TRS Standard pair #487067867

details

property	value
status	complete
benchmark	2.24.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n180.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.385982 seconds
cpu usage	0.538231
user time	0.418881
system time	0.11935
max virtual memory	96176.0
max residence set size	56876.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 fib(0()) -> 0()
 fib(s(0())) -> s(0())
 fib(s(s(x))) -> +(fib(s(x)),fib(x))

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [fib](x0) = x0,
   
   [+](x0, x1) = x0 + 2x1 + 1,
   
   [0] = 0,
   
   [s](x0) = 2x0 + 1
  orientation:
   fib(0()) = 0 >= 0 = 0()
   
   fib(s(0())) = 1 >= 1 = s(0())
   
   fib(s(s(x))) = 4x + 3 >= 4x + 2 = +(fib(s(x)),fib(x))
  problem:
   fib(0()) -> 0()
   fib(s(0())) -> s(0())
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                [1 0 0]     [1]
    [fib](x0) = [0 0 0]x0 + [1]
                [0 0 0]     [0],
    
          [0]
    [0] = [1]
          [0],
    
              [1 0 0]  
    [s](x0) = [0 1 0]x0
              [0 0 0]  
   orientation:
               [1]    [0]      
    fib(0()) = [1] >= [1] = 0()
               [0]    [0]      
    
                  [1]    [0]         
    fib(s(0())) = [1] >= [1] = s(0())
                  [0]    [0]         
   problem:
    
   Qed

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