Problem Zantema 08 ex5

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Zantema 08 ex5

stdout:

MAYBE

Problem:
f(x,f(y,z)) -> f(f(x,y),z)
f(x,y) -> s(f(y,x))
s(s(x)) -> c()

Proof:
Complexity Transformation Processor:
  strict:
   f(x,f(y,z)) -> f(f(x,y),z)
   f(x,y) -> s(f(y,x))
   s(s(x)) -> c()
  weak:

  Bounds Processor:
   bound: 0
   enrichment: match
   automaton:
    final states: {3,2}
    transitions:
     f0(1,1) -> 2*
     s0(2) -> 2*
     s0(1) -> 3*
     c0() -> 2,1
   problem:
    strict:
     f(x,y) -> s(f(y,x))
     s(s(x)) -> c()
    weak:
     f(x,f(y,z)) -> f(f(x,y),z)
   Matrix Interpretation Processor:
    dimension: 1
    max_matrix:
     1
     interpretation:
      [c] = 0,

      [s](x0) = x0 + 195,

      [f](x0, x1) = x0 + x1 + 1
     orientation:
      f(x,y) = x + y + 1 >= x + y + 196 = s(f(y,x))

      s(s(x)) = x + 390 >= 0 = c()

      f(x,f(y,z)) = x + y + z + 2 >= x + y + z + 2 = f(f(x,y),z)
     problem:
      strict:
       f(x,y) -> s(f(y,x))
      weak:
       s(s(x)) -> c()
       f(x,f(y,z)) -> f(f(x,y),z)
     Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Zantema 08 ex5

stdout:

MAYBE
Warning when parsing problem:

Unsupported strategy 'OUTERMOST'

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Zantema 08 ex5

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  f(x, f(y, z)) -> f(f(x, y), z)
     , f(x, y) -> s(f(y, x))
     , s(s(x)) -> c()}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Zantema 08 ex5

stdout:

MAYBE
Warning when parsing problem:

Unsupported strategy 'OUTERMOST'

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Zantema 08 ex5

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  f(x, f(y, z)) -> f(f(x, y), z)
     , f(x, y) -> s(f(y, x))
     , s(s(x)) -> c()}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds