* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
+ Considered Problem:
- Strict TRS:
eq0(0(),0()) -> S(0())
eq0(0(),S(x)) -> 0()
eq0(S(x),0()) -> 0()
eq0(S(x'),S(x)) -> eq0(x',x)
- Signature:
{eq0/2} / {0/0,S/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {eq0} and constructors {0,S}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
eq0(0(),0()) -> S(0())
eq0(0(),S(x)) -> 0()
eq0(S(x),0()) -> 0()
eq0(S(x'),S(x)) -> eq0(x',x)
- Signature:
{eq0/2} / {0/0,S/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {eq0} and constructors {0,S}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
eq0(x,y){x -> S(x),y -> S(y)} =
eq0(S(x),S(y)) ->^+ eq0(x,y)
= C[eq0(x,y) = eq0(x,y){}]
** Step 1.b:1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
eq0(0(),0()) -> S(0())
eq0(0(),S(x)) -> 0()
eq0(S(x),0()) -> 0()
eq0(S(x'),S(x)) -> eq0(x',x)
- Signature:
{eq0/2} / {0/0,S/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {eq0} and constructors {0,S}
+ Applied Processor:
Bounds {initialAutomaton = perSymbol, enrichment = match}
+ Details:
The problem is match-bounded by 1.
The enriched problem is compatible with follwoing automaton.
0_0() -> 1
0_1() -> 3
0_1() -> 4
S_0(1) -> 2
S_0(2) -> 2
S_1(4) -> 3
eq0_0(1,1) -> 3
eq0_0(1,2) -> 3
eq0_0(2,1) -> 3
eq0_0(2,2) -> 3
eq0_1(1,1) -> 3
eq0_1(1,2) -> 3
eq0_1(2,1) -> 3
eq0_1(2,2) -> 3
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
eq0(0(),0()) -> S(0())
eq0(0(),S(x)) -> 0()
eq0(S(x),0()) -> 0()
eq0(S(x'),S(x)) -> eq0(x',x)
- Signature:
{eq0/2} / {0/0,S/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {eq0} and constructors {0,S}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(Omega(n^1),O(n^1))