YES

The TRS could be proven terminating. The proof took 21 ms.

The following DP Processors were used

Problem 1 was processed with processor SubtermCriterion (1ms).
 | – Problem 2 was processed with processor DependencyGraph (0ms).

Problem 1: SubtermCriterion

Dependency Pair Problem

Dependency Pairs

append^#(l1, l2)

→

ifappend^#(l1, l2, l1)

ifappend^#(l1, l2, cons(x, l))

→

append^#(l, l2)

Rewrite Rules

is_empty(nil)	→	true		is_empty(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))

Original Signature

Termination of terms over the following signature is verified: append, tl, ifappend, true, false, hd, is_empty, nil, cons

Strategy

Projection

The following projection was used:

π (append#): 1
π (ifappend#): 3

Thus, the following dependency pairs are removed:

ifappend^#(l1, l2, cons(x, l))

→

append^#(l, l2)

Problem 2: DependencyGraph

Dependency Pair Problem

Dependency Pairs

append^#(l1, l2)

→

ifappend^#(l1, l2, l1)

Rewrite Rules

is_empty(nil)	→	true		is_empty(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))

Original Signature

Termination of terms over the following signature is verified: append, ifappend, tl, false, true, hd, is_empty, cons, nil

Strategy

There are no SCCs!