TRS Standard pair #516966104

details

property	value
status	complete
benchmark	4.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n034.star.cs.uiowa.edu
space	Secret_06_TRS

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	1.73007011414 seconds
cpu usage	5.625871578
max memory	1.018011648E9

stage attributes

key	value
output-size	4228
starexec-result	YES

output

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


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


YES

Problem:
 c(c(b(c(x)))) -> b(a(0(),c(x)))
 c(c(x)) -> b(c(b(c(x))))
 a(0(),x) -> c(c(x))

Proof:
 DP Processor:
  DPs:
   c#(c(b(c(x)))) -> a#(0(),c(x))
   c#(c(x)) -> c#(b(c(x)))
   a#(0(),x) -> c#(x)
   a#(0(),x) -> c#(c(x))
  TRS:
   c(c(b(c(x)))) -> b(a(0(),c(x)))
   c(c(x)) -> b(c(b(c(x))))
   a(0(),x) -> c(c(x))
  TDG Processor:
   DPs:
    c#(c(b(c(x)))) -> a#(0(),c(x))
    c#(c(x)) -> c#(b(c(x)))
    a#(0(),x) -> c#(x)
    a#(0(),x) -> c#(c(x))
   TRS:
    c(c(b(c(x)))) -> b(a(0(),c(x)))
    c(c(x)) -> b(c(b(c(x))))
    a(0(),x) -> c(c(x))
   graph:
    a#(0(),x) -> c#(c(x)) -> c#(c(x)) -> c#(b(c(x)))
    a#(0(),x) -> c#(c(x)) -> c#(c(b(c(x)))) -> a#(0(),c(x))
    a#(0(),x) -> c#(x) -> c#(c(x)) -> c#(b(c(x)))
    a#(0(),x) -> c#(x) -> c#(c(b(c(x)))) -> a#(0(),c(x))
    c#(c(b(c(x)))) -> a#(0(),c(x)) -> a#(0(),x) -> c#(c(x))
    c#(c(b(c(x)))) -> a#(0(),c(x)) -> a#(0(),x) -> c#(x)
    c#(c(x)) -> c#(b(c(x))) -> c#(c(x)) -> c#(b(c(x)))
    c#(c(x)) -> c#(b(c(x))) -> c#(c(b(c(x)))) -> a#(0(),c(x))
   EDG Processor:
    DPs:
     c#(c(b(c(x)))) -> a#(0(),c(x))
     c#(c(x)) -> c#(b(c(x)))
     a#(0(),x) -> c#(x)
     a#(0(),x) -> c#(c(x))
    TRS:
     c(c(b(c(x)))) -> b(a(0(),c(x)))
     c(c(x)) -> b(c(b(c(x))))
     a(0(),x) -> c(c(x))
    graph:
     a#(0(),x) -> c#(c(x)) -> c#(c(b(c(x)))) -> a#(0(),c(x))
     a#(0(),x) -> c#(c(x)) -> c#(c(x)) -> c#(b(c(x)))
     a#(0(),x) -> c#(x) -> c#(c(b(c(x)))) -> a#(0(),c(x))
     a#(0(),x) -> c#(x) -> c#(c(x)) -> c#(b(c(x)))
     c#(c(b(c(x)))) -> a#(0(),c(x)) -> a#(0(),x) -> c#(x)
     c#(c(b(c(x)))) -> a#(0(),c(x)) -> a#(0(),x) -> c#(c(x))
    SCC Processor:
     #sccs: 1
     #rules: 3
     #arcs: 6/16
     DPs:
      a#(0(),x) -> c#(c(x))
      c#(c(b(c(x)))) -> a#(0(),c(x))
      a#(0(),x) -> c#(x)
     TRS:
      c(c(b(c(x)))) -> b(a(0(),c(x)))
      c(c(x)) -> b(c(b(c(x))))
      a(0(),x) -> c(c(x))
     Arctic Interpretation Processor:
      dimension: 1
      usable rules:
       c(c(b(c(x)))) -> b(a(0(),c(x)))
       c(c(x)) -> b(c(b(c(x))))
       a(0(),x) -> c(c(x))
      interpretation:
       [c#](x0) = x0,
       
       [b](x0) = x0 + 0,
       
       [a](x0, x1) = -6x0 + 2x1 + 1,
       
       [a#](x0, x1) = -7x0 + 1x1 + 0,
       
       [c](x0) = 1x0 + 0,
       
       [0] = 5
      orientation:
       a#(0(),x) = 1x + 0 >= 1x + 0 = c#(c(x))
       
       c#(c(b(c(x)))) = 2x + 1 >= 2x + 1 = a#(0(),c(x))
       
       a#(0(),x) = 1x + 0 >= x = c#(x)
       
       c(c(b(c(x)))) = 3x + 2 >= 3x + 2 = b(a(0(),c(x)))
       
       c(c(x)) = 2x + 1 >= 2x + 1 = b(c(b(c(x))))

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