first(0,

first(s(

from(

R

↳Dependency Pair Analysis

FIRST(s(X), cons(Y,Z)) -> FIRST(X,Z)

FROM(X) -> FROM(s(X))

Furthermore,

R

↳DPs

→DP Problem 1

↳Remaining Obligation(s)

→DP Problem 2

↳Remaining Obligation(s)

The following remains to be proven:

**Dependency Pair:****FIRST(s(***X*), cons(*Y*,*Z*)) -> FIRST(*X*,*Z*)**Rules:**

first(0,*X*) -> nil

first(s(*X*), cons(*Y*,*Z*)) -> cons(*Y*, first(*X*,*Z*))

from(*X*) -> cons(*X*, from(s(*X*)))**Dependency Pair:****FROM(***X*) -> FROM(s(*X*))**Rules:**

first(0,*X*) -> nil

first(s(*X*), cons(*Y*,*Z*)) -> cons(*Y*, first(*X*,*Z*))

from(*X*) -> cons(*X*, from(s(*X*)))

R

↳DPs

→DP Problem 1

↳Remaining Obligation(s)

→DP Problem 2

↳Remaining Obligation(s)

The following remains to be proven:

**Dependency Pair:****FIRST(s(***X*), cons(*Y*,*Z*)) -> FIRST(*X*,*Z*)**Rules:**

first(0,*X*) -> nil

first(s(*X*), cons(*Y*,*Z*)) -> cons(*Y*, first(*X*,*Z*))

from(*X*) -> cons(*X*, from(s(*X*)))**Dependency Pair:****FROM(***X*) -> FROM(s(*X*))**Rules:**

first(0,*X*) -> nil

first(s(*X*), cons(*Y*,*Z*)) -> cons(*Y*, first(*X*,*Z*))

from(*X*) -> cons(*X*, from(s(*X*)))

Duration:

0:00 minutes