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