(VAR X N M)
(STRATEGY CONTEXTSENSITIVE 
  (and 1)
  (tt)
  (plus 1 2)
  (0)
  (s 1)
  (x 1 2)
)
(RULES 
and(tt,X) -> X
plus(N,0) -> N
plus(N,s(M)) -> s(plus(N,M))
x(N,0) -> 0
x(N,s(M)) -> plus(x(N,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:

-> Dependency pairs:
nF_and(tt,X) -> X
nF_plus(N,s(M)) -> nF_plus(N,M)
nF_x(N,s(M)) -> nF_plus(x(N,M),N)
nF_x(N,s(M)) -> nF_x(N,M)

-> Proof of termination for MYNAT_nosorts_1_1:
-> -> Dependency pairs in cycle:
nF_x(N,s(M)) -> nF_x(N,M)

Termination proved: Cycles verify subterm criterion.

-> Proof of termination for MYNAT_nosorts_1_2:
-> -> Dependency pairs in cycle:
nF_plus(N,s(M)) -> 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.