Term Rewriting System R:
[n, m]
ackin(0, n) -> ackout(s(n))
ackin(s(m), 0) -> u11(ackin(m, s(0)))
ackin(s(m), s(n)) -> u21(ackin(s(m), n), m)
u11(ackout(n)) -> ackout(n)
u21(ackout(n), m) -> u22(ackin(m, n))
u22(ackout(n)) -> ackout(n)

Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

ACKIN(s(m), 0) -> U11(ackin(m, s(0)))
ACKIN(s(m), 0) -> ACKIN(m, s(0))
ACKIN(s(m), s(n)) -> U21(ackin(s(m), n), m)
ACKIN(s(m), s(n)) -> ACKIN(s(m), n)
U21(ackout(n), m) -> U22(ackin(m, n))
U21(ackout(n), m) -> ACKIN(m, n)

Furthermore, R contains one SCC. 


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




The following remains to be proven:
Dependency Pairs:

ACKIN(s(m), s(n)) -> ACKIN(s(m), n)
U21(ackout(n), m) -> ACKIN(m, n)
ACKIN(s(m), s(n)) -> U21(ackin(s(m), n), m)
ACKIN(s(m), 0) -> ACKIN(m, s(0))


Rules:


ackin(0, n) -> ackout(s(n))
ackin(s(m), 0) -> u11(ackin(m, s(0)))
ackin(s(m), s(n)) -> u21(ackin(s(m), n), m)
u11(ackout(n)) -> ackout(n)
u21(ackout(n), m) -> u22(ackin(m, n))
u22(ackout(n)) -> ackout(n)




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