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)) -> l
append(l1, l2) -> ifappend(l1, l2, l1)
ifappend(l1, l2, nil) -> l2
ifappend(l1, l2, cons(x, l)) -> cons(x, append(l, l2))

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

APPEND(l1, l2) -> IFAPPEND(l1, l2, l1)
IFAPPEND(l1, l2, cons(x, l)) -> APPEND(l, l2)

Furthermore, R contains one SCC. 


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




The following remains to be proven:
Dependency Pairs:

IFAPPEND(l1, l2, cons(x, l)) -> APPEND(l, l2)
APPEND(l1, l2) -> IFAPPEND(l1, l2, l1)


Rules:


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




Termination of R could not be shown.
Duration:
0:34 minutes