/export/starexec/sandbox2/solver/bin/starexec_run_hrs /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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NO

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: f(X,g(X)) -> f(1(),g(X))
    2: g(1()) -> g(0())
Number of strict rules: 2
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #g(1()) -> #g(0())
   #2: #f(X,g(X)) -> #f(1(),g(X))
Number of SCCs: 1, DPs: 1
  SCC { #2 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  found.
  #f(1(),g(1()))	-#2->
  #f(1(),g(1()))	--->*
  #f(1(),g(1()))
  Looping with: [ ]

...
Input TRS:
    1: f(X,g(X)) -> f(1(),g(X))
    2: g(1()) -> g(0())
Number of strict rules: 2
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #g(1()) -> #g(0())
   #2: #f(X,g(X)) -> #f(1(),g(X))
Number of SCCs: 1, DPs: 1
  SCC { #2 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  found.
  #f(1(),g(1()))	-#2->
  #f(1(),g(1()))	--->*
  #f(1(),g(1()))
  Looping with: [ ]
>>NO


******** Signature ********
 0 : b
 1 : b
 cons : (e,f) -> f
 f : (b,c) -> a
 false : d
 filter : ((e -> d),f) -> f
 filter2 : (d,(e -> d),e,f) -> f
 g : b -> c
 map : ((e -> e),f) -> f
 nil : f
 true : d
******** Computation Rules ********
 (1)  f(X,g(X)) => f(1,g(X))
 (2)  g(1) => g(0)
 (3)  map(Z,nil) => nil
 (4)  map(G,cons(V,W)) => cons(G[V],map(G,W))
 (5)  filter(J,nil) => nil
 (6)  filter(F1,cons(Y1,U1)) => filter2(F1[Y1],F1,Y1,U1)
 (7)  filter2(true,H1,W1,P1) => cons(W1,filter(H1,P1))
 (8)  filter2(false,F2,Y2,U2) => filter(F2,U2)

NO