(VAR X Y)
(STRATEGY CONTEXTSENSITIVE 
  (nats)
  (adx 1)
  (zeros)
  (cons)
  (0)
  (incr 1)
  (s)
  (hd 1)
  (tl 1)
)
(RULES 
nats -> adx(zeros)
zeros -> cons(0,zeros)
incr(cons(X,Y)) -> cons(s(X),incr(Y))
adx(cons(X,Y)) -> incr(cons(X,adx(Y)))
hd(cons(X,Y)) -> X
tl(cons(X,Y)) -> Y
)

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 ExIntrod_GM04:

-> Dependency pairs:
nF_nats -> nF_adx(zeros)
nF_nats -> nF_zeros
nF_adx(cons(X,Y)) -> nF_incr(cons(X,adx(Y)))
nF_hd(cons(X,Y)) -> X
nF_tl(cons(X,Y)) -> Y

-> Proof of termination for ExIntrod_GM04_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.