Problem Waldmann 07 size12 size-12-alpha-3-num-65

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Waldmann 07 size12 size-12-alpha-3-num-65

stdout:

MAYBE

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

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

  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [c](x0) = x0 + 64,

     [b](x0) = x0 + 16,

     [a](x0) = x0 + 64
    orientation:
     a(x1) = x1 + 64 >= x1 = x1

     a(a(x1)) = x1 + 128 >= x1 + 224 = a(b(c(a(b(x1)))))

     c(b(x1)) = x1 + 80 >= x1 + 128 = a(c(x1))
    problem:
     strict:
      a(a(x1)) -> a(b(c(a(b(x1)))))
      c(b(x1)) -> a(c(x1))
     weak:
      a(x1) -> x1
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [c](x0) = x0 + 192,

       [b](x0) = x0 + 1,

       [a](x0) = x0
      orientation:
       a(a(x1)) = x1 >= x1 + 194 = a(b(c(a(b(x1)))))

       c(b(x1)) = x1 + 193 >= x1 + 192 = a(c(x1))

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

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Waldmann 07 size12 size-12-alpha-3-num-65

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Waldmann 07 size12 size-12-alpha-3-num-65

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)) -> a(b(c(a(b(x1)))))
     , c(b(x1)) -> a(c(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-65

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Waldmann 07 size12 size-12-alpha-3-num-65

stdout:

TIMEOUT

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

Proof Output:
  Computation stopped due to timeout after 60.0 seconds