TRS Standard pair #516967849

details

property	value
status	complete
benchmark	list-sum-prod-bin.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n117.star.cs.uiowa.edu
space	CiME_04

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	1.35305404663 seconds
cpu usage	3.871698845
max memory	5.9828224E8

stage attributes

key	value
output-size	15068
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:
 0(#()) -> #()
 +(x,#()) -> x
 +(#(),x) -> x
 +(0(x),0(y)) -> 0(+(x,y))
 +(0(x),1(y)) -> 1(+(x,y))
 +(1(x),0(y)) -> 1(+(x,y))
 +(1(x),1(y)) -> 0(+(+(x,y),1(#())))
 *(#(),x) -> #()
 *(0(x),y) -> 0(*(x,y))
 *(1(x),y) -> +(0(*(x,y)),y)
 sum(nil()) -> 0(#())
 sum(cons(x,l)) -> +(x,sum(l))
 prod(nil()) -> 1(#())
 prod(cons(x,l)) -> *(x,prod(l))

Proof:
 DP Processor:
  DPs:
   +#(0(x),0(y)) -> +#(x,y)
   +#(0(x),0(y)) -> 0#(+(x,y))
   +#(0(x),1(y)) -> +#(x,y)
   +#(1(x),0(y)) -> +#(x,y)
   +#(1(x),1(y)) -> +#(x,y)
   +#(1(x),1(y)) -> +#(+(x,y),1(#()))
   +#(1(x),1(y)) -> 0#(+(+(x,y),1(#())))
   *#(0(x),y) -> *#(x,y)
   *#(0(x),y) -> 0#(*(x,y))
   *#(1(x),y) -> *#(x,y)
   *#(1(x),y) -> 0#(*(x,y))
   *#(1(x),y) -> +#(0(*(x,y)),y)
   sum#(nil()) -> 0#(#())
   sum#(cons(x,l)) -> sum#(l)
   sum#(cons(x,l)) -> +#(x,sum(l))
   prod#(cons(x,l)) -> prod#(l)
   prod#(cons(x,l)) -> *#(x,prod(l))
  TRS:
   0(#()) -> #()
   +(x,#()) -> x
   +(#(),x) -> x
   +(0(x),0(y)) -> 0(+(x,y))
   +(0(x),1(y)) -> 1(+(x,y))
   +(1(x),0(y)) -> 1(+(x,y))
   +(1(x),1(y)) -> 0(+(+(x,y),1(#())))
   *(#(),x) -> #()
   *(0(x),y) -> 0(*(x,y))
   *(1(x),y) -> +(0(*(x,y)),y)
   sum(nil()) -> 0(#())
   sum(cons(x,l)) -> +(x,sum(l))
   prod(nil()) -> 1(#())
   prod(cons(x,l)) -> *(x,prod(l))
  TDG Processor:
   DPs:
    +#(0(x),0(y)) -> +#(x,y)
    +#(0(x),0(y)) -> 0#(+(x,y))
    +#(0(x),1(y)) -> +#(x,y)
    +#(1(x),0(y)) -> +#(x,y)
    +#(1(x),1(y)) -> +#(x,y)
    +#(1(x),1(y)) -> +#(+(x,y),1(#()))
    +#(1(x),1(y)) -> 0#(+(+(x,y),1(#())))
    *#(0(x),y) -> *#(x,y)
    *#(0(x),y) -> 0#(*(x,y))
    *#(1(x),y) -> *#(x,y)
    *#(1(x),y) -> 0#(*(x,y))
    *#(1(x),y) -> +#(0(*(x,y)),y)
    sum#(nil()) -> 0#(#())
    sum#(cons(x,l)) -> sum#(l)
    sum#(cons(x,l)) -> +#(x,sum(l))
    prod#(cons(x,l)) -> prod#(l)
    prod#(cons(x,l)) -> *#(x,prod(l))
   TRS:
    0(#()) -> #()
    +(x,#()) -> x
    +(#(),x) -> x
    +(0(x),0(y)) -> 0(+(x,y))
    +(0(x),1(y)) -> 1(+(x,y))
    +(1(x),0(y)) -> 1(+(x,y))
    +(1(x),1(y)) -> 0(+(+(x,y),1(#())))
    *(#(),x) -> #()
    *(0(x),y) -> 0(*(x,y))
    *(1(x),y) -> +(0(*(x,y)),y)
    sum(nil()) -> 0(#())
    sum(cons(x,l)) -> +(x,sum(l))
    prod(nil()) -> 1(#())
    prod(cons(x,l)) -> *(x,prod(l))
   graph:
    prod#(cons(x,l)) -> prod#(l) -> prod#(cons(x,l)) -> *#(x,prod(l))
    prod#(cons(x,l)) -> prod#(l) -> prod#(cons(x,l)) -> prod#(l)
    prod#(cons(x,l)) -> *#(x,prod(l)) ->
    *#(1(x),y) -> +#(0(*(x,y)),y)
    prod#(cons(x,l)) -> *#(x,prod(l)) -> *#(1(x),y) -> 0#(*(x,y))
    prod#(cons(x,l)) -> *#(x,prod(l)) -> *#(1(x),y) -> *#(x,y)

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job log

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