Tool CaT
stdout:
MAYBE
Problem:
ge(x,0()) -> true()
ge(0(),s(y)) -> false()
ge(s(x),s(y)) -> ge(x,y)
rev(x) -> if(x,eq(0(),length(x)),nil(),0(),length(x))
if(x,true(),z,c,l) -> z
if(x,false(),z,c,l) -> help(s(c),l,x,z)
help(c,l,cons(x,y),z) -> if(append(y,cons(x,nil())),ge(c,l),cons(x,z),c,l)
append(nil(),y) -> y
append(cons(x,y),z) -> cons(x,append(y,z))
length(nil()) -> 0()
length(cons(x,y)) -> s(length(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:
{ ge(x, 0()) -> true()
, ge(0(), s(y)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, rev(x) -> if(x, eq(0(), length(x)), nil(), 0(), length(x))
, if(x, true(), z, c, l) -> z
, if(x, false(), z, c, l) -> help(s(c), l, x, z)
, help(c, l, cons(x, y), z) ->
if(append(y, cons(x, nil())), ge(c, l), cons(x, z), c, l)
, append(nil(), y) -> y
, append(cons(x, y), z) -> cons(x, append(y, z))
, length(nil()) -> 0()
, length(cons(x, y)) -> s(length(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:
{ ge(x, 0()) -> true()
, ge(0(), s(y)) -> false()
, ge(s(x), s(y)) -> ge(x, y)
, rev(x) -> if(x, eq(0(), length(x)), nil(), 0(), length(x))
, if(x, true(), z, c, l) -> z
, if(x, false(), z, c, l) -> help(s(c), l, x, z)
, help(c, l, cons(x, y), z) ->
if(append(y, cons(x, nil())), ge(c, l), cons(x, z), c, l)
, append(nil(), y) -> y
, append(cons(x, y), z) -> cons(x, append(y, z))
, length(nil()) -> 0()
, length(cons(x, y)) -> s(length(y))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds