Tool CaT
stdout:
MAYBE
Problem:
f(0(x1)) -> s(0(x1))
d(0(x1)) -> 0(x1)
d(s(x1)) -> s(s(d(x1)))
f(s(x1)) -> d(f(x1))
Proof:
Complexity Transformation Processor:
strict:
f(0(x1)) -> s(0(x1))
d(0(x1)) -> 0(x1)
d(s(x1)) -> s(s(d(x1)))
f(s(x1)) -> d(f(x1))
weak:
Arctic Interpretation Processor:
dimension: 1
interpretation:
[d](x0) = x0,
[s](x0) = x0,
[f](x0) = 2x0,
[0](x0) = x0
orientation:
f(0(x1)) = 2x1 >= x1 = s(0(x1))
d(0(x1)) = x1 >= x1 = 0(x1)
d(s(x1)) = x1 >= x1 = s(s(d(x1)))
f(s(x1)) = 2x1 >= 2x1 = d(f(x1))
problem:
strict:
d(0(x1)) -> 0(x1)
d(s(x1)) -> s(s(d(x1)))
f(s(x1)) -> d(f(x1))
weak:
f(0(x1)) -> s(0(x1))
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[d](x0) = x0 + 75,
[s](x0) = x0 + 131,
[f](x0) = x0 + 131,
[0](x0) = x0 + 20
orientation:
d(0(x1)) = x1 + 95 >= x1 + 20 = 0(x1)
d(s(x1)) = x1 + 206 >= x1 + 337 = s(s(d(x1)))
f(s(x1)) = x1 + 262 >= x1 + 206 = d(f(x1))
f(0(x1)) = x1 + 151 >= x1 + 151 = s(0(x1))
problem:
strict:
d(s(x1)) -> s(s(d(x1)))
weak:
d(0(x1)) -> 0(x1)
f(s(x1)) -> d(f(x1))
f(0(x1)) -> s(0(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:
{ f(0(x1)) -> s(0(x1))
, d(0(x1)) -> 0(x1)
, d(s(x1)) -> s(s(d(x1)))
, f(s(x1)) -> d(f(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:
{ f(0(x1)) -> s(0(x1))
, d(0(x1)) -> 0(x1)
, d(s(x1)) -> s(s(d(x1)))
, f(s(x1)) -> d(f(x1))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds