f(+(

+(

R

↳Dependency Pair Analysis

F(+(x, 0)) -> F(x)

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

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

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

→DP Problem 2

↳AFS

**F(+( x, 0)) -> F(x)**

f(+(x, 0)) -> f(x)

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

innermost

The following dependency pair can be strictly oriented:

F(+(x, 0)) -> F(x)

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

Used ordering: Lexicographic Path Order with Non-Strict Precedence with Quasi Precedence:

trivial

resulting in one new DP problem.

Used Argument Filtering System:

F(x) -> F(_{1}x)_{1}

+(x,_{1}x) -> +(_{2}x,_{1}x)_{2}

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 3

↳Dependency Graph

→DP Problem 2

↳AFS

f(+(x, 0)) -> f(x)

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

innermost

Using the Dependency Graph resulted in no new DP problems.

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Argument Filtering and Ordering

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

f(+(x, 0)) -> f(x)

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

innermost

The following dependency pair can be strictly oriented:

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

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

Used ordering: Lexicographic Path Order with Non-Strict Precedence with Quasi Precedence:

trivial

resulting in one new DP problem.

Used Argument Filtering System:

+'(x,_{1}x) -> +'(_{2}x,_{1}x)_{2}

+(x,_{1}x) -> +(_{2}x,_{1}x)_{2}

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳AFS

→DP Problem 4

↳Dependency Graph

f(+(x, 0)) -> f(x)

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

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes