f(a,

h(g(

h(h(

g(h(

R

↳Dependency Pair Analysis

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

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

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

→DP Problem 2

↳Remaining

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

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

Additionally, the following rules can be oriented:

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

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

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

h(h(x)) ->x

Used ordering: Polynomial ordering with Polynomial interpretation:

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

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 3

↳Dependency Graph

→DP Problem 2

↳Remaining

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

↳Remaining Obligation(s)

The following remains to be proven:

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

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

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

h(h(x)) ->x

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

Duration:

0:00 minutes