YES
  TPA v.1.0

Result: TRS is terminating

Default interpretations for symbols are not printed. For polynomial interpretations
and semantic labelling over N\{0,1} defaults are 2 for constants, identity for unary
symbols and x+y-2 for binary symbols. For semantic labelling over {0,1} (booleans)
defaults are 0 for constants, identity for unary symbols and disjunction for binary symbols.

[1]  TRS loaded from input file:
(1) minus(X,0) -> X
(2) minus(s(X),s(Y)) -> p(minus(X,Y))
(3) p(s(X)) -> X
(4) div(0,s(Y)) -> 0
(5) div(s(X),s(Y)) -> s(div(minus(X,Y),s(Y)))

[2]  Apply the Dependency Pair transformation resulting in the following dependency pairs:
<Minus(s(X),s(Y)), P(minus(X,Y))>
<Minus(s(X),s(Y)), Minus(X,Y)>
<Div(s(X),s(Y)), Div(minus(X,Y),s(Y))>
<Div(s(X),s(Y)), Minus(X,Y)>
 and 2 SCCs in the dependency graph. Proofs for those SCCs follow.

[2a-1]  Consider the following SCC obtained from analysis of dependency graph:
(1) minus(X,0) ->= X
(2) minus(s(X),s(Y)) ->= p(minus(X,Y))
(3) p(s(X)) ->= X
(4) div(0,s(Y)) ->= 0
(5) div(s(X),s(Y)) ->= s(div(minus(X,Y),s(Y)))
(DP3) Div(s(X),s(Y)) -> Div(minus(X,Y),s(Y))

[2a-2]  Use following polynomial interpretation:
[minus(x,y)] = x
[s(x)] = x + 1
rest default

  Remove rules with left hand side strictly bigger than right hand side:
(2)-(4), (DP3)

[2a-3]  Since there are no remaining strict rules, relative termination is proved!

[2b-1]  Consider the following SCC obtained from analysis of dependency graph:
(1) minus(X,0) ->= X
(2) minus(s(X),s(Y)) ->= p(minus(X,Y))
(3) p(s(X)) ->= X
(4) div(0,s(Y)) ->= 0
(5) div(s(X),s(Y)) ->= s(div(minus(X,Y),s(Y)))
(DP2) Minus(s(X),s(Y)) -> Minus(X,Y)

[2b-2]  Use following polynomial interpretation:
[minus(x,y)] = x
[s(x)] = x + 1
rest default

  Remove rules with left hand side strictly bigger than right hand side:
(2)-(4), (DP2)

[2b-3]  Since there are no remaining strict rules, relative termination is proved!



../tpdb/TRS/Rubio/gm.trs, 0.01, Y
Couldn't open file <60>: 60: No such file or directory