Tool CaT
stdout:
MAYBE
Problem:
g(A()) -> A()
g(B()) -> A()
g(B()) -> B()
g(C()) -> A()
g(C()) -> B()
g(C()) -> C()
foldf(x,nil()) -> x
foldf(x,cons(y,z)) -> f(foldf(x,z),y)
f(t,x) -> f'(t,g(x))
f'(triple(a,b,c),C()) -> triple(a,b,cons(C(),c))
f'(triple(a,b,c),B()) -> f(triple(a,b,c),A())
f'(triple(a,b,c),A()) -> f''(foldf(triple(cons(A(),a),nil(),c),b))
f''(triple(a,b,c)) -> foldf(triple(a,b,nil()),c)
Proof:
OpenTool IRC1
stdout:
MAYBE
Tool IRC2
stdout:
TIMEOUT
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: TIMEOUT
Input Problem: innermost runtime-complexity with respect to
Rules:
{ g(A()) -> A()
, g(B()) -> A()
, g(B()) -> B()
, g(C()) -> A()
, g(C()) -> B()
, g(C()) -> C()
, foldf(x, nil()) -> x
, foldf(x, cons(y, z)) -> f(foldf(x, z), y)
, f(t, x) -> f'(t, g(x))
, f'(triple(a, b, c), C()) -> triple(a, b, cons(C(), c))
, f'(triple(a, b, c), B()) -> f(triple(a, b, c), A())
, f'(triple(a, b, c), A()) ->
f''(foldf(triple(cons(A(), a), nil(), c), b))
, f''(triple(a, b, c)) -> foldf(triple(a, b, nil()), c)}
Proof Output:
Computation stopped due to timeout after 60.0 secondsTool RC1
stdout:
MAYBE
Tool RC2
stdout:
TIMEOUT
'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer: TIMEOUT
Input Problem: runtime-complexity with respect to
Rules:
{ g(A()) -> A()
, g(B()) -> A()
, g(B()) -> B()
, g(C()) -> A()
, g(C()) -> B()
, g(C()) -> C()
, foldf(x, nil()) -> x
, foldf(x, cons(y, z)) -> f(foldf(x, z), y)
, f(t, x) -> f'(t, g(x))
, f'(triple(a, b, c), C()) -> triple(a, b, cons(C(), c))
, f'(triple(a, b, c), B()) -> f(triple(a, b, c), A())
, f'(triple(a, b, c), A()) ->
f''(foldf(triple(cons(A(), a), nil(), c), b))
, f''(triple(a, b, c)) -> foldf(triple(a, b, nil()), c)}
Proof Output:
Computation stopped due to timeout after 60.0 seconds