from(

first(0,

first(s(

sel(0, cons(

sel(s(

R

↳Dependency Pair Analysis

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

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Usable Rules (Innermost)

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

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

first(0,Z) -> nil

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

sel(0, cons(X,Z)) ->X

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

innermost

As we are in the innermost case, we can delete all 5 non-usable-rules.

R

↳DPs

→DP Problem 1

↳UsableRules

→DP Problem 4

↳Non Termination

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

none

innermost

Found an infinite P-chain over R:

P =

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

R = none

s = FROM(

evaluates to t =FROM(s(

Thus, s starts an infinite chain as s matches t.

Duration:

0:01 minutes