(VAR X)
(STRATEGY CONTEXTSENSITIVE 
  (from 1)
  (cons 1)
  (s 1)
)
(RULES 
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 Ex14_AEGL02_1:

-> Dependency pairs:
No dependency pairs found.

-> Proof of termination for Ex14_AEGL02_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

(VAR X Y)
(STRATEGY CONTEXTSENSITIVE 
  (length)
  (cons 1)
  (s 1)
  (length1)
  (nil)
  (0)
)
(RULES 
length(cons(X,Y)) -> s(length1(Y))
length(nil) -> 0
length1(X) -> length(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 Ex14_AEGL02_2:

-> Dependency pairs:
nF_length(cons(X,Y)) -> nF_length1(Y)
nF_length1(X) -> nF_length(X)

-> Proof of termination for Ex14_AEGL02_2:
-> -> Dependency pairs in cycle:
nF_length(cons(X,Y)) -> nF_length1(Y)
nF_length1(X) -> nF_length(X)


Polynomial Interpretation:

[cons](X1,X2) = X2 + 1

TIME: 1.5557e-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.