Term Rewriting System R:
[x, l, l1, l2]
isempty(nil) -> true
isempty(cons(x, l)) -> false
hd(cons(x, l)) -> x
tl(cons(x, l)) -> cons(x, l)
append(l1, l2) -> ifappend(l1, l2, isempty(l1))
ifappend(l1, l2, true) -> l2
ifappend(l1, l2, false) -> cons(hd(l1), append(tl(l1), l2))

Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

APPEND(l1, l2) -> IFAPPEND(l1, l2, isempty(l1))
APPEND(l1, l2) -> ISEMPTY(l1)
IFAPPEND(l1, l2, false) -> HD(l1)
IFAPPEND(l1, l2, false) -> APPEND(tl(l1), l2)
IFAPPEND(l1, l2, false) -> TL(l1)

Furthermore, R contains one SCC.

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳Remaining Obligation(s)`

The following remains to be proven:
Dependency Pairs:

IFAPPEND(l1, l2, false) -> APPEND(tl(l1), l2)
APPEND(l1, l2) -> IFAPPEND(l1, l2, isempty(l1))

Rules:

isempty(nil) -> true
isempty(cons(x, l)) -> false
hd(cons(x, l)) -> x
tl(cons(x, l)) -> cons(x, l)
append(l1, l2) -> ifappend(l1, l2, isempty(l1))
ifappend(l1, l2, true) -> l2
ifappend(l1, l2, false) -> cons(hd(l1), append(tl(l1), l2))

Termination of R could not be shown.
Duration:
0:01 minutes