|
| 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}.