/export/starexec/sandbox2/solver/bin/starexec_run_default /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: if(true(),X,Y) -> X
    2: if(false(),X,Y) -> Y
    3: _(X1,X2) -> X1
    4: _(X1,X2) -> X2
Number of strict rules: 4
Direct POLO(bPol) ... removes: 4 1 3 2
      false	w: 7720
      _ 	w: x1 + 2 * x2 + 1
      true	w: 1
      if	w: 2 * x1 + 2 * x2 + 2 * x3
Number of strict rules: 0

...
Input TRS:
    1: if(true(),X,Y) -> X
    2: if(false(),X,Y) -> Y
    3: _(X1,X2) -> X1
    4: _(X1,X2) -> X2
Number of strict rules: 4
Direct POLO(bPol) ... removes: 4 1 3 2
      false	w: 7720
      _ 	w: x1 + 2 * x2 + 1
      true	w: 1
      if	w: 2 * x1 + 2 * x2 + 2 * x3
Number of strict rules: 0
>>YES

******** Signature ********
 h : ((nat -> bool),(nat -> nat),nat) -> nat
 0 : nat
 s : nat -> nat
 if : (bool,nat,nat) -> nat
******** Computation rules ********
 (3)  h(F,G,0) => 0
 (4)  h(F,G,s(Y)) => G[h(F,G,if(F[Y],Y,0))]


******** General Schema criterion ********
Found constructors: 0, true, false, s
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>OK
Checking  (1) if(true,X,Y) => X
 (meta X)[is acc in true,X,Y] [is positive in true] [is acc in X]  >>True
Checking  (2) if(false,X,Y) => Y
 (meta Y)[is acc in false,X,Y] [is positive in false] [is acc in Y]  >>True
Checking  (3) h(F,G,0) => 0
 (fun h>0) >>True
Checking  (4) h(F,G,s(Y)) => G[h(F,G,if(F[Y],Y,0))]
 (meta G)[is acc in F,G,s(Y)] [is acc in G] 
 (fun h=h) subterm comparison of args w. LR LR >>False

Try again using status RL
Checking  (1) if(true,X,Y) => X
 (meta X)[is acc in true,X,Y] [is positive in true] [is acc in X]  >>True
Checking  (2) if(false,X,Y) => Y
 (meta Y)[is acc in false,X,Y] [is positive in false] [is acc in Y]  >>True
Checking  (3) h(F,G,0) => 0
 (fun h>0) >>True
Checking  (4) h(F,G,s(Y)) => G[h(F,G,if(F[Y],Y,0))]
 (meta G)[is acc in F,G,s(Y)] [is acc in G] 
 (fun h=h) subterm comparison of args w. RL RL >>False

Try again using status Mul
Checking  (1) if(true,X,Y) => X
 (meta X)[is acc in true,X,Y] [is positive in true] [is acc in X]  >>True
Checking  (2) if(false,X,Y) => Y
 (meta Y)[is acc in false,X,Y] [is positive in false] [is acc in Y]  >>True
Checking  (3) h(F,G,0) => 0
 (fun h>0) >>True
Checking  (4) h(F,G,s(Y)) => G[h(F,G,if(F[Y],Y,0))]
 (meta G)[is acc in F,G,s(Y)] [is acc in G] 
 (fun h=h) subterm comparison of args w. Mul Mul >>False
Found constructors: 0, s, if
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>OK
Checking  (3) h(F,G,0) => 0
 (fun h>0) >>True
Checking  (4) h(F,G,s(Y)) => G[h(F,G,if(F[Y],Y,0))]
 (meta G)[is acc in F,G,s(Y)] [is acc in G] 
 (fun h=h) subterm comparison of args w. LR LR >>False

Try again using status RL
Checking  (3) h(F,G,0) => 0
 (fun h>0) >>True
Checking  (4) h(F,G,s(Y)) => G[h(F,G,if(F[Y],Y,0))]
 (meta G)[is acc in F,G,s(Y)] [is acc in G] 
 (fun h=h) subterm comparison of args w. RL RL >>False

Try again using status Mul
Checking  (3) h(F,G,0) => 0
 (fun h>0) >>True
Checking  (4) h(F,G,s(Y)) => G[h(F,G,if(F[Y],Y,0))]
 (meta G)[is acc in F,G,s(Y)] [is acc in G] 
 (fun h=h) subterm comparison of args w. Mul Mul >>False
#No idea..
******** Signature ********
 0 : nat
 h : ((nat -> bool),(nat -> nat),nat) -> nat
 if : (bool,nat,nat) -> nat
 true : bool
 false : bool
 s : nat -> nat
******** Computation Rules ********
 (1)  if(true,X,Y) => X
 (2)  if(false,X,Y) => Y
 (3)  h(F,G,0) => 0
 (4)  h(F,G,s(Y)) => G[h(F,G,if(F[Y],Y,0))]

MAYBE