Runtime Complexity proof of /tmp/tmp2XhwNl/pl2.3.1.pl

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

0 Prolog

↳1 LPReorderTransformerProof (⇔, 0 ms)

↳2 Prolog

↳3 PrologToCdtProblemTransformerProof (UPPER BOUND (ID), 60 ms)

↳4 CdtProblem

    ↳5 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳6 CdtProblem

    ↳7 CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳8 CdtProblem

    ↳9 CdtKnowledgeProof (⇔, 0 ms)

    ↳10 BOUNDS(O(1), O(1))

↳11 PrologToCdtProblemTransformerProof (UPPER BOUND (ID), 63 ms)

↳12 CdtProblem

    ↳13 CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳14 CdtProblem

    ↳15 CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID), 0 ms)

    ↳16 CdtProblem

(0) Obligation:

Clauses:

p(X, Z) :- ','(q(X, Y), p(Y, Z)).
p(X, X).
q(a, b).

Query: p(g,a)

(1) LPReorderTransformerProof (EQUIVALENT transformation)

Reordered facts before rules in definite LP [PROLOG].

(2) Obligation:

Clauses:

p(X, X).
q(a, b).
p(X, Z) :- ','(q(X, Y), p(Y, Z)).

Query: p(g,a)

(3) 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: p(T1, T2)\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
3 [label="3: p(T1, T2), SCOPE: 1, CLAUSE: 0 | p(T1, T2), SCOPE: 1, CLAUSE: 2\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
5 [label="5: true | p(T5, T2), SCOPE: 1, CLAUSE: 2\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
7 [label="7: p(T1, T2), SCOPE: 1, CLAUSE: 2\n\nT1 is ground\nX3 is free\np(T1, T2) !=? p(X3, X3)", fontsize=16, style=filled, fillcolor=lightyellow];
11 [label="11: p(T5, T2), SCOPE: 1, CLAUSE: 2\n\nT5 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
15 [label="15: ','(q(T12, X13), p(X13, T14))\n\nT12 is ground\nX13 is free", fontsize=16, style=filled, fillcolor=lightyellow];
16 [label="16: ','(q(T12, X13), p(X13, T14)), SCOPE: 2, CLAUSE: 1\n\nT12 is ground\nX13 is free", fontsize=16, style=filled, fillcolor=lightyellow];
17 [label="17: p(b, T14)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
18 [label="18: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
23 [label="23: p(b, T14), SCOPE: 3, CLAUSE: 0 | p(b, T14), SCOPE: 3, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
24 [label="24: true | p(b, T14), SCOPE: 3, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
29 [label="29: p(b, T14), SCOPE: 3, CLAUSE: 2\n\nX20 is free\np(b, T14) !=? p(X20, X20)", fontsize=16, style=filled, fillcolor=lightyellow];
30 [label="30: p(b, T14), SCOPE: 3, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
34 [label="34: ','(q(b, X30), p(X30, T21))\n\nX30 is free", fontsize=16, style=filled, fillcolor=lightyellow];
36 [label="36: ','(q(b, X30), p(X30, T21)), SCOPE: 4, CLAUSE: 1\n\nX30 is free", fontsize=16, style=filled, fillcolor=lightyellow];
38 [label="38: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="40: ','(q(b, X42), p(X42, T28))\n\nX42 is free", fontsize=16, style=filled, fillcolor=lightyellow];
41 [label="41: ','(q(b, X42), p(X42, T28)), SCOPE: 5, CLAUSE: 1\n\nX42 is free", fontsize=16, style=filled, fillcolor=lightyellow];
42 [label="42: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
43 [label="43: ','(q(T36, X54), p(X54, T38))\n\nT36 is ground\nX3 is free\nX54 is free\np(T36, T2) !=? p(X3, X3)", fontsize=16, style=filled, fillcolor=lightyellow];
44 [label="44: ','(q(T36, X54), p(X54, T38)), SCOPE: 6, CLAUSE: 1\n\nT36 is ground\nX3 is free\nX54 is free\np(T36, T2) !=? p(X3, X3)", fontsize=16, style=filled, fillcolor=lightyellow];
45 [label="45: p(b, T38)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
46 [label="46: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
47 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
1 -> 47 [arrowhead = none ];
47 -> 3;

48 [label="EVAL with clause\np(X3, X3).\nand substitutionT1 -> T5,\nX3 -> T5,\nT2 -> T5", fontsize=14, style = filled, fillcolor = lightblue];
3 -> 48 [arrowhead = none ];
48 -> 5;

49 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
3 -> 49 [arrowhead = none ];
49 -> 7;

50 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
5 -> 50 [arrowhead = none ];
50 -> 11;

51 [label="ONLY EVAL with clause\np(X52, X53) :- ','(q(X52, X54), p(X54, X53)).\nand substitutionT1 -> T36,\nX52 -> T36,\nT2 -> T38,\nX53 -> T38,\nT37 -> T38", fontsize=14, style = filled, fillcolor = lightblue];
7 -> 51 [arrowhead = none ];
51 -> 43;

52 [label="ONLY EVAL with clause\np(X11, X12) :- ','(q(X11, X13), p(X13, X12)).\nand substitutionT5 -> T12,\nX11 -> T12,\nT2 -> T14,\nX12 -> T14,\nT13 -> T14", fontsize=14, style = filled, fillcolor = lightblue];
11 -> 52 [arrowhead = none ];
52 -> 15;

53 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
15 -> 53 [arrowhead = none ];
53 -> 16;

54 [label="EVAL with clause\nq(a, b).\nand substitutionT12 -> a,\nX13 -> b", fontsize=14, style = filled, fillcolor = lightblue];
16 -> 54 [arrowhead = none ];
54 -> 17;

55 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
16 -> 55 [arrowhead = none ];
55 -> 18;

56 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
17 -> 56 [arrowhead = none ];
56 -> 23;

57 [label="EVAL with clause\np(X20, X20).\nand substitutionX20 -> b,\nT14 -> b", fontsize=14, style = filled, fillcolor = lightblue];
23 -> 57 [arrowhead = none ];
57 -> 24;

58 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
23 -> 58 [arrowhead = none ];
58 -> 29;

59 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
24 -> 59 [arrowhead = none ];
59 -> 30;

60 [label="ONLY EVAL with clause\np(X40, X41) :- ','(q(X40, X42), p(X42, X41)).\nand substitutionX40 -> b,\nT14 -> T28,\nX41 -> T28,\nT27 -> T28", fontsize=14, style = filled, fillcolor = lightblue];
29 -> 60 [arrowhead = none ];
60 -> 40;

61 [label="ONLY EVAL with clause\np(X28, X29) :- ','(q(X28, X30), p(X30, X29)).\nand substitutionX28 -> b,\nT14 -> T21,\nX29 -> T21,\nT20 -> T21", fontsize=14, style = filled, fillcolor = lightblue];
30 -> 61 [arrowhead = none ];
61 -> 34;

62 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
34 -> 62 [arrowhead = none ];
62 -> 36;

63 [label="BACKTRACK\nfor clause: q(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
36 -> 63 [arrowhead = none ];
63 -> 38;

64 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
40 -> 64 [arrowhead = none ];
64 -> 41;

65 [label="BACKTRACK\nfor clause: q(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
41 -> 65 [arrowhead = none ];
65 -> 42;

66 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
43 -> 66 [arrowhead = none ];
66 -> 44;

67 [label="EVAL with clause\nq(a, b).\nand substitutionT36 -> a,\nX54 -> b", fontsize=14, style = filled, fillcolor = lightblue];
44 -> 67 [arrowhead = none ];
67 -> 45;

68 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
44 -> 68 [arrowhead = none ];
68 -> 46;

69 [label="INSTANCE with matching:\nT14 -> T38", fontsize=14, style = filled, fillcolor = lightgrey];
45 -> 69 [arrowhead = none , style=dashed];
69 -> 17[style=dashed];

}

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0) → f1_out1(z0)
f1_in(a) → U1(f17_in, a)
f1_in(a) → U2(f17_in, a)
U1(f17_out1(z0), a) → f1_out1(z0)
U2(f17_out1(z0), a) → f1_out1(z0)
f17_in → f17_out1(b)

