Term Rewriting System R:
[X, XS]
zeros -> cons(0, zeros)
tail(cons(X, XS)) -> XS

Innermost Termination of R to be shown.

`   R`
`     ↳Removing Redundant Rules`

Removing the following rules from R which fullfill a polynomial ordering:

tail(cons(X, XS)) -> XS

where the Polynomial interpretation:
 POL(0) =  0 POL(cons(x1, x2)) =  x1 + x2 POL(tail(x1)) =  1 + x1 POL(zeros) =  0
was used.

Not all Rules of R can be deleted, so we still have to regard a part of R.

`   R`
`     ↳RRRPolo`
`       →TRS2`
`         ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

ZEROS -> ZEROS

Furthermore, R contains one SCC.

`   R`
`     ↳RRRPolo`
`       →TRS2`
`         ↳DPs`
`           →DP Problem 1`
`             ↳Usable Rules (Innermost)`

Dependency Pair:

ZEROS -> ZEROS

Rule:

zeros -> cons(0, zeros)

Strategy:

innermost

As we are in the innermost case, we can delete all 1 non-usable-rules.

`   R`
`     ↳RRRPolo`
`       →TRS2`
`         ↳DPs`
`           →DP Problem 1`
`             ↳UsableRules`
`             ...`
`               →DP Problem 2`
`                 ↳Non Termination`

Dependency Pair:

ZEROS -> ZEROS

Rule:

none

Strategy:

innermost

Found an infinite P-chain over R:
P =

ZEROS -> ZEROS

R = none

s = ZEROS
evaluates to t =ZEROS

Thus, s starts an infinite chain.

Innermost Non-Termination of R could be shown.
Duration:
0:03 minutes