f(a) -> b

f(c) -> d

f(g(

f(h(

g(

R

↳Dependency Pair Analysis

F(g(x,y)) -> G(f(x), f(y))

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

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

F(h(x,y)) -> G(h(y, f(x)), h(x, f(y)))

F(h(x,y)) -> F(x)

F(h(x,y)) -> F(y)

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

**F(h( x, y)) -> F(y)**

f(a) -> b

f(c) -> d

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

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

g(x,x) -> h(e,x)

innermost

The following dependency pairs can be strictly oriented:

F(h(x,y)) -> F(y)

F(h(x,y)) -> F(x)

There are no usable rules for innermost that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

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

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polynomial Ordering

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

f(a) -> b

f(c) -> d

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

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

g(x,x) -> h(e,x)

innermost

The following dependency pairs can be strictly oriented:

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

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

There are no usable rules for innermost that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

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

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polo

...

→DP Problem 3

↳Dependency Graph

f(a) -> b

f(c) -> d

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

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

g(x,x) -> h(e,x)

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes