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

↳Argument Filtering and 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)

The following usable rules for innermost can be oriented:

b -> f(a, a)

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

g(a) -> g(b)

Used ordering: Lexicographic Path Order with Non-Strict Precedence with Quasi Precedence:

a > {f, b} > d

a > {f, b} > g

resulting in one new DP problem.

Used Argument Filtering System:

G(x) -> G(_{1}x)_{1}

b -> b

f(x,_{1}x) -> f_{2}

g(x) -> g(_{1}x)_{1}

R

↳DPs

→DP Problem 1

↳AFS

→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