Tool CaT
stdout:
MAYBE
Problem:
a() -> f(a())
f(f(x)) -> b()
0(f(x)) -> 1(x)
1(f(x)) -> 2(x)
2(f(x)) -> f(0(x))
Proof:
Complexity Transformation Processor:
strict:
a() -> f(a())
f(f(x)) -> b()
0(f(x)) -> 1(x)
1(f(x)) -> 2(x)
2(f(x)) -> f(0(x))
weak:
Bounds Processor:
bound: 0
enrichment: match
automaton:
final states: {6,5,4,3,2}
transitions:
a0() -> 2*
f0(15) -> 16*
f0(1) -> 3*
b0() -> 1*
00(1) -> 4*
10(1) -> 5*
20(1) -> 6*
1 -> 16*
2 -> 15*
16 -> 2*
problem:
strict:
a() -> f(a())
f(f(x)) -> b()
0(f(x)) -> 1(x)
1(f(x)) -> 2(x)
weak:
2(f(x)) -> f(0(x))
Bounds Processor:
bound: 0
enrichment: match
automaton:
final states: {6,5,4,3,2}
transitions:
a0() -> 2*
f0(1) -> 3*
f0(13) -> 14*
b0() -> 1*
00(1) -> 4*
10(1) -> 5*
20(1) -> 6*
1 -> 14*
2 -> 13*
14 -> 2*
problem:
strict:
a() -> f(a())
f(f(x)) -> b()
0(f(x)) -> 1(x)
weak:
1(f(x)) -> 2(x)
2(f(x)) -> f(0(x))
Bounds Processor:
bound: 0
enrichment: match
automaton:
final states: {6,5,4,3,2}
transitions:
a0() -> 2*
f0(11) -> 12*
f0(1) -> 3*
b0() -> 1*
00(1) -> 4*
10(1) -> 5*
20(1) -> 6*
1 -> 12*
2 -> 11*
12 -> 2*
problem:
strict:
a() -> f(a())
f(f(x)) -> b()
weak:
0(f(x)) -> 1(x)
1(f(x)) -> 2(x)
2(f(x)) -> f(0(x))
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[2](x0) = x0 + 184,
[1](x0) = x0 + 42,
[0](x0) = x0 + 162,
[b] = 0,
[f](x0) = x0 + 154,
[a] = 17
orientation:
a() = 17 >= 171 = f(a())
f(f(x)) = x + 308 >= 0 = b()
0(f(x)) = x + 316 >= x + 42 = 1(x)
1(f(x)) = x + 196 >= x + 184 = 2(x)
2(f(x)) = x + 338 >= x + 316 = f(0(x))
problem:
strict:
a() -> f(a())
weak:
f(f(x)) -> b()
0(f(x)) -> 1(x)
1(f(x)) -> 2(x)
2(f(x)) -> f(0(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:
{ a() -> f(a())
, f(f(x)) -> b()
, 0(f(x)) -> 1(x)
, 1(f(x)) -> 2(x)
, 2(f(x)) -> f(0(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:
{ a() -> f(a())
, f(f(x)) -> b()
, 0(f(x)) -> 1(x)
, 1(f(x)) -> 2(x)
, 2(f(x)) -> f(0(x))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds