR vNonEmpty x vNonEmpty x)
(STRATEGY CONTEXTSENSITIVE
(g 1)
(a)
(b)
(f 1 2)
(fSNonEmpty)
)
(RULES
g(x) -> g(x) | g(x) ->* f(a,b)
g(x) -> f(x,x)
)
]

Infeasibility Conditions:
g(x) ->* f(a,b)

Problem 1: 

Obtaining a model using Mace4:

 -> Usable Rules:
g(x) -> g(x) | g(x) ->* f(a,b)
g(x) -> f(x,x)

 -> Mace4 Output:
============================== Mace4 =================================
Mace4 (64) version 2009-11A, November 2009.
Process 3279345 was started by sandbox on z013.star.cs.uiowa.edu,
Tue Jul 30 09:07:55 2024
The command was "./mace4 -c -f /tmp/mace43279332-2.in".
============================== end of head ===========================

============================== INPUT =================================

% Reading from file /tmp/mace43279332-2.in

assign(max_seconds,100).

formulas(assumptions).
->(x1,y) -> ->(g(x1),g(y)) # label(congruence).
->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence).
->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence).
->*(g(x1),f(a,b)) -> ->(g(x1),g(x1)) # label(replacement).
->(g(x1),f(x1,x1)) # label(replacement).
->*(x,x) # label(reflexivity).
->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity).
end_of_list.

formulas(goals).
(exists x3 ->*(g(x3),f(a,b))) # label(goal).
end_of_list.

============================== end of input ==========================

============================== PROCESS NON-CLAUSAL FORMULAS ==========

% Formulas that are not ordinary clauses:
1 ->(x1,y) -> ->(g(x1),g(y)) # label(congruence) # label(non_clause).  [assumption].
2 ->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause).  [assumption].
3 ->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause).  [assumption].
4 ->*(g(x1),f(a,b)) -> ->(g(x1),g(x1)) # label(replacement) # label(non_clause).  [assumption].
5 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause).  [assumption].
6 (exists x3 ->*(g(x3),f(a,b))) # label(goal) # label(non_clause) # label(goal).  [goal].

============================== end of process non-clausal formulas ===

============================== CLAUSES FOR SEARCH ====================

formulas(mace4_clauses).
-->(x,y) | ->(g(x),g(y)) # label(congruence).
-->(x,y) | ->(f(x,z),f(y,z)) # label(congruence).
-->(x,y) | ->(f(z,x),f(z,y)) # label(congruence).
-->*(g(x),f(a,b)) | ->(g(x),g(x)) # label(replacement).
->(g(x),f(x,x)) # label(replacement).
->*(x,x) # label(reflexivity).
-->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity).
-->*(g(x),f(a,b)) # label(goal).
end_of_list.

============================== end of clauses for search =============

% There are no natural numbers in the input.

============================== DOMAIN SIZE 2 =========================

============================== MODEL =================================

interpretation( 2, [number=1, seconds=0], [

        function(a, [ 0 ]),

        function(b, [ 1 ]),

        function(g(_), [ 0, 0 ]),

        function(f(_,_), [
			   0, 1,
			   0, 0 ]),

        relation(->*(_,_), [
			   1, 0,
			   0, 1 ]),

        relation(->(_,_), [
			   1, 0,
			   0, 1 ])
]).

============================== end of model ==========================

============================== STATISTICS ============================

For domain size 2.

Current CPU time: 0.00 seconds (total CPU time: 0.01 seconds).
Ground clauses: seen=36, kept=32.
Selections=6, assignments=8, propagations=17, current_models=1.
Rewrite_terms=112, rewrite_bools=47, indexes=34.
Rules_from_neg_clauses=6, cross_offs=6.

============================== end of statistics =====================

User_CPU=0.01, System_CPU=0.00, Wall_clock=0.

Exiting with 1 model.

Process 3279345 exit (max_models) Tue Jul 30 09:07:55 2024
The process finished Tue Jul 30 09:07:55 2024


Mace4 cooked interpretation:

% number = 1
% seconds = 0

% Interpretation of size 2

a = 0.

b = 1.

g(0) = 0.
g(1) = 0.

f(0,0) = 0.
f(0,1) = 1.
f(1,0) = 0.
f(1,1) = 0.

  ->*(0,0).
- ->*(0,1).
- ->*(1,0).
  ->*(1,1).

  ->(0,0).
- ->(0,1).
- ->(1,0).
  ->(1,1).


The problem is infeasible.