(VAR )
(STRATEGY CONTEXTSENSITIVE 
  (f 1)
  (0)
  (cons 1)
  (s 1)
  (p 1)
)
(RULES 
f(0) -> cons(0,f(s(0)))
f(s(0)) -> f(p(s(0)))
p(s(0)) -> 0
)

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 Ex4_7_15_Bor03:

-> Dependency pairs:
nF_f(s(0)) -> nF_f(p(s(0)))
nF_f(s(0)) -> nF_p(s(0))

-> Dependency pairs narrowed: 
nF_f(s(0)) -> nF_f(p(s(0)))

-> New dependency pairs: 
nF_f(s(0)) -> nF_f(0)

-> Proof of termination for Ex4_7_15_Bor03_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.