f(f(a, f(

R

↳Dependency Pair Analysis

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

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

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

The following dependency pair can be strictly oriented:

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

Additionally, the following rule can be oriented:

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

Used ordering: Polynomial ordering with Polynomial interpretation:

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

resulting in one new DP problem.

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↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Dependency Graph

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

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes