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

(0) Obligation:

Clauses:

dcsolve(X, Y) :- ','(base(X), conquer(X, Y)).
dcsolve(X, Y) :- ','(divide(X, X0, X1, X2), ','(dcsolve(X1, Y1), ','(dcsolve(X2, Y2), merge(X0, Y1, Y2, Y)))).

Query: dcsolve(g,a)

(1) PrologToTRSTransformerProof (SOUND transformation)

Transformed Prolog program to TRS.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
3 [label="3: dcsolve(T1, T2)\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
6 [label="6: dcsolve(T1, T2), SCOPE: 1, CLAUSE: 0 | dcsolve(T1, T2), SCOPE: 1, CLAUSE: 1\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: ','(base(T8), conquer(T8, T10)) | dcsolve(T8, T2), SCOPE: 1, CLAUSE: 1\n\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 12 [arrowhead = none ];
12 -> 6;

13 [label="ONLY EVAL with clause\ndcsolve(X7, X8) :- ','(base(X7), conquer(X7, X8)).\nand substitutionT1 -> T8,\nX7 -> T8,\nT2 -> T10,\nX8 -> T10,\nT9 -> T10", fontsize=14, style = filled, fillcolor = lightblue];
6 -> 13 [arrowhead = none ];
13 -> 9;

14 [label="UNDEFINED ERROR", fontsize=14, style = filled, fillcolor = lightgreen];
9 -> 14 [arrowhead = none ];
14 -> 11;

}

(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