(VAR X XS)
(STRATEGY CONTEXTSENSITIVE 
  (nats)
  (cons 1)
  (0)
  (incr 1)
  (pairs)
  (odds)
  (s 1)
  (head 1)
  (tail 1)
)
(RULES 
nats -> cons(0,incr(nats))
pairs -> cons(0,incr(odds))
odds -> incr(pairs)
incr(cons(X,XS)) -> cons(s(X),incr(XS))
head(cons(X,XS)) -> X
tail(cons(X,XS)) -> XS
)

The TRS is orthogonal, thus termination of innermost context-sensitive rewriting is equivalent to termination of context-sensitive rewriting.

Proving termination of context-sensitive rewriting for Ex1_Luc04b:

-> Dependency pairs:
nF_odds -> nF_incr(pairs)
nF_odds -> nF_pairs
nF_tail(cons(X,XS)) -> XS

-> Proof of termination for Ex1_Luc04b_1:
Termination proved: No cycles in dependency graph.

SETTINGS:
Base ordering: Polynomial ordering
Proof mode: SCCs in CSDG + base ordering
Upper bound for coeffs: 1
Rationals below 1 for all non-replacing args: No
Polynomial interpretation: Linear
Coeffs in polynomials: No rationals
Delta: automatic



Termination was proved succesfully.