|
1: |
|
app(app(eq,0),0) |
→ true |
2: |
|
app(app(eq,0),app(s,x)) |
→ false |
3: |
|
app(app(eq,app(s,x)),0) |
→ false |
4: |
|
app(app(eq,app(s,x)),app(s,y)) |
→ app(app(eq,x),y) |
5: |
|
app(app(or,true),y) |
→ true |
6: |
|
app(app(or,false),y) |
→ y |
7: |
|
app(app(union,empty),h) |
→ h |
8: |
|
app(app(union,app(app(app(edge,x),y),i)),h) |
→ app(app(app(edge,x),y),app(app(union,i),h)) |
9: |
|
app(app(app(app(reach,x),y),empty),h) |
→ false |
10: |
|
app(app(app(app(reach,x),y),app(app(app(edge,u),v),i)),h) |
→ app(app(app(app(app(if_reach_1,app(app(eq,x),u)),x),y),app(app(app(edge,u),v),i)),h) |
11: |
|
app(app(app(app(app(if_reach_1,true),x),y),app(app(app(edge,u),v),i)),h) |
→ app(app(app(app(app(if_reach_2,app(app(eq,y),v)),x),y),app(app(app(edge,u),v),i)),h) |
12: |
|
app(app(app(app(app(if_reach_1,false),x),y),app(app(app(edge,u),v),i)),h) |
→ app(app(app(app(reach,x),y),i),app(app(app(edge,u),v),h)) |
13: |
|
app(app(app(app(app(if_reach_2,true),x),y),app(app(app(edge,u),v),i)),h) |
→ true |
14: |
|
app(app(app(app(app(if_reach_2,false),x),y),app(app(app(edge,u),v),i)),h) |
→ app(app(or,app(app(app(app(reach,x),y),i),h)),app(app(app(app(reach,v),y),app(app(union,i),h)),empty)) |
|
There are 36 dependency pairs:
|
15: |
|
APP(app(eq,app(s,x)),app(s,y)) |
→ APP(app(eq,x),y) |
16: |
|
APP(app(eq,app(s,x)),app(s,y)) |
→ APP(eq,x) |
17: |
|
APP(app(union,app(app(app(edge,x),y),i)),h) |
→ APP(app(app(edge,x),y),app(app(union,i),h)) |
18: |
|
APP(app(union,app(app(app(edge,x),y),i)),h) |
→ APP(app(union,i),h) |
19: |
|
APP(app(union,app(app(app(edge,x),y),i)),h) |
→ APP(union,i) |
20: |
|
APP(app(app(app(reach,x),y),app(app(app(edge,u),v),i)),h) |
→ APP(app(app(app(app(if_reach_1,app(app(eq,x),u)),x),y),app(app(app(edge,u),v),i)),h) |
21: |
|
APP(app(app(app(reach,x),y),app(app(app(edge,u),v),i)),h) |
→ APP(app(app(app(if_reach_1,app(app(eq,x),u)),x),y),app(app(app(edge,u),v),i)) |
22: |
|
APP(app(app(app(reach,x),y),app(app(app(edge,u),v),i)),h) |
→ APP(app(app(if_reach_1,app(app(eq,x),u)),x),y) |
23: |
|
APP(app(app(app(reach,x),y),app(app(app(edge,u),v),i)),h) |
→ APP(app(if_reach_1,app(app(eq,x),u)),x) |
24: |
|
APP(app(app(app(reach,x),y),app(app(app(edge,u),v),i)),h) |
→ APP(if_reach_1,app(app(eq,x),u)) |
25: |
|
APP(app(app(app(reach,x),y),app(app(app(edge,u),v),i)),h) |
→ APP(app(eq,x),u) |
26: |
|
APP(app(app(app(reach,x),y),app(app(app(edge,u),v),i)),h) |
→ APP(eq,x) |
27: |
|
APP(app(app(app(app(if_reach_1,true),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(app(app(app(app(if_reach_2,app(app(eq,y),v)),x),y),app(app(app(edge,u),v),i)),h) |
28: |
|
APP(app(app(app(app(if_reach_1,true),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(app(app(app(if_reach_2,app(app(eq,y),v)),x),y),app(app(app(edge,u),v),i)) |
29: |
|
APP(app(app(app(app(if_reach_1,true),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(app(app(if_reach_2,app(app(eq,y),v)),x),y) |
30: |
|
APP(app(app(app(app(if_reach_1,true),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(app(if_reach_2,app(app(eq,y),v)),x) |
31: |
|
APP(app(app(app(app(if_reach_1,true),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(if_reach_2,app(app(eq,y),v)) |
32: |
|
APP(app(app(app(app(if_reach_1,true),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(app(eq,y),v) |
33: |
|
APP(app(app(app(app(if_reach_1,true),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(eq,y) |
34: |
|
APP(app(app(app(app(if_reach_1,false),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(app(app(app(reach,x),y),i),app(app(app(edge,u),v),h)) |
35: |
|
APP(app(app(app(app(if_reach_1,false),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(app(app(reach,x),y),i) |
36: |
|
APP(app(app(app(app(if_reach_1,false),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(app(reach,x),y) |
37: |
|
APP(app(app(app(app(if_reach_1,false),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(reach,x) |
38: |
|
APP(app(app(app(app(if_reach_1,false),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(app(app(edge,u),v),h) |
39: |
|
APP(app(app(app(app(if_reach_2,false),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(app(or,app(app(app(app(reach,x),y),i),h)),app(app(app(app(reach,v),y),app(app(union,i),h)),empty)) |
40: |
|
APP(app(app(app(app(if_reach_2,false),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(or,app(app(app(app(reach,x),y),i),h)) |
41: |
|
APP(app(app(app(app(if_reach_2,false),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(app(app(app(reach,x),y),i),h) |
42: |
|
APP(app(app(app(app(if_reach_2,false),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(app(app(reach,x),y),i) |
43: |
|
APP(app(app(app(app(if_reach_2,false),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(app(reach,x),y) |
44: |
|
APP(app(app(app(app(if_reach_2,false),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(reach,x) |
45: |
|
APP(app(app(app(app(if_reach_2,false),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(app(app(app(reach,v),y),app(app(union,i),h)),empty) |
46: |
|
APP(app(app(app(app(if_reach_2,false),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(app(app(reach,v),y),app(app(union,i),h)) |
47: |
|
APP(app(app(app(app(if_reach_2,false),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(app(reach,v),y) |
48: |
|
APP(app(app(app(app(if_reach_2,false),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(reach,v) |
49: |
|
APP(app(app(app(app(if_reach_2,false),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(app(union,i),h) |
50: |
|
APP(app(app(app(app(if_reach_2,false),x),y),app(app(app(edge,u),v),i)),h) |
→ APP(union,i) |
|
The approximated dependency graph contains one SCC:
{15,18,20-23,25,27-30,32,34-36,39,41-43,45-47,49}.