Term Rewriting System R:
[y, x, f]
app(app(plus, 0), y) -> y
app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y))
app(app(app(curry, f), x), y) -> app(app(f, x), y)

Innermost Termination of R to be shown.

`   R`
`     ↳Removing Redundant Rules`

Removing the following rules from R which fullfill a polynomial ordering:

app(app(plus, 0), y) -> y

where the Polynomial interpretation:
 POL(plus) =  0 POL(0) =  1 POL(curry) =  0 POL(s) =  0 POL(app(x1, x2)) =  x1 + x2 POL(add) =  0
was used.

Not all Rules of R can be deleted, so we still have to regard a part of R.

`   R`
`     ↳RRRPolo`
`       →TRS2`
`         ↳Removing Redundant Rules`

Removing the following rules from R which fullfill a polynomial ordering:

where the Polynomial interpretation:
 POL(plus) =  0 POL(curry) =  0 POL(s) =  0 POL(app(x1, x2)) =  x1 + x2 POL(add) =  1
was used.

Not all Rules of R can be deleted, so we still have to regard a part of R.

`   R`
`     ↳RRRPolo`
`       →TRS2`
`         ↳RRRPolo`
`           →TRS3`
`             ↳Removing Redundant Rules`

Removing the following rules from R which fullfill a polynomial ordering:

app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y))
app(app(app(curry, f), x), y) -> app(app(f, x), y)

where the Polynomial interpretation:
 POL(plus) =  0 POL(curry) =  4 POL(s) =  0 POL(app(x1, x2)) =  1 + 2·x1 + x2
was used.

All Rules of R can be deleted.

`   R`
`     ↳RRRPolo`
`       →TRS2`
`         ↳RRRPolo`
`           →TRS3`
`             ↳RRRPolo`
`             ...`
`               →TRS4`
`                 ↳Dependency Pair Analysis`

R contains no Dependency Pairs and therefore no SCCs.

Innermost Termination of R successfully shown.
Duration:
0:00 minutes