f(a) -> f(c(a))

f(c(

f(c(a)) -> f(d(b))

f(a) -> f(d(a))

f(d(

f(c(b)) -> f(d(a))

e(g(

R

↳Dependency Pair Analysis

F(a) -> F(c(a))

F(c(a)) -> F(d(b))

F(a) -> F(d(a))

F(c(b)) -> F(d(a))

E(g(X)) -> E(X)

Furthermore,

R

↳DPs

→DP Problem 1

↳Forward Instantiation Transformation

**E(g( X)) -> E(X)**

f(a) -> f(c(a))

f(c(X)) ->X

f(c(a)) -> f(d(b))

f(a) -> f(d(a))

f(d(X)) ->X

f(c(b)) -> f(d(a))

e(g(X)) -> e(X)

innermost

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

As a result of transforming the rule

one new Dependency Pair is created:

E(g(X)) -> E(X)

E(g(g(X''))) -> E(g(X''))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳FwdInst

→DP Problem 2

↳Forward Instantiation Transformation

**E(g(g( X''))) -> E(g(X''))**

f(a) -> f(c(a))

f(c(X)) ->X

f(c(a)) -> f(d(b))

f(a) -> f(d(a))

f(d(X)) ->X

f(c(b)) -> f(d(a))

e(g(X)) -> e(X)

innermost

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

As a result of transforming the rule

one new Dependency Pair is created:

E(g(g(X''))) -> E(g(X''))

E(g(g(g(X'''')))) -> E(g(g(X'''')))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳FwdInst

→DP Problem 2

↳FwdInst

...

→DP Problem 3

↳Polynomial Ordering

**E(g(g(g( X'''')))) -> E(g(g(X'''')))**

f(a) -> f(c(a))

f(c(X)) ->X

f(c(a)) -> f(d(b))

f(a) -> f(d(a))

f(d(X)) ->X

f(c(b)) -> f(d(a))

e(g(X)) -> e(X)

innermost

The following dependency pair can be strictly oriented:

E(g(g(g(X'''')))) -> E(g(g(X'''')))

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(E(x)_{1})= 1 + x _{1}_{ }^{ }_{ }^{ }POL(g(x)_{1})= 1 + x _{1}_{ }^{ }

resulting in one new DP problem.

R

↳DPs

→DP Problem 1

↳FwdInst

→DP Problem 2

↳FwdInst

...

→DP Problem 4

↳Dependency Graph

f(a) -> f(c(a))

f(c(X)) ->X

f(c(a)) -> f(d(b))

f(a) -> f(d(a))

f(d(X)) ->X

f(c(b)) -> f(d(a))

e(g(X)) -> e(X)

innermost

Using the Dependency Graph resulted in no new DP problems.

Duration:

0:00 minutes