s1(s1(s0(s0(

R

↳Dependency Pair Analysis

S1(s1(s0(s0(x)))) -> S1(s1(s1(x)))

S1(s1(s0(s0(x)))) -> S1(s1(x))

S1(s1(s0(s0(x)))) -> S1(x)

Furthermore,

R

↳DPs

→DP Problem 1

↳Narrowing Transformation

**S1(s1(s0(s0( x)))) -> S1(x)**

s1(s1(s0(s0(x)))) -> s0(s0(s0(s1(s1(s1(x))))))

innermost

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

As a result of transforming the rule

two new Dependency Pairs are created:

S1(s1(s0(s0(x)))) -> S1(s1(s1(x)))

S1(s1(s0(s0(s0(s0(x'')))))) -> S1(s0(s0(s0(s1(s1(s1(x'')))))))

S1(s1(s0(s0(s1(s0(s0(x''))))))) -> S1(s1(s0(s0(s0(s1(s1(s1(x''))))))))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳Forward Instantiation Transformation

**S1(s1(s0(s0(s1(s0(s0( x''))))))) -> S1(s1(s0(s0(s0(s1(s1(s1(x''))))))))**

s1(s1(s0(s0(x)))) -> s0(s0(s0(s1(s1(s1(x))))))

innermost

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

As a result of transforming the rule

two new Dependency Pairs are created:

S1(s1(s0(s0(x)))) -> S1(x)

S1(s1(s0(s0(s1(s0(s0(x''))))))) -> S1(s1(s0(s0(x''))))

S1(s1(s0(s0(s1(s0(s0(s1(s0(s0(x'''')))))))))) -> S1(s1(s0(s0(s1(s0(s0(x'''')))))))

The transformation is resulting in one new DP problem:

R

↳DPs

→DP Problem 1

↳Nar

→DP Problem 2

↳FwdInst

...

→DP Problem 3

↳Remaining Obligation(s)

The following remains to be proven:

**S1(s1(s0(s0(s1(s0(s0(s1(s0(s0( x'''')))))))))) -> S1(s1(s0(s0(s1(s0(s0(x'''')))))))**

s1(s1(s0(s0(x)))) -> s0(s0(s0(s1(s1(s1(x))))))

innermost

Duration:

0:00 minutes