f(h(

g(i(

h(a) -> b

i(a) -> b

R

↳Dependency Pair Analysis

F(h(x)) -> F(i(x))

F(h(x)) -> I(x)

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

G(i(x)) -> H(x)

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

→DP Problem 2

↳Polo

**F(h( x)) -> F(i(x))**

f(h(x)) -> f(i(x))

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

h(a) -> b

i(a) -> b

The following dependency pair can be strictly oriented:

F(h(x)) -> F(i(x))

Additionally, the following usable rule using the Ce-refinement can be oriented:

i(a) -> b

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(i(x)_{1})= 0 _{ }^{ }_{ }^{ }POL(b)= 0 _{ }^{ }_{ }^{ }POL(h(x)_{1})= 1 _{ }^{ }_{ }^{ }POL(a)= 0 _{ }^{ }_{ }^{ }POL(F(x)_{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(h(x)) -> f(i(x))

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

h(a) -> b

i(a) -> b

Using the Dependency Graph resulted in no new DP problems.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polynomial Ordering

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

f(h(x)) -> f(i(x))

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

h(a) -> b

i(a) -> b

The following dependency pair can be strictly oriented:

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

Additionally, the following usable rule using the Ce-refinement can be oriented:

h(a) -> b

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(i(x)_{1})= 1 _{ }^{ }_{ }^{ }POL(G(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(b)= 0 _{ }^{ }_{ }^{ }POL(h(x)_{1})= 0 _{ }^{ }_{ }^{ }POL(a)= 0 _{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polo

→DP Problem 4

↳Dependency Graph

f(h(x)) -> f(i(x))

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

h(a) -> b

i(a) -> b

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes