Problem Waldmann 07 size12 size-12-alpha-3-num-92

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Waldmann 07 size12 size-12-alpha-3-num-92

stdout:

MAYBE

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

Proof:
Complexity Transformation Processor:
  strict:
   a(x1) -> x1
   a(a(x1)) -> b(c(x1))
   a(b(b(x1))) -> b(b(a(a(x1))))
  weak:

  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [b](x0) = x0,

     [c](x0) = x0 + 8,

     [a](x0) = x0 + 1
    orientation:
     a(x1) = x1 + 1 >= x1 = x1

     a(a(x1)) = x1 + 2 >= x1 + 8 = b(c(x1))

     a(b(b(x1))) = x1 + 1 >= x1 + 2 = b(b(a(a(x1))))
    problem:
     strict:
      a(a(x1)) -> b(c(x1))
      a(b(b(x1))) -> b(b(a(a(x1))))
     weak:
      a(x1) -> x1
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [b](x0) = x0 + 3,

       [c](x0) = x0,

       [a](x0) = x0 + 2
      orientation:
       a(a(x1)) = x1 + 4 >= x1 + 3 = b(c(x1))

       a(b(b(x1))) = x1 + 8 >= x1 + 10 = b(b(a(a(x1))))

       a(x1) = x1 + 2 >= x1 = x1
      problem:
       strict:
        a(b(b(x1))) -> b(b(a(a(x1))))
       weak:
        a(a(x1)) -> b(c(x1))
        a(x1) -> x1
      Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Waldmann 07 size12 size-12-alpha-3-num-92

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Waldmann 07 size12 size-12-alpha-3-num-92

stdout:

TIMEOUT

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

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Waldmann 07 size12 size-12-alpha-3-num-92

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Waldmann 07 size12 size-12-alpha-3-num-92

stdout:

TIMEOUT

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

Proof Output:
  Computation stopped due to timeout after 60.0 seconds