TRS Standard pair #487068082

details

property	value
status	complete
benchmark	4.28.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n070.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.712014 seconds
cpu usage	1.50563
user time	1.26747
system time	0.238163
max virtual memory	1764088.0
max residence set size	72000.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 f(x,nil()) -> g(nil(),x)
 f(x,g(y,z)) -> g(f(x,y),z)
 ++(x,nil()) -> x
 ++(x,g(y,z)) -> g(++(x,y),z)
 null(nil()) -> true()
 null(g(x,y)) -> false()
 mem(nil(),y) -> false()
 mem(g(x,y),z) -> or(=(y,z),mem(x,z))
 mem(x,max(x)) -> not(null(x))
 max(g(g(nil(),x),y)) -> max'(x,y)
 max(g(g(g(x,y),z),u())) -> max'(max(g(g(x,y),z)),u())

Proof:
 DP Processor:
  DPs:
   f#(x,g(y,z)) -> f#(x,y)
   ++#(x,g(y,z)) -> ++#(x,y)
   mem#(g(x,y),z) -> mem#(x,z)
   mem#(x,max(x)) -> null#(x)
   max#(g(g(g(x,y),z),u())) -> max#(g(g(x,y),z))
  TRS:
   f(x,nil()) -> g(nil(),x)
   f(x,g(y,z)) -> g(f(x,y),z)
   ++(x,nil()) -> x
   ++(x,g(y,z)) -> g(++(x,y),z)
   null(nil()) -> true()
   null(g(x,y)) -> false()
   mem(nil(),y) -> false()
   mem(g(x,y),z) -> or(=(y,z),mem(x,z))
   mem(x,max(x)) -> not(null(x))
   max(g(g(nil(),x),y)) -> max'(x,y)
   max(g(g(g(x,y),z),u())) -> max'(max(g(g(x,y),z)),u())
  TDG Processor:
   DPs:
    f#(x,g(y,z)) -> f#(x,y)
    ++#(x,g(y,z)) -> ++#(x,y)
    mem#(g(x,y),z) -> mem#(x,z)
    mem#(x,max(x)) -> null#(x)
    max#(g(g(g(x,y),z),u())) -> max#(g(g(x,y),z))
   TRS:
    f(x,nil()) -> g(nil(),x)
    f(x,g(y,z)) -> g(f(x,y),z)
    ++(x,nil()) -> x
    ++(x,g(y,z)) -> g(++(x,y),z)
    null(nil()) -> true()
    null(g(x,y)) -> false()
    mem(nil(),y) -> false()
    mem(g(x,y),z) -> or(=(y,z),mem(x,z))
    mem(x,max(x)) -> not(null(x))
    max(g(g(nil(),x),y)) -> max'(x,y)
    max(g(g(g(x,y),z),u())) -> max'(max(g(g(x,y),z)),u())
   graph:
    max#(g(g(g(x,y),z),u())) -> max#(g(g(x,y),z)) ->
    max#(g(g(g(x,y),z),u())) -> max#(g(g(x,y),z))
    mem#(g(x,y),z) -> mem#(x,z) -> mem#(x,max(x)) -> null#(x)
    mem#(g(x,y),z) -> mem#(x,z) -> mem#(g(x,y),z) -> mem#(x,z)
    ++#(x,g(y,z)) -> ++#(x,y) -> ++#(x,g(y,z)) -> ++#(x,y)
    f#(x,g(y,z)) -> f#(x,y) -> f#(x,g(y,z)) -> f#(x,y)
   SCC Processor:
    #sccs: 4
    #rules: 4
    #arcs: 5/25
    DPs:
     f#(x,g(y,z)) -> f#(x,y)
    TRS:
     f(x,nil()) -> g(nil(),x)
     f(x,g(y,z)) -> g(f(x,y),z)
     ++(x,nil()) -> x
     ++(x,g(y,z)) -> g(++(x,y),z)
     null(nil()) -> true()
     null(g(x,y)) -> false()
     mem(nil(),y) -> false()
     mem(g(x,y),z) -> or(=(y,z),mem(x,z))
     mem(x,max(x)) -> not(null(x))
     max(g(g(nil(),x),y)) -> max'(x,y)
     max(g(g(g(x,y),z),u())) -> max'(max(g(g(x,y),z)),u())
    Subterm Criterion Processor:
     simple projection:
      pi(f#) = 1
     problem:
      DPs:
       
      TRS:
       f(x,nil()) -> g(nil(),x)
       f(x,g(y,z)) -> g(f(x,y),z)
       ++(x,nil()) -> x
       ++(x,g(y,z)) -> g(++(x,y),z)
       null(nil()) -> true()
       null(g(x,y)) -> false()
       mem(nil(),y) -> false()
       mem(g(x,y),z) -> or(=(y,z),mem(x,z))
       mem(x,max(x)) -> not(null(x))
       max(g(g(nil(),x),y)) -> max'(x,y)
       max(g(g(g(x,y),z),u())) -> max'(max(g(g(x,y),z)),u())
     Qed
    
    DPs:

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