TRS Standard pair #615305660

details

property	value
status	complete
benchmark	4.20.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n148.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.449273109436 seconds
cpu usage	0.718921476
max memory	1.6611328E8

stage attributes

key	value
output-size	3544
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:
 not(x) -> xor(x,true())
 or(x,y) -> xor(and(x,y),xor(x,y))
 implies(x,y) -> xor(and(x,y),xor(x,true()))
 and(x,true()) -> x
 and(x,false()) -> false()
 and(x,x) -> x
 xor(x,false()) -> x
 xor(x,x) -> false()
 and(xor(x,y),z) -> xor(and(x,z),and(y,z))

Proof:
 DP Processor:
  DPs:
   not#(x) -> xor#(x,true())
   or#(x,y) -> xor#(x,y)
   or#(x,y) -> and#(x,y)
   or#(x,y) -> xor#(and(x,y),xor(x,y))
   implies#(x,y) -> xor#(x,true())
   implies#(x,y) -> and#(x,y)
   implies#(x,y) -> xor#(and(x,y),xor(x,true()))
   and#(xor(x,y),z) -> and#(y,z)
   and#(xor(x,y),z) -> and#(x,z)
   and#(xor(x,y),z) -> xor#(and(x,z),and(y,z))
  TRS:
   not(x) -> xor(x,true())
   or(x,y) -> xor(and(x,y),xor(x,y))
   implies(x,y) -> xor(and(x,y),xor(x,true()))
   and(x,true()) -> x
   and(x,false()) -> false()
   and(x,x) -> x
   xor(x,false()) -> x
   xor(x,x) -> false()
   and(xor(x,y),z) -> xor(and(x,z),and(y,z))
  TDG Processor:
   DPs:
    not#(x) -> xor#(x,true())
    or#(x,y) -> xor#(x,y)
    or#(x,y) -> and#(x,y)
    or#(x,y) -> xor#(and(x,y),xor(x,y))
    implies#(x,y) -> xor#(x,true())
    implies#(x,y) -> and#(x,y)
    implies#(x,y) -> xor#(and(x,y),xor(x,true()))
    and#(xor(x,y),z) -> and#(y,z)
    and#(xor(x,y),z) -> and#(x,z)
    and#(xor(x,y),z) -> xor#(and(x,z),and(y,z))
   TRS:
    not(x) -> xor(x,true())
    or(x,y) -> xor(and(x,y),xor(x,y))
    implies(x,y) -> xor(and(x,y),xor(x,true()))
    and(x,true()) -> x
    and(x,false()) -> false()
    and(x,x) -> x
    xor(x,false()) -> x
    xor(x,x) -> false()
    and(xor(x,y),z) -> xor(and(x,z),and(y,z))
   graph:
    implies#(x,y) -> and#(x,y) ->
    and#(xor(x,y),z) -> xor#(and(x,z),and(y,z))
    implies#(x,y) -> and#(x,y) -> and#(xor(x,y),z) -> and#(x,z)
    implies#(x,y) -> and#(x,y) -> and#(xor(x,y),z) -> and#(y,z)
    and#(xor(x,y),z) -> and#(y,z) ->
    and#(xor(x,y),z) -> xor#(and(x,z),and(y,z))
    and#(xor(x,y),z) -> and#(y,z) -> and#(xor(x,y),z) -> and#(x,z)
    and#(xor(x,y),z) -> and#(y,z) -> and#(xor(x,y),z) -> and#(y,z)
    and#(xor(x,y),z) -> and#(x,z) ->
    and#(xor(x,y),z) -> xor#(and(x,z),and(y,z))
    and#(xor(x,y),z) -> and#(x,z) -> and#(xor(x,y),z) -> and#(x,z)
    and#(xor(x,y),z) -> and#(x,z) -> and#(xor(x,y),z) -> and#(y,z)
    or#(x,y) -> and#(x,y) -> and#(xor(x,y),z) -> xor#(and(x,z),and(y,z))
    or#(x,y) -> and#(x,y) -> and#(xor(x,y),z) -> and#(x,z)
    or#(x,y) -> and#(x,y) -> and#(xor(x,y),z) -> and#(y,z)
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 12/100
    DPs:
     and#(xor(x,y),z) -> and#(y,z)
     and#(xor(x,y),z) -> and#(x,z)
    TRS:
     not(x) -> xor(x,true())
     or(x,y) -> xor(and(x,y),xor(x,y))
     implies(x,y) -> xor(and(x,y),xor(x,true()))
     and(x,true()) -> x
     and(x,false()) -> false()
     and(x,x) -> x
     xor(x,false()) -> x
     xor(x,x) -> false()
     and(xor(x,y),z) -> xor(and(x,z),and(y,z))
    Subterm Criterion Processor:
     simple projection:
      pi(and#) = 0

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