Runtime Complexity of the query pattern
dcsolve(g,a)
w.r.t. the given Prolog program could be shown to be BOUNDS(O(1), O(1)).

(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) PrologToCdtProblemTransformerProof (UPPER BOUND (ID) transformation)

Built complexity over-approximating cdt problems from derivation graph.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: dcsolve(T1, T2)\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
3 [label="3: dcsolve(T1, T2), SCOPE: 1, CLAUSE: 0 | dcsolve(T1, T2), SCOPE: 1, CLAUSE: 1\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: ','(base(T8), conquer(T8, T10)) | dcsolve(T8, T2), SCOPE: 1, CLAUSE: 1\n\nT8 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 9 [arrowhead = none ];
9 -> 3;

10 [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];
3 -> 10 [arrowhead = none ];
10 -> 6;

11 [label="UNDEFINED ERROR", fontsize=14, style = filled, fillcolor = lightgreen];
6 -> 11 [arrowhead = none ];
11 -> 8;

}

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:none

Compound Symbols:none

(3) SIsEmptyProof (EQUIVALENT transformation)

The set S is empty

(4) BOUNDS(O(1), O(1))

(5) PrologToCdtProblemTransformerProof (UPPER BOUND (ID) transformation)

Built complexity over-approximating cdt problems from derivation graph.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
2 [label="2: dcsolve(T1, T2)\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
4 [label="4: dcsolve(T1, T2), SCOPE: 1, CLAUSE: 0 | dcsolve(T1, T2), SCOPE: 1, CLAUSE: 1\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: ','(base(T5), conquer(T5, T7)) | dcsolve(T5, T2), SCOPE: 1, CLAUSE: 1\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2 -> 8 [arrowhead = none ];
8 -> 4;

9 [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];
4 -> 9 [arrowhead = none ];
9 -> 5;

10 [label="UNDEFINED ERROR", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 10 [arrowhead = none ];
10 -> 7;

}

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:none
Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:none

Defined Pair Symbols:none

Compound Symbols:none