Term Rewriting System R:
[x, y, z, t, a, b, c]
g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldf(x, nil) -> x
foldf(x, cons(y, z)) -> f(foldf(x, z), y)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, cons(C, c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldf(triple(cons(A, a), nil, c), b))
f''(triple(a, b, c)) -> foldf(triple(a, b, nil), c)

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

FOLDF(x, cons(y, z)) -> F(foldf(x, z), y)
FOLDF(x, cons(y, z)) -> FOLDF(x, z)
F(t, x) -> F'(t, g(x))
F(t, x) -> G(x)
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F'(triple(a, b, c), A) -> F''(foldf(triple(cons(A, a), nil, c), b))
F'(triple(a, b, c), A) -> FOLDF(triple(cons(A, a), nil, c), b)
F''(triple(a, b, c)) -> FOLDF(triple(a, b, nil), c)

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Remaining Obligation(s)




The following remains to be proven:
Dependency Pairs:

F'(triple(a, b, c), A) -> FOLDF(triple(cons(A, a), nil, c), b)
FOLDF(x, cons(y, z)) -> FOLDF(x, z)
F''(triple(a, b, c)) -> FOLDF(triple(a, b, nil), c)
F'(triple(a, b, c), A) -> F''(foldf(triple(cons(A, a), nil, c), b))
F'(triple(a, b, c), B) -> F(triple(a, b, c), A)
F(t, x) -> F'(t, g(x))
FOLDF(x, cons(y, z)) -> F(foldf(x, z), y)


Rules:


g(A) -> A
g(B) -> A
g(B) -> B
g(C) -> A
g(C) -> B
g(C) -> C
foldf(x, nil) -> x
foldf(x, cons(y, z)) -> f(foldf(x, z), y)
f(t, x) -> f'(t, g(x))
f'(triple(a, b, c), C) -> triple(a, b, cons(C, c))
f'(triple(a, b, c), B) -> f(triple(a, b, c), A)
f'(triple(a, b, c), A) -> f''(foldf(triple(cons(A, a), nil, c), b))
f''(triple(a, b, c)) -> foldf(triple(a, b, nil), c)




Termination of R could not be shown.
Duration:
0:00 minutes