TRS Standard pair #487068672

details

property	value
status	complete
benchmark	jw27.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n192.star.cs.uiowa.edu
space	Zantema_05

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.832267 seconds
cpu usage	2.11642
user time	1.49296
system time	0.623459
max virtual memory	4370352.0
max residence set size	72152.0

stage attributes

key	value
starexec-result	YES

output

YES

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

Proof:
 Extended Uncurrying Processor:
  application symbol: f
  symbol table:
   a ==> a0/0 a1/1 a2/2
   
  uncurry-rules:
   f(a1(x1),x2) -> a2(x1,x2)
   f(a0(),x1) -> a1(x1)
  eta-rules:
   
  problem:
   a2(x,a0()) -> a1(f(f(x,a1(a0())),a0()))
   f(a1(x1),x2) -> a2(x1,x2)
   f(a0(),x1) -> a1(x1)
  DP Processor:
   DPs:
    a{2,#}(x,a0()) -> f#(x,a1(a0()))
    a{2,#}(x,a0()) -> f#(f(x,a1(a0())),a0())
    f#(a1(x1),x2) -> a{2,#}(x1,x2)
   TRS:
    a2(x,a0()) -> a1(f(f(x,a1(a0())),a0()))
    f(a1(x1),x2) -> a2(x1,x2)
    f(a0(),x1) -> a1(x1)
   TDG Processor:
    DPs:
     a{2,#}(x,a0()) -> f#(x,a1(a0()))
     a{2,#}(x,a0()) -> f#(f(x,a1(a0())),a0())
     f#(a1(x1),x2) -> a{2,#}(x1,x2)
    TRS:
     a2(x,a0()) -> a1(f(f(x,a1(a0())),a0()))
     f(a1(x1),x2) -> a2(x1,x2)
     f(a0(),x1) -> a1(x1)
    graph:
     f#(a1(x1),x2) -> a{2,#}(x1,x2) ->
     a{2,#}(x,a0()) -> f#(f(x,a1(a0())),a0())
     f#(a1(x1),x2) -> a{2,#}(x1,x2) ->
     a{2,#}(x,a0()) -> f#(x,a1(a0()))
     a{2,#}(x,a0()) -> f#(f(x,a1(a0())),a0()) ->
     f#(a1(x1),x2) -> a{2,#}(x1,x2)
     a{2,#}(x,a0()) -> f#(x,a1(a0())) -> f#(a1(x1),x2) -> a{2,#}(x1,x2)
    Bounds Processor:
     bound: 0
     enrichment: match-dp
     automaton:
      final states: {1}
      transitions:
       f70() -> 4*
       a{2,#,0}(4,3) -> 1*
       f{#,0}(4,3) -> 1*
       a{0,0}() -> 2*
       a{1,0}(2) -> 3*
     problem:
      DPs:
       a{2,#}(x,a0()) -> f#(f(x,a1(a0())),a0())
       f#(a1(x1),x2) -> a{2,#}(x1,x2)
      TRS:
       a2(x,a0()) -> a1(f(f(x,a1(a0())),a0()))
       f(a1(x1),x2) -> a2(x1,x2)
       f(a0(),x1) -> a1(x1)
     Bounds Processor:
      bound: 1
      enrichment: match-dp
      automaton:
       final states: {1}
       transitions:
        a{1,1}(11) -> 12*
        a{0,1}() -> 11*
        a{2,0}(4,3) -> 5*
        f150() -> 4*
        a{2,#,0}(3,2) -> 1*
        f0(4,3) -> 5*
        f{#,0}(5,2) -> 1*
        a{0,0}() -> 2*
        a{1,0}(2) -> 3*
        a{1,0}(3) -> 5*
        f{#,1}(13,11) -> 1*
        f1(3,12) -> 13*
        a{2,1}(2,12) -> 13*
      problem:
       DPs:
        f#(a1(x1),x2) -> a{2,#}(x1,x2)
       TRS:
        a2(x,a0()) -> a1(f(f(x,a1(a0())),a0()))
        f(a1(x1),x2) -> a2(x1,x2)
        f(a0(),x1) -> a1(x1)
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 4/1

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