f(a, h(

h(g(

h(h(

g(h(

R

↳Dependency Pair Analysis

F(a, h(x)) -> F(g(x), h(x))

F(a, h(x)) -> G(x)

H(g(x)) -> H(a)

G(h(x)) -> G(x)

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

→DP Problem 2

↳Polo

**G(h( x)) -> G(x)**

f(a, h(x)) -> f(g(x), h(x))

h(g(x)) -> h(a)

h(h(x)) ->x

g(h(x)) -> g(x)

The following dependency pair can be strictly oriented:

G(h(x)) -> G(x)

There are no usable rules w.r.t. to the implicit AFS that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(G(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(h(x)_{1})= 1 + x _{1}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 3

↳Dependency Graph

→DP Problem 2

↳Polo

f(a, h(x)) -> f(g(x), h(x))

h(g(x)) -> h(a)

h(h(x)) ->x

g(h(x)) -> g(x)

Using the Dependency Graph resulted in no new DP problems.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polynomial Ordering

**F(a, h( x)) -> F(g(x), h(x))**

f(a, h(x)) -> f(g(x), h(x))

h(g(x)) -> h(a)

h(h(x)) ->x

g(h(x)) -> g(x)

The following dependency pair can be strictly oriented:

F(a, h(x)) -> F(g(x), h(x))

Additionally, the following usable rule w.r.t. to the implicit AFS can be oriented:

g(h(x)) -> g(x)

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(g(x)_{1})= 0 _{ }^{ }_{ }^{ }POL(h(x)_{1})= 0 _{ }^{ }_{ }^{ }POL(a)= 1 _{ }^{ }_{ }^{ }POL(F(x)_{1}, x_{2})= x _{1}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polo

→DP Problem 4

↳Dependency Graph

f(a, h(x)) -> f(g(x), h(x))

h(g(x)) -> h(a)

h(h(x)) ->x

g(h(x)) -> g(x)

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes