+(*(

+(+(

+(*(

R

↳Dependency Pair Analysis

+'(*(x,y), *(x,z)) -> +'(y,z)

+'(+(x,y),z) -> +'(x, +(y,z))

+'(+(x,y),z) -> +'(y,z)

+'(*(x,y), +(*(x,z), u)) -> +'(*(x, +(y,z)), u)

+'(*(x,y), +(*(x,z), u)) -> +'(y,z)

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

**+'(+( x, y), z) -> +'(y, z)**

+(*(x,y), *(x,z)) -> *(x, +(y,z))

+(+(x,y),z) -> +(x, +(y,z))

+(*(x,y), +(*(x,z), u)) -> +(*(x, +(y,z)), u)

innermost

The following dependency pairs can be strictly oriented:

+'(*(x,y), +(*(x,z), u)) -> +'(y,z)

+'(*(x,y), *(x,z)) -> +'(y,z)

Additionally, the following usable rules for innermost can be oriented:

+(*(x,y), *(x,z)) -> *(x, +(y,z))

+(+(x,y),z) -> +(x, +(y,z))

+(*(x,y), +(*(x,z), u)) -> +(*(x, +(y,z)), u)

Used ordering: Polynomial ordering with Polynomial interpretation:

_{ }^{ }POL(*(x)_{1}, x_{2})= 1 + x _{2}_{ }^{ }_{ }^{ }POL(+(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(u)= 0 _{ }^{ }_{ }^{ }POL(+'(x)_{1}, x_{2})= 1 + x _{1}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳Dependency Graph

**+'(+( x, y), z) -> +'(y, z)**

+(*(x,y), *(x,z)) -> *(x, +(y,z))

+(+(x,y),z) -> +(x, +(y,z))

+(*(x,y), +(*(x,z), u)) -> +(*(x, +(y,z)), u)

innermost

Using the Dependency Graph the DP problem was split into 1 DP problems.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳DGraph

...

→DP Problem 3

↳Polynomial Ordering

**+'(+( x, y), z) -> +'(y, z)**

+(*(x,y), *(x,z)) -> *(x, +(y,z))

+(+(x,y),z) -> +(x, +(y,z))

+(*(x,y), +(*(x,z), u)) -> +(*(x, +(y,z)), u)

innermost

The following dependency pair can be strictly oriented:

+'(+(x,y),z) -> +'(y,z)

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

Used ordering: Polynomial ordering with Polynomial interpretation:

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

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳Polo

→DP Problem 2

↳DGraph

...

→DP Problem 4

↳Dependency Graph

+(*(x,y), *(x,z)) -> *(x, +(y,z))

+(+(x,y),z) -> +(x, +(y,z))

+(*(x,y), +(*(x,z), u)) -> +(*(x, +(y,z)), u)

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes