* Step 1: ToInnermost WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
f(0()) -> s(0())
f(s(x)) -> s(s(g(x)))
g(0()) -> 0()
g(s(x)) -> f(x)
- Signature:
{f/1,g/1} / {0/0,s/1}
- Obligation:
runtime complexity wrt. defined symbols {f,g} and constructors {0,s}
+ Applied Processor:
ToInnermost
+ Details:
switch to innermost, as the system is overlay and right linear and does not contain weak rules
* Step 2: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
f(0()) -> s(0())
f(s(x)) -> s(s(g(x)))
g(0()) -> 0()
g(s(x)) -> f(x)
- Signature:
{f/1,g/1} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,s}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 1.
The enriched problem is compatible with follwoing automaton.
0_0() -> 2
0_1() -> 1
0_1() -> 3
0_1() -> 4
f_0(2) -> 1
f_1(2) -> 1
f_1(2) -> 4
g_0(2) -> 1
g_1(2) -> 4
s_0(2) -> 2
s_1(3) -> 1
s_1(4) -> 3
s_1(4) -> 4
* Step 3: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
f(0()) -> s(0())
f(s(x)) -> s(s(g(x)))
g(0()) -> 0()
g(s(x)) -> f(x)
- Signature:
{f/1,g/1} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,s}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(?,O(n^1))