TRS Stand 20472 pair #381712245

details

property	value
status	complete
benchmark	gen-18.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n112.star.cs.uiowa.edu
space	Secret_06_TRS

run statistics

property	value
solver	ttt2-1.17+nonreach
configuration	ttt2-1.17+nonreach
runtime (wallclock)	2.08497810364 seconds
cpu usage	6.906526115
max memory	7.87521536E8

stage attributes

key	value
output-size	4702
starexec-result	YES

output

/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:
 b(b(y,z),c(a(),a(),a())) -> f(c(z,y,z))
 f(b(b(a(),z),c(a(),x,y))) -> z
 c(y,x,f(z)) -> b(f(b(z,x)),z)

Proof:
 DP Processor:
  DPs:
   b#(b(y,z),c(a(),a(),a())) -> c#(z,y,z)
   b#(b(y,z),c(a(),a(),a())) -> f#(c(z,y,z))
   c#(y,x,f(z)) -> b#(z,x)
   c#(y,x,f(z)) -> f#(b(z,x))
   c#(y,x,f(z)) -> b#(f(b(z,x)),z)
  TRS:
   b(b(y,z),c(a(),a(),a())) -> f(c(z,y,z))
   f(b(b(a(),z),c(a(),x,y))) -> z
   c(y,x,f(z)) -> b(f(b(z,x)),z)
  TDG Processor:
   DPs:
    b#(b(y,z),c(a(),a(),a())) -> c#(z,y,z)
    b#(b(y,z),c(a(),a(),a())) -> f#(c(z,y,z))
    c#(y,x,f(z)) -> b#(z,x)
    c#(y,x,f(z)) -> f#(b(z,x))
    c#(y,x,f(z)) -> b#(f(b(z,x)),z)
   TRS:
    b(b(y,z),c(a(),a(),a())) -> f(c(z,y,z))
    f(b(b(a(),z),c(a(),x,y))) -> z
    c(y,x,f(z)) -> b(f(b(z,x)),z)
   graph:
    c#(y,x,f(z)) -> b#(f(b(z,x)),z) ->
    b#(b(y,z),c(a(),a(),a())) -> f#(c(z,y,z))
    c#(y,x,f(z)) -> b#(f(b(z,x)),z) ->
    b#(b(y,z),c(a(),a(),a())) -> c#(z,y,z)
    c#(y,x,f(z)) -> b#(z,x) -> b#(b(y,z),c(a(),a(),a())) -> f#(c(z,y,z))
    c#(y,x,f(z)) -> b#(z,x) ->
    b#(b(y,z),c(a(),a(),a())) -> c#(z,y,z)
    b#(b(y,z),c(a(),a(),a())) -> c#(z,y,z) ->
    c#(y,x,f(z)) -> b#(f(b(z,x)),z)
    b#(b(y,z),c(a(),a(),a())) -> c#(z,y,z) ->
    c#(y,x,f(z)) -> f#(b(z,x))
    b#(b(y,z),c(a(),a(),a())) -> c#(z,y,z) -> c#(y,x,f(z)) -> b#(z,x)
   SCC Processor:
    #sccs: 1
    #rules: 3
    #arcs: 7/25
    DPs:
     c#(y,x,f(z)) -> b#(f(b(z,x)),z)
     b#(b(y,z),c(a(),a(),a())) -> c#(z,y,z)
     c#(y,x,f(z)) -> b#(z,x)
    TRS:
     b(b(y,z),c(a(),a(),a())) -> f(c(z,y,z))
     f(b(b(a(),z),c(a(),x,y))) -> z
     c(y,x,f(z)) -> b(f(b(z,x)),z)
    Arctic Interpretation Processor:
     dimension: 1
     usable rules:
      b(b(y,z),c(a(),a(),a())) -> f(c(z,y,z))
      f(b(b(a(),z),c(a(),x,y))) -> z
      c(y,x,f(z)) -> b(f(b(z,x)),z)
     interpretation:
      [c#](x0, x1, x2) = -16x0 + 1x1 + 1x2 + 0,
      
      [b#](x0, x1) = x0 + x1 + -16,
      
      [f](x0) = x0 + -8,
      
      [c](x0, x1, x2) = x0 + 2x1 + 2x2 + 1,
      
      [a] = 2,
      
      [b](x0, x1) = 1x0 + 1x1 + 0
     orientation:
      c#(y,x,f(z)) = 1x + -16y + 1z + 0 >= 1x + 1z + 0 = b#(f(b(z,x)),z)
      
      b#(b(y,z),c(a(),a(),a())) = 1y + 1z + 4 >= 1y + 1z + 0 = c#(z,y,z)
      
      c#(y,x,f(z)) = 1x + -16y + 1z + 0 >= x + z + -16 = b#(z,x)
      
      b(b(y,z),c(a(),a(),a())) = 2y + 2z + 5 >= 2y + 2z + 1 = f(c(z,y,z))
      
      f(b(b(a(),z),c(a(),x,y))) = 3x + 3y + 2z + 4 >= z = z
      
      c(y,x,f(z)) = 2x + y + 2z + 1 >= 2x + 2z + 1 = b(f(b(z,x)),z)
     problem:
      DPs:
       c#(y,x,f(z)) -> b#(f(b(z,x)),z)
       b#(b(y,z),c(a(),a(),a())) -> c#(z,y,z)
      TRS:
       b(b(y,z),c(a(),a(),a())) -> f(c(z,y,z))
       f(b(b(a(),z),c(a(),x,y))) -> z
       c(y,x,f(z)) -> b(f(b(z,x)),z)
     Restore Modifier:

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