/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

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

Proof:
 DP Processor:
  DPs:
   f#(f(x,a()),y) -> f#(x,y)
   f#(f(x,a()),y) -> f#(y,f(x,y))
  TRS:
   f(f(x,a()),y) -> f(y,f(x,y))
  Bounds Processor:
   bound: 2
   enrichment: top-dp
   automaton:
    final states: {20,14}
    transitions:
     f{#,1}(12,22) -> 16*
     f{#,1}(17,24) -> 16*
     f{#,1}(12,24) -> 16*
     f{#,1}(18,21) -> 20*
     f{#,1}(18,27) -> 16*
     f{#,1}(13,29) -> 14*
     f{#,1}(20,21) -> 20*
     f{#,1}(10,21) -> 20*
     f{#,1}(10,23) -> 16*
     f{#,1}(15,29) -> 14*
     f{#,1}(11,24) -> 16*
     f{#,1}(16,28) -> 16*
     f{#,1}(17,21) -> 20*
     f{#,1}(12,21) -> 20*
     f{#,1}(19,21) -> 20*
     f{#,1}(10,24) -> 16*
     f{#,1}(20,26) -> 16*
     f{#,1}(16,21) -> 20*
     f{#,1}(11,21) -> 20*
     f{#,1}(11,25) -> 16*
     f1(17,16) -> 28*
     f1(12,16) -> 28*
     f1(17,18) -> 27*
     f1(12,18) -> 27*
     f1(17,20) -> 26*
     f1(12,20) -> 26*
     f1(12,22) -> 22*
     f1(17,24) -> 24*
     f1(18,11) -> 25*
     f1(18,15) -> 29*
     f1(18,17) -> 24*
     f1(18,19) -> 21*
     f1(18,27) -> 27*
     f1(19,10) -> 23*
     f1(19,12) -> 22*
     f1(19,16) -> 28*
     f1(19,18) -> 27*
     f1(19,20) -> 26*
     f1(29,30) -> 29*
     f1(20,11) -> 25*
     f1(24,32) -> 24*
     f1(10,11) -> 25*
     f1(20,15) -> 29*
     f1(10,15) -> 29*
     f1(20,17) -> 24*
     f1(10,17) -> 24*
     f1(20,19) -> 21*
     f1(10,19) -> 21*
     f1(10,23) -> 23*
     f1(15,29) -> 29*
     f1(16,10) -> 23*
     f1(11,10) -> 23*
     f1(16,12) -> 22*
     f1(11,12) -> 22*
     f1(16,16) -> 28*
     f1(11,16) -> 28*
     f1(16,18) -> 27*
     f1(11,18) -> 27*
     f1(16,20) -> 26*
     f1(11,20) -> 26*
     f1(16,28) -> 28*
     f1(17,11) -> 25*
     f1(12,11) -> 25*
     f1(17,15) -> 29*
     f1(12,15) -> 29*
     f1(17,17) -> 24*
     f1(12,17) -> 24*
     f1(17,19) -> 21*
     f1(12,19) -> 21*
     f1(18,10) -> 23*
     f1(18,12) -> 22*
     f1(18,16) -> 28*
     f1(18,18) -> 27*
     f1(18,20) -> 26*
     f1(19,11) -> 25*
     f1(19,15) -> 29*
     f1(19,17) -> 24*
     f1(19,19) -> 21*
     f1(19,21) -> 21*
     f1(20,10) -> 23*
     f1(20,12) -> 22*
     f1(10,10) -> 23*
     f1(10,12) -> 22*
     f1(20,16) -> 28*
     f1(10,16) -> 28*
     f1(20,18) -> 27*
     f1(10,18) -> 27*
     f1(20,20) -> 26*
     f1(10,20) -> 26*
     f1(20,26) -> 26*
     f1(16,11) -> 25*
     f1(11,11) -> 25*
     f1(16,15) -> 29*
     f1(11,15) -> 29*
     f1(16,17) -> 24*
     f1(11,17) -> 24*
     f1(16,19) -> 21*
     f1(11,19) -> 21*
     f1(11,25) -> 25*
     f1(17,10) -> 23*
     f1(21,31) -> 21*
     f1(12,10) -> 23*
     f1(17,12) -> 22*
     f1(12,12) -> 22*
     f{#,2}(29,30) -> 14*
     f{#,2}(24,32) -> 16*
     f{#,2}(21,31) -> 20*
     f2(12,24) -> 32*
     f2(18,21) -> 31*
     f2(13,29) -> 30*
     f2(20,21) -> 31*
     f2(10,21) -> 31*
     f2(11,24) -> 32*
     f2(17,21) -> 31*
     f2(12,21) -> 31*
     f2(19,21) -> 31*
     f2(10,24) -> 32*
     f2(16,21) -> 31*
     f2(11,21) -> 31*
     f2(21,31) -> 31*
     f{#,0}(17,16) -> 16*
     f{#,0}(12,16) -> 16*
     f{#,0}(17,18) -> 16*
     f{#,0}(12,18) -> 16*
     f{#,0}(17,20) -> 16*
     f{#,0}(12,20) -> 16*
     f{#,0}(18,11) -> 16*
     f{#,0}(18,15) -> 14*
     f{#,0}(13,15) -> 14*
     f{#,0}(18,17) -> 16*
     f{#,0}(18,19) -> 20*
     f{#,0}(13,19) -> 14*
     f{#,0}(19,10) -> 16*
     f{#,0}(19,12) -> 16*
     f{#,0}(19,16) -> 16*
     f{#,0}(19,18) -> 16*
     f{#,0}(19,20) -> 16*
     f{#,0}(20,11) -> 16*
     f{#,0}(10,11) -> 16*
     f{#,0}(20,15) -> 14*
     f{#,0}(10,15) -> 14*
     f{#,0}(20,17) -> 16*
     f{#,0}(20,19) -> 20*
     f{#,0}(10,17) -> 16*
     f{#,0}(10,19) -> 20,16
     f{#,0}(16,10) -> 16*
     f{#,0}(11,10) -> 16*
     f{#,0}(16,12) -> 16*
     f{#,0}(11,12) -> 16*
     f{#,0}(16,16) -> 16*
     f{#,0}(11,16) -> 16*
     f{#,0}(16,18) -> 16*
     f{#,0}(11,18) -> 16*
     f{#,0}(16,20) -> 16*
     f{#,0}(11,20) -> 16*
     f{#,0}(17,11) -> 16*
     f{#,0}(12,11) -> 16*
     f{#,0}(17,15) -> 14*
     f{#,0}(12,15) -> 14*
     f{#,0}(17,17) -> 16*
     f{#,0}(12,17) -> 16*
     f{#,0}(17,19) -> 20*
     f{#,0}(12,19) -> 20,16
     f{#,0}(18,10) -> 16*
     f{#,0}(18,12) -> 16*
     f{#,0}(18,16) -> 16*
     f{#,0}(18,18) -> 16*
     f{#,0}(18,20) -> 16*
     f{#,0}(19,11) -> 16*
     f{#,0}(19,15) -> 14*
     f{#,0}(19,17) -> 16*
     f{#,0}(19,19) -> 20*
     f{#,0}(20,10) -> 16*
     f{#,0}(20,12) -> 16*
     f{#,0}(10,10) -> 16*
     f{#,0}(10,12) -> 16*
     f{#,0}(20,16) -> 16*
     f{#,0}(20,18) -> 16*
     f{#,0}(10,16) -> 16*
     f{#,0}(20,20) -> 16*
     f{#,0}(10,18) -> 16*
     f{#,0}(10,20) -> 16*
     f{#,0}(16,11) -> 16*
     f{#,0}(11,11) -> 16*
     f{#,0}(16,15) -> 14*
     f{#,0}(11,15) -> 14*
     f{#,0}(16,17) -> 16*
     f{#,0}(11,17) -> 16*
     f{#,0}(16,19) -> 20*
     f{#,0}(11,19) -> 20,16
     f{#,0}(17,10) -> 16*
     f{#,0}(12,10) -> 16*
     f{#,0}(17,12) -> 16*
     f{#,0}(12,12) -> 16*
     f0(17,16) -> 19*
     f0(12,16) -> 17*
     f0(17,18) -> 19*
     f0(12,18) -> 17*
     f0(17,20) -> 19*
     f0(12,20) -> 17*
     f0(18,11) -> 17*
     f0(18,13) -> 15*
     f0(13,13) -> 15*
     f0(13,15) -> 15*
     f0(18,17) -> 19*
     f0(13,17) -> 15*
     f0(18,19) -> 19*
     f0(13,19) -> 15*
     f0(19,10) -> 17*
     f0(19,12) -> 17*
     f0(19,16) -> 19*
     f0(19,18) -> 19*
     f0(19,20) -> 19*
     f0(20,11) -> 17*
     f0(20,13) -> 15*
     f0(10,11) -> 17*
     f0(10,13) -> 13*
     f0(20,17) -> 19*
     f0(20,19) -> 19*
     f0(10,17) -> 17*
     f0(10,19) -> 17*
     f0(16,10) -> 17*
     f0(11,10) -> 17*
     f0(16,12) -> 17*
     f0(11,12) -> 17*
     f0(16,16) -> 19*
     f0(11,16) -> 17*
     f0(16,18) -> 19*
     f0(11,18) -> 17*
     f0(16,20) -> 19*
     f0(11,20) -> 17*
     f0(17,11) -> 17*
     f0(12,11) -> 17*
     f0(17,13) -> 15*
     f0(12,13) -> 13*
     f0(17,17) -> 19*
     f0(12,17) -> 17*
     f0(17,19) -> 19*
     f0(12,19) -> 17*
     f0(18,10) -> 17*
     f0(18,12) -> 17*
     f0(18,16) -> 19*
     f0(13,16) -> 15*
     f0(18,18) -> 19*
     f0(13,18) -> 15*
     f0(18,20) -> 19*
     f0(13,20) -> 15*
     f0(19,11) -> 17*
     f0(19,13) -> 15*
     f0(19,17) -> 19*
     f0(19,19) -> 19*
     f0(20,10) -> 17*
     f0(20,12) -> 17*
     f0(10,10) -> 17*
     f0(10,12) -> 17*
     f0(20,16) -> 19*
     f0(20,18) -> 19*
     f0(10,16) -> 17*
     f0(20,20) -> 19*
     f0(10,18) -> 17*
     f0(10,20) -> 17*
     f0(16,11) -> 17*
     f0(11,11) -> 17*
     f0(16,13) -> 15*
     f0(11,13) -> 13*
     f0(16,17) -> 19*
     f0(11,17) -> 17*
     f0(16,19) -> 19*
     f0(11,19) -> 17*
     f0(17,10) -> 17*
     f0(12,10) -> 17*
     f0(17,12) -> 17*
     f0(12,12) -> 17*
     a0() -> 18*
   problem:
    DPs:
     f#(f(x,a()),y) -> f#(x,y)
    TRS:
     f(f(x,a()),y) -> f(y,f(x,y))
   Size-Change Termination Processor:
    DPs:
     
    TRS:
     f(f(x,a()),y) -> f(y,f(x,y))
    The DP: f#(f(x,a()),y) -> f#(x,y) has the edges:
      0 >   0
      1 >=  1
    Qed