/export/starexec/sandbox2/solver/bin/starexec_run_hrs /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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: f(X) -> X
    2: _(X1,X2) -> X1
    3: _(X1,X2) -> X2
Number of strict rules: 3
Direct POLO(bPol) ... removes: 1 3 2
      _ 	w: 2 * x1 + 2 * x2 + 1
      f 	w: 2 * x1 + 1
Number of strict rules: 0

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

******** Signature ********
 g : (((b,d) -> e),b,e) -> f
 s : c -> e
 0 : d
******** Computation rules ********
 (2)  g(Z,U,s(V)) => g(Z,U,Z[U,0])


******** General Schema criterion ********
Found constructors: 0, s
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>OK
Checking  (1) f(X) => X
 (meta X)[is acc in X] [is acc in X]  >>True
Checking  (2) g(Z,U,s(V)) => g(Z,U,Z[U,0])
 (fun g=g) subterm comparison of args w. LR LR >>False

Try again using status RL
Checking  (1) f(X) => X
 (meta X)[is acc in X] [is acc in X]  >>True
Checking  (2) g(Z,U,s(V)) => g(Z,U,Z[U,0])
 (fun g=g) subterm comparison of args w. RL RL >>False

Try again using status Mul
Checking  (1) f(X) => X
 (meta X)[is acc in X] [is acc in X]  >>True
Checking  (2) g(Z,U,s(V)) => g(Z,U,Z[U,0])
 (fun g=g) subterm comparison of args w. Mul Mul >>False
Found constructors: s, 0
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>OK
Checking  (2) g(Z,U,s(V)) => g(Z,U,Z[U,0])
 (fun g=g) subterm comparison of args w. LR LR >>False

Try again using status RL
Checking  (2) g(Z,U,s(V)) => g(Z,U,Z[U,0])
 (fun g=g) subterm comparison of args w. RL RL >>False

Try again using status Mul
Checking  (2) g(Z,U,s(V)) => g(Z,U,Z[U,0])
 (fun g=g) subterm comparison of args w. Mul Mul >>False
#No idea..
******** Signature ********
 0 : d
 f : a -> a
 g : (((b,d) -> e),b,e) -> f
 s : c -> e
******** Computation Rules ********
 (1)  f(X) => X
 (2)  g(Z,U,s(V)) => g(Z,U,Z[U,0])

MAYBE