Tool CaT
stdout:
MAYBE
Problem:
function(iszero(),0(),dummy,dummy2) -> true()
function(iszero(),s(x),dummy,dummy2) -> false()
function(p(),0(),dummy,dummy2) -> 0()
function(p(),s(0()),dummy,dummy2) -> 0()
function(p(),s(s(x)),dummy,dummy2) -> s(function(p(),s(x),x,x))
function(plus(),dummy,x,y) -> function(if(),function(iszero(),x,x,x),x,y)
function(if(),true(),x,y) -> y
function(if(),false(),x,y) -> function(plus(),function(third(),x,y,y),function(p(),x,x,y),s(y))
function(third(),x,y,z) -> z
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:
{ function(iszero(), 0(), dummy, dummy2) -> true()
, function(iszero(), s(x), dummy, dummy2) -> false()
, function(p(), 0(), dummy, dummy2) -> 0()
, function(p(), s(0()), dummy, dummy2) -> 0()
, function(p(), s(s(x)), dummy, dummy2) ->
s(function(p(), s(x), x, x))
, function(plus(), dummy, x, y) ->
function(if(), function(iszero(), x, x, x), x, y)
, function(if(), true(), x, y) -> y
, function(if(), false(), x, y) ->
function(plus(),
function(third(), x, y, y),
function(p(), x, x, y),
s(y))
, function(third(), x, y, z) -> z}
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:
{ function(iszero(), 0(), dummy, dummy2) -> true()
, function(iszero(), s(x), dummy, dummy2) -> false()
, function(p(), 0(), dummy, dummy2) -> 0()
, function(p(), s(0()), dummy, dummy2) -> 0()
, function(p(), s(s(x)), dummy, dummy2) ->
s(function(p(), s(x), x, x))
, function(plus(), dummy, x, y) ->
function(if(), function(iszero(), x, x, x), x, y)
, function(if(), true(), x, y) -> y
, function(if(), false(), x, y) ->
function(plus(),
function(third(), x, y, y),
function(p(), x, x, y),
s(y))
, function(third(), x, y, z) -> z}
Proof Output:
Computation stopped due to timeout after 60.0 seconds