TRS Standard pair #487067967

details

property	value
status	complete
benchmark	4.42.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n179.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.46896 seconds
cpu usage	0.788603
user time	0.582504
system time	0.206099
max virtual memory	96176.0
max residence set size	60664.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 f(a(),g(y)) -> g(g(y))
 f(g(x),a()) -> f(x,g(a()))
 f(g(x),g(y)) -> h(g(y),x,g(y))
 h(g(x),y,z) -> f(y,h(x,y,z))
 h(a(),y,z) -> z

Proof:
 DP Processor:
  DPs:
   f#(g(x),a()) -> f#(x,g(a()))
   f#(g(x),g(y)) -> h#(g(y),x,g(y))
   h#(g(x),y,z) -> h#(x,y,z)
   h#(g(x),y,z) -> f#(y,h(x,y,z))
  TRS:
   f(a(),g(y)) -> g(g(y))
   f(g(x),a()) -> f(x,g(a()))
   f(g(x),g(y)) -> h(g(y),x,g(y))
   h(g(x),y,z) -> f(y,h(x,y,z))
   h(a(),y,z) -> z
  TDG Processor:
   DPs:
    f#(g(x),a()) -> f#(x,g(a()))
    f#(g(x),g(y)) -> h#(g(y),x,g(y))
    h#(g(x),y,z) -> h#(x,y,z)
    h#(g(x),y,z) -> f#(y,h(x,y,z))
   TRS:
    f(a(),g(y)) -> g(g(y))
    f(g(x),a()) -> f(x,g(a()))
    f(g(x),g(y)) -> h(g(y),x,g(y))
    h(g(x),y,z) -> f(y,h(x,y,z))
    h(a(),y,z) -> z
   graph:
    h#(g(x),y,z) -> h#(x,y,z) -> h#(g(x),y,z) -> f#(y,h(x,y,z))
    h#(g(x),y,z) -> h#(x,y,z) -> h#(g(x),y,z) -> h#(x,y,z)
    h#(g(x),y,z) -> f#(y,h(x,y,z)) ->
    f#(g(x),g(y)) -> h#(g(y),x,g(y))
    h#(g(x),y,z) -> f#(y,h(x,y,z)) -> f#(g(x),a()) -> f#(x,g(a()))
    f#(g(x),g(y)) -> h#(g(y),x,g(y)) ->
    h#(g(x),y,z) -> f#(y,h(x,y,z))
    f#(g(x),g(y)) -> h#(g(y),x,g(y)) -> h#(g(x),y,z) -> h#(x,y,z)
    f#(g(x),a()) -> f#(x,g(a())) -> f#(g(x),g(y)) -> h#(g(y),x,g(y))
    f#(g(x),a()) -> f#(x,g(a())) -> f#(g(x),a()) -> f#(x,g(a()))
   Subterm Criterion Processor:
    simple projection:
     pi(f#) = 0
     pi(h#) = 1
    problem:
     DPs:
      h#(g(x),y,z) -> h#(x,y,z)
      h#(g(x),y,z) -> f#(y,h(x,y,z))
     TRS:
      f(a(),g(y)) -> g(g(y))
      f(g(x),a()) -> f(x,g(a()))
      f(g(x),g(y)) -> h(g(y),x,g(y))
      h(g(x),y,z) -> f(y,h(x,y,z))
      h(a(),y,z) -> z
    SCC Processor:
     #sccs: 1
     #rules: 1
     #arcs: 8/4
     DPs:
      h#(g(x),y,z) -> h#(x,y,z)
     TRS:
      f(a(),g(y)) -> g(g(y))
      f(g(x),a()) -> f(x,g(a()))
      f(g(x),g(y)) -> h(g(y),x,g(y))
      h(g(x),y,z) -> f(y,h(x,y,z))
      h(a(),y,z) -> z
     Subterm Criterion Processor:
      simple projection:
       pi(h#) = 0
      problem:
       DPs:
        
       TRS:
        f(a(),g(y)) -> g(g(y))
        f(g(x),a()) -> f(x,g(a()))
        f(g(x),g(y)) -> h(g(y),x,g(y))
        h(g(x),y,z) -> f(y,h(x,y,z))
        h(a(),y,z) -> z
      Qed

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