/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: g(P) -> true()
    2: pred(0()) -> 0()
    3: pred(s(P1)) -> P1
    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(P) -> true()
    2: pred(0()) -> 0()
    3: pred(s(P1)) -> P1
    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
 s : N -> N
 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 ********
 (8)  g2(X2) => iszero(X2,0)
 (1)  rec(F,Z[0]) => Z
 (2)  rec(G,H[s(W)]) => G[W,rec(G,H[W])]
 (4)  h(X1,Z1,U1) => false
 (5)  iszero(V1,W1) => rec(h,g(V1),W1)
 (9)  h2(Y2,G2,V2) => G2[pred(V2)]
 (10)  geq(W2,P2) => rec(h2,g2(W2),P2)


******** 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, s, false, g, pred
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>OK
Checking  (8) g2(X2) => iszero(X2,0)
 (fun g2>iszero)
 (meta X2)[is acc in X2] [is acc in X2] 
 (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  (8) g2(X2) => iszero(X2,0)
 (fun g2>iszero)
 (meta X2)[is acc in X2] [is acc in X2] 
 (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  (8) g2(X2) => iszero(X2,0)
 (fun g2>iszero)
 (meta X2)[is acc in X2] [is acc in X2] 
 (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)  rec(G,H[s(W)]) => G[W,rec(G,H[W])]
 (3)  g(P) => true
 (4)  h(X1,Z1,U1) => false
 (5)  iszero(V1,W1) => rec(h,g(V1),W1)
 (6)  pred(0) => 0
 (7)  pred(s(P1)) => P1
 (8)  g2(X2) => iszero(X2,0)
 (9)  h2(Y2,G2,V2) => G2[pred(V2)]
 (10)  geq(W2,P2) => rec(h2,g2(W2),P2)

MAYBE