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) PrologToDTProblemTransformerProof (SOUND transformation)

Built DT problem from termination graph DT10.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="A: dcsolve(T1, T2)\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: dcsolve(T1, T2), SCOPE: 1, CLAUSE: 0 | dcsolve(T1, T2), SCOPE: 1, CLAUSE: 1\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: ','(base(T5), conquer(T5, T7)) | dcsolve(T5, T2), SCOPE: 1, CLAUSE: 1\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 5 [arrowhead = none ];
5 -> 2;

6 [label="ONLY EVAL with clause\ndcsolve(X5, X6) :- ','(base(X5), conquer(X5, X6)).\nand substitutionT1 -> T5,\nX5 -> T5,\nT2 -> T7,\nX6 -> T7,\nT6 -> T7", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 6 [arrowhead = none ];
6 -> 3;

7 [label="UNDEFINED ERROR", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 7 [arrowhead = none ];
7 -> 4;

}

(2) Obligation:

Triples:


Clauses:


Afs:

(3) TPisEmptyProof (EQUIVALENT transformation)

There are no more dependency triples. Hence, the dependency triple problem trivially terminates.

(4) YES