(VAR X Y)
(STRATEGY CONTEXTSENSITIVE 
  (f 1)
  (if 1 2)
  (c)
  (true)
  (false)
)
(RULES 
f(X) -> if(X,c,f(true))
if(true,X,Y) -> X
if(false,X,Y) -> 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 Ex5_Zan97:

-> Dependency pairs:
nF_f(X) -> nF_if(X,c,f(true))
nF_if(false,X,Y) -> Y

-> Proof of termination for Ex5_Zan97_1:
-> -> Dependency pairs in cycle:
nF_f(X) -> nF_if(X,c,f(true))
nF_if(false,X,Y) -> Y

Usable Rules:
f(X) -> if(X,c,f(true))
if(true,X,Y) -> X
if(false,X,Y) -> Y

Polynomial Interpretation:

[f](X) = X
[if](X1,X2,X3) = X1 + X2 + X3
[c] = 0
[true] = 0
[false] = 1
[nF_f](X) = X
[nF_if](X1,X2,X3) = X1 + X3

TIME: 1.6891e-2


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.