/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:
 a(f(),a(f(),a(g(),a(g(),x)))) -> a(g(),a(g(),a(g(),a(f(),a(f(),a(f(),x))))))

Proof:
 Extended Uncurrying Processor:
  application symbol: a
  symbol table:
   g ==> g0/0 g1/1
   f ==> f0/0 f1/1
   
  uncurry-rules:
   a(f0(),x1) -> f1(x1)
   a(g0(),x3) -> g1(x3)
  eta-rules:
   
  problem:
   f1(f1(g1(g1(x)))) -> g1(g1(g1(f1(f1(f1(x))))))
   a(f0(),x1) -> f1(x1)
   a(g0(),x3) -> g1(x3)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
               [1 0 0]  
    [g1](x0) = [0 0 0]x0
               [0 0 0]  ,
    
           [0]
    [g0] = [1]
           [0],
    
               [1 0 0]  
    [f1](x0) = [0 0 0]x0
               [0 0 0]  ,
    
           [0]
    [f0] = [0]
           [1],
    
                  [1 0 0]     [1 1 1]     [1]
    [a](x0, x1) = [0 1 1]x0 + [1 1 1]x1 + [0]
                  [0 0 0]     [1 1 1]     [0]
   orientation:
                        [1 0 0]     [1 0 0]                             
    f1(f1(g1(g1(x)))) = [0 0 0]x >= [0 0 0]x = g1(g1(g1(f1(f1(f1(x))))))
                        [0 0 0]     [0 0 0]                             
    
                 [1 1 1]     [1]    [1 0 0]           
    a(f0(),x1) = [1 1 1]x1 + [1] >= [0 0 0]x1 = f1(x1)
                 [1 1 1]     [0]    [0 0 0]           
    
                 [1 1 1]     [1]    [1 0 0]           
    a(g0(),x3) = [1 1 1]x3 + [1] >= [0 0 0]x3 = g1(x3)
                 [1 1 1]     [0]    [0 0 0]           
   problem:
    f1(f1(g1(g1(x)))) -> g1(g1(g1(f1(f1(f1(x))))))
   DP Processor:
    DPs:
     f{1,#}(f1(g1(g1(x)))) -> f{1,#}(x)
     f{1,#}(f1(g1(g1(x)))) -> f{1,#}(f1(x))
     f{1,#}(f1(g1(g1(x)))) -> f{1,#}(f1(f1(x)))
    TRS:
     f1(f1(g1(g1(x)))) -> g1(g1(g1(f1(f1(f1(x))))))
    Bounds Processor:
     bound: 3
     enrichment: match
     automaton:
      final states: {7,5,3,1}
      transitions:
       f80() -> 2*
       f{1,#,0}(2) -> 1*
       f{1,#,0}(4) -> 3*
       f{1,#,0}(6) -> 5*
       f{1,0}(2) -> 4*
       f{1,0}(4) -> 6*
       f{1,0}(6) -> 8*
       g{1,0}(10) -> 7*
       g{1,0}(9) -> 10*
       g{1,0}(8) -> 9*
       g{1,1}(25) -> 26*
       g{1,1}(52) -> 53*
       g{1,1}(24) -> 25*
       g{1,1}(51) -> 52*
       g{1,1}(26) -> 27*
       g{1,1}(53) -> 54*
       f{1,1}(50) -> 51*
       f{1,1}(15) -> 16*
       f{1,1}(39) -> 40*
       f{1,1}(41) -> 42*
       f{1,1}(21) -> 22*
       f{1,1}(23) -> 24*
       f{1,#,1}(35) -> 36*
       f{1,#,1}(11) -> 12*
       g{1,2}(70) -> 71*
       g{1,2}(97) -> 98*
       g{1,2}(69) -> 70*
       g{1,2}(96) -> 97*
       g{1,2}(68) -> 69*
       g{1,2}(95) -> 96*
       f{1,2}(85) -> 86*
       f{1,2}(65) -> 66*
       f{1,2}(67) -> 68*
       f{1,2}(94) -> 95*
       f{1,2}(59) -> 60*
       f{1,2}(83) -> 84*
       f{1,#,2}(55) -> 56*
       f{1,#,2}(79) -> 80*
       g{1,3}(112) -> 113*
       g{1,3}(114) -> 115*
       g{1,3}(113) -> 114*
       f{1,3}(109) -> 110*
       f{1,3}(111) -> 112*
       f{1,3}(103) -> 104*
       f{1,#,3}(99) -> 100*
       1 -> 3*
       3 -> 1*
       5 -> 3*
       7 -> 4,6
       9 -> 15,11
       12 -> 5,1
       16 -> 21,11
       22 -> 23,11
       24 -> 59,55
       26 -> 39,35
       27 -> 8*
       36 -> 12,5
       40 -> 41,11
       42 -> 50,11
       52 -> 83,79
       54 -> 22,11,23
       56 -> 12,5
       60 -> 65,55
       66 -> 67,55
       71 -> 42,11,50
       80 -> 56,12
       84 -> 85,55
       86 -> 94,55
       96 -> 103,99
       98 -> 60,55,65
       100 -> 56,12
       104 -> 109,99
       110 -> 111,99
       115 -> 68*
     problem:
      DPs:
       
      TRS:
       f1(f1(g1(g1(x)))) -> g1(g1(g1(f1(f1(f1(x))))))
     Qed