f(a,

g(a) -> b

g(b) -> b

R

↳Dependency Pair Analysis

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

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

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

g(a) -> b

g(b) -> b

The following dependency pair can be strictly oriented:

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

The following rules can be oriented:

g(a) -> b

g(b) -> b

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

Used ordering: Polynomial ordering with Polynomial interpretation:

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

resulting in one new DP problem.

Used Argument Filtering System:

F(x,_{1}x) -> F(_{2}x,_{1}x)_{2}

g(x) -> g_{1}

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Dependency Graph

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

g(a) -> b

g(b) -> b

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes