Tool CaT
stdout:
MAYBE
Problem:
le(0(),y) -> true()
le(s(x),0()) -> false()
le(s(x),s(y)) -> le(x,y)
zero(0()) -> true()
zero(s(x)) -> false()
id(0()) -> 0()
id(s(x)) -> s(id(x))
minus(x,0()) -> x
minus(s(x),s(y)) -> minus(x,y)
mod(x,y) -> if_mod(zero(x),zero(y),le(y,x),id(x),id(y))
if_mod(true(),b1,b2,x,y) -> 0()
if_mod(false(),b1,b2,x,y) -> if2(b1,b2,x,y)
if2(true(),b2,x,y) -> 0()
if2(false(),b2,x,y) -> if3(b2,x,y)
if3(true(),x,y) -> mod(minus(x,y),s(y))
if3(false(),x,y) -> 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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, zero(0()) -> true()
, zero(s(x)) -> false()
, id(0()) -> 0()
, id(s(x)) -> s(id(x))
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, mod(x, y) -> if_mod(zero(x), zero(y), le(y, x), id(x), id(y))
, if_mod(true(), b1, b2, x, y) -> 0()
, if_mod(false(), b1, b2, x, y) -> if2(b1, b2, x, y)
, if2(true(), b2, x, y) -> 0()
, if2(false(), b2, x, y) -> if3(b2, x, y)
, if3(true(), x, y) -> mod(minus(x, y), s(y))
, if3(false(), x, y) -> 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:
{ le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, zero(0()) -> true()
, zero(s(x)) -> false()
, id(0()) -> 0()
, id(s(x)) -> s(id(x))
, minus(x, 0()) -> x
, minus(s(x), s(y)) -> minus(x, y)
, mod(x, y) -> if_mod(zero(x), zero(y), le(y, x), id(x), id(y))
, if_mod(true(), b1, b2, x, y) -> 0()
, if_mod(false(), b1, b2, x, y) -> if2(b1, b2, x, y)
, if2(true(), b2, x, y) -> 0()
, if2(false(), b2, x, y) -> if3(b2, x, y)
, if3(true(), x, y) -> mod(minus(x, y), s(y))
, if3(false(), x, y) -> x}
Proof Output:
Computation stopped due to timeout after 60.0 seconds