TRS Standard pair #516964559

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	n029.star.cs.uiowa.edu
space	Mixed_TRS

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.664160966873 seconds
cpu usage	1.283886839
max memory	4.2713088E8

stage attributes

key	value
output-size	1820
starexec-result	YES

output

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


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YES

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

Proof:
 DP Processor:
  DPs:
   f#(x,f(a(),y)) -> f#(a(),a())
   f#(x,f(a(),y)) -> f#(f(a(),a()),a())
   f#(x,f(a(),y)) -> f#(y,f(f(a(),a()),a()))
   f#(x,f(a(),y)) -> f#(f(y,f(f(a(),a()),a())),x)
  TRS:
   f(x,f(a(),y)) -> f(f(y,f(f(a(),a()),a())),x)
  EDG Processor:
   DPs:
    f#(x,f(a(),y)) -> f#(a(),a())
    f#(x,f(a(),y)) -> f#(f(a(),a()),a())
    f#(x,f(a(),y)) -> f#(y,f(f(a(),a()),a()))
    f#(x,f(a(),y)) -> f#(f(y,f(f(a(),a()),a())),x)
   TRS:
    f(x,f(a(),y)) -> f(f(y,f(f(a(),a()),a())),x)
   graph:
    f#(x,f(a(),y)) -> f#(f(y,f(f(a(),a()),a())),x) ->
    f#(x,f(a(),y)) -> f#(a(),a())
    f#(x,f(a(),y)) -> f#(f(y,f(f(a(),a()),a())),x) ->
    f#(x,f(a(),y)) -> f#(f(a(),a()),a())
    f#(x,f(a(),y)) -> f#(f(y,f(f(a(),a()),a())),x) ->
    f#(x,f(a(),y)) -> f#(y,f(f(a(),a()),a()))
    f#(x,f(a(),y)) -> f#(f(y,f(f(a(),a()),a())),x) ->
    f#(x,f(a(),y)) -> f#(f(y,f(f(a(),a()),a())),x)
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 4/16
    DPs:
     f#(x,f(a(),y)) -> f#(f(y,f(f(a(),a()),a())),x)
    TRS:
     f(x,f(a(),y)) -> f(f(y,f(f(a(),a()),a())),x)
    Bounds Processor:
     bound: 0
     enrichment: match
     automaton:
      final states: {7,1}
      transitions:
       f0(6,6) -> 7*
       f0(6,2) -> 7*
       f0(5,5) -> 6*
       f0(2,5) -> 6*
       f0(4,3) -> 5*
       f0(3,3) -> 4*
       a0() -> 3*
       f30() -> 2*
       f{#,0}(6,2) -> 1*
       f{#,0}(6,6) -> 1*
     problem:
      DPs:
       
      TRS:
       f(x,f(a(),y)) -> f(f(y,f(f(a(),a()),a())),x)
     Qed

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