Tuples:

F1_IN(a) → c1(U1'(f17_in, a), F17_IN)
F1_IN(a) → c2(U2'(f17_in, a), F17_IN)

S tuples:

F1_IN(a) → c1(U1'(f17_in, a), F17_IN)
F1_IN(a) → c2(U2'(f17_in, a), F17_IN)

K tuples:none
Defined Rule Symbols:

f1_in, U1, U2, f17_in

Defined Pair Symbols:

F1_IN

Compound Symbols:

c1, c2

(5) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)

Split RHS of tuples not part of any SCC

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0) → f1_out1(z0)
f1_in(a) → U1(f17_in, a)
f1_in(a) → U2(f17_in, a)
U1(f17_out1(z0), a) → f1_out1(z0)
U2(f17_out1(z0), a) → f1_out1(z0)
f17_in → f17_out1(b)

Tuples:

F1_IN(a) → c(U1'(f17_in, a))
F1_IN(a) → c(F17_IN)
F1_IN(a) → c(U2'(f17_in, a))

S tuples:

F1_IN(a) → c(U1'(f17_in, a))
F1_IN(a) → c(F17_IN)
F1_IN(a) → c(U2'(f17_in, a))

K tuples:none
Defined Rule Symbols:

f1_in, U1, U2, f17_in

Defined Pair Symbols:

F1_IN

Compound Symbols:

c

(7) CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID) transformation)

Removed 4 trailing tuple parts

(8) Obligation:

Complexity Dependency Tuples Problem
Rules:

f1_in(z0) → f1_out1(z0)
f1_in(a) → U1(f17_in, a)
f1_in(a) → U2(f17_in, a)
U1(f17_out1(z0), a) → f1_out1(z0)
U2(f17_out1(z0), a) → f1_out1(z0)
f17_in → f17_out1(b)

Tuples:

F1_IN(a) → c

S tuples:

F1_IN(a) → c

K tuples:none
Defined Rule Symbols:

f1_in, U1, U2, f17_in

Defined Pair Symbols:

F1_IN

Compound Symbols:

c

(9) CdtKnowledgeProof (EQUIVALENT transformation)

The following tuples could be moved from S to K by knowledge propagation:

F1_IN(a) → c
F1_IN(a) → c
F1_IN(a) → c
F1_IN(a) → c

Now S is empty

(10) BOUNDS(O(1), O(1))

