* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
plus(0(),y) -> y
plus(s(x),y) -> s(plus(x,y))
quot(x,0(),s(z)) -> s(quot(x,plus(z,s(0())),s(z)))
quot(0(),s(y),s(z)) -> 0()
quot(s(x),s(y),z) -> quot(x,y,z)
- Signature:
{plus/2,quot/3} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {plus,quot} and constructors {0,s}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
plus(0(),y) -> y
plus(s(x),y) -> s(plus(x,y))
quot(x,0(),s(z)) -> s(quot(x,plus(z,s(0())),s(z)))
quot(0(),s(y),s(z)) -> 0()
quot(s(x),s(y),z) -> quot(x,y,z)
- Signature:
{plus/2,quot/3} / {0/0,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {plus,quot} and constructors {0,s}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
plus(x,y){x -> s(x)} =
plus(s(x),y) ->^+ s(plus(x,y))
= C[plus(x,y) = plus(x,y){}]
WORST_CASE(Omega(n^1),?)