(VAR X)
(STRATEGY CONTEXTSENSITIVE 
  (g)
  (h)
  (c)
  (d)
)
(RULES 
g(X) -> h(X)
c -> d
h(d) -> g(c)
)

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_Zan97:

-> Dependency pairs:
nF_g(X) -> nF_h(X)
nF_h(d) -> nF_g(c)

-> Proof of termination for Ex1_Zan97_1:
-> -> Dependency pairs in cycle:
nF_g(X) -> nF_h(X)
nF_h(d) -> nF_g(c)


Polynomial Interpretation:

[d] = 1
[c] = 0

TIME: 1.5719e-2

Termination proved: There exists a projection such that there are no minimal mu-rewrite sequences in cycle.

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.