w(r(

b(r(

b(w(

R

↳Dependency Pair Analysis

W(r(x)) -> W(x)

B(r(x)) -> B(x)

B(w(x)) -> W(b(x))

B(w(x)) -> B(x)

Furthermore,

R

↳DPs

→DP Problem 1

↳Argument Filtering and Ordering

→DP Problem 2

↳AFS

→DP Problem 3

↳AFS

**W(r( x)) -> W(x)**

w(r(x)) -> r(w(x))

b(r(x)) -> r(b(x))

b(w(x)) -> w(b(x))

innermost

The following dependency pair can be strictly oriented:

W(r(x)) -> W(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:

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 4

↳Dependency Graph

→DP Problem 2

↳AFS

→DP Problem 3

↳AFS

w(r(x)) -> r(w(x))

b(r(x)) -> r(b(x))

b(w(x)) -> w(b(x))

innermost

Using the Dependency Graph resulted in no new DP problems.

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳Argument Filtering and Ordering

→DP Problem 3

↳AFS

**B(r( x)) -> B(x)**

w(r(x)) -> r(w(x))

b(r(x)) -> r(b(x))

b(w(x)) -> w(b(x))

innermost

The following dependency pair can be strictly oriented:

B(r(x)) -> B(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:

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳AFS

→DP Problem 5

↳Dependency Graph

→DP Problem 3

↳AFS

w(r(x)) -> r(w(x))

b(r(x)) -> r(b(x))

b(w(x)) -> w(b(x))

innermost

Using the Dependency Graph resulted in no new DP problems.

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳AFS

→DP Problem 3

↳Argument Filtering and Ordering

**B(w( x)) -> B(x)**

w(r(x)) -> r(w(x))

b(r(x)) -> r(b(x))

b(w(x)) -> w(b(x))

innermost

The following dependency pair can be strictly oriented:

B(w(x)) -> B(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:

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

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

R

↳DPs

→DP Problem 1

↳AFS

→DP Problem 2

↳AFS

→DP Problem 3

↳AFS

→DP Problem 6

↳Dependency Graph

w(r(x)) -> r(w(x))

b(r(x)) -> r(b(x))

b(w(x)) -> w(b(x))

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes