Termination Proof using AProVE

Term Rewriting System R:
[x]
f(h(x)) -> f(i(x))
g(i(x)) -> g(h(x))
h(a) -> b
i(a) -> b

Innermost Termination of R to be shown.

     ↳Dependency Pair Analysis

R contains the following Dependency Pairs:

F(h(x)) -> F(i(x))
F(h(x)) -> I(x)
G(i(x)) -> G(h(x))
G(i(x)) -> H(x)

Furthermore, R contains two SCCs.

     ↳DPs

       →DP Problem 1

         ↳Remaining Obligation(s)

       →DP Problem 2

         ↳Remaining Obligation(s)

The following remains to be proven:

Dependency Pair:
F(h(x)) -> F(i(x))

Rules:

f(h(x)) -> f(i(x))
g(i(x)) -> g(h(x))
h(a) -> b
i(a) -> b

Strategy:
innermost
Dependency Pair:
G(i(x)) -> G(h(x))

Rules:

f(h(x)) -> f(i(x))
g(i(x)) -> g(h(x))
h(a) -> b
i(a) -> b

Strategy:
innermost

     ↳DPs

       →DP Problem 1

         ↳Remaining Obligation(s)

       →DP Problem 2

         ↳Remaining Obligation(s)

The following remains to be proven:

Dependency Pair:
F(h(x)) -> F(i(x))

Rules:

f(h(x)) -> f(i(x))
g(i(x)) -> g(h(x))
h(a) -> b
i(a) -> b

Strategy:
innermost
Dependency Pair:
G(i(x)) -> G(h(x))

Rules:

f(h(x)) -> f(i(x))
g(i(x)) -> g(h(x))
h(a) -> b
i(a) -> b

Strategy:
innermost

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