/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


MAYBE

We split firstr-order part and higher-order part, and do modular checking by a general modularity.

******** FO SN check ********
Check SN using NaTT (Nagoya Termination Tool)
Input TRS:
    1: dom(s(X),s(Y),s(Z)) -> s(dom(X,Y,Z))
    2: dom(o(),s(Y),s(Z)) -> s(dom(o(),Y,Z))
    3: dom(X,Y,o()) -> X
    4: dom(o(),o(),Z) -> o()
    5: _(X1,X2) -> X1
    6: _(X1,X2) -> X2
Number of strict rules: 6
Direct POLO(bPol) ... removes: 4 1 3 5 6 2
      s 	w: 2 * x1 + 4
      _ 	w: 2 * x1 + 2 * x2 + 1
      o 	w: 3
      dom	w: 2 * x1 + 2 * x2 + 2 * x3 + 3
Number of strict rules: 0

...
Input TRS:
    1: dom(s(X),s(Y),s(Z)) -> s(dom(X,Y,Z))
    2: dom(o(),s(Y),s(Z)) -> s(dom(o(),Y,Z))
    3: dom(X,Y,o()) -> X
    4: dom(o(),o(),Z) -> o()
    5: _(X1,X2) -> X1
    6: _(X1,X2) -> X2
Number of strict rules: 6
Direct POLO(bPol) ... removes: 4 1 3 5 6 2
      s 	w: 2 * x1 + 4
      _ 	w: 2 * x1 + 2 * x2 + 1
      o 	w: 3
      dom	w: 2 * x1 + 2 * x2 + 2 * x3 + 3
Number of strict rules: 0
>>YES

******** Signature ********
 eval : (N,N) -> N
 fun : ((N -> N),N,N) -> N
 dom : (N,N,N) -> N
******** Computation rules ********
 (1)  eval(fun(F,X,Y),Z) => F[dom(X,Y,Z)]


******** General Schema criterion ********
Found constructors: o, s, fun
Checking type order >>OK
Checking positivity of constructors >>NO
Checking  (1) eval(fun(F,X,Y),Z) => F[dom(X,Y,Z)]
 (meta F)[is acc in fun(F,X,Y),Z] [is positive in fun(F,X,Y)]  >>False
Found constructors: fun, dom
Checking type order >>OK
Checking positivity of constructors >>NO
#No idea..
******** Signature ********
 o : N
 s : N -> N
 fun : ((N -> N),N,N) -> N
 dom : (N,N,N) -> N
 eval : (N,N) -> N
******** Computation Rules ********
 (1)  eval(fun(F,X,Y),Z) => F[dom(X,Y,Z)]
 (2)  dom(s(X),s(Y),s(Z)) => s(dom(X,Y,Z))
 (3)  dom(o,s(Y),s(Z)) => s(dom(o,Y,Z))
 (4)  dom(X,Y,o) => X
 (5)  dom(o,o,Z) => o

MAYBE