TRS Standard pair #516966209

details

property	value
status	complete
benchmark	sumList.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n166.star.cs.uiowa.edu
space	Secret_06_TRS

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	4.2892780304 seconds
cpu usage	15.376889356
max memory	1.3514752E9

stage attributes

key	value
output-size	16891
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:
 isEmpty(cons(x,xs)) -> false()
 isEmpty(nil()) -> true()
 isZero(0()) -> true()
 isZero(s(x)) -> false()
 head(cons(x,xs)) -> x
 tail(cons(x,xs)) -> xs
 tail(nil()) -> nil()
 p(s(s(x))) -> s(p(s(x)))
 p(s(0())) -> 0()
 p(0()) -> 0()
 inc(s(x)) -> s(inc(x))
 inc(0()) -> s(0())
 sumList(xs,y) -> if(isEmpty(xs),isZero(head(xs)),y,tail(xs),cons(p(head(xs)),tail(xs)),inc(y))
 if(true(),b,y,xs,ys,x) -> y
 if(false(),true(),y,xs,ys,x) -> sumList(xs,y)
 if(false(),false(),y,xs,ys,x) -> sumList(ys,x)
 sum(xs) -> sumList(xs,0())

Proof:
 DP Processor:
  DPs:
   p#(s(s(x))) -> p#(s(x))
   inc#(s(x)) -> inc#(x)
   sumList#(xs,y) -> inc#(y)
   sumList#(xs,y) -> p#(head(xs))
   sumList#(xs,y) -> tail#(xs)
   sumList#(xs,y) -> head#(xs)
   sumList#(xs,y) -> isZero#(head(xs))
   sumList#(xs,y) -> isEmpty#(xs)
   sumList#(xs,y) -> if#(isEmpty(xs),isZero(head(xs)),y,tail(xs),cons(p(head(xs)),tail(xs)),inc(y))
   if#(false(),true(),y,xs,ys,x) -> sumList#(xs,y)
   if#(false(),false(),y,xs,ys,x) -> sumList#(ys,x)
   sum#(xs) -> sumList#(xs,0())
  TRS:
   isEmpty(cons(x,xs)) -> false()
   isEmpty(nil()) -> true()
   isZero(0()) -> true()
   isZero(s(x)) -> false()
   head(cons(x,xs)) -> x
   tail(cons(x,xs)) -> xs
   tail(nil()) -> nil()
   p(s(s(x))) -> s(p(s(x)))
   p(s(0())) -> 0()
   p(0()) -> 0()
   inc(s(x)) -> s(inc(x))
   inc(0()) -> s(0())
   sumList(xs,y) -> if(isEmpty(xs),isZero(head(xs)),y,tail(xs),cons(p(head(xs)),tail(xs)),inc(y))
   if(true(),b,y,xs,ys,x) -> y
   if(false(),true(),y,xs,ys,x) -> sumList(xs,y)
   if(false(),false(),y,xs,ys,x) -> sumList(ys,x)
   sum(xs) -> sumList(xs,0())
  TDG Processor:
   DPs:
    p#(s(s(x))) -> p#(s(x))
    inc#(s(x)) -> inc#(x)
    sumList#(xs,y) -> inc#(y)
    sumList#(xs,y) -> p#(head(xs))
    sumList#(xs,y) -> tail#(xs)
    sumList#(xs,y) -> head#(xs)
    sumList#(xs,y) -> isZero#(head(xs))
    sumList#(xs,y) -> isEmpty#(xs)
    sumList#(xs,y) ->
    if#(isEmpty(xs),isZero(head(xs)),y,tail(xs),cons(p(head(xs)),tail(xs)),inc(y))
    if#(false(),true(),y,xs,ys,x) -> sumList#(xs,y)
    if#(false(),false(),y,xs,ys,x) -> sumList#(ys,x)
    sum#(xs) -> sumList#(xs,0())
   TRS:
    isEmpty(cons(x,xs)) -> false()
    isEmpty(nil()) -> true()
    isZero(0()) -> true()
    isZero(s(x)) -> false()
    head(cons(x,xs)) -> x
    tail(cons(x,xs)) -> xs
    tail(nil()) -> nil()
    p(s(s(x))) -> s(p(s(x)))
    p(s(0())) -> 0()
    p(0()) -> 0()
    inc(s(x)) -> s(inc(x))
    inc(0()) -> s(0())
    sumList(xs,y) -> if(isEmpty(xs),isZero(head(xs)),y,tail(xs),cons(p(head(xs)),tail(xs)),inc(y))
    if(true(),b,y,xs,ys,x) -> y
    if(false(),true(),y,xs,ys,x) -> sumList(xs,y)
    if(false(),false(),y,xs,ys,x) -> sumList(ys,x)
    sum(xs) -> sumList(xs,0())
   graph:
    sum#(xs) -> sumList#(xs,0()) ->
    sumList#(xs,y) ->
    if#(isEmpty(xs),isZero(head(xs)),y,tail(xs),cons(p(head(xs)),tail(xs)),inc(y))
    sum#(xs) -> sumList#(xs,0()) -> sumList#(xs,y) -> isEmpty#(xs)
    sum#(xs) -> sumList#(xs,0()) -> sumList#(xs,y) -> isZero#(head(xs))
    sum#(xs) -> sumList#(xs,0()) -> sumList#(xs,y) -> head#(xs)

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