* Step 1: Sum WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
f(t,x) -> f'(t,g(x))
f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b))
f'(triple(a,b,c),B()) -> f(triple(a,b,c),A())
f'(triple(a,b,c),C()) -> triple(a,b,s(c))
f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c)
fold(t,x,0()) -> t
fold(t,x,s(n)) -> f(fold(t,x,n),x)
foldB(t,0()) -> t
foldB(t,s(n)) -> f(foldB(t,n),B())
foldC(t,0()) -> t
foldC(t,s(n)) -> f(foldC(t,n),C())
g(A()) -> A()
g(B()) -> A()
g(B()) -> B()
g(C()) -> A()
g(C()) -> B()
g(C()) -> C()
- Signature:
{f/2,f'/2,f''/1,fold/3,foldB/2,foldC/2,g/1} / {0/0,A/0,B/0,C/0,s/1,triple/3}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,f',f'',fold,foldB,foldC,g} and constructors {0,A,B,C,s
,triple}
+ Applied Processor:
Sum {left = someStrategy, right = someStrategy}
+ Details:
()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
+ Considered Problem:
- Strict TRS:
f(t,x) -> f'(t,g(x))
f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b))
f'(triple(a,b,c),B()) -> f(triple(a,b,c),A())
f'(triple(a,b,c),C()) -> triple(a,b,s(c))
f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c)
fold(t,x,0()) -> t
fold(t,x,s(n)) -> f(fold(t,x,n),x)
foldB(t,0()) -> t
foldB(t,s(n)) -> f(foldB(t,n),B())
foldC(t,0()) -> t
foldC(t,s(n)) -> f(foldC(t,n),C())
g(A()) -> A()
g(B()) -> A()
g(B()) -> B()
g(C()) -> A()
g(C()) -> B()
g(C()) -> C()
- Signature:
{f/2,f'/2,f''/1,fold/3,foldB/2,foldC/2,g/1} / {0/0,A/0,B/0,C/0,s/1,triple/3}
- Obligation:
innermost runtime complexity wrt. defined symbols {f,f',f'',fold,foldB,foldC,g} and constructors {0,A,B,C,s
,triple}
+ Applied Processor:
DecreasingLoops {bound = AnyLoop, narrow = 10}
+ Details:
The system has following decreasing Loops:
fold(x,y,z){z -> s(z)} =
fold(x,y,s(z)) ->^+ f(fold(x,y,z),y)
= C[fold(x,y,z) = fold(x,y,z){}]
WORST_CASE(Omega(n^1),?)