(11) 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: p(T1, T2)\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow, color=red];
4 [label="4: p(T1, T2), SCOPE: 1, CLAUSE: 0 | p(T1, T2), SCOPE: 1, CLAUSE: 2\n\nT1 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
6 [label="6: true | p(T4, T2), SCOPE: 1, CLAUSE: 2\n\nT4 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
8 [label="8: p(T1, T2), SCOPE: 1, CLAUSE: 2\n\nT1 is ground\nX2 is free\np(T1, T2) !=? p(X2, X2)", fontsize=16, style=filled, fillcolor=lightyellow];
9 [label="9: p(T4, T2), SCOPE: 1, CLAUSE: 2\n\nT4 is ground", fontsize=16, style=filled, fillcolor=lightyellow];
10 [label="10: ','(q(T7, X7), p(X7, T9))\n\nT7 is ground\nX7 is free", fontsize=16, style=filled, fillcolor=lightyellow];
12 [label="12: ','(q(T7, X7), p(X7, T9)), SCOPE: 2, CLAUSE: 1\n\nT7 is ground\nX7 is free", fontsize=16, style=filled, fillcolor=lightyellow];
13 [label="13: p(b, T9)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
14 [label="14: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
19 [label="19: p(b, T9), SCOPE: 3, CLAUSE: 0 | p(b, T9), SCOPE: 3, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
20 [label="20: true | p(b, T9), SCOPE: 3, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
21 [label="21: p(b, T9), SCOPE: 3, CLAUSE: 2\n\nX12 is free\np(b, T9) !=? p(X12, X12)", fontsize=16, style=filled, fillcolor=lightyellow];
22 [label="22: p(b, T9), SCOPE: 3, CLAUSE: 2\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
25 [label="25: ','(q(b, X22), p(X22, T15))\n\nX22 is free", fontsize=16, style=filled, fillcolor=lightyellow];
26 [label="26: ','(q(b, X22), p(X22, T15)), SCOPE: 4, CLAUSE: 1\n\nX22 is free", fontsize=16, style=filled, fillcolor=lightyellow];
27 [label="27: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
28 [label="28: ','(q(b, X34), p(X34, T22))\n\nX34 is free", fontsize=16, style=filled, fillcolor=lightyellow];
31 [label="31: ','(q(b, X34), p(X34, T22)), SCOPE: 5, CLAUSE: 1\n\nX34 is free", fontsize=16, style=filled, fillcolor=lightyellow];
32 [label="32: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
33 [label="33: ','(q(T26, X41), p(X41, T28))\n\nT26 is ground\nX2 is free\nX41 is free\np(T26, T2) !=? p(X2, X2)", fontsize=16, style=filled, fillcolor=lightyellow];
35 [label="35: ','(q(T26, X41), p(X41, T28)), SCOPE: 6, CLAUSE: 1\n\nT26 is ground\nX2 is free\nX41 is free\np(T26, T2) !=? p(X2, X2)", fontsize=16, style=filled, fillcolor=lightyellow];
37 [label="37: p(b, T28)\n\n", fontsize=16, style=filled, fillcolor=lightyellow];
39 [label="39: \n\n", fontsize=16, style=filled, fillcolor=lightyellow];
40 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
2 -> 40 [arrowhead = none ];
40 -> 4;

41 [label="EVAL with clause\np(X2, X2).\nand substitutionT1 -> T4,\nX2 -> T4,\nT2 -> T4", fontsize=14, style = filled, fillcolor = lightblue];
4 -> 41 [arrowhead = none ];
41 -> 6;

42 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
4 -> 42 [arrowhead = none ];
42 -> 8;

43 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
6 -> 43 [arrowhead = none ];
43 -> 9;

44 [label="ONLY EVAL with clause\np(X39, X40) :- ','(q(X39, X41), p(X41, X40)).\nand substitutionT1 -> T26,\nX39 -> T26,\nT2 -> T28,\nX40 -> T28,\nT27 -> T28", fontsize=14, style = filled, fillcolor = lightblue];
8 -> 44 [arrowhead = none ];
44 -> 33;

45 [label="ONLY EVAL with clause\np(X5, X6) :- ','(q(X5, X7), p(X7, X6)).\nand substitutionT4 -> T7,\nX5 -> T7,\nT2 -> T9,\nX6 -> T9,\nT8 -> T9", fontsize=14, style = filled, fillcolor = lightblue];
9 -> 45 [arrowhead = none ];
45 -> 10;

46 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
10 -> 46 [arrowhead = none ];
46 -> 12;

47 [label="EVAL with clause\nq(a, b).\nand substitutionT7 -> a,\nX7 -> b", fontsize=14, style = filled, fillcolor = lightblue];
12 -> 47 [arrowhead = none ];
47 -> 13;

48 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
12 -> 48 [arrowhead = none ];
48 -> 14;

49 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
13 -> 49 [arrowhead = none ];
49 -> 19;

50 [label="EVAL with clause\np(X12, X12).\nand substitutionX12 -> b,\nT9 -> b", fontsize=14, style = filled, fillcolor = lightblue];
19 -> 50 [arrowhead = none ];
50 -> 20;

51 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
19 -> 51 [arrowhead = none ];
51 -> 21;

52 [label="SUCCESS", fontsize=14, style = filled, fillcolor = lightgreen];
20 -> 52 [arrowhead = none ];
52 -> 22;

53 [label="ONLY EVAL with clause\np(X32, X33) :- ','(q(X32, X34), p(X34, X33)).\nand substitutionX32 -> b,\nT9 -> T22,\nX33 -> T22,\nT21 -> T22", fontsize=14, style = filled, fillcolor = lightblue];
21 -> 53 [arrowhead = none ];
53 -> 28;

