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


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YES
Input TRS:
    1: a__pairNs() -> cons(0(),incr(oddNs()))
    2: a__oddNs() -> a__incr(a__pairNs())
    3: a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
    4: a__take(0(),XS) -> nil()
    5: a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
    6: a__zip(nil(),XS) -> nil()
    7: a__zip(X,nil()) -> nil()
    8: a__zip(cons(X,XS),cons(Y,YS)) -> cons(pair(mark(X),mark(Y)),zip(XS,YS))
    9: a__tail(cons(X,XS)) -> mark(XS)
    10: a__repItems(nil()) -> nil()
    11: a__repItems(cons(X,XS)) -> cons(mark(X),cons(X,repItems(XS)))
    12: mark(pairNs()) -> a__pairNs()
    13: mark(incr(X)) -> a__incr(mark(X))
    14: mark(oddNs()) -> a__oddNs()
    15: mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
    16: mark(zip(X1,X2)) -> a__zip(mark(X1),mark(X2))
    17: mark(tail(X)) -> a__tail(mark(X))
    18: mark(repItems(X)) -> a__repItems(mark(X))
    19: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    20: mark(0()) -> 0()
    21: mark(s(X)) -> s(mark(X))
    22: mark(nil()) -> nil()
    23: mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
    24: a__pairNs() -> pairNs()
    25: a__incr(X) -> incr(X)
    26: a__oddNs() -> oddNs()
    27: a__take(X1,X2) -> take(X1,X2)
    28: a__zip(X1,X2) -> zip(X1,X2)
    29: a__tail(X) -> tail(X)
    30: a__repItems(X) -> repItems(X)
Number of strict rules: 30
Direct POLO(bPol) ... removes: 4 10 7 9 6
      repItems	w: 2 * x1 + 8
      incr	w: x1
      s 	w: x1
      a__incr	w: x1
      take	w: x1 + 2 * x2 + 2
      pair	w: x1 + x2
      tail	w: x1 + 3
      0 	w: 0
      a__repItems	w: 2 * x1 + 8
      nil	w: 1
      mark	w: x1
      pairNs	w: 1
      a__zip	w: 2 * x1 + x2 + 5
      oddNs	w: 1
      cons	w: x1 + x2
      a__oddNs	w: 1
      a__take	w: x1 + 2 * x2 + 2
      a__pairNs	w: 1
      a__tail	w: x1 + 3
      zip	w: 2 * x1 + x2 + 5
Number of strict rules: 25
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
   #1: #a__oddNs() -> #a__incr(a__pairNs())
   #2: #a__oddNs() -> #a__pairNs()
   #3: #mark(incr(X)) -> #a__incr(mark(X))
   #4: #mark(incr(X)) -> #mark(X)
   #5: #a__repItems(cons(X,XS)) -> #mark(X)
   #6: #mark(pair(X1,X2)) -> #mark(X1)
   #7: #mark(pair(X1,X2)) -> #mark(X2)
   #8: #mark(pairNs()) -> #a__pairNs()
   #9: #mark(oddNs()) -> #a__oddNs()
   #10: #a__take(s(N),cons(X,XS)) -> #mark(X)
   #11: #mark(tail(X)) -> #a__tail(mark(X))
   #12: #mark(tail(X)) -> #mark(X)
   #13: #mark(cons(X1,X2)) -> #mark(X1)
   #14: #mark(s(X)) -> #mark(X)
   #15: #mark(zip(X1,X2)) -> #a__zip(mark(X1),mark(X2))
   #16: #mark(zip(X1,X2)) -> #mark(X1)
   #17: #mark(zip(X1,X2)) -> #mark(X2)
   #18: #a__incr(cons(X,XS)) -> #mark(X)
   #19: #a__zip(cons(X,XS),cons(Y,YS)) -> #mark(X)
   #20: #a__zip(cons(X,XS),cons(Y,YS)) -> #mark(Y)
   #21: #mark(take(X1,X2)) -> #a__take(mark(X1),mark(X2))
   #22: #mark(take(X1,X2)) -> #mark(X1)
   #23: #mark(take(X1,X2)) -> #mark(X2)
   #24: #mark(repItems(X)) -> #a__repItems(mark(X))
   #25: #mark(repItems(X)) -> #mark(X)
Number of SCCs: 1, DPs: 22
  SCC { #1 #3..7 #9 #10 #12..25 }
POLO(Sum)... succeeded.
