(VAR M N)
(STRATEGY CONTEXTSENSITIVE 
  (U11 1)
  (tt)
  (U12 1)
  (s 1)
  (plus 1 2)
  (0)
)
(RULES 
U11(tt,M,N) -> U12(tt,M,N)
U12(tt,M,N) -> s(plus(N,M))
plus(N,0) -> N
plus(N,s(M)) -> U11(tt,M,N)
)

The TRS is orthogonal, thus termination of innermost context-sensitive rewriting is equivalent to termination of context-sensitive rewriting.

Proving termination of context-sensitive rewriting for MYNAT_nosorts_noand:

-> Dependency pairs:
nF_U11(tt,M,N) -> nF_U12(tt,M,N)
nF_U12(tt,M,N) -> nF_plus(N,M)
nF_U12(tt,M,N) -> N
nF_U12(tt,M,N) -> M
nF_plus(N,s(M)) -> nF_U11(tt,M,N)

-> Proof of termination for MYNAT_nosorts_noand_1:
-> -> Dependency pairs in cycle:
nF_U11(tt,M,N) -> nF_U12(tt,M,N)
nF_plus(N,s(M)) -> nF_U11(tt,M,N)
nF_U12(tt,M,N) -> nF_plus(N,M)

Termination proved: Cycles verify subterm criterion.

SETTINGS:
Base ordering: Polynomial ordering
Proof mode: SCCs in CSDG + base ordering
Upper bound for coeffs: 1
Rationals below 1 for all non-replacing args: No
Polynomial interpretation: Linear
Coeffs in polynomials: No rationals
Delta: automatic



Termination was proved succesfully.