/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


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: avg(s(X),Y) -> avg(X,s(Y))
    2: avg(U,s(s(s(V)))) -> s(avg(s(U),V))
    3: avg(0(),0()) -> 0()
    4: avg(0(),s(0())) -> 0()
    5: avg(0(),s(s(0()))) -> s(0())
    6: check(s(X1)) -> s(check(X1))
    7: check(0()) -> 0()
    8: _(X1,X2) -> X1
    9: _(X1,X2) -> X2
Number of strict rules: 9
Direct POLO(bPol) ... removes: 4 8 1 3 5 7 9 6
      s 	w: x1 + 975
      _ 	w: 2 * x1 + 2 * x2 + 1
      check	w: 2 * x1 + 1
      0 	w: 1143
      avg	w: 2 * x1 + x2 + 8456
Number of strict rules: 1
Direct POLO(bPol) ... removes: 2
      s 	w: x1 + 975
      _ 	w: 2 * x1 + 2 * x2 + 1
      check	w: 2 * x1 + 1
      0 	w: 1143
      avg	w: 2 * x1 + 2 * x2 + 8456
Number of strict rules: 0

...
Input TRS:
    1: avg(s(X),Y) -> avg(X,s(Y))
    2: avg(U,s(s(s(V)))) -> s(avg(s(U),V))
    3: avg(0(),0()) -> 0()
    4: avg(0(),s(0())) -> 0()
    5: avg(0(),s(s(0()))) -> s(0())
    6: check(s(X1)) -> s(check(X1))
    7: check(0()) -> 0()
    8: _(X1,X2) -> X1
    9: _(X1,X2) -> X2
Number of strict rules: 9
Direct POLO(bPol) ... removes: 4 8 1 3 5 7 9 6
      s 	w: x1 + 975
      _ 	w: 2 * x1 + 2 * x2 + 1
      check	w: 2 * x1 + 1
      0 	w: 1143
      avg	w: 2 * x1 + x2 + 8456
Number of strict rules: 1
Direct POLO(bPol) ... removes: 2
      s 	w: x1 + 975
      _ 	w: 2 * x1 + 2 * x2 + 1
      check	w: 2 * x1 + 1
      0 	w: 1143
      avg	w: 2 * x1 + 2 * x2 + 8456
Number of strict rules: 0
>>YES

******** Signature ********
 apply : (nat,nat) -> nat
 fun : (nat -> nat) -> nat
 check : nat -> nat
******** Computation rules ********
 (6)  apply(fun(I),P) => I[check(P)]


******** General Schema criterion ********
Found constructors: 0, fun, s
Checking type order >>OK
Checking positivity of constructors >>NO
Checking  (1) avg(s(X),Y) => avg(X,s(Y))
 (fun avg=avg) subterm comparison of args w. LR LR
 (meta X)[is acc in s(X),Y] [is positive in s(X)] [is acc in X] 
 (fun avg>s)
 (meta Y)[is acc in s(X),Y] [is positive in s(X)] [is acc in Y]  >>True
Checking  (2) avg(U,s(s(s(V)))) => s(avg(s(U),V))
 (fun avg>s)
 (fun avg=avg) subterm comparison of args w. LR LR >>False
Found constructors: fun, check
Checking type order >>OK
Checking positivity of constructors >>NO
#No idea..
******** Signature ********
 0 : nat
 apply : (nat,nat) -> nat
 avg : (nat,nat) -> nat
 check : nat -> nat
 fun : (nat -> nat) -> nat
 s : nat -> nat
******** Computation Rules ********
 (1)  avg(s(X),Y) => avg(X,s(Y))
 (2)  avg(U,s(s(s(V)))) => s(avg(s(U),V))
 (3)  avg(0,0) => 0
 (4)  avg(0,s(0)) => 0
 (5)  avg(0,s(s(0))) => s(0)
 (6)  apply(fun(I),P) => I[check(P)]
 (7)  check(s(X1)) => s(check(X1))
 (8)  check(0) => 0

MAYBE