Term Rewriting System R:
[]
g(a) -> g(b)
b -> f(a, a)
f(a, a) -> g(d)

Termination of R to be shown.

R
Dependency Pair Analysis

R contains the following Dependency Pairs:

G(a) -> G(b)
G(a) -> B
B -> F(a, a)
F(a, a) -> G(d)

Furthermore, R contains one SCC.

R
DPs
→DP Problem 1
Narrowing Transformation

Dependency Pair:

G(a) -> G(b)

Rules:

g(a) -> g(b)
b -> f(a, a)
f(a, a) -> g(d)

On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

G(a) -> G(b)
one new Dependency Pair is created:

G(a) -> G(f(a, a))

The transformation is resulting in one new DP problem:

R
DPs
→DP Problem 1
Nar
→DP Problem 2
Narrowing Transformation

Dependency Pair:

G(a) -> G(f(a, a))

Rules:

g(a) -> g(b)
b -> f(a, a)
f(a, a) -> g(d)

On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

G(a) -> G(f(a, a))
one new Dependency Pair is created:

G(a) -> G(g(d))

The transformation is resulting in one new DP problem:

R
DPs
→DP Problem 1
Nar
→DP Problem 2
Nar
...
→DP Problem 3
Narrowing Transformation

Dependency Pair:

G(a) -> G(g(d))

Rules:

g(a) -> g(b)
b -> f(a, a)
f(a, a) -> g(d)

On this DP problem, a Narrowing SCC transformation can be performed.
As a result of transforming the rule

G(a) -> G(g(d))
no new Dependency Pairs are created.
The transformation is resulting in no new DP problems.

Termination of R successfully shown.
Duration:
0:00 minutes