* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
h(f(x,y)) -> f(y,f(h(h(x)),a()))
- Signature:
{h/1} / {a/0,f/2}
- Obligation:
innermost runtime complexity wrt. defined symbols {h} and constructors {a,f}
+ Applied Processor:
Bounds {initialAutomaton = perSymbol, enrichment = match}
+ Details:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
a_0() -> 1
a_1() -> 6
a_2() -> 10
f_0(1,1) -> 2
f_0(1,2) -> 2
f_0(2,1) -> 2
f_0(2,2) -> 2
f_1(1,4) -> 3
f_1(1,4) -> 7
f_1(1,4) -> 11
f_1(2,4) -> 3
f_1(2,4) -> 7
f_1(2,4) -> 11
f_1(5,6) -> 4
f_2(4,8) -> 5
f_2(4,8) -> 9
f_2(9,10) -> 8
h_0(1) -> 3
h_0(2) -> 3
h_1(1) -> 7
h_1(2) -> 7
h_1(7) -> 5
h_2(1) -> 11
h_2(2) -> 11
h_2(11) -> 9
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
h(f(x,y)) -> f(y,f(h(h(x)),a()))
- Signature:
{h/1} / {a/0,f/2}
- Obligation:
innermost runtime complexity wrt. defined symbols {h} and constructors {a,f}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(?,O(n^1))