|
1: |
|
active(fib(N)) |
→ mark(sel(N,fib1(s(0),s(0)))) |
2: |
|
active(fib1(X,Y)) |
→ mark(cons(X,fib1(Y,add(X,Y)))) |
3: |
|
active(add(0,X)) |
→ mark(X) |
4: |
|
active(add(s(X),Y)) |
→ mark(s(add(X,Y))) |
5: |
|
active(sel(0,cons(X,XS))) |
→ mark(X) |
6: |
|
active(sel(s(N),cons(X,XS))) |
→ mark(sel(N,XS)) |
7: |
|
active(fib(X)) |
→ fib(active(X)) |
8: |
|
active(sel(X1,X2)) |
→ sel(active(X1),X2) |
9: |
|
active(sel(X1,X2)) |
→ sel(X1,active(X2)) |
10: |
|
active(fib1(X1,X2)) |
→ fib1(active(X1),X2) |
11: |
|
active(fib1(X1,X2)) |
→ fib1(X1,active(X2)) |
12: |
|
active(s(X)) |
→ s(active(X)) |
13: |
|
active(cons(X1,X2)) |
→ cons(active(X1),X2) |
14: |
|
active(add(X1,X2)) |
→ add(active(X1),X2) |
15: |
|
active(add(X1,X2)) |
→ add(X1,active(X2)) |
16: |
|
fib(mark(X)) |
→ mark(fib(X)) |
17: |
|
sel(mark(X1),X2) |
→ mark(sel(X1,X2)) |
18: |
|
sel(X1,mark(X2)) |
→ mark(sel(X1,X2)) |
19: |
|
fib1(mark(X1),X2) |
→ mark(fib1(X1,X2)) |
20: |
|
fib1(X1,mark(X2)) |
→ mark(fib1(X1,X2)) |
21: |
|
s(mark(X)) |
→ mark(s(X)) |
22: |
|
cons(mark(X1),X2) |
→ mark(cons(X1,X2)) |
23: |
|
add(mark(X1),X2) |
→ mark(add(X1,X2)) |
24: |
|
add(X1,mark(X2)) |
→ mark(add(X1,X2)) |
25: |
|
proper(fib(X)) |
→ fib(proper(X)) |
26: |
|
proper(sel(X1,X2)) |
→ sel(proper(X1),proper(X2)) |
27: |
|
proper(fib1(X1,X2)) |
→ fib1(proper(X1),proper(X2)) |
28: |
|
proper(s(X)) |
→ s(proper(X)) |
29: |
|
proper(0) |
→ ok(0) |
30: |
|
proper(cons(X1,X2)) |
→ cons(proper(X1),proper(X2)) |
31: |
|
proper(add(X1,X2)) |
→ add(proper(X1),proper(X2)) |
32: |
|
fib(ok(X)) |
→ ok(fib(X)) |
33: |
|
sel(ok(X1),ok(X2)) |
→ ok(sel(X1,X2)) |
34: |
|
fib1(ok(X1),ok(X2)) |
→ ok(fib1(X1,X2)) |
35: |
|
s(ok(X)) |
→ ok(s(X)) |
36: |
|
cons(ok(X1),ok(X2)) |
→ ok(cons(X1,X2)) |
37: |
|
add(ok(X1),ok(X2)) |
→ ok(add(X1,X2)) |
38: |
|
top(mark(X)) |
→ top(proper(X)) |
39: |
|
top(ok(X)) |
→ top(active(X)) |
|
There are 62 dependency pairs:
|
40: |
|
ACTIVE(fib(N)) |
→ SEL(N,fib1(s(0),s(0))) |
41: |
|
ACTIVE(fib(N)) |
→ FIB1(s(0),s(0)) |
42: |
|
ACTIVE(fib(N)) |
→ S(0) |
43: |
|
ACTIVE(fib1(X,Y)) |
→ CONS(X,fib1(Y,add(X,Y))) |
44: |
|
ACTIVE(fib1(X,Y)) |
→ FIB1(Y,add(X,Y)) |
45: |
|
ACTIVE(fib1(X,Y)) |
→ ADD(X,Y) |
46: |
|
ACTIVE(add(s(X),Y)) |
→ S(add(X,Y)) |
47: |
|
ACTIVE(add(s(X),Y)) |
→ ADD(X,Y) |
48: |
|
ACTIVE(sel(s(N),cons(X,XS))) |
→ SEL(N,XS) |
49: |
|
ACTIVE(fib(X)) |
→ FIB(active(X)) |
50: |
|
ACTIVE(fib(X)) |
→ ACTIVE(X) |
51: |
|
ACTIVE(sel(X1,X2)) |
