Tool CaT
stdout:
MAYBE
Problem:
b(b(b(x1))) -> a(x1)
a(a(x1)) -> a(b(a(x1)))
b(c(x1)) -> c(a(a(x1)))
a(c(x1)) -> c(b(b(x1)))
a(a(a(x1))) -> b(a(a(x1)))
Proof:
Complexity Transformation Processor:
strict:
b(b(b(x1))) -> a(x1)
a(a(x1)) -> a(b(a(x1)))
b(c(x1)) -> c(a(a(x1)))
a(c(x1)) -> c(b(b(x1)))
a(a(a(x1))) -> b(a(a(x1)))
weak:
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[c](x0) = x0 + 1,
[a](x0) = x0 + 5,
[b](x0) = x0 + 64
orientation:
b(b(b(x1))) = x1 + 192 >= x1 + 5 = a(x1)
a(a(x1)) = x1 + 10 >= x1 + 74 = a(b(a(x1)))
b(c(x1)) = x1 + 65 >= x1 + 11 = c(a(a(x1)))
a(c(x1)) = x1 + 6 >= x1 + 129 = c(b(b(x1)))
a(a(a(x1))) = x1 + 15 >= x1 + 74 = b(a(a(x1)))
problem:
strict:
a(a(x1)) -> a(b(a(x1)))
a(c(x1)) -> c(b(b(x1)))
a(a(a(x1))) -> b(a(a(x1)))
weak:
b(b(b(x1))) -> a(x1)
b(c(x1)) -> c(a(a(x1)))
Open
Tool IRC1
stdout:
MAYBE
Tool IRC2
stdout:
TIMEOUT
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: TIMEOUT
Input Problem: innermost runtime-complexity with respect to
Rules:
{ b(b(b(x1))) -> a(x1)
, a(a(x1)) -> a(b(a(x1)))
, b(c(x1)) -> c(a(a(x1)))
, a(c(x1)) -> c(b(b(x1)))
, a(a(a(x1))) -> b(a(a(x1)))}
Proof Output:
Computation stopped due to timeout after 60.0 secondsTool RC1
stdout:
MAYBE
Tool RC2
stdout:
TIMEOUT
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: TIMEOUT
Input Problem: runtime-complexity with respect to
Rules:
{ b(b(b(x1))) -> a(x1)
, a(a(x1)) -> a(b(a(x1)))
, b(c(x1)) -> c(a(a(x1)))
, a(c(x1)) -> c(b(b(x1)))
, a(a(a(x1))) -> b(a(a(x1)))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds