(VAR X Y)
(STRATEGY CONTEXTSENSITIVE 
  (f 1)
  (g 1)
)
(RULES 
f(g(X),Y) -> f(X,f(g(X),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 Ex4_4_Luc96b:

-> Dependency pairs:
nF_f(g(X),Y) -> nF_f(X,f(g(X),Y))

-> Proof of termination for Ex4_4_Luc96b_1:
-> -> Dependency pairs in cycle:
nF_f(g(X),Y) -> nF_f(X,f(g(X),Y))

Termination proved: Cycles verify subterm criterion.

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.