Tool CaT
stdout:
MAYBE
Problem:
cond1(true(),x,y,z) -> cond2(gr(x,0()),x,y,z)
cond2(true(),x,y,z) -> cond1(or(gr(x,z),gr(y,z)),p(x),y,z)
cond2(false(),x,y,z) -> cond3(gr(y,0()),x,y,z)
cond3(true(),x,y,z) -> cond1(or(gr(x,z),gr(y,z)),x,p(y),z)
cond3(false(),x,y,z) -> cond1(or(gr(x,z),gr(y,z)),x,y,z)
gr(0(),x) -> false()
gr(s(x),0()) -> true()
gr(s(x),s(y)) -> gr(x,y)
or(false(),false()) -> false()
or(true(),x) -> true()
or(x,true()) -> true()
p(0()) -> 0()
p(s(x)) -> 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:
{ cond1(true(), x, y, z) -> cond2(gr(x, 0()), x, y, z)
, cond2(true(), x, y, z) ->
cond1(or(gr(x, z), gr(y, z)), p(x), y, z)
, cond2(false(), x, y, z) -> cond3(gr(y, 0()), x, y, z)
, cond3(true(), x, y, z) ->
cond1(or(gr(x, z), gr(y, z)), x, p(y), z)
, cond3(false(), x, y, z) -> cond1(or(gr(x, z), gr(y, z)), x, y, z)
, gr(0(), x) -> false()
, gr(s(x), 0()) -> true()
, gr(s(x), s(y)) -> gr(x, y)
, or(false(), false()) -> false()
, or(true(), x) -> true()
, or(x, true()) -> true()
, p(0()) -> 0()
, p(s(x)) -> 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:
{ cond1(true(), x, y, z) -> cond2(gr(x, 0()), x, y, z)
, cond2(true(), x, y, z) ->
cond1(or(gr(x, z), gr(y, z)), p(x), y, z)
, cond2(false(), x, y, z) -> cond3(gr(y, 0()), x, y, z)
, cond3(true(), x, y, z) ->
cond1(or(gr(x, z), gr(y, z)), x, p(y), z)
, cond3(false(), x, y, z) -> cond1(or(gr(x, z), gr(y, z)), x, y, z)
, gr(0(), x) -> false()
, gr(s(x), 0()) -> true()
, gr(s(x), s(y)) -> gr(x, y)
, or(false(), false()) -> false()
, or(true(), x) -> true()
, or(x, true()) -> true()
, p(0()) -> 0()
, p(s(x)) -> x}
Proof Output:
Computation stopped due to timeout after 60.0 seconds