+(+(

+(f(

+(f(

R

↳Dependency Pair Analysis

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

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

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

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Polynomial Ordering

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

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

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

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

innermost

The following dependency pairs can be strictly oriented:

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

+'(f(x), f(y)) -> +'(x,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(+(x)_{1}, x_{2})= x _{1}+ x_{2}_{ }^{ }_{ }^{ }POL(f(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(+'(x)_{1}, x_{2})= 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),z) -> +(x, +(y,z))

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

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

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

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

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

innermost

The following dependency pair can be strictly oriented:

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

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

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

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

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes