Term Rewriting System R:
[x]
+(1, x) -> +(+(0, 1), x)
+(0, x) -> x

Innermost Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

+'(1, x) -> +'(+(0, 1), x)
+'(1, x) -> +'(0, 1)

Furthermore, R contains one SCC.

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳Rewriting Transformation`

Dependency Pair:

+'(1, x) -> +'(+(0, 1), x)

Rules:

+(1, x) -> +(+(0, 1), x)
+(0, x) -> x

Strategy:

innermost

On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

+'(1, x) -> +'(+(0, 1), x)
one new Dependency Pair is created:

+'(1, x) -> +'(1, x)

The transformation is resulting in one new DP problem:

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳Rw`
`           →DP Problem 2`
`             ↳Remaining Obligation(s)`

The following remains to be proven:
Dependency Pair:

+'(1, x) -> +'(1, x)

Rules:

+(1, x) -> +(+(0, 1), x)
+(0, x) -> x

Strategy:

innermost

Innermost Termination of R could not be shown.
Duration:
0:00 minutes