      repItems	w: x1 + 1
      incr	w: x1
      s 	w: x1
      #a__zip	w: x1 + x2
      a__incr	w: x1
      take	w: x1 + x2 + 1
      pair	w: x1 + x2 + 1
      #a__take	w: x2 + 1
      #a__pairNs	w: 0
      tail	w: x1 + 1
      #mark	w: x1 + 2
      0 	w: 1
      a__repItems	w: x1 + 1
      nil	w: 1
      #a__oddNs	w: 5
      mark	w: x1
      pairNs	w: 2
      a__zip	w: x1 + x2 + 1
      #a__repItems	w: x1 + 2
      oddNs	w: 4
      #a__incr	w: x1 + 2
      cons	w: x1 + 1
      a__oddNs	w: 4
      a__take	w: x1 + x2 + 1
      a__pairNs	w: 2
      a__tail	w: x1 + 1
      #a__tail	w: 0
      zip	w: x1 + x2 + 1
    USABLE RULES: { 1..3 5 8 11..30 }
    Removed DPs: #1 #5..7 #9 #12 #13 #15..18 #21..25
Number of SCCs: 1, DPs: 2
  SCC { #4 #14 }
POLO(Sum)... succeeded.
      repItems	w: x1 + 1
      incr	w: x1 + 1
      s 	w: x1
      #a__zip	w: x1 + x2
      a__incr	w: x1 + 1
      take	w: x1 + x2 + 1
      pair	w: x1 + x2 + 1
      #a__take	w: x2 + 1
      #a__pairNs	w: 0
      tail	w: x1 + 1
      #mark	w: x1 + 2
      0 	w: 1
      a__repItems	w: x1 + 1
      nil	w: 1
      #a__oddNs	w: 5
      mark	w: x1
      pairNs	w: 2
      a__zip	w: x1 + x2 + 1
      #a__repItems	w: x1 + 2
      oddNs	w: 4
      #a__incr	w: x1 + 2
      cons	w: x1 + 1
      a__oddNs	w: 4
      a__take	w: x1 + x2 + 1
      a__pairNs	w: 2
      a__tail	w: x1 + 1
      #a__tail	w: 0
      zip	w: x1 + x2 + 1
    USABLE RULES: { 1..3 5 8 11..30 }
    Removed DPs: #4
Number of SCCs: 1, DPs: 1
  SCC { #14 }
POLO(Sum)... succeeded.
      repItems	w: x1 + 1
      incr	w: x1 + 2
      s 	w: x1 + 1
      #a__zip	w: x1 + x2
      a__incr	w: x1 + 2
      take	w: x1 + x2 + 1
      pair	w: x1 + x2 + 1
      #a__take	w: x2 + 1
      #a__pairNs	w: 0
      tail	w: x1 + 1
      #mark	w: x1 + 2
      0 	w: 1
      a__repItems	w: x1 + 1
      nil	w: 1
      #a__oddNs	w: 5
      mark	w: x1
      pairNs	w: 2
      a__zip	w: x1 + x2 + 1
      #a__repItems	w: x1 + 2
      oddNs	w: 4
      #a__incr	w: x1 + 2
      cons	w: x1 + 1
      a__oddNs	w: 4
      a__take	w: x1 + x2 + 1
      a__pairNs	w: 2
      a__tail	w: x1 + 1
      #a__tail	w: 0
      zip	w: x1 + x2 + 1
    USABLE RULES: { 1..3 5 8 11..30 }
    Removed DPs: #14
Number of SCCs: 0, DPs: 0