/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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


YES

Problem:
 strict:
  a(b(b(x1))) -> c(b(c(x1)))
  c(a(b(x1))) -> a(c(b(x1)))
  c(c(a(x1))) -> c(b(b(x1)))
 weak:
  b(c(c(x1))) -> b(a(c(x1)))
  a(c(b(x1))) -> c(b(a(x1)))
  c(c(b(x1))) -> c(a(c(x1)))

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
             [1 1]  
   [a](x0) = [0 0]x0,
   
             [1 1]     [0]
   [b](x0) = [0 0]x0 + [1],
   
             [1 0]     [1]
   [c](x0) = [0 0]x0 + [0]
  orientation:
                 [1 1]     [2]    [1 0]     [2]              
   a(b(b(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = c(b(c(x1)))
   
                 [1 1]     [2]    [1 1]     [1]              
   c(a(b(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = a(c(b(x1)))
   
                 [1 1]     [2]    [1 1]     [2]              
   c(c(a(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = c(b(b(x1)))
   
                 [1 0]     [2]    [1 0]     [1]              
   b(c(c(x1))) = [0 0]x1 + [1] >= [0 0]x1 + [1] = b(a(c(x1)))
   
                 [1 1]     [1]    [1 1]     [1]              
   a(c(b(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = c(b(a(x1)))
   
