/export/starexec/sandbox/solver/bin/starexec_run_default /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: h(0()) -> a(0())
    2: h(s(Y)) -> a(h(Y))
    3: i(0()) -> 0()
    4: i(a(Y)) -> s(i(Y))
    5: _(X1,X2) -> X1
    6: _(X1,X2) -> X2
Number of strict rules: 6
Direct POLO(bPol) ... removes: 4 1 3 5 6 2
      a 	w: 2 * x1 + 3
      h 	w: 2 * x1 + 4
      s 	w: 2 * x1 + 4
      _ 	w: 2 * x1 + 2 * x2 + 1
      0 	w: 2438
      i 	w: 2 * x1 + 1
Number of strict rules: 0

...
Input TRS:
    1: h(0()) -> a(0())
    2: h(s(Y)) -> a(h(Y))
    3: i(0()) -> 0()
    4: i(a(Y)) -> s(i(Y))
    5: _(X1,X2) -> X1
    6: _(X1,X2) -> X2
Number of strict rules: 6
Direct POLO(bPol) ... removes: 4 1 3 5 6 2
      a 	w: 2 * x1 + 3
      h 	w: 2 * x1 + 4
      s 	w: 2 * x1 + 4
      _ 	w: 2 * x1 + 2 * x2 + 1
      0 	w: 2438
      i 	w: 2 * x1 + 1
Number of strict rules: 0
>>YES

******** Signature ********
 f : ((nat -> nat),nat,nat) -> nat
 g : (nat,nat,(nat -> nat),nat) -> nat
 s : nat -> nat
 0 : nat
 h : nat -> nat
******** Computation rules ********
 (1)  f(F,Y,U) => g(Y,U,F,Y)
 (2)  g(s(Y),s(U),F,V) => g(Y,U,F,V)
 (3)  g(0,0,F,V) => f(F,s(V),F[h(V)])


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

Try again using status RL
Checking  (1) f(F,Y,U) => g(Y,U,F,Y)
 (fun f=g) subterm comparison of args w. RL RL >>False

Try again using status Mul
Checking  (1) f(F,Y,U) => g(Y,U,F,Y)
 (fun f=g) subterm comparison of args w. Mul Mul >>False
Found constructors: s, 0, h
Checking type order >>OK
Checking positivity of constructors >>OK
Checking function dependency >>Regared as equal: g, f
Checking  (1) f(F,Y,U) => g(Y,U,F,Y)
 (fun f=g) subterm comparison of args w. LR LR >>False

Try again using status RL
Checking  (1) f(F,Y,U) => g(Y,U,F,Y)
 (fun f=g) subterm comparison of args w. RL RL >>False

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

MAYBE