TRS Standard pair #516966604

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	n031.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.716698169708 seconds
cpu usage	1.503737996
max memory	2.60173824E8

stage attributes

key	value
output-size	5983
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:
 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))

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