/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem:
 f(y,f(y,x)) -> f(f(a(),y),f(a(),y))

Proof:
 DP Processor:
  DPs:
   f#(y,f(y,x)) -> f#(a(),y)
   f#(y,f(y,x)) -> f#(f(a(),y),f(a(),y))
  TRS:
   f(y,f(y,x)) -> f(f(a(),y),f(a(),y))
  Arctic Interpretation Processor:
   dimension: 1
   usable rules:
    f(y,f(y,x)) -> f(f(a(),y),f(a(),y))
   interpretation:
    [f#](x0, x1) = -9x0 + x1,
    
    [a] = 1,
    
    [f](x0, x1) = 1x0 + 1x1 + 2
   orientation:
    f#(y,f(y,x)) = 1x + 1y + 2 >= y + -8 = f#(a(),y)
    
    f#(y,f(y,x)) = 1x + 1y + 2 >= 1y + 2 = f#(f(a(),y),f(a(),y))
    
    f(y,f(y,x)) = 2x + 2y + 3 >= 2y + 3 = f(f(a(),y),f(a(),y))
   problem:
    DPs:
     f#(y,f(y,x)) -> f#(f(a(),y),f(a(),y))
    TRS:
     f(y,f(y,x)) -> f(f(a(),y),f(a(),y))
   Restore Modifier:
    DPs:
     f#(y,f(y,x)) -> f#(f(a(),y),f(a(),y))
    TRS:
     f(y,f(y,x)) -> f(f(a(),y),f(a(),y))
    Bounds Processor:
     bound: 3
     enrichment: match
     automaton:
      final states: {3}
      transitions:
       f{#,0}(1,35) -> 3*
       f{#,0}(27,30) -> 3*
       f{#,0}(2,30) -> 3*
       f{#,0}(29,2) -> 3*
       f{#,0}(35,1) -> 3*
       f{#,0}(35,27) -> 3*
       f{#,0}(30,27) -> 3*
       f{#,0}(1,2) -> 3*
       f{#,0}(35,29) -> 3*
       f{#,0}(35,35) -> 3*
       f{#,0}(30,35) -> 3*
       f{#,0}(35,37) -> 3*
       f{#,0}(27,1) -> 3*
       f{#,0}(2,1) -> 3*
       f{#,0}(37,27) -> 3*
       f{#,0}(27,27) -> 3*
       f{#,0}(27,29) -> 3*
       f{#,0}(2,27) -> 3*
       f{#,0}(37,35) -> 3*
       f{#,0}(2,29) -> 3*
       f{#,0}(27,35) -> 3*
       f{#,0}(27,37) -> 3*
       f{#,0}(2,35) -> 3*
       f{#,0}(2,37) -> 3*
       f{#,0}(35,2) -> 3*
       f{#,0}(30,2) -> 3*
       f{#,0}(29,27) -> 3*
       f{#,0}(29,35) -> 3*
       f{#,0}(35,30) -> 3*
       f{#,0}(37,2) -> 3*
       f{#,0}(27,2) -> 3*
       f{#,0}(2,2) -> 3*
       f{#,0}(1,27) -> 3*
       f0(1,35) -> 1*
       f0(29,2) -> 1*
       f0(30,27) -> 1*
       f0(1,2) -> 1*
       f0(30,35) -> 1*
       f0(37,27) -> 1*
       f0(37,35) -> 1*
       f0(30,2) -> 1*
       f0(29,27) -> 1*
       f0(29,35) -> 1*
       f0(37,2) -> 1*
       f0(1,27) -> 1*
       f1(1,37) -> 1*
       f1(37,30) -> 1*
       f1(27,30) -> 1*
       f1(2,30) -> 1*
       f1(35,1) -> 1*
       f1(30,1) -> 1*
       f1(29,30) -> 1*
       f1(35,27) -> 1*
       f1(35,29) -> 1*
       f1(30,29) -> 1*
       f1(35,35) -> 1*
       f1(35,37) -> 1*
       f1(30,37) -> 1*
       f1(37,1) -> 1*
       f1(27,1) -> 1*
       f1(2,1) -> 1*
       f1(1,30) -> 1*
       f1(27,27) -> 1*
       f1(37,29) -> 1*
       f1(27,29) -> 1*
       f1(2,27) -> 1*
       f1(2,29) -> 1*
       f1(37,37) -> 1*
       f1(27,35) -> 1*
       f1(27,37) -> 1*
