Tool CaT
stdout:
MAYBE
Problem:
a() -> f(a())
f(f(f(x))) -> b()
g(f(f(x)),f(f(y))) -> f(g(x,y))
Proof:
Complexity Transformation Processor:
strict:
a() -> f(a())
f(f(f(x))) -> b()
g(f(f(x)),f(f(y))) -> f(g(x,y))
weak:
Bounds Processor:
bound: 0
enrichment: match
automaton:
final states: {4,3,2}
transitions:
a0() -> 2*
f0(7) -> 8*
f0(1) -> 3*
b0() -> 1*
g0(1,1) -> 4*
1 -> 8*
2 -> 7*
8 -> 2*
problem:
strict:
a() -> f(a())
f(f(f(x))) -> b()
weak:
g(f(f(x)),f(f(y))) -> f(g(x,y))
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[g](x0, x1) = x0 + x1 + 86,
[b] = 0,
[f](x0) = x0 + 4,
[a] = 4
orientation:
a() = 4 >= 8 = f(a())
f(f(f(x))) = x + 12 >= 0 = b()
g(f(f(x)),f(f(y))) = x + y + 102 >= x + y + 90 = f(g(x,y))
problem:
strict:
a() -> f(a())
weak:
f(f(f(x))) -> b()
g(f(f(x)),f(f(y))) -> f(g(x,y))
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:
{ a() -> f(a())
, f(f(f(x))) -> b()
, g(f(f(x)), f(f(y))) -> f(g(x, y))}
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:
{ a() -> f(a())
, f(f(f(x))) -> b()
, g(f(f(x)), f(f(y))) -> f(g(x, y))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds