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

(0) Obligation:

Clauses:

gtsolve(X, Y) :- ','(generate(X, Y), test(Y)).

Query: gtsolve(g,a)

(1) PrologToDTProblemTransformerProof (SOUND transformation)

Built DT problem from termination graph DT10.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="A: gtsolve(T1, T2)\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: gtsolve(T1, T2), SCOPE: 1, CLAUSE: 0\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: ','(generate(T5, T7), test(T7))\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\ngtsolve(X3, X4) :- ','(generate(X3, X4), test(X4)).\nand substitutionT1 -> T5,\nX3 -> T5,\nT2 -> T7,\nX4 -> 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