Tool CaT
stdout:
MAYBE
Problem:
p(s(x)) -> x
p(0()) -> 0()
le(0(),y) -> true()
le(s(x),0()) -> false()
le(s(x),s(y)) -> le(x,y)
average(x,y) -> if(le(x,0()),le(y,0()),le(y,s(0())),le(y,s(s(0()))),x,y)
if(true(),b1,b2,b3,x,y) -> if2(b1,b2,b3,x,y)
if(false(),b1,b2,b3,x,y) -> average(p(x),s(y))
if2(true(),b2,b3,x,y) -> 0()
if2(false(),b2,b3,x,y) -> if3(b2,b3,x,y)
if3(true(),b3,x,y) -> 0()
if3(false(),b3,x,y) -> if4(b3,x,y)
if4(true(),x,y) -> s(0())
if4(false(),x,y) -> average(s(x),p(p(y)))
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:
{ p(s(x)) -> x
, p(0()) -> 0()
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, average(x, y) ->
if(le(x, 0()), le(y, 0()), le(y, s(0())), le(y, s(s(0()))), x, y)
, if(true(), b1, b2, b3, x, y) -> if2(b1, b2, b3, x, y)
, if(false(), b1, b2, b3, x, y) -> average(p(x), s(y))
, if2(true(), b2, b3, x, y) -> 0()
, if2(false(), b2, b3, x, y) -> if3(b2, b3, x, y)
, if3(true(), b3, x, y) -> 0()
, if3(false(), b3, x, y) -> if4(b3, x, y)
, if4(true(), x, y) -> s(0())
, if4(false(), x, y) -> average(s(x), p(p(y)))}
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:
{ p(s(x)) -> x
, p(0()) -> 0()
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, average(x, y) ->
if(le(x, 0()), le(y, 0()), le(y, s(0())), le(y, s(s(0()))), x, y)
, if(true(), b1, b2, b3, x, y) -> if2(b1, b2, b3, x, y)
, if(false(), b1, b2, b3, x, y) -> average(p(x), s(y))
, if2(true(), b2, b3, x, y) -> 0()
, if2(false(), b2, b3, x, y) -> if3(b2, b3, x, y)
, if3(true(), b3, x, y) -> 0()
, if3(false(), b3, x, y) -> if4(b3, x, y)
, if4(true(), x, y) -> s(0())
, if4(false(), x, y) -> average(s(x), p(p(y)))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds