half(0) -> 0

half(s(s(

log(s(0)) -> 0

log(s(s(

R

↳Dependency Pair Analysis

HALF(s(s(x))) -> HALF(x)

LOG(s(s(x))) -> LOG(s(half(x)))

LOG(s(s(x))) -> HALF(x)

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

→DP Problem 2

↳Polo

**HALF(s(s( x))) -> HALF(x)**

half(0) -> 0

half(s(s(x))) -> s(half(x))

log(s(0)) -> 0

log(s(s(x))) -> s(log(s(half(x))))

The following dependency pair can be strictly oriented:

HALF(s(s(x))) -> HALF(x)

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

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(HALF(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(s(x)_{1})= 1 + x _{1}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 3

↳Dependency Graph

→DP Problem 2

↳Polo

half(0) -> 0

half(s(s(x))) -> s(half(x))

log(s(0)) -> 0

log(s(s(x))) -> s(log(s(half(x))))

Using the Dependency Graph resulted in no new DP problems.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polynomial Ordering

**LOG(s(s( x))) -> LOG(s(half(x)))**

half(0) -> 0

half(s(s(x))) -> s(half(x))

log(s(0)) -> 0

log(s(s(x))) -> s(log(s(half(x))))

The following dependency pair can be strictly oriented:

LOG(s(s(x))) -> LOG(s(half(x)))

Additionally, the following usable rules w.r.t. to the implicit AFS can be oriented:

half(0) -> 0

half(s(s(x))) -> s(half(x))

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(0)= 0 _{ }^{ }_{ }^{ }POL(s(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(half(x)_{1})= x _{1}_{ }^{ }_{ }^{ }POL(LOG(x)_{1})= 1 + x _{1}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Polo

→DP Problem 4

↳Dependency Graph

half(0) -> 0

half(s(s(x))) -> s(half(x))

log(s(0)) -> 0

log(s(s(x))) -> s(log(s(half(x))))

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes