(VAR X L)
(STRATEGY CONTEXTSENSITIVE 
  (incr 1)
  (nil)
  (cons 1)
  (s 1)
  (adx 1)
  (nats)
  (zeros)
  (0)
  (head 1)
  (tail 1)
)
(RULES 
incr(nil) -> nil
incr(cons(X,L)) -> cons(s(X),incr(L))
adx(nil) -> nil
adx(cons(X,L)) -> incr(cons(X,adx(L)))
nats -> adx(zeros)
zeros -> cons(0,zeros)
head(cons(X,L)) -> X
tail(cons(X,L)) -> L
)

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_GM01:

-> Dependency pairs:
nF_adx(cons(X,L)) -> nF_incr(cons(X,adx(L)))
nF_nats -> nF_adx(zeros)
nF_nats -> nF_zeros
nF_tail(cons(X,L)) -> L

-> Proof of termination for ExIntrod_GM01_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.