       f1(2,35) -> 1*
       f1(29,1) -> 1*
       f1(2,37) -> 1*
       f1(35,2) -> 1*
       f1(29,29) -> 1*
       f1(29,37) -> 1*
       f1(1,1) -> 1*
       f1(35,30) -> 1*
       f1(30,30) -> 1*
       f1(27,2) -> 1*
       f1(2,2) -> 1*
       f1(1,29) -> 1*
       f{#,1}(1,37) -> 3*
       f{#,1}(37,30) -> 3*
       f{#,1}(30,1) -> 3*
       f{#,1}(29,30) -> 3*
       f{#,1}(30,29) -> 3*
       f{#,1}(30,37) -> 3*
       f{#,1}(37,1) -> 3*
       f{#,1}(1,30) -> 3*
       f{#,1}(37,29) -> 3*
       f{#,1}(37,37) -> 3*
       f{#,1}(29,1) -> 3*
       f{#,1}(29,29) -> 3*
       f{#,1}(29,37) -> 3*
       f{#,1}(1,1) -> 3*
       f{#,1}(30,30) -> 3*
       f{#,1}(1,29) -> 3*
       f2(26,37) -> 1*
       f2(37,24) -> 1*
       f2(37,26) -> 1*
       f2(37,30) -> 1*
       f2(27,30) -> 1,16,29*,18
       f2(17,30) -> 18*
       f2(28,29) -> 1*
       f2(29,16) -> 1*
       f2(35,1) -> 1,16,29*,18
       f2(15,1) -> 16*
       f2(29,28) -> 1*
       f2(35,27) -> 30*
       f2(35,29) -> 1,16,29*,18
       f2(15,27) -> 26*
       f2(15,29) -> 16*
       f2(35,35) -> 30*
       f2(35,37) -> 1,18,29*,16
       f2(30,37) -> 1*
       f2(25,37) -> 1*
       f2(15,35) -> 26*
       f2(16,16) -> 1*
       f2(15,37) -> 16*
       f2(27,1) -> 28,29*,1,16,18
       f2(17,1) -> 18*
       f2(26,24) -> 1*
       f2(26,26) -> 1*
       f2(26,30) -> 1*
       f2(16,28) -> 1*
       f2(27,27) -> 26,30*,1
       f2(27,29) -> 1,16,29*,18
       f2(17,29) -> 18*
       f2(37,37) -> 1*
       f2(27,35) -> 1,30*
       f2(28,16) -> 1*
       f2(27,37) -> 1,29*,18,16
       f2(17,37) -> 18*
       f2(28,28) -> 1*
       f2(35,2) -> 1,30*
       f2(15,2) -> 26*,25,24
       f2(29,29) -> 1*
       f2(30,24) -> 1*
       f2(25,24) -> 1*
       f2(30,26) -> 1*
       f2(25,26) -> 1*
       f2(35,30) -> 1,29*,18,16
       f2(30,30) -> 1*
       f2(25,30) -> 1*
       f2(15,30) -> 16*
       f2(27,2) -> 26,30*,1
       f2(16,29) -> 1*
       f{#,2}(28,29) -> 3*
       f{#,2}(18,29) -> 3*
       f{#,2}(29,16) -> 3*
       f{#,2}(29,28) -> 3*
       f{#,2}(28,16) -> 3*
       f{#,2}(18,16) -> 3*
       f{#,2}(28,28) -> 3*
       f{#,2}(18,28) -> 3*
       f{#,2}(29,29) -> 3*
       f3(37,32) -> 29*
       f3(37,36) -> 29*
       f3(33,27) -> 34*
       f3(33,35) -> 34*
       f3(34,32) -> 29*
       f3(34,36) -> 29*
       f3(35,27) -> 36,30,37*,1,34,32
       f3(35,35) -> 36,30,37*,1,34,32
       f3(36,32) -> 29*
       f3(36,36) -> 29*
       f3(37,37) -> 1,29*
       f3(34,37) -> 29*
       f3(31,27) -> 32*
       f3(31,35) -> 32*
       f3(36,37) -> 29*
       a3() -> 27,35*,15,17,2,33,31
     problem:
      DPs:
       
      TRS:
       f(y,f(y,x)) -> f(f(a(),y),f(a(),y))
     Qed