c(b(a(

c(

a(

b(

R

↳Dependency Pair Analysis

C(b(a(X))) -> A(a(b(b(c(c(X))))))

C(b(a(X))) -> A(b(b(c(c(X)))))

C(b(a(X))) -> B(b(c(c(X))))

C(b(a(X))) -> B(c(c(X)))

C(b(a(X))) -> C(c(X))

C(b(a(X))) -> C(X)

Furthermore,

R

↳DPs

→DP Problem 1

↳Forward Instantiation Transformation

**C(b(a( X))) -> C(X)**

c(b(a(X))) -> a(a(b(b(c(c(X))))))

c(X) -> e

a(X) -> e

b(X) -> e

On this DP problem, a Forward Instantiation SCC transformation can be performed.

As a result of transforming the rule

no new Dependency Pairs are created.

C(b(a(X))) -> C(c(X))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳FwdInst

→DP Problem 2

↳Polynomial Ordering

**C(b(a( X))) -> C(X)**

c(b(a(X))) -> a(a(b(b(c(c(X))))))

c(X) -> e

a(X) -> e

b(X) -> e

The following dependency pair can be strictly oriented:

C(b(a(X))) -> C(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(C(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(b(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(a(x)_{1})= x _{1}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳FwdInst

→DP Problem 2

↳Polo

...

→DP Problem 3

↳Dependency Graph

c(b(a(X))) -> a(a(b(b(c(c(X))))))

c(X) -> e

a(X) -> e

b(X) -> e

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes