g(a) -> g(b)

b -> f(a, a)

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

R

↳Dependency Pair Analysis

G(a) -> G(b)

G(a) -> B

B -> F(a, a)

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

**G(a) -> G(b)**

g(a) -> g(b)

b -> f(a, a)

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

innermost

The following dependency pair can be strictly oriented:

G(a) -> G(b)

Additionally, the following usable rules for innermost can be oriented:

b -> f(a, a)

g(a) -> g(b)

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(g(x)_{1})= 0 _{ }^{ }_{ }^{ }POL(G(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(b)= 0 _{ }^{ }_{ }^{ }POL(d)= 0 _{ }^{ }_{ }^{ }POL(a)= 1 _{ }^{ }_{ }^{ }POL(f(x)_{1}, x_{2})= 0 _{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Dependency Graph

g(a) -> g(b)

b -> f(a, a)

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

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes