Tool CaT
stdout:
MAYBE
Problem:
f(g(a())) -> a()
f(f(x)) -> b()
g(x) -> f(g(x))
Proof:
Complexity Transformation Processor:
strict:
f(g(a())) -> a()
f(f(x)) -> b()
g(x) -> f(g(x))
weak:
Bounds Processor:
bound: 1
enrichment: match
automaton:
final states: {4,3}
transitions:
f1(26) -> 27*
g1(25) -> 26*
g1(37) -> 38*
b1() -> 39*
a1() -> 15*
f0(5) -> 6*
f0(2) -> 3*
f0(1) -> 3*
g0(2) -> 4*
g0(1) -> 4*
a0() -> 1*
b0() -> 2*
1 -> 25*
2 -> 37,6
4 -> 5*
6 -> 4*
15 -> 27,6
27 -> 38,4
38 -> 26*
39 -> 27,6
problem:
strict:
f(f(x)) -> b()
g(x) -> f(g(x))
weak:
f(g(a())) -> a()
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[b] = 0,
[f](x0) = x0 + 1,
[g](x0) = x0 + 4,
[a] = 0
orientation:
f(f(x)) = x + 2 >= 0 = b()
g(x) = x + 4 >= x + 5 = f(g(x))
f(g(a())) = 5 >= 0 = a()
problem:
strict:
g(x) -> f(g(x))
weak:
f(f(x)) -> b()
f(g(a())) -> a()
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:
{ f(g(a())) -> a()
, f(f(x)) -> b()
, g(x) -> f(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:
{ f(g(a())) -> a()
, f(f(x)) -> b()
, g(x) -> f(g(x))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds