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

(0) Obligation:

Clauses:

factorial1(N, F) :- ','(>(N, 0), ','(is(N1, -(N, 1)), ','(factorial1(N1, F1), is(F, *(N, F1))))).
factorial1(0, 1).
factorial2(N, F) :- factorial2(0, N, 1, F).
factorial2(I, N, T, F) :- ','(<(I, N), ','(is(I1, +(I, 1)), ','(is(T1, *(T, I1)), factorial2(I1, N, T1, F)))).
factorial2(N, N, F, F).
factorial3(N, F) :- factorial3(N, 1, F).
factorial3(N, T, F) :- ','(>(N, 0), ','(is(T1, *(T, N)), ','(is(N1, -(N, 1)), factorial3(N1, T1, F)))).
factorial3(0, F, F).

Query: factorial(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];
2 [label="2: factorial(T2, T3)\n\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
3 [label="3: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="UNDEFINED ERROR", fontsize=14, style = filled, fillcolor = lightgreen];
2 -> 4 [arrowhead = none ];
4 -> 3;

}

(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];
1 [label="1: factorial(T2, T3)\n\nT2 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
4 [label="4: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="UNDEFINED ERROR", fontsize=14, style = filled, fillcolor = lightgreen];
1 -> 5 [arrowhead = none ];
5 -> 4;

}

(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