54 [label="ONLY EVAL with clause\np(X20, X21) :- ','(q(X20, X22), p(X22, X21)).\nand substitutionX20 -> b,\nT9 -> T15,\nX21 -> T15,\nT14 -> T15", fontsize=14, style = filled, fillcolor = lightblue];
22 -> 54 [arrowhead = none ];
54 -> 25;

55 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
25 -> 55 [arrowhead = none ];
55 -> 26;

56 [label="BACKTRACK\nfor clause: q(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
26 -> 56 [arrowhead = none ];
56 -> 27;

57 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
28 -> 57 [arrowhead = none ];
57 -> 31;

58 [label="BACKTRACK\nfor clause: q(a, b)because of non-unification", fontsize=14, style = filled, fillcolor = lightgreen];
31 -> 58 [arrowhead = none ];
58 -> 32;

59 [label="CASE", fontsize=14, style = filled, fillcolor = lightcyan];
33 -> 59 [arrowhead = none ];
59 -> 35;

60 [label="EVAL with clause\nq(a, b).\nand substitutionT26 -> a,\nX41 -> b", fontsize=14, style = filled, fillcolor = lightblue];
35 -> 60 [arrowhead = none ];
60 -> 37;

61 [label="EVAL-BACKTRACK", fontsize=14, style = filled, fillcolor = lightgreen];
35 -> 61 [arrowhead = none ];
61 -> 39;

62 [label="INSTANCE with matching:\nT9 -> T28", fontsize=14, style = filled, fillcolor = lightgrey];
37 -> 62 [arrowhead = none , style=dashed];
62 -> 13[style=dashed];

}

(12) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0) → f2_out1(z0)
f2_in(a) → U1(f13_in, a)
f2_in(a) → U2(f13_in, a)
U1(f13_out1(z0), a) → f2_out1(z0)
U2(f13_out1(z0), a) → f2_out1(z0)
f13_in → f13_out1(b)

Tuples:

F2_IN(a) → c1(U1'(f13_in, a), F13_IN)
F2_IN(a) → c2(U2'(f13_in, a), F13_IN)

S tuples:

F2_IN(a) → c1(U1'(f13_in, a), F13_IN)
F2_IN(a) → c2(U2'(f13_in, a), F13_IN)

K tuples:none
Defined Rule Symbols:

f2_in, U1, U2, f13_in

Defined Pair Symbols:

F2_IN

Compound Symbols:

c1, c2

(13) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID) transformation)

Split RHS of tuples not part of any SCC

(14) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0) → f2_out1(z0)
f2_in(a) → U1(f13_in, a)
f2_in(a) → U2(f13_in, a)
U1(f13_out1(z0), a) → f2_out1(z0)
U2(f13_out1(z0), a) → f2_out1(z0)
f13_in → f13_out1(b)

Tuples:

F2_IN(a) → c(U1'(f13_in, a))
F2_IN(a) → c(F13_IN)
F2_IN(a) → c(U2'(f13_in, a))

S tuples:

F2_IN(a) → c(U1'(f13_in, a))
F2_IN(a) → c(F13_IN)
F2_IN(a) → c(U2'(f13_in, a))

K tuples:none
Defined Rule Symbols:

f2_in, U1, U2, f13_in

Defined Pair Symbols:

F2_IN

Compound Symbols:

c

(15) CdtGraphRemoveTrailingTuplepartsProof (BOTH BOUNDS(ID, ID) transformation)

Removed 4 trailing tuple parts

(16) Obligation:

Complexity Dependency Tuples Problem
Rules:

f2_in(z0) → f2_out1(z0)
f2_in(a) → U1(f13_in, a)
f2_in(a) → U2(f13_in, a)
U1(f13_out1(z0), a) → f2_out1(z0)
U2(f13_out1(z0), a) → f2_out1(z0)
f13_in → f13_out1(b)

Tuples:

F2_IN(a) → c

S tuples:

F2_IN(a) → c

K tuples:none
Defined Rule Symbols:

f2_in, U1, U2, f13_in

Defined Pair Symbols:

F2_IN

Compound Symbols:

c