TRS Standard pair #487067767

details

property	value
status	complete
benchmark	2.22.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n192.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.467388 seconds
cpu usage	0.753547
user time	0.580892
system time	0.172655
max virtual memory	96176.0
max residence set size	60268.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 exp(x,0()) -> s(0())
 exp(x,s(y)) -> *(x,exp(x,y))
 *(0(),y) -> 0()
 *(s(x),y) -> +(y,*(x,y))
 -(0(),y) -> 0()
 -(x,0()) -> x
 -(s(x),s(y)) -> -(x,y)

Proof:
 DP Processor:
  DPs:
   exp#(x,s(y)) -> exp#(x,y)
   exp#(x,s(y)) -> *#(x,exp(x,y))
   *#(s(x),y) -> *#(x,y)
   -#(s(x),s(y)) -> -#(x,y)
  TRS:
   exp(x,0()) -> s(0())
   exp(x,s(y)) -> *(x,exp(x,y))
   *(0(),y) -> 0()
   *(s(x),y) -> +(y,*(x,y))
   -(0(),y) -> 0()
   -(x,0()) -> x
   -(s(x),s(y)) -> -(x,y)
  TDG Processor:
   DPs:
    exp#(x,s(y)) -> exp#(x,y)
    exp#(x,s(y)) -> *#(x,exp(x,y))
    *#(s(x),y) -> *#(x,y)
    -#(s(x),s(y)) -> -#(x,y)
   TRS:
    exp(x,0()) -> s(0())
    exp(x,s(y)) -> *(x,exp(x,y))
    *(0(),y) -> 0()
    *(s(x),y) -> +(y,*(x,y))
    -(0(),y) -> 0()
    -(x,0()) -> x
    -(s(x),s(y)) -> -(x,y)
   graph:
    -#(s(x),s(y)) -> -#(x,y) -> -#(s(x),s(y)) -> -#(x,y)
    *#(s(x),y) -> *#(x,y) -> *#(s(x),y) -> *#(x,y)
    exp#(x,s(y)) -> *#(x,exp(x,y)) -> *#(s(x),y) -> *#(x,y)
    exp#(x,s(y)) -> exp#(x,y) -> exp#(x,s(y)) -> *#(x,exp(x,y))
    exp#(x,s(y)) -> exp#(x,y) -> exp#(x,s(y)) -> exp#(x,y)
   SCC Processor:
    #sccs: 3
    #rules: 3
    #arcs: 5/16
    DPs:
     exp#(x,s(y)) -> exp#(x,y)
    TRS:
     exp(x,0()) -> s(0())
     exp(x,s(y)) -> *(x,exp(x,y))
     *(0(),y) -> 0()
     *(s(x),y) -> +(y,*(x,y))
     -(0(),y) -> 0()
     -(x,0()) -> x
     -(s(x),s(y)) -> -(x,y)
    Subterm Criterion Processor:
     simple projection:
      pi(exp#) = 1
     problem:
      DPs:
       
      TRS:
       exp(x,0()) -> s(0())
       exp(x,s(y)) -> *(x,exp(x,y))
       *(0(),y) -> 0()
       *(s(x),y) -> +(y,*(x,y))
       -(0(),y) -> 0()
       -(x,0()) -> x
       -(s(x),s(y)) -> -(x,y)
     Qed
    
    DPs:
     *#(s(x),y) -> *#(x,y)
    TRS:
     exp(x,0()) -> s(0())
     exp(x,s(y)) -> *(x,exp(x,y))
     *(0(),y) -> 0()
     *(s(x),y) -> +(y,*(x,y))
     -(0(),y) -> 0()
     -(x,0()) -> x
     -(s(x),s(y)) -> -(x,y)
    Subterm Criterion Processor:
     simple projection:
      pi(*#) = 0
     problem:
      DPs:
       
      TRS:
       exp(x,0()) -> s(0())
       exp(x,s(y)) -> *(x,exp(x,y))
       *(0(),y) -> 0()
       *(s(x),y) -> +(y,*(x,y))
       -(0(),y) -> 0()
       -(x,0()) -> x
       -(s(x),s(y)) -> -(x,y)

popout

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

job log

popout

actions all output return to TRS Standard