TRS Standard pair #615305030

details

property	value
status	complete
benchmark	2.19.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n045.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.485147953033 seconds
cpu usage	0.822191763
max memory	1.7463296E8

stage attributes

key	value
output-size	3749
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:
 sqr(0()) -> 0()
 sqr(s(x)) -> +(sqr(x),s(double(x)))
 double(0()) -> 0()
 double(s(x)) -> s(s(double(x)))
 +(x,0()) -> x
 +(x,s(y)) -> s(+(x,y))
 sqr(s(x)) -> s(+(sqr(x),double(x)))

Proof:
 DP Processor:
  DPs:
   sqr#(s(x)) -> double#(x)
   sqr#(s(x)) -> sqr#(x)
   sqr#(s(x)) -> +#(sqr(x),s(double(x)))
   double#(s(x)) -> double#(x)
   +#(x,s(y)) -> +#(x,y)
   sqr#(s(x)) -> +#(sqr(x),double(x))
  TRS:
   sqr(0()) -> 0()
   sqr(s(x)) -> +(sqr(x),s(double(x)))
   double(0()) -> 0()
   double(s(x)) -> s(s(double(x)))
   +(x,0()) -> x
   +(x,s(y)) -> s(+(x,y))
   sqr(s(x)) -> s(+(sqr(x),double(x)))
  TDG Processor:
   DPs:
    sqr#(s(x)) -> double#(x)
    sqr#(s(x)) -> sqr#(x)
    sqr#(s(x)) -> +#(sqr(x),s(double(x)))
    double#(s(x)) -> double#(x)
    +#(x,s(y)) -> +#(x,y)
    sqr#(s(x)) -> +#(sqr(x),double(x))
   TRS:
    sqr(0()) -> 0()
    sqr(s(x)) -> +(sqr(x),s(double(x)))
    double(0()) -> 0()
    double(s(x)) -> s(s(double(x)))
    +(x,0()) -> x
    +(x,s(y)) -> s(+(x,y))
    sqr(s(x)) -> s(+(sqr(x),double(x)))
   graph:
    +#(x,s(y)) -> +#(x,y) -> +#(x,s(y)) -> +#(x,y)
    double#(s(x)) -> double#(x) -> double#(s(x)) -> double#(x)
    sqr#(s(x)) -> +#(sqr(x),double(x)) ->
    +#(x,s(y)) -> +#(x,y)
    sqr#(s(x)) -> +#(sqr(x),s(double(x))) -> +#(x,s(y)) -> +#(x,y)
    sqr#(s(x)) -> double#(x) -> double#(s(x)) -> double#(x)
    sqr#(s(x)) -> sqr#(x) -> sqr#(s(x)) -> +#(sqr(x),double(x))
    sqr#(s(x)) -> sqr#(x) -> sqr#(s(x)) -> +#(sqr(x),s(double(x)))
    sqr#(s(x)) -> sqr#(x) -> sqr#(s(x)) -> sqr#(x)
    sqr#(s(x)) -> sqr#(x) -> sqr#(s(x)) -> double#(x)
   SCC Processor:
    #sccs: 3
    #rules: 3
    #arcs: 9/36
    DPs:
     sqr#(s(x)) -> sqr#(x)
    TRS:
     sqr(0()) -> 0()
     sqr(s(x)) -> +(sqr(x),s(double(x)))
     double(0()) -> 0()
     double(s(x)) -> s(s(double(x)))
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
     sqr(s(x)) -> s(+(sqr(x),double(x)))
    Subterm Criterion Processor:
     simple projection:
      pi(sqr#) = 0
     problem:
      DPs:
       
      TRS:
       sqr(0()) -> 0()
       sqr(s(x)) -> +(sqr(x),s(double(x)))
       double(0()) -> 0()
       double(s(x)) -> s(s(double(x)))
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
       sqr(s(x)) -> s(+(sqr(x),double(x)))
     Qed
    
    DPs:
     double#(s(x)) -> double#(x)
    TRS:
     sqr(0()) -> 0()
     sqr(s(x)) -> +(sqr(x),s(double(x)))
     double(0()) -> 0()
     double(s(x)) -> s(s(double(x)))
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to TRS Standard