→ SEL(active(X1),X2) |
52: |
|
ACTIVE(sel(X1,X2)) |
→ ACTIVE(X1) |
53: |
|
ACTIVE(sel(X1,X2)) |
→ SEL(X1,active(X2)) |
54: |
|
ACTIVE(sel(X1,X2)) |
→ ACTIVE(X2) |
55: |
|
ACTIVE(fib1(X1,X2)) |
→ FIB1(active(X1),X2) |
56: |
|
ACTIVE(fib1(X1,X2)) |
→ ACTIVE(X1) |
57: |
|
ACTIVE(fib1(X1,X2)) |
→ FIB1(X1,active(X2)) |
58: |
|
ACTIVE(fib1(X1,X2)) |
→ ACTIVE(X2) |
59: |
|
ACTIVE(s(X)) |
→ S(active(X)) |
60: |
|
ACTIVE(s(X)) |
→ ACTIVE(X) |
61: |
|
ACTIVE(cons(X1,X2)) |
→ CONS(active(X1),X2) |
62: |
|
ACTIVE(cons(X1,X2)) |
→ ACTIVE(X1) |
63: |
|
ACTIVE(add(X1,X2)) |
→ ADD(active(X1),X2) |
64: |
|
ACTIVE(add(X1,X2)) |
→ ACTIVE(X1) |
65: |
|
ACTIVE(add(X1,X2)) |
→ ADD(X1,active(X2)) |
66: |
|
ACTIVE(add(X1,X2)) |
→ ACTIVE(X2) |
67: |
|
FIB(mark(X)) |
→ FIB(X) |
68: |
|
SEL(mark(X1),X2) |
→ SEL(X1,X2) |
69: |
|
SEL(X1,mark(X2)) |
→ SEL(X1,X2) |
70: |
|
FIB1(mark(X1),X2) |
→ FIB1(X1,X2) |
71: |
|
FIB1(X1,mark(X2)) |
→ FIB1(X1,X2) |
72: |
|
S(mark(X)) |
→ S(X) |
73: |
|
CONS(mark(X1),X2) |
→ CONS(X1,X2) |
74: |
|
ADD(mark(X1),X2) |
→ ADD(X1,X2) |
75: |
|
ADD(X1,mark(X2)) |
→ ADD(X1,X2) |
76: |
|
PROPER(fib(X)) |
→ FIB(proper(X)) |
77: |
|
PROPER(fib(X)) |
→ PROPER(X) |
78: |
|
PROPER(sel(X1,X2)) |
→ SEL(proper(X1),proper(X2)) |
79: |
|
PROPER(sel(X1,X2)) |
→ PROPER(X1) |
80: |
|
PROPER(sel(X1,X2)) |
→ PROPER(X2) |
81: |
|
PROPER(fib1(X1,X2)) |
→ FIB1(proper(X1),proper(X2)) |
82: |
|
PROPER(fib1(X1,X2)) |
→ PROPER(X1) |
83: |
|
PROPER(fib1(X1,X2)) |
→ PROPER(X2) |
84: |
|
PROPER(s(X)) |
→ S(proper(X)) |
85: |
|
PROPER(s(X)) |
→ PROPER(X) |
86: |
|
PROPER(cons(X1,X2)) |
→ CONS(proper(X1),proper(X2)) |
87: |
|
PROPER(cons(X1,X2)) |
→ PROPER(X1) |
88: |
|
PROPER(cons(X1,X2)) |
→ PROPER(X2) |
89: |
|
PROPER(add(X1,X2)) |
→ ADD(proper(X1),proper(X2)) |
90: |
|
PROPER(add(X1,X2)) |
→ PROPER(X1) |
91: |
|
PROPER(add(X1,X2)) |
→ PROPER(X2) |
92: |
|
FIB(ok(X)) |
→ FIB(X) |
93: |
|
SEL(ok(X1),ok(X2)) |
→ SEL(X1,X2) |
94: |
|
FIB1(ok(X1),ok(X2)) |
→ FIB1(X1,X2) |
95: |
|
S(ok(X)) |
→ S(X) |
96: |
|
CONS(ok(X1),ok(X2)) |
→ CONS(X1,X2) |
97: |
|
ADD(ok(X1),ok(X2)) |
→ ADD(X1,X2) |
98: |
|
TOP(mark(X)) |
→ TOP(proper(X)) |
99: |
|
TOP(mark(X)) |
→ PROPER(X) |
100: |
|
TOP(ok(X)) |
→ TOP(active(X)) |
101: |
|
TOP(ok(X)) |
→ ACTIVE(X) |
|
The approximated dependency graph contains 9 SCCs:
{74,75,97},
{73,96},
{67,92},
{70,71,94},
{72,95},
{68,69,93},
{77,79,80,82,83,85,87,88,90,91},
{50,52,54,56,58,60,62,64,66}
and {98,100}.