* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
+ Considered Problem:
- Strict TRS:
+(0(),y) -> y
+(s(x),y) -> s(+(x,y))
-(x,0()) -> x
-(0(),y) -> 0()
-(s(x),s(y)) -> -(x,y)
- Signature:
{+/2,-/2} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {+,-} 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:
+(0(),y) -> y
+(s(x),y) -> s(+(x,y))
-(x,0()) -> x
-(0(),y) -> 0()
-(s(x),s(y)) -> -(x,y)
- Signature:
{+/2,-/2} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {+,-} and constructors {0,s}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
+(x,y){x -> s(x)} =
+(s(x),y) ->^+ s(+(x,y))
= C[+(x,y) = +(x,y){}]
** Step 1.b:1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
+(0(),y) -> y
+(s(x),y) -> s(+(x,y))
-(x,0()) -> x
-(0(),y) -> 0()
-(s(x),s(y)) -> -(x,y)
- Signature:
{+/2,-/2} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {+,-} 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(2,2) -> 1
+_1(2,2) -> 3
-_0(2,2) -> 1
-_1(2,2) -> 1
0_0() -> 1
0_0() -> 2
0_0() -> 3
0_1() -> 1
s_0(2) -> 1
s_0(2) -> 2
s_0(2) -> 3
s_1(3) -> 1
s_1(3) -> 3
2 -> 1
2 -> 3
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
+(0(),y) -> y
+(s(x),y) -> s(+(x,y))
-(x,0()) -> x
-(0(),y) -> 0()
-(s(x),s(y)) -> -(x,y)
- Signature:
{+/2,-/2} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {+,-} 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))