Term Rewriting System R:
[x, u, v, z, y]
admit(x, .(u, .(v, .(w, z)))) -> cond(=(sum(x, u, v), w), .(u, .(v, .(w, admit(carry(x, u, v), z)))))
cond(true, y) -> y

Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

ADMIT(x, .(u, .(v, .(w, z)))) -> COND(=(sum(x, u, v), w), .(u, .(v, .(w, admit(carry(x, u, v), z)))))

Furthermore, R contains one SCC.

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳Polynomial Ordering`

Dependency Pair:

Rules:

admit(x, .(u, .(v, .(w, z)))) -> cond(=(sum(x, u, v), w), .(u, .(v, .(w, admit(carry(x, u, v), z)))))
cond(true, y) -> y

The following dependency pair can be strictly oriented:

Additionally, the following rules can be oriented:

admit(x, .(u, .(v, .(w, z)))) -> cond(=(sum(x, u, v), w), .(u, .(v, .(w, admit(carry(x, u, v), z)))))
cond(true, y) -> y

Used ordering: Polynomial ordering with Polynomial interpretation:
 POL(cond(x1, x2)) =  x2 POL(=(x1, x2)) =  0 POL(carry(x1, x2, x3)) =  0 POL(nil) =  0 POL(true) =  1 POL(.(x1, x2)) =  x1 + x2 POL(sum(x1, x2, x3)) =  0 POL(admit(x1, x2)) =  x2 POL(w) =  1 POL(ADMIT(x1, x2)) =  1 + x2

resulting in one new DP problem.

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳Polo`
`           →DP Problem 2`
`             ↳Dependency Graph`

Dependency Pair:

Rules: