R
↳Dependency Pair Analysis
F(cons(x, k), l) -> G(k, l, cons(x, k))
G(a, b, c) -> F(a, cons(b, c))
R
↳DPs
→DP Problem 1
↳Instantiation Transformation
G(a, b, c) -> F(a, cons(b, c))
F(cons(x, k), l) -> G(k, l, cons(x, k))
f(empty, l) -> l
f(cons(x, k), l) -> g(k, l, cons(x, k))
g(a, b, c) -> f(a, cons(b, c))
one new Dependency Pair is created:
F(cons(x, k), l) -> G(k, l, cons(x, k))
F(cons(x', k'), cons(b'', c'')) -> G(k', cons(b'', c''), cons(x', k'))
R
↳DPs
→DP Problem 1
↳Inst
→DP Problem 2
↳Instantiation Transformation
F(cons(x', k'), cons(b'', c'')) -> G(k', cons(b'', c''), cons(x', k'))
G(a, b, c) -> F(a, cons(b, c))
f(empty, l) -> l
f(cons(x, k), l) -> g(k, l, cons(x, k))
g(a, b, c) -> f(a, cons(b, c))
one new Dependency Pair is created:
G(a, b, c) -> F(a, cons(b, c))
G(a', cons(b'''', c''''), cons(x''', k'''')) -> F(a', cons(cons(b'''', c''''), cons(x''', k'''')))
R
↳DPs
→DP Problem 1
↳Inst
→DP Problem 2
↳Inst
...
→DP Problem 3
↳Remaining Obligation(s)
G(a', cons(b'''', c''''), cons(x''', k'''')) -> F(a', cons(cons(b'''', c''''), cons(x''', k'''')))
F(cons(x', k'), cons(b'', c'')) -> G(k', cons(b'', c''), cons(x', k'))
f(empty, l) -> l
f(cons(x, k), l) -> g(k, l, cons(x, k))
g(a, b, c) -> f(a, cons(b, c))