/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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(0(),1(),g(X,Y),U) -> f(g(X,Y),g(X,Y),g(X,Y),h(X))
    2: g(0(),1()) -> 0()
    3: g(0(),1()) -> 1()
    4: h(g(V,W)) -> h(V)
Number of strict rules: 4
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #f(0(),1(),g(X,Y),U) -> #f(g(X,Y),g(X,Y),g(X,Y),h(X))
   #2: #f(0(),1(),g(X,Y),U) -> #h(X)
   #3: #h(g(V,W)) -> #h(V)
Number of SCCs: 2, DPs: 2
  SCC { #3 }
POLO(Sum)... succeeded.
      h 	w: 0
      1 	w: 0
      f 	w: 0
      0 	w: 0
      #h 	w: x1
      #f 	w: 0
      #g 	w: 0
      g 	w: x1 + 1
    USABLE RULES: { }
    Removed DPs: #3
Number of SCCs: 1, DPs: 1
  SCC { #1 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  found.
  #f(0(),1(),g(0(),1()),U)	-#1->
  #f(g(0(),1()),g(0(),1()),g(0(),1()),h(0()))	--->*
  #f(0(),1(),g(0(),1()),h(0()))
  Looping with: [ U := h(0()); ]

...
Input TRS:
    1: f(0(),1(),g(X,Y),U) -> f(g(X,Y),g(X,Y),g(X,Y),h(X))
    2: g(0(),1()) -> 0()
    3: g(0(),1()) -> 1()
    4: h(g(V,W)) -> h(V)
Number of strict rules: 4
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #f(0(),1(),g(X,Y),U) -> #f(g(X,Y),g(X,Y),g(X,Y),h(X))
   #2: #f(0(),1(),g(X,Y),U) -> #h(X)
   #3: #h(g(V,W)) -> #h(V)
Number of SCCs: 2, DPs: 2
  SCC { #3 }
POLO(Sum)... succeeded.
      h 	w: 0
      1 	w: 0
      f 	w: 0
      0 	w: 0
      #h 	w: x1
      #f 	w: 0
      #g 	w: 0
      g 	w: x1 + 1
    USABLE RULES: { }
    Removed DPs: #3
Number of SCCs: 1, DPs: 1
  SCC { #1 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  found.
  #f(0(),1(),g(0(),1()),U)	-#1->
  #f(g(0(),1()),g(0(),1()),g(0(),1()),h(0()))	--->*
  #f(0(),1(),g(0(),1()),h(0()))
  Looping with: [ U := h(0()); ]
>>NO


******** Signature ********
 0 : b
 1 : b
 cons : (e,f) -> f
 f : (b,b,b,c) -> a
 false : d
 filter : ((e -> d),f) -> f
 filter2 : (d,(e -> d),e,f) -> f
 g : (b,b) -> b
 h : b -> c
 map : ((e -> e),f) -> f
 nil : f
 true : d
******** Computation Rules ********
 (1)  f(0,1,g(X,Y),U) => f(g(X,Y),g(X,Y),g(X,Y),h(X))
 (2)  g(0,1) => 0
 (3)  g(0,1) => 1
 (4)  h(g(V,W)) => h(V)
 (5)  map(J,nil) => nil
 (6)  map(F1,cons(Y1,U1)) => cons(F1[Y1],map(F1,U1))
 (7)  filter(H1,nil) => nil
 (8)  filter(I1,cons(P1,X2)) => filter2(I1[P1],I1,P1,X2)
 (9)  filter2(true,Z2,U2,V2) => cons(U2,filter(Z2,V2))
 (10)  filter2(false,I2,P2,X3) => filter(I2,X3)

NO