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

↳Argument Filtering and Ordering

→DP Problem 2

↳AFS

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

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

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

h(a) -> b

i(a) -> b

innermost

The following dependency pair can be strictly oriented:

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

The following usable rule for innermost can be oriented:

i(a) -> b

Used ordering: Polynomial ordering with Polynomial interpretation:

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

resulting in one new DP problem.

Used Argument Filtering System:

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

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 3

↳Dependency Graph

→DP Problem 2

↳AFS

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

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

h(a) -> b

i(a) -> b

innermost

Using the Dependency Graph resulted in no new DP problems.

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Argument Filtering and 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

innermost

The following dependency pair can be strictly oriented:

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

The following usable rule for innermost can be oriented:

h(a) -> b

Used ordering: Polynomial ordering with Polynomial interpretation:

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

resulting in one new DP problem.

Used Argument Filtering System:

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

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳AFS

→DP Problem 4

↳Dependency Graph

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

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

h(a) -> b

i(a) -> b

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes