/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(U) -> true()
    2: pred(0()) -> 0()
    3: pred(s(U1)) -> U1
    4: _(X1,X2) -> X1
    5: _(X1,X2) -> X2
Number of strict rules: 5
Direct POLO(bPol) ... removes: 4 1 3 5 2
      s 	w: 2 * x1 + 1
      _ 	w: 2 * x1 + 2 * x2 + 1
      true	w: 0
      pred	w: 2 * x1 + 7719
      0 	w: 1
      g 	w: x1 + 1
Number of strict rules: 0

...
Input TRS:
    1: g(U) -> true()
    2: pred(0()) -> 0()
    3: pred(s(U1)) -> U1
    4: _(X1,X2) -> X1
    5: _(X1,X2) -> X2
Number of strict rules: 5
Direct POLO(bPol) ... removes: 4 1 3 5 2
      s 	w: 2 * x1 + 1
      _ 	w: 2 * x1 + 2 * x2 + 1
      true	w: 0
      pred	w: 2 * x1 + 7719
      0 	w: 1
      g 	w: x1 + 1
Number of strict rules: 0
>>YES

******** Signature ********
 g2 : N -> B
 iszero : (N,N) -> B
 0 : N
 rec : (((N,(N -> B),N) -> B),B,N) -> B
 h : (N,(N -> B),N) -> B
 false : B
 g : N -> B
 h2 : (N,(N -> B),N) -> B
 pred : N -> N
 geq : (N,N) -> B
******** Computation rules ********
 (7)  g2(V1) => iszero(V1,0)
 (1)  rec(F,Z[0]) => Z
 (3)  h(V,I,P) => false
 (4)  iszero(X1,Y1) => rec(h,g(X1),Y1)
 (8)  h2(W1,J1,X2) => J1[pred(X2)]
 (9)  geq(Y2,U2) => rec(h2,g2(Y2),U2)


******** General Schema criterion ********
Found constructors: 0, false, s, true
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>OK
Checking  (1) rec(F,Z[0]) => Z
 (meta Z)[is acc in F,Z[0]] [is acc in Z[0]]  >>False

Try again using status RL
Checking  (1) rec(F,Z[0]) => Z
 (meta Z)[is acc in F,Z[0]] [is acc in Z[0]]  >>False

Try again using status Mul
Checking  (1) rec(F,Z[0]) => Z
 (meta Z)[is acc in F,Z[0]] [is acc in Z[0]]  >>False
Found constructors: 0, false, g, pred
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>OK
Checking  (7) g2(V1) => iszero(V1,0)
 (fun g2>iszero)
 (meta V1)[is acc in V1] [is acc in V1] 
 (fun g2>0) >>True
Checking  (1) rec(F,Z[0]) => Z
 (meta Z)[is acc in F,Z[0]] [is acc in Z[0]]  >>False

Try again using status RL
Checking  (7) g2(V1) => iszero(V1,0)
 (fun g2>iszero)
 (meta V1)[is acc in V1] [is acc in V1] 
 (fun g2>0) >>True
Checking  (1) rec(F,Z[0]) => Z
 (meta Z)[is acc in F,Z[0]] [is acc in Z[0]]  >>False

Try again using status Mul
Checking  (7) g2(V1) => iszero(V1,0)
 (fun g2>iszero)
 (meta V1)[is acc in V1] [is acc in V1] 
 (fun g2>0) >>True
Checking  (1) rec(F,Z[0]) => Z
 (meta Z)[is acc in F,Z[0]] [is acc in Z[0]]  >>False
#No idea..
******** Signature ********
 0 : N
 false : B
 g : N -> B
 g2 : N -> B
 geq : (N,N) -> B
 h : (N,(N -> B),N) -> B
 h2 : (N,(N -> B),N) -> B
 iszero : (N,N) -> B
 pred : N -> N
 rec : (((N,(N -> B),N) -> B),B,N) -> B
 s : N -> N
 true : B
******** Computation Rules ********
 (1)  rec(F,Z[0]) => Z
 (2)  g(U) => true
 (3)  h(V,I,P) => false
 (4)  iszero(X1,Y1) => rec(h,g(X1),Y1)
 (5)  pred(0) => 0
 (6)  pred(s(U1)) => U1
 (7)  g2(V1) => iszero(V1,0)
 (8)  h2(W1,J1,X2) => J1[pred(X2)]
 (9)  geq(Y2,U2) => rec(h2,g2(Y2),U2)

MAYBE