f(

f(s(

R

↳Dependency Pair Analysis

F(x, c(y)) -> F(x, s(f(y,y)))

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

F(s(x), s(y)) -> F(x, s(c(s(y))))

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

→DP Problem 2

↳Polo

**F(s( x), s(y)) -> F(x, s(c(s(y))))**

f(x, c(y)) -> f(x, s(f(y,y)))

f(s(x), s(y)) -> f(x, s(c(s(y))))

innermost

The following dependency pair can be strictly oriented:

F(s(x), s(y)) -> F(x, s(c(s(y))))

There are no usable rules for innermost w.r.t. to the implicit AFS that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

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

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 3

↳Dependency Graph

→DP Problem 2

↳Polo

f(x, c(y)) -> f(x, s(f(y,y)))

f(s(x), s(y)) -> f(x, s(c(s(y))))

innermost

Using the Dependency Graph resulted in no new DP problems.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polynomial Ordering

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

f(x, c(y)) -> f(x, s(f(y,y)))

f(s(x), s(y)) -> f(x, s(c(s(y))))

innermost

The following dependency pair can be strictly oriented:

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

There are no usable rules for innermost w.r.t. to the implicit AFS that need to be oriented.

Used ordering: Polynomial ordering with Polynomial interpretation:

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

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polo

→DP Problem 4

↳Dependency Graph

f(x, c(y)) -> f(x, s(f(y,y)))

f(s(x), s(y)) -> f(x, s(c(s(y))))

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes