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

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

******** Signature ********
 min : (nat,nat) -> nat
 0 : nat
 s : nat -> nat
 nul : ((nat -> nat),nat) -> nat
 find0 : ((nat -> nat),nat,nat) -> nat
 if : (nat,nat,nat) -> nat
******** Computation rules ********
 (3)  min(0,X) => 0
 (2)  min(X,0) => 0
 (1)  min(s(X),s(Y)) => min(X,Y)
 (4)  min(nul(F,Y),Z) => nul(F,min(Y,Z))
 (5)  nul(F,X) => find0(F,0,X)
 (6)  find0(F,X,0) => X
 (7)  find0(F,X,s(Y)) => if(F[X],find0(F,s(X),Y),X)


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

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

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

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

Try again using status Mul
Checking  (3) min(0,X) => 0
 (fun min>0) >>True
Checking  (2) min(X,0) => 0
 (fun min>0) >>True
Checking  (1) min(s(X),s(Y)) => min(X,Y)
 (fun min=min) subterm comparison of args w. Mul Mul
 (meta X)[is acc in s(X),s(Y)] [is positive in s(X)] [is acc in X] 
 (meta Y)[is acc in s(X),s(Y)] [is positive in s(X)] [is positive in s(Y)] [is acc in Y]  >>True
Checking  (4) min(nul(F,Y),Z) => nul(F,min(Y,Z))
 (fun min>nul)
 (meta F)[is acc in nul(F,Y),Z] [is positive in nul(F,Y)]  >>False
#No idea..
******** Signature ********
 min : (nat,nat) -> nat
 0 : nat
 s : nat -> nat
 nul : ((nat -> nat),nat) -> nat
 if : (nat,nat,nat) -> nat
 find0 : ((nat -> nat),nat,nat) -> nat
******** Computation Rules ********
 (1)  min(s(X),s(Y)) => min(X,Y)
 (2)  min(X,0) => 0
 (3)  min(0,X) => 0
 (4)  min(nul(F,Y),Z) => nul(F,min(Y,Z))
 (5)  nul(F,X) => find0(F,0,X)
 (6)  find0(F,X,0) => X
 (7)  find0(F,X,s(Y)) => if(F[X],find0(F,s(X),Y),X)
 (8)  if(s(Z),X,Y) => X
 (9)  if(0,X,Y) => Y

MAYBE