Problem Zantema 06 15

Tool CaT

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 06 15

stdout:

YES(?,O(n^1))

Problem:
a(x1) -> b(x1)
a(a(x1)) -> a(b(a(x1)))
a(b(x1)) -> b(b(b(x1)))
a(a(a(x1))) -> a(a(b(a(a(x1)))))
a(a(b(x1))) -> a(b(b(a(b(x1)))))
a(b(a(x1))) -> b(a(b(b(a(x1)))))
a(b(b(x1))) -> b(b(b(b(b(x1)))))
a(a(a(a(x1)))) -> a(a(a(b(a(a(a(x1)))))))
a(a(a(b(x1)))) -> a(a(b(b(a(a(b(x1)))))))
a(a(b(a(x1)))) -> a(b(a(b(a(b(a(x1)))))))
a(a(b(b(x1)))) -> a(b(b(b(a(b(b(x1)))))))
a(b(a(a(x1)))) -> b(a(a(b(b(a(a(x1)))))))
a(b(a(b(x1)))) -> b(a(b(b(b(a(b(x1)))))))
a(b(b(a(x1)))) -> b(b(a(b(b(b(a(x1)))))))
a(b(b(b(x1)))) -> b(b(b(b(b(b(b(x1)))))))

Proof:
Bounds Processor:
  bound: 1
  enrichment: match
  automaton:
   final states: {2}
   transitions:
    b1(5) -> 6*
    b1(7) -> 8*
    a0(1) -> 2*
    b0(1) -> 1*
    1 -> 5*
    6 -> 7,2
    8 -> 5*
  problem:

  Qed

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 06 15

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Zantema 06 15

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  a(x1) -> b(x1)
     , a(a(x1)) -> a(b(a(x1)))
     , a(b(x1)) -> b(b(b(x1)))
     , a(a(a(x1))) -> a(a(b(a(a(x1)))))
     , a(a(b(x1))) -> a(b(b(a(b(x1)))))
     , a(b(a(x1))) -> b(a(b(b(a(x1)))))
     , a(b(b(x1))) -> b(b(b(b(b(x1)))))
     , a(a(a(a(x1)))) -> a(a(a(b(a(a(a(x1)))))))
     , a(a(a(b(x1)))) -> a(a(b(b(a(a(b(x1)))))))
     , a(a(b(a(x1)))) -> a(b(a(b(a(b(a(x1)))))))
     , a(a(b(b(x1)))) -> a(b(b(b(a(b(b(x1)))))))
     , a(b(a(a(x1)))) -> b(a(a(b(b(a(a(x1)))))))
     , a(b(a(b(x1)))) -> b(a(b(b(b(a(b(x1)))))))
     , a(b(b(a(x1)))) -> b(b(a(b(b(b(a(x1)))))))
     , a(b(b(b(x1)))) -> b(b(b(b(b(b(b(x1)))))))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Zantema 06 15

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Zantema 06 15

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  a(x1) -> b(x1)
     , a(a(x1)) -> a(b(a(x1)))
     , a(b(x1)) -> b(b(b(x1)))
     , a(a(a(x1))) -> a(a(b(a(a(x1)))))
     , a(a(b(x1))) -> a(b(b(a(b(x1)))))
     , a(b(a(x1))) -> b(a(b(b(a(x1)))))
     , a(b(b(x1))) -> b(b(b(b(b(x1)))))
     , a(a(a(a(x1)))) -> a(a(a(b(a(a(a(x1)))))))
     , a(a(a(b(x1)))) -> a(a(b(b(a(a(b(x1)))))))
     , a(a(b(a(x1)))) -> a(b(a(b(a(b(a(x1)))))))
     , a(a(b(b(x1)))) -> a(b(b(b(a(b(b(x1)))))))
     , a(b(a(a(x1)))) -> b(a(a(b(b(a(a(x1)))))))
     , a(b(a(b(x1)))) -> b(a(b(b(b(a(b(x1)))))))
     , a(b(b(a(x1)))) -> b(b(a(b(b(b(a(x1)))))))
     , a(b(b(b(x1)))) -> b(b(b(b(b(b(b(x1)))))))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds