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


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


YES
Input TRS:
    1: f(a(),x) -> f(b(),f(c(),x))
    2: f(a(),f(b(),x)) -> f(b(),f(a(),x))
    3: f(d(),f(c(),x)) -> f(d(),f(a(),x))
    4: f(a(),f(c(),x)) -> f(c(),f(a(),x))
Number of strict rules: 4
Direct POLO(bPol) ... failed.
Uncurrying f
1: f^1_a(x) -> f^1_b(f^1_c(x))
2: f^1_a(f^1_b(x)) -> f^1_b(f^1_a(x))
3: f^1_d(f^1_c(x)) -> f^1_d(f^1_a(x))
4: f^1_a(f^1_c(x)) -> f^1_c(f^1_a(x))
5: f(a(),_1) ->= f^1_a(_1)
6: f(d(),_1) ->= f^1_d(_1)
7: f(c(),_1) ->= f^1_c(_1)
8: f(b(),_1) ->= f^1_b(_1)
Number of strict rules: 4
Direct POLO(bPol) ... removes: 8 5 7 6
      a 	w: 2
      d 	w: 1
      b 	w: 1
      f^1_b	w: x1
      c 	w: 1
      f 	w: 2 * x1 + x2
      f^1_a	w: x1 + 1
      f^1_c	w: x1 + 1
      f^1_d	w: x1
Number of strict rules: 4
Direct POLO(bPol) ... failed.
Dependency Pairs:
   #1: #f^1_a(f^1_b(x)) -> #f^1_a(x)
   #2: #f^1_d(f^1_c(x)) -> #f^1_d(f^1_a(x))
   #3: #f^1_d(f^1_c(x)) -> #f^1_a(x)
   #4: #f^1_a(f^1_c(x)) -> #f^1_a(x)
Number of SCCs: 2, DPs: 3
  SCC { #2 }
POLO(Sum)... succeeded.
      a 	w: 0
      #f^1_a	w: 0
      d 	w: 0
      b 	w: 0
      f^1_b	w: 1
      c 	w: 0
      f 	w: 0
      f^1_a	w: x1 + 1
      f^1_c	w: x1 + 2
      f^1_d	w: 0
      #f^1_d	w: x1
    USABLE RULES: { 1 2 4 }
    Removed DPs: #2
Number of SCCs: 1, DPs: 2
  SCC { #1 #4 }
POLO(Sum)... succeeded.
      a 	w: 0
      #f^1_a	w: x1
      d 	w: 0
      b 	w: 0
      f^1_b	w: x1 + 1
      c 	w: 0
      f 	w: 0
      f^1_a	w: x1 + 2
      f^1_c	w: x1 + 1
      f^1_d	w: 0
      #f^1_d	w: x1
    USABLE RULES: { 1 2 4 }
    Removed DPs: #1 #4
Number of SCCs: 0, DPs: 0