TRS Standard pair #615296910

details

property	value
status	complete
benchmark	logarithm.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n036.star.cs.uiowa.edu
space	Secret_06_TRS

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	77.6846580505 seconds
cpu usage	308.573062776
max memory	1.704542208E9

stage attributes

key	value
output-size	28541
starexec-result	"YES"

output

/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem:
 half(0()) -> 0()
 half(s(0())) -> 0()
 half(s(s(x))) -> s(half(x))
 le(0(),y) -> true()
 le(s(x),0()) -> false()
 le(s(x),s(y)) -> le(x,y)
 inc(s(x)) -> s(inc(x))
 inc(0()) -> s(0())
 logarithm(x) -> logIter(x,0())
 logIter(x,y) -> if(le(s(0()),x),le(s(s(0())),x),half(x),inc(y))
 if(false(),b,x,y) -> logZeroError()
 if(true(),false(),x,s(y)) -> y
 if(true(),true(),x,y) -> logIter(x,y)
 f() -> g()
 f() -> h()

Proof:
 DP Processor:
  DPs:
   half#(s(s(x))) -> half#(x)
   le#(s(x),s(y)) -> le#(x,y)
   inc#(s(x)) -> inc#(x)
   logarithm#(x) -> logIter#(x,0())
   logIter#(x,y) -> inc#(y)
   logIter#(x,y) -> half#(x)
   logIter#(x,y) -> le#(s(s(0())),x)
   logIter#(x,y) -> le#(s(0()),x)
   logIter#(x,y) -> if#(le(s(0()),x),le(s(s(0())),x),half(x),inc(y))
   if#(true(),true(),x,y) -> logIter#(x,y)
  TRS:
   half(0()) -> 0()
   half(s(0())) -> 0()
   half(s(s(x))) -> s(half(x))
   le(0(),y) -> true()
   le(s(x),0()) -> false()
   le(s(x),s(y)) -> le(x,y)
   inc(s(x)) -> s(inc(x))
   inc(0()) -> s(0())
   logarithm(x) -> logIter(x,0())
   logIter(x,y) -> if(le(s(0()),x),le(s(s(0())),x),half(x),inc(y))
   if(false(),b,x,y) -> logZeroError()
   if(true(),false(),x,s(y)) -> y
   if(true(),true(),x,y) -> logIter(x,y)
   f() -> g()
   f() -> h()
  TDG Processor:
   DPs:
    half#(s(s(x))) -> half#(x)
    le#(s(x),s(y)) -> le#(x,y)
    inc#(s(x)) -> inc#(x)
    logarithm#(x) -> logIter#(x,0())
    logIter#(x,y) -> inc#(y)
    logIter#(x,y) -> half#(x)
    logIter#(x,y) -> le#(s(s(0())),x)
    logIter#(x,y) -> le#(s(0()),x)
    logIter#(x,y) -> if#(le(s(0()),x),le(s(s(0())),x),half(x),inc(y))
    if#(true(),true(),x,y) -> logIter#(x,y)
   TRS:
    half(0()) -> 0()
    half(s(0())) -> 0()
    half(s(s(x))) -> s(half(x))
    le(0(),y) -> true()
    le(s(x),0()) -> false()
    le(s(x),s(y)) -> le(x,y)
    inc(s(x)) -> s(inc(x))
    inc(0()) -> s(0())
    logarithm(x) -> logIter(x,0())
    logIter(x,y) -> if(le(s(0()),x),le(s(s(0())),x),half(x),inc(y))
    if(false(),b,x,y) -> logZeroError()
    if(true(),false(),x,s(y)) -> y
    if(true(),true(),x,y) -> logIter(x,y)
    f() -> g()
    f() -> h()
   graph:
    if#(true(),true(),x,y) -> logIter#(x,y) ->
    logIter#(x,y) -> if#(le(s(0()),x),le(s(s(0())),x),half(x),inc(y))
    if#(true(),true(),x,y) -> logIter#(x,y) ->
    logIter#(x,y) -> le#(s(0()),x)
    if#(true(),true(),x,y) -> logIter#(x,y) ->
    logIter#(x,y) -> le#(s(s(0())),x)
    if#(true(),true(),x,y) -> logIter#(x,y) ->
    logIter#(x,y) -> half#(x)
    if#(true(),true(),x,y) -> logIter#(x,y) ->
    logIter#(x,y) -> inc#(y)
    logIter#(x,y) -> if#(le(s(0()),x),le(s(s(0())),x),half(x),inc(y)) ->
    if#(true(),true(),x,y) -> logIter#(x,y)
    logIter#(x,y) -> inc#(y) -> inc#(s(x)) -> inc#(x)
    logIter#(x,y) -> le#(s(s(0())),x) -> le#(s(x),s(y)) -> le#(x,y)
    logIter#(x,y) -> le#(s(0()),x) -> le#(s(x),s(y)) -> le#(x,y)
    logIter#(x,y) -> half#(x) -> half#(s(s(x))) -> half#(x)
    logarithm#(x) -> logIter#(x,0()) ->

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