                 [1 1]     [2]    [1 0]     [2]              
   c(c(b(x1))) = [0 0]x1 + [0] >= [0 0]x1 + [0] = c(a(c(x1)))
  problem:
   strict:
    a(b(b(x1))) -> c(b(c(x1)))
    c(c(a(x1))) -> c(b(b(x1)))
   weak:
    a(c(b(x1))) -> c(b(a(x1)))
    c(c(b(x1))) -> c(a(c(x1)))
  RT Transformation Processor:
   a(b(b(x1))) -> c(b(c(x1)))
   c(c(a(x1))) -> c(b(b(x1)))
   a(c(b(x1))) -> c(b(a(x1)))
   c(c(b(x1))) -> c(a(c(x1)))
   DP Processor:
    DPs:
     a#(b(b(x1))) -> c#(x1)
     a#(b(b(x1))) -> c#(b(c(x1)))
     c#(c(a(x1))) -> c#(b(b(x1)))
     a#(c(b(x1))) -> a#(x1)
     a#(c(b(x1))) -> c#(b(a(x1)))
     c#(c(b(x1))) -> c#(x1)
     c#(c(b(x1))) -> a#(c(x1))
     c#(c(b(x1))) -> c#(a(c(x1)))
    TRS:
     a(b(b(x1))) -> c(b(c(x1)))
     c(c(a(x1))) -> c(b(b(x1)))
     a(c(b(x1))) -> c(b(a(x1)))
     c(c(b(x1))) -> c(a(c(x1)))
    TDG Processor:
     DPs:
      a#(b(b(x1))) -> c#(x1)
      a#(b(b(x1))) -> c#(b(c(x1)))
      c#(c(a(x1))) -> c#(b(b(x1)))
      a#(c(b(x1))) -> a#(x1)
      a#(c(b(x1))) -> c#(b(a(x1)))
      c#(c(b(x1))) -> c#(x1)
      c#(c(b(x1))) -> a#(c(x1))
      c#(c(b(x1))) -> c#(a(c(x1)))
     TRS:
      a(b(b(x1))) -> c(b(c(x1)))
      c(c(a(x1))) -> c(b(b(x1)))
      a(c(b(x1))) -> c(b(a(x1)))
      c(c(b(x1))) -> c(a(c(x1)))
     graph:
      c#(c(a(x1))) -> c#(b(b(x1))) -> c#(c(b(x1))) -> c#(a(c(x1)))
      c#(c(a(x1))) -> c#(b(b(x1))) -> c#(c(b(x1))) -> a#(c(x1))
      c#(c(a(x1))) -> c#(b(b(x1))) -> c#(c(b(x1))) -> c#(x1)
      c#(c(a(x1))) -> c#(b(b(x1))) -> c#(c(a(x1))) -> c#(b(b(x1)))
      c#(c(b(x1))) -> c#(a(c(x1))) -> c#(c(b(x1))) -> c#(a(c(x1)))
      c#(c(b(x1))) -> c#(a(c(x1))) -> c#(c(b(x1))) -> a#(c(x1))
      c#(c(b(x1))) -> c#(a(c(x1))) -> c#(c(b(x1))) -> c#(x1)
      c#(c(b(x1))) -> c#(a(c(x1))) -> c#(c(a(x1))) -> c#(b(b(x1)))
      c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(a(c(x1)))
      c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(c(x1))
      c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1)
      c#(c(b(x1))) -> c#(x1) -> c#(c(a(x1))) -> c#(b(b(x1)))
      c#(c(b(x1))) -> a#(c(x1)) -> a#(c(b(x1))) -> c#(b(a(x1)))
      c#(c(b(x1))) -> a#(c(x1)) -> a#(c(b(x1))) -> a#(x1)
      c#(c(b(x1))) -> a#(c(x1)) -> a#(b(b(x1))) -> c#(b(c(x1)))
      c#(c(b(x1))) -> a#(c(x1)) -> a#(b(b(x1))) -> c#(x1)
      a#(c(b(x1))) -> c#(b(a(x1))) -> c#(c(b(x1))) -> c#(a(c(x1)))
      a#(c(b(x1))) -> c#(b(a(x1))) -> c#(c(b(x1))) -> a#(c(x1))
      a#(c(b(x1))) -> c#(b(a(x1))) -> c#(c(b(x1))) -> c#(x1)
      a#(c(b(x1))) -> c#(b(a(x1))) -> c#(c(a(x1))) -> c#(b(b(x1)))
      a#(c(b(x1))) -> a#(x1) -> a#(c(b(x1))) -> c#(b(a(x1)))
      a#(c(b(x1))) -> a#(x1) -> a#(c(b(x1))) -> a#(x1)
      a#(c(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> c#(b(c(x1)))
      a#(c(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> c#(x1)
      a#(b(b(x1))) -> c#(b(c(x1))) -> c#(c(b(x1))) -> c#(a(c(x1)))
      a#(b(b(x1))) -> c#(b(c(x1))) -> c#(c(b(x1))) -> a#(c(x1))
      a#(b(b(x1))) -> c#(b(c(x1))) -> c#(c(b(x1))) -> c#(x1)
      a#(b(b(x1))) -> c#(b(c(x1))) -> c#(c(a(x1))) -> c#(b(b(x1)))
      a#(b(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(a(c(x1)))
      a#(b(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(c(x1))
      a#(b(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1)
      a#(b(b(x1))) -> c#(x1) -> c#(c(a(x1))) -> c#(b(b(x1)))
     EDG Processor:
      DPs:
       a#(b(b(x1))) -> c#(x1)
       a#(b(b(x1))) -> c#(b(c(x1)))
       c#(c(a(x1))) -> c#(b(b(x1)))
       a#(c(b(x1))) -> a#(x1)
       a#(c(b(x1))) -> c#(b(a(x1)))
       c#(c(b(x1))) -> c#(x1)
       c#(c(b(x1))) -> a#(c(x1))
       c#(c(b(x1))) -> c#(a(c(x1)))
      TRS:
       a(b(b(x1))) -> c(b(c(x1)))
       c(c(a(x1))) -> c(b(b(x1)))
       a(c(b(x1))) -> c(b(a(x1)))
       c(c(b(x1))) -> c(a(c(x1)))
      graph:
       c#(c(b(x1))) -> c#(a(c(x1))) -> c#(c(a(x1))) -> c#(b(b(x1)))
       c#(c(b(x1))) -> c#(a(c(x1))) -> c#(c(b(x1))) -> c#(x1)
