Determinacy proof of /tmp/tmpPnPTBB/latesplit.pl

Determinacy of the query pattern
q(a)
w.r.t. the given Prolog program could successfully be proven:

0 Prolog

↳1 PrologDeterminacyProcessorProof (⇔, 0 ms)

↳2 YES

(0) Obligation:

Clauses:

q(X) :- ','(p(s(s(0)), X), r(X)).
p(0, 0).
p(s(X), s(Y)) :- p(X, Y).
r(s(s(0))) :- !.
r(X) :- r(X).

Query: q(a)

(1) PrologDeterminacyProcessorProof (EQUIVALENT transformation)

The root node satisfies the determinacy criterion.

digraph dp_graph {
node [outthreshold=100, inthreshold=100];
1 [label="1: q(T1)\n\n", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
2 [label="2: q(T1), SCOPE: 1, CLAUSE: 0\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
3 [label="3: ','(p(s(s(0)), T4), r(T4))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
4 [label="4: ','(p(s(s(0)), T4), r(T4)), SCOPE: 2, CLAUSE: 1 | ','(p(s(s(0)), T4), r(T4)), SCOPE: 2, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: ','(p(s(s(0)), T4), r(T4)), SCOPE: 2, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: ','(p(s(0), T8), r(s(T8)))\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: p(s(0), T8)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: r(s(T9))\n\nT9 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: p(s(0), T8), SCOPE: 3, CLAUSE: 1 | p(s(0), T8), SCOPE: 3, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: p(s(0), T8), SCOPE: 3, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: p(0, T13)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: p(0, T13), SCOPE: 4, CLAUSE: 1 | p(0, T13), SCOPE: 4, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: p(0, T13), SCOPE: 4, CLAUSE: 1\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: p(0, T13), SCOPE: 4, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: r(s(T9)), SCOPE: 5, CLAUSE: 3 | r(s(T9)), SCOPE: 5, CLAUSE: 4\n\nT9 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: !_5 | r(s(s(0))), SCOPE: 5, CLAUSE: 4\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: r(s(T9)), SCOPE: 5, CLAUSE: 4\n\nT9 is ground\nr(s(T9)) !=? r(s(s(0)))", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: true\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: r(s(T17))\n\nT17 is ground\nr(s(T17)) !=? r(s(s(0)))", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 27 [arrowhead = none ];
27 -> 2;

28 [label="ONLY EVAL with clause\nq(X2) :- ','(p(s(s(0)), X2), r(X2)).\nand substitutionT1 -> T4,\nX2 -> T4,\nT3 -> T4", fontsize=14, style = filled, fillcolor = lightblue];
2 -> 28 [arrowhead = none ];
28 -> 3;

29 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
3 -> 29 [arrowhead = none ];
29 -> 4;

30 [label="BACKTRACK\nfor clause: p(0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
4 -> 30 [arrowhead = none ];
30 -> 5;

31 [label="EVAL with clause\np(s(X7), s(X8)) :- p(X7, X8).\nand substitutionX7 -> s(0),\nX8 -> T8,\nT4 -> s(T8),\nT7 -> T8", fontsize=14, style = filled, fillcolor = lightblue];
5 -> 31 [arrowhead = none ];
31 -> 6;

32 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 32 [arrowhead = none ];
32 -> 7;

33 [label="SPLIT 1", fontsize=14, style = filled, fillcolor = violet];
6 -> 33 [arrowhead = none ];
33 -> 8;

34 [label="SPLIT 2\nnew knowledge:\nT9 is ground\nreplacements:T8 -> T9", fontsize=14, style = filled, fillcolor = violet];
6 -> 34 [arrowhead = none ];
34 -> 9;

35 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
8 -> 35 [arrowhead = none ];
35 -> 10;

36 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
9 -> 36 [arrowhead = none ];
36 -> 21;

37 [label="BACKTRACK\nfor clause: p(0, 0)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
10 -> 37 [arrowhead = none ];
37 -> 11;

38 [label="EVAL with clause\np(s(X13), s(X14)) :- p(X13, X14).\nand substitutionX13 -> 0,\nX14 -> T13,\nT8 -> s(T13),\nT12 -> T13", fontsize=14, style = filled, fillcolor = lightblue];
11 -> 38 [arrowhead = none ];
38 -> 12;

39 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
11 -> 39 [arrowhead = none ];
39 -> 13;

40 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
12 -> 40 [arrowhead = none ];
40 -> 14;

41 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
14 -> 41 [arrowhead = none ];
41 -> 15;

42 [label="PARALLEL", fontsize=14, style = filled, fillcolor = violet];
14 -> 42 [arrowhead = none ];
42 -> 16;

43 [label="EVAL with clause\np(0, 0).\nand substitutionT13 -> 0", fontsize=14, style = filled, fillcolor = lightblue];
15 -> 43 [arrowhead = none ];
43 -> 17;

44 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
15 -> 44 [arrowhead = none ];
44 -> 18;

45 [label="BACKTRACK\nfor clause: p(s(X), s(Y)) :- p(X, Y)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
16 -> 45 [arrowhead = none ];
45 -> 20;

46 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
17 -> 46 [arrowhead = none ];
46 -> 19;

47 [label="EVAL with clause\nr(s(s(0))) :- !_5.\nand substitutionT9 -> s(0)", fontsize=14, style = filled, fillcolor = lightblue];
21 -> 47 [arrowhead = none ];
47 -> 22;

48 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
21 -> 48 [arrowhead = none ];
48 -> 23;

49 [label="CUT", fontsize=14, style = filled, fillcolor = lightgreen];
22 -> 49 [arrowhead = none ];
49 -> 24;

50 [label="ONLY EVAL with clause\nr(X20) :- r(X20).\nand substitutionT9 -> T17,\nX20 -> s(T17)", fontsize=14, style = filled, fillcolor = lightblue];
23 -> 50 [arrowhead = none ];
50 -> 26;

51 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
24 -> 51 [arrowhead = none ];
51 -> 25;

52 [label="INSTANCE with matching:\nT9 -> T17", fontsize=14, style = filled, fillcolor = lightgrey];
26 -> 52 [arrowhead = none , style=dashed];
52 -> 9[style=dashed];

}

(0) Obligation:

(1) PrologDeterminacyProcessorProof (EQUIVALENT transformation)

(2) YES