/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: g(Y) -> h(Y,Y)
    2: h(0(),U) -> U
    3: h(s(V),0()) -> g(V)
    4: _(X1,X2) -> X1
    5: _(X1,X2) -> X2
Number of strict rules: 5
Direct POLO(bPol) ... removes: 4 1 3 5 2
      h 	w: x1 + x2
      s 	w: 2 * x1 + 1
      _ 	w: 2 * x1 + 2 * x2 + 1
      0 	w: 1
      g 	w: 2 * x1 + 1
Number of strict rules: 0

...
Input TRS:
    1: g(Y) -> h(Y,Y)
    2: h(0(),U) -> U
    3: h(s(V),0()) -> g(V)
    4: _(X1,X2) -> X1
    5: _(X1,X2) -> X2
Number of strict rules: 5
Direct POLO(bPol) ... removes: 4 1 3 5 2
      h 	w: x1 + x2
      s 	w: 2 * x1 + 1
      _ 	w: 2 * x1 + 2 * x2 + 1
      0 	w: 1
      g 	w: 2 * x1 + 1
Number of strict rules: 0
>>YES

******** Signature ********
 a : o
 f : (o -> o) -> o
 g : o -> o
******** Computation rules ********
 (1)  a => f(%X.g(%X))
 (2)  f(%Y.X) => a


******** General Schema criterion ********
Found constructors: 0, s
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>Regared as equal: h, g
Checking  (1) a => f(%X.g(%X))
 (fun a>f)
 (fun a>g) >>True
Checking  (2) f(%Y.X) => a
 (fun f>a) >>True
Checking  (3) g(Y) => h(Y,Y)
 (fun g=h) subterm comparison of args w. LR LR >>False

Try again using status RL
Checking  (1) a => f(%X.g(%X))
 (fun a>f)
 (fun a>g) >>True
Checking  (2) f(%Y.X) => a
 (fun f>a) >>True
Checking  (3) g(Y) => h(Y,Y)
 (fun g=h) subterm comparison of args w. RL RL >>False

Try again using status Mul
Checking  (1) a => f(%X.g(%X))
 (fun a>f)
 (fun a>g) >>True
Checking  (2) f(%Y.X) => a
 (fun f>a) >>True
Checking  (3) g(Y) => h(Y,Y)
 (fun g=h) subterm comparison of args w. Mul Mul >>False
Found constructors: g
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>Regared as equal: f, a
Checking  (1) a => f(%X.g(%X))
 (fun a=f) subterm comparison of args w. LR LR >>False

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

Try again using status Mul
Checking  (1) a => f(%X.g(%X))
 (fun a=f) subterm comparison of args w. Mul Mul >>False
#No idea..
******** Signature ********
 0 : o
 a : o
 f : (o -> o) -> o
 g : o -> o
 h : (o,o) -> o
 s : o -> o
******** Computation Rules ********
 (1)  a => f(%X.g(%X))
 (2)  f(%Y.X) => a
 (3)  g(Y) => h(Y,Y)
 (4)  h(0,U) => U
 (5)  h(s(V),0) => g(V)

MAYBE