       c#(c(b(x1))) -> c#(a(c(x1))) -> c#(c(b(x1))) -> a#(c(x1))
       c#(c(b(x1))) -> c#(a(c(x1))) -> c#(c(b(x1))) -> c#(a(c(x1)))
       c#(c(b(x1))) -> c#(x1) -> c#(c(a(x1))) -> c#(b(b(x1)))
       c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1)
       c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(c(x1))
       c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(a(c(x1)))
       c#(c(b(x1))) -> a#(c(x1)) -> a#(c(b(x1))) -> a#(x1)
       c#(c(b(x1))) -> a#(c(x1)) -> a#(c(b(x1))) -> c#(b(a(x1)))
       a#(c(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> c#(x1)
       a#(c(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> c#(b(c(x1)))
       a#(c(b(x1))) -> a#(x1) -> a#(c(b(x1))) -> a#(x1)
       a#(c(b(x1))) -> a#(x1) -> a#(c(b(x1))) -> c#(b(a(x1)))
       a#(b(b(x1))) -> c#(x1) -> c#(c(a(x1))) -> c#(b(b(x1)))
       a#(b(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1)
       a#(b(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(c(x1))
       a#(b(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(a(c(x1)))
      SCC Processor:
       #sccs: 1
       #rules: 5
       #arcs: 18/64
       DPs:
        c#(c(b(x1))) -> c#(a(c(x1)))
        c#(c(b(x1))) -> a#(c(x1))
        a#(c(b(x1))) -> a#(x1)
        a#(b(b(x1))) -> c#(x1)
        c#(c(b(x1))) -> c#(x1)
       TRS:
        a(b(b(x1))) -> c(b(c(x1)))
        c(c(a(x1))) -> c(b(b(x1)))
        a(c(b(x1))) -> c(b(a(x1)))
        c(c(b(x1))) -> c(a(c(x1)))
       Subterm Criterion Processor:
        simple projection:
         pi(b) = [0,0]
         pi(a) = [0,0]
         pi(c) = [0,0]
         pi(a#) = 0
         pi(c#) = [0,0]
        problem:
         DPs:
          c#(c(b(x1))) -> c#(a(c(x1)))
         TRS:
          a(b(b(x1))) -> c(b(c(x1)))
          c(c(a(x1))) -> c(b(b(x1)))
          a(c(b(x1))) -> c(b(a(x1)))
          c(c(b(x1))) -> c(a(c(x1)))
        Bounds Processor:
         bound: 3
         enrichment: match
         automaton:
          final states: {13,10,7,5,1}
          transitions:
           f50() -> 2*
           c{#,1}(28) -> 29*
           a2(57) -> 58*
           a2(87) -> 88*
           a2(78) -> 79*
           a0(3) -> 4*
           a0(2) -> 11*
           c{#,0}(4) -> 1*
           a1(27) -> 28*
           a1(14) -> 15*
           a1(46) -> 47*
           a1(48) -> 49*
           b1(70) -> 71*
           b1(49) -> 50*
           b1(15) -> 16*
           c0(4) -> 13*
           c0(2) -> 3*
           c0(12) -> 10*
           c0(9) -> 7*
           c0(6) -> 5*
           c1(40) -> 41*
           c1(30) -> 31*
           c1(34) -> 35*
           c1(50) -> 51*
           c1(16) -> 17*
           c1(26) -> 27*
           c1(45) -> 46*
           b0(2) -> 8*
           b0(8) -> 9*
           b0(3) -> 6*
           b0(11) -> 12*
           b2(68) -> 69*
           b2(67) -> 68*
           b2(79) -> 80*
           a3(95) -> 96*
           c3(94) -> 95*
           c3(96) -> 97*
           c2(58) -> 59*
           c2(92) -> 93*
           c2(86) -> 87*
           c2(80) -> 81*
           c2(88) -> 89*
           c2(56) -> 57*
           27 -> 57,67,35
           68 -> 78*
           47 -> 40*
           17 -> 15,26,4
           35 -> 27*
           69 -> 58*
           7 -> 41,14,3
           93 -> 87*
           28 -> 30*
           11 -> 34*
           2 -> 48*
           79 -> 94,86
           13 -> 41,14,3
           71 -> 68*
           8 -> 45,14
           49 -> 56*
           31 -> 27,13
           59 -> 41,14
           5 -> 49,56,15,26,11
           3 -> 70,40
           41 -> 14*
           15 -> 92,26
           97 -> 93,87
           51 -> 47,40
           10 -> 49,56,11,4
           81 -> 15,26
           89 -> 93,87,35,67
           29 -> 1*
         problem:
          DPs:
           
          TRS:
           a(b(b(x1))) -> c(b(c(x1)))
           c(c(a(x1))) -> c(b(b(x1)))
           a(c(b(x1))) -> c(b(a(x1)))
           c(c(b(x1))) -> c(a(c(x1)))
         Qed