/export/starexec/sandbox/solver/bin/starexec_run_hrs /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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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: b() -> a()
    2: _(X1,X2) -> X1
    3: _(X1,X2) -> X2
Number of strict rules: 3
Direct POLO(bPol) ... removes: 1 3 2
      a 	w: 0
      b 	w: 1
      _ 	w: 2 * x1 + 2 * x2 + 1
Number of strict rules: 0

...
Input TRS:
    1: b() -> a()
    2: _(X1,X2) -> X1
    3: _(X1,X2) -> X2
Number of strict rules: 3
Direct POLO(bPol) ... removes: 1 3 2
      a 	w: 0
      b 	w: 1
      _ 	w: 2 * x1 + 2 * x2 + 1
Number of strict rules: 0
>>YES

******** Signature ********
 g : (o,o,(o -> o)) -> o
 f : (o,(o -> o)) -> o
 b : o
 a : o
******** Computation rules ********
 (1)  g(X,Y,F) => f(f(X,F),F)
 (2)  f(X,F) => b
 (4)  f(b,z.g(z,z,F)) => g(f(a,z.g(z,z,F)),f(b,z.b),F)


******** General Schema criterion ********
Found constructors: a
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>Regared as equal: f, g
Checking  (1) g(X,Y,F) => f(f(X,F),F)
 (fun g=f) subterm comparison of args w. LR LR >>False

Try again using status RL
Checking  (1) g(X,Y,F) => f(f(X,F),F)
 (fun g=f) subterm comparison of args w. RL RL >>False

Try again using status Mul
Checking  (1) g(X,Y,F) => f(f(X,F),F)
 (fun g=f) subterm comparison of args w. Mul Mul >>False
Found constructors: b, a
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>Regared as equal: f, g
Checking  (1) g(X,Y,F) => f(f(X,F),F)
 (fun g=f) subterm comparison of args w. LR LR >>False

Try again using status RL
Checking  (1) g(X,Y,F) => f(f(X,F),F)
 (fun g=f) subterm comparison of args w. RL RL >>False

Try again using status Mul
Checking  (1) g(X,Y,F) => f(f(X,F),F)
 (fun g=f) subterm comparison of args w. Mul Mul >>False
#No idea..
******** Signature ********
 f : (o,(o -> o)) -> o
 g : (o,o,(o -> o)) -> o
 b : o
 a : o
******** Computation Rules ********
 (1)  g(X,Y,F) => f(f(X,F),F)
 (2)  f(X,F) => b
 (3)  b => a
 (4)  f(b,z.g(z,z,F)) => g(f(a,z.g(z,z,F)),f(b,z.b),F)

MAYBE