Tool CaT
stdout:
MAYBE
Problem:
active(f(b(),c(),x)) -> mark(f(x,x,x))
active(f(x,y,z)) -> f(x,y,active(z))
active(d()) -> m(b())
f(x,y,mark(z)) -> mark(f(x,y,z))
active(d()) -> mark(c())
proper(b()) -> ok(b())
proper(c()) -> ok(c())
proper(d()) -> ok(d())
proper(f(x,y,z)) -> f(proper(x),proper(y),proper(z))
f(ok(x),ok(y),ok(z)) -> ok(f(x,y,z))
top(mark(x)) -> top(proper(x))
top(ok(x)) -> top(active(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:
{ active(f(b(), c(), x)) -> mark(f(x, x, x))
, active(f(x, y, z)) -> f(x, y, active(z))
, active(d()) -> m(b())
, f(x, y, mark(z)) -> mark(f(x, y, z))
, active(d()) -> mark(c())
, proper(b()) -> ok(b())
, proper(c()) -> ok(c())
, proper(d()) -> ok(d())
, proper(f(x, y, z)) -> f(proper(x), proper(y), proper(z))
, f(ok(x), ok(y), ok(z)) -> ok(f(x, y, z))
, top(mark(x)) -> top(proper(x))
, top(ok(x)) -> top(active(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:
{ active(f(b(), c(), x)) -> mark(f(x, x, x))
, active(f(x, y, z)) -> f(x, y, active(z))
, active(d()) -> m(b())
, f(x, y, mark(z)) -> mark(f(x, y, z))
, active(d()) -> mark(c())
, proper(b()) -> ok(b())
, proper(c()) -> ok(c())
, proper(d()) -> ok(d())
, proper(f(x, y, z)) -> f(proper(x), proper(y), proper(z))
, f(ok(x), ok(y), ok(z)) -> ok(f(x, y, z))
, top(mark(x)) -> top(proper(x))
, top(ok(x)) -> top(active(x))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds