Tool CaT
stdout:
MAYBE
Problem:
b(f(f(f(x)))) -> x
b(u(x)) -> b(f(x))
f(g(x)) -> f(f(x))
f(b(x)) -> u(g(b(x)))
f(u(x)) -> u(g(x))
Proof:
Complexity Transformation Processor:
strict:
b(f(f(f(x)))) -> x
b(u(x)) -> b(f(x))
f(g(x)) -> f(f(x))
f(b(x)) -> u(g(b(x)))
f(u(x)) -> u(g(x))
weak:
Bounds Processor:
bound: 0
enrichment: match
automaton:
final states: {4,3}
transitions:
b0(2) -> 3*
b0(11) -> 12*
b0(1) -> 3*
u0(2) -> 1*
u0(1) -> 1*
f0(2) -> 4*
f0(1) -> 4*
f0(18) -> 19*
g0(2) -> 2*
g0(1) -> 2*
1 -> 12,19,4
2 -> 12*
4 -> 18,11
12 -> 3*
18 -> 12*
19 -> 4*
problem:
strict:
b(u(x)) -> b(f(x))
f(g(x)) -> f(f(x))
f(u(x)) -> u(g(x))
b(f(f(f(x)))) -> x
weak:
f(b(x)) -> u(g(b(x)))
Arctic Interpretation Processor:
dimension: 1
interpretation:
[g](x0) = x0,
[u](x0) = x0,
[b](x0) = 1x0,
[f](x0) = x0
orientation:
b(u(x)) = 1x >= 1x = b(f(x))
f(g(x)) = x >= x = f(f(x))
f(u(x)) = x >= x = u(g(x))
b(f(f(f(x)))) = 1x >= x = x
f(b(x)) = 1x >= 1x = u(g(b(x)))
problem:
strict:
b(u(x)) -> b(f(x))
f(g(x)) -> f(f(x))
f(u(x)) -> u(g(x))
weak:
b(f(f(f(x)))) -> x
f(b(x)) -> u(g(b(x)))
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[g](x0) = x0 + 2,
[u](x0) = x0,
[b](x0) = x0 + 2,
[f](x0) = x0 + 4
orientation:
b(u(x)) = x + 2 >= x + 6 = b(f(x))
f(g(x)) = x + 6 >= x + 8 = f(f(x))
f(u(x)) = x + 4 >= x + 2 = u(g(x))
b(f(f(f(x)))) = x + 14 >= x = x
f(b(x)) = x + 6 >= x + 4 = u(g(b(x)))
problem:
strict:
b(u(x)) -> b(f(x))
f(g(x)) -> f(f(x))
weak:
f(u(x)) -> u(g(x))
b(f(f(f(x)))) -> x
f(b(x)) -> u(g(b(x)))
Open
Tool IRC1
stdout:
MAYBE
Warning when parsing problem:
Unsupported strategy 'OUTERMOST'Tool IRC2
stdout:
TIMEOUT
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: TIMEOUT
Input Problem: innermost runtime-complexity with respect to
Rules:
{ b(f(f(f(x)))) -> x
, b(u(x)) -> b(f(x))
, f(g(x)) -> f(f(x))
, f(b(x)) -> u(g(b(x)))
, f(u(x)) -> u(g(x))}
Proof Output:
Computation stopped due to timeout after 60.0 secondsTool RC1
stdout:
MAYBE
Warning when parsing problem:
Unsupported strategy 'OUTERMOST'Tool RC2
stdout:
TIMEOUT
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: TIMEOUT
Input Problem: runtime-complexity with respect to
Rules:
{ b(f(f(f(x)))) -> x
, b(u(x)) -> b(f(x))
, f(g(x)) -> f(f(x))
, f(b(x)) -> u(g(b(x)))
, f(u(x)) -> u(g(x))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds