Tool CaT
stdout:
MAYBE
Problem:
eq(0(),0()) -> true()
eq(0(),s(x)) -> false()
eq(s(x),0()) -> false()
eq(s(x),s(y)) -> eq(x,y)
or(true(),y) -> true()
or(false(),y) -> y
and(true(),y) -> y
and(false(),y) -> false()
size(empty()) -> 0()
size(edge(x,y,i)) -> s(size(i))
le(0(),y) -> true()
le(s(x),0()) -> false()
le(s(x),s(y)) -> le(x,y)
reachable(x,y,i) -> reach(x,y,0(),i,i)
reach(x,y,c,i,j) -> if1(eq(x,y),x,y,c,i,j)
if1(true(),x,y,c,i,j) -> true()
if1(false(),x,y,c,i,j) -> if2(le(c,size(j)),x,y,c,i,j)
if2(false(),x,y,c,i,j) -> false()
if2(true(),x,y,c,empty(),j) -> false()
if2(true(),x,y,c,edge(u,v,i),j) -> or(if2(true(),x,y,c,i,j),and(eq(x,u),reach(v,y,s(c),j,j)))
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:
{ eq(0(), 0()) -> true()
, eq(0(), s(x)) -> false()
, eq(s(x), 0()) -> false()
, eq(s(x), s(y)) -> eq(x, y)
, or(true(), y) -> true()
, or(false(), y) -> y
, and(true(), y) -> y
, and(false(), y) -> false()
, size(empty()) -> 0()
, size(edge(x, y, i)) -> s(size(i))
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, reachable(x, y, i) -> reach(x, y, 0(), i, i)
, reach(x, y, c, i, j) -> if1(eq(x, y), x, y, c, i, j)
, if1(true(), x, y, c, i, j) -> true()
, if1(false(), x, y, c, i, j) -> if2(le(c, size(j)), x, y, c, i, j)
, if2(false(), x, y, c, i, j) -> false()
, if2(true(), x, y, c, empty(), j) -> false()
, if2(true(), x, y, c, edge(u, v, i), j) ->
or(if2(true(), x, y, c, i, j),
and(eq(x, u), reach(v, y, s(c), j, j)))}
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:
{ eq(0(), 0()) -> true()
, eq(0(), s(x)) -> false()
, eq(s(x), 0()) -> false()
, eq(s(x), s(y)) -> eq(x, y)
, or(true(), y) -> true()
, or(false(), y) -> y
, and(true(), y) -> y
, and(false(), y) -> false()
, size(empty()) -> 0()
, size(edge(x, y, i)) -> s(size(i))
, le(0(), y) -> true()
, le(s(x), 0()) -> false()
, le(s(x), s(y)) -> le(x, y)
, reachable(x, y, i) -> reach(x, y, 0(), i, i)
, reach(x, y, c, i, j) -> if1(eq(x, y), x, y, c, i, j)
, if1(true(), x, y, c, i, j) -> true()
, if1(false(), x, y, c, i, j) -> if2(le(c, size(j)), x, y, c, i, j)
, if2(false(), x, y, c, i, j) -> false()
, if2(true(), x, y, c, empty(), j) -> false()
, if2(true(), x, y, c, edge(u, v, i), j) ->
or(if2(true(), x, y, c, i, j),
and(eq(x, u), reach(v, y, s(c), j, j)))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds