* Step 1: Sum WORST_CASE(Omega(n^1),O(n^1))
+ Considered Problem:
- Strict TRS:
f(c(X,s(Y))) -> f(c(s(X),Y))
g(c(s(X),Y)) -> f(c(X,s(Y)))
- Signature:
{f/1,g/1} / {c/2,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
f(c(X,s(Y))) -> f(c(s(X),Y))
g(c(s(X),Y)) -> f(c(X,s(Y)))
- Signature:
{f/1,g/1} / {c/2,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
f(c(x,y)){y -> s(y)} =
f(c(x,s(y))) ->^+ f(c(s(x),y))
= C[f(c(s(x),y)) = f(c(x,y)){x -> s(x)}]
** Step 1.b:1: Bounds WORST_CASE(?,O(n^1))
+ Considered Problem:
- Strict TRS:
f(c(X,s(Y))) -> f(c(s(X),Y))
g(c(s(X),Y)) -> f(c(X,s(Y)))
- Signature:
{f/1,g/1} / {c/2,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s}
+ Applied Processor:
Bounds {initialAutomaton = perSymbol, enrichment = match}
+ Details:
The problem is match-bounded by 2.
The enriched problem is compatible with follwoing automaton.
c_0(1,1) -> 1
c_0(1,4) -> 1
c_0(4,1) -> 1
c_0(4,4) -> 1
c_1(1,6) -> 7
c_1(4,6) -> 7
c_1(6,1) -> 5
c_1(6,4) -> 5
c_1(10,1) -> 7
c_1(10,4) -> 7
c_2(9,1) -> 8
c_2(9,4) -> 8
c_2(9,6) -> 8
f_0(1) -> 2
f_0(4) -> 2
f_1(5) -> 2
f_1(7) -> 3
f_2(8) -> 3
g_0(1) -> 3
g_0(4) -> 3
s_0(1) -> 4
s_0(4) -> 4
s_1(1) -> 6
s_1(4) -> 6
s_1(6) -> 6
s_1(9) -> 10
s_1(10) -> 10
s_2(1) -> 9
s_2(4) -> 9
s_2(9) -> 9
** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1))
+ Considered Problem:
- Weak TRS:
f(c(X,s(Y))) -> f(c(s(X),Y))
g(c(s(X),Y)) -> f(c(X,s(Y)))
- Signature:
{f/1,g/1} / {c/2,s/1}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s}
+ Applied Processor:
EmptyProcessor
+ Details:
The problem is already closed. The intended complexity is O(1).
WORST_CASE(Omega(n^1),O(n^1))