TRS Standard pair #487067932

details

property	value
status	complete
benchmark	2.16.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n187.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.506118 seconds
cpu usage	0.869862
user time	0.663412
system time	0.20645
max virtual memory	96176.0
max residence set size	61356.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 f(0()) -> 1()
 f(s(x)) -> g(x,s(x))
 g(0(),y) -> y
 g(s(x),y) -> g(x,+(y,s(x)))
 +(x,0()) -> x
 +(x,s(y)) -> s(+(x,y))
 g(s(x),y) -> g(x,s(+(y,x)))

Proof:
 DP Processor:
  DPs:
   f#(s(x)) -> g#(x,s(x))
   g#(s(x),y) -> +#(y,s(x))
   g#(s(x),y) -> g#(x,+(y,s(x)))
   +#(x,s(y)) -> +#(x,y)
   g#(s(x),y) -> +#(y,x)
   g#(s(x),y) -> g#(x,s(+(y,x)))
  TRS:
   f(0()) -> 1()
   f(s(x)) -> g(x,s(x))
   g(0(),y) -> y
   g(s(x),y) -> g(x,+(y,s(x)))
   +(x,0()) -> x
   +(x,s(y)) -> s(+(x,y))
   g(s(x),y) -> g(x,s(+(y,x)))
  TDG Processor:
   DPs:
    f#(s(x)) -> g#(x,s(x))
    g#(s(x),y) -> +#(y,s(x))
    g#(s(x),y) -> g#(x,+(y,s(x)))
    +#(x,s(y)) -> +#(x,y)
    g#(s(x),y) -> +#(y,x)
    g#(s(x),y) -> g#(x,s(+(y,x)))
   TRS:
    f(0()) -> 1()
    f(s(x)) -> g(x,s(x))
    g(0(),y) -> y
    g(s(x),y) -> g(x,+(y,s(x)))
    +(x,0()) -> x
    +(x,s(y)) -> s(+(x,y))
    g(s(x),y) -> g(x,s(+(y,x)))
   graph:
    +#(x,s(y)) -> +#(x,y) -> +#(x,s(y)) -> +#(x,y)
    g#(s(x),y) -> +#(y,s(x)) -> +#(x,s(y)) -> +#(x,y)
    g#(s(x),y) -> +#(y,x) -> +#(x,s(y)) -> +#(x,y)
    g#(s(x),y) -> g#(x,+(y,s(x))) -> g#(s(x),y) -> g#(x,s(+(y,x)))
    g#(s(x),y) -> g#(x,+(y,s(x))) -> g#(s(x),y) -> +#(y,x)
    g#(s(x),y) -> g#(x,+(y,s(x))) -> g#(s(x),y) -> g#(x,+(y,s(x)))
    g#(s(x),y) -> g#(x,+(y,s(x))) -> g#(s(x),y) -> +#(y,s(x))
    g#(s(x),y) -> g#(x,s(+(y,x))) -> g#(s(x),y) -> g#(x,s(+(y,x)))
    g#(s(x),y) -> g#(x,s(+(y,x))) -> g#(s(x),y) -> +#(y,x)
    g#(s(x),y) -> g#(x,s(+(y,x))) -> g#(s(x),y) -> g#(x,+(y,s(x)))
    g#(s(x),y) -> g#(x,s(+(y,x))) -> g#(s(x),y) -> +#(y,s(x))
    f#(s(x)) -> g#(x,s(x)) -> g#(s(x),y) -> g#(x,s(+(y,x)))
    f#(s(x)) -> g#(x,s(x)) -> g#(s(x),y) -> +#(y,x)
    f#(s(x)) -> g#(x,s(x)) -> g#(s(x),y) -> g#(x,+(y,s(x)))
    f#(s(x)) -> g#(x,s(x)) -> g#(s(x),y) -> +#(y,s(x))
   SCC Processor:
    #sccs: 2
    #rules: 3
    #arcs: 15/36
    DPs:
     g#(s(x),y) -> g#(x,+(y,s(x)))
     g#(s(x),y) -> g#(x,s(+(y,x)))
    TRS:
     f(0()) -> 1()
     f(s(x)) -> g(x,s(x))
     g(0(),y) -> y
     g(s(x),y) -> g(x,+(y,s(x)))
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
     g(s(x),y) -> g(x,s(+(y,x)))
    Subterm Criterion Processor:
     simple projection:
      pi(g#) = 0
     problem:
      DPs:
       
      TRS:
       f(0()) -> 1()
       f(s(x)) -> g(x,s(x))
       g(0(),y) -> y
       g(s(x),y) -> g(x,+(y,s(x)))
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
       g(s(x),y) -> g(x,s(+(y,x)))
     Qed
    
    DPs:
     +#(x,s(y)) -> +#(x,y)
    TRS:
     f(0()) -> 1()
     f(s(x)) -> g(x,s(x))
     g(0(),y) -> y
     g(s(x),y) -> g(x,+(y,s(x)))
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))

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