(VAR X Y Z X1)
(STRATEGY CONTEXTSENSITIVE 
  (2nd 1)
  (cons1 1 2)
  (cons 1)
  (from 1)
  (s 1)
)
(RULES 
2nd(cons1(X,cons(Y,Z))) -> Y
2nd(cons(X,X1)) -> 2nd(cons1(X,X1))
from(X) -> cons(X,from(s(X)))
)

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 Ex6_9_Luc02c:

-> Dependency pairs:
nF_2nd(cons(X,X1)) -> nF_2nd(cons1(X,X1))
nF_2nd(cons(X,X1)) -> X1

-> Proof of termination for Ex6_9_Luc02c_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.