Term Rewriting System R:
[x, y]
not(true) -> false
not(false) -> true
odd(0) -> false
odd(s(x)) -> not(odd(x))
+(x, 0) -> x
+(x, s(y)) -> s(+(x, y))
+(s(x), y) -> s(+(x, y))

Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

ODD(s(x)) -> NOT(odd(x))
ODD(s(x)) -> ODD(x)
+'(x, s(y)) -> +'(x, y)
+'(s(x), y) -> +'(x, y)

Furthermore, R contains two SCCs.

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

The following remains to be proven:
• Dependency Pair:

ODD(s(x)) -> ODD(x)

Rules:

not(true) -> false
not(false) -> true
odd(0) -> false
odd(s(x)) -> not(odd(x))
+(x, 0) -> x
+(x, s(y)) -> s(+(x, y))
+(s(x), y) -> s(+(x, y))

• Dependency Pairs:

+'(s(x), y) -> +'(x, y)
+'(x, s(y)) -> +'(x, y)

Rules:

not(true) -> false
not(false) -> true
odd(0) -> false
odd(s(x)) -> not(odd(x))
+(x, 0) -> x
+(x, s(y)) -> s(+(x, y))
+(s(x), y) -> s(+(x, y))

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

The following remains to be proven:
• Dependency Pair:

ODD(s(x)) -> ODD(x)

Rules:

not(true) -> false
not(false) -> true
odd(0) -> false
odd(s(x)) -> not(odd(x))
+(x, 0) -> x
+(x, s(y)) -> s(+(x, y))
+(s(x), y) -> s(+(x, y))

• Dependency Pairs:

+'(s(x), y) -> +'(x, y)
+'(x, s(y)) -> +'(x, y)

Rules:

not(true) -> false
not(false) -> true
odd(0) -> false
odd(s(x)) -> not(odd(x))
+(x, 0) -> x
+(x, s(y)) -> s(+(x, y))
+(s(x), y) -> s(+(x, y))

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