Tool CaT
stdout:
MAYBE
Problem:
g(A()) -> A()
g(B()) -> A()
g(B()) -> B()
g(C()) -> A()
g(C()) -> B()
g(C()) -> C()
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())
f(t,x) -> f'(t,g(x))
f'(triple(a,b,c),C()) -> triple(a,b,s(c))
f'(triple(a,b,c),B()) -> f(triple(a,b,c),A())
f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b))
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)
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()
, 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())
, f(t, x) -> f'(t, g(x))
, f'(triple(a, b, c), C()) -> triple(a, b, s(c))
, f'(triple(a, b, c), B()) -> f(triple(a, b, c), A())
, f'(triple(a, b, c), A()) -> f''(foldB(triple(s(a), 0(), c), b))
, 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)}
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()
, 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())
, f(t, x) -> f'(t, g(x))
, f'(triple(a, b, c), C()) -> triple(a, b, s(c))
, f'(triple(a, b, c), B()) -> f(triple(a, b, c), A())
, f'(triple(a, b, c), A()) -> f''(foldB(triple(s(a), 0(), c), b))
, 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)}
Proof Output:
Computation stopped due to timeout after 60.0 seconds