* Step 1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
f(+(x,y)) -> *(f(x),f(y))
f(+(x,s(0()))) -> +(s(s(0())),f(x))
f(0()) -> s(0())
f(s(0())) -> *(s(s(0())),f(0()))
f(s(0())) -> s(s(0()))
- Signature:
{f/1} / {*/2,+/2,0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f} and constructors {*,+,0,s}
+ Applied Processor:
Bounds {initialAutomaton = minimal, enrichment = match}
+ Details:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
*_0(2,2) -> 2
*_1(3,4) -> 1
*_1(4,4) -> 3
*_1(4,4) -> 4
*_1(5,8) -> 1
*_1(5,8) -> 3
*_1(5,8) -> 4
+_0(2,2) -> 2
+_1(5,4) -> 1
+_1(5,4) -> 3
+_1(5,4) -> 4
0_0() -> 2
0_1() -> 7
0_2() -> 9
f_0(2) -> 1
f_1(2) -> 3
f_1(2) -> 4
f_1(7) -> 8
s_0(2) -> 2
s_1(6) -> 1
s_1(6) -> 3
s_1(6) -> 4
s_1(6) -> 5
s_1(7) -> 1
s_1(7) -> 3
s_1(7) -> 4
s_1(7) -> 6
s_2(9) -> 8
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
f(+(x,y)) -> *(f(x),f(y))
f(+(x,s(0()))) -> +(s(s(0())),f(x))
f(0()) -> s(0())
f(s(0())) -> *(s(s(0())),f(0()))
f(s(0())) -> s(s(0()))
- Signature:
{f/1} / {*/2,+/2,0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f} and constructors {*,+,0,s}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))