Left Termination of the query pattern
even(g)
w.r.t. the given Prolog program could successfully be proven:

(0) Obligation:

Clauses:

even(X) :- ','(eq(Y, f(e, f(o, Y))), c(Y, X)).
c(f(e, X1), 0).
c(f(X2, X), s(Y)) :- c(X, Y).
eq(X, X).

Query: even(g)

(1) PrologToTRSTransformerProof (SOUND transformation)

Transformed Prolog program to TRS.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
2 [label="2: even(T1)\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
6 [label="6: even(T1), SCOPE: 1, CLAUSE: 0\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: ','(eq(X11, f(e, f(o, X11))), c(X11, T4))\n\nT4 is ground\nX11 is free", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: ','(eq(X11, f(e, f(o, X11))), c(X11, T4)), SCOPE: 2, CLAUSE: 3\n\nT4 is ground\nX11 is free", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2 -> 14 [arrowhead = none ];
14 -> 6;

15 [label="ONLY EVAL with clause\neven(X10) :- ','(eq(X11, f(e, f(o, X11))), c(X11, X10)).\nand substitutionT1 -> T4,\nX10 -> T4", fontsize=14, style = filled, fillcolor = lightblue];
6 -> 15 [arrowhead = none ];
15 -> 9;

16 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
9 -> 16 [arrowhead = none ];
16 -> 12;

17 [label="BACKTRACK\nfor clause: eq(X, X)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
12 -> 17 [arrowhead = none ];
17 -> 13;

}

(2) Obligation:

Q restricted rewrite system:
R is empty.
Q is empty.

(3) RisEmptyProof (EQUIVALENT transformation)

The TRS R is empty. Hence, termination is trivially proven.

(4) YES