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
union(empty(),h) -> h
union(edge(x,y,i),h) -> edge(x,y,union(i,h))
isEmpty(empty()) -> true()
isEmpty(edge(x,y,i)) -> false()
from(edge(x,y,i)) -> x
to(edge(x,y,i)) -> y
rest(edge(x,y,i)) -> i
rest(empty()) -> empty()
reach(x,y,i,h) -> if1(eq(x,y),isEmpty(i),eq(x,from(i)),eq(y,to(i)),x,y,i,h)
if1(true(),b1,b2,b3,x,y,i,h) -> true()
if1(false(),b1,b2,b3,x,y,i,h) -> if2(b1,b2,b3,x,y,i,h)
if2(true(),b2,b3,x,y,i,h) -> false()
if2(false(),b2,b3,x,y,i,h) -> if3(b2,b3,x,y,i,h)
if3(false(),b3,x,y,i,h) -> reach(x,y,rest(i),edge(from(i),to(i),h))
if3(true(),b3,x,y,i,h) -> if4(b3,x,y,i,h)
if4(true(),x,y,i,h) -> true()
if4(false(),x,y,i,h) -> or(reach(x,y,rest(i),h),reach(to(i),y,union(rest(i),h),empty()))
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
, union(empty(), h) -> h
, union(edge(x, y, i), h) -> edge(x, y, union(i, h))
, isEmpty(empty()) -> true()
, isEmpty(edge(x, y, i)) -> false()
, from(edge(x, y, i)) -> x
, to(edge(x, y, i)) -> y
, rest(edge(x, y, i)) -> i
, rest(empty()) -> empty()
, reach(x, y, i, h) ->
if1(eq(x, y), isEmpty(i), eq(x, from(i)), eq(y, to(i)), x, y, i, h)
, if1(true(), b1, b2, b3, x, y, i, h) -> true()
, if1(false(), b1, b2, b3, x, y, i, h) ->
if2(b1, b2, b3, x, y, i, h)
, if2(true(), b2, b3, x, y, i, h) -> false()
, if2(false(), b2, b3, x, y, i, h) -> if3(b2, b3, x, y, i, h)
, if3(false(), b3, x, y, i, h) ->
reach(x, y, rest(i), edge(from(i), to(i), h))
, if3(true(), b3, x, y, i, h) -> if4(b3, x, y, i, h)
, if4(true(), x, y, i, h) -> true()
, if4(false(), x, y, i, h) ->
or(reach(x, y, rest(i), h),
reach(to(i), y, union(rest(i), h), empty()))}
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
, union(empty(), h) -> h
, union(edge(x, y, i), h) -> edge(x, y, union(i, h))
, isEmpty(empty()) -> true()
, isEmpty(edge(x, y, i)) -> false()
, from(edge(x, y, i)) -> x
, to(edge(x, y, i)) -> y
, rest(edge(x, y, i)) -> i
, rest(empty()) -> empty()
, reach(x, y, i, h) ->
if1(eq(x, y), isEmpty(i), eq(x, from(i)), eq(y, to(i)), x, y, i, h)
, if1(true(), b1, b2, b3, x, y, i, h) -> true()
, if1(false(), b1, b2, b3, x, y, i, h) ->
if2(b1, b2, b3, x, y, i, h)
, if2(true(), b2, b3, x, y, i, h) -> false()
, if2(false(), b2, b3, x, y, i, h) -> if3(b2, b3, x, y, i, h)
, if3(false(), b3, x, y, i, h) ->
reach(x, y, rest(i), edge(from(i), to(i), h))
, if3(true(), b3, x, y, i, h) -> if4(b3, x, y, i, h)
, if4(true(), x, y, i, h) -> true()
, if4(false(), x, y, i, h) ->
or(reach(x, y, rest(i), h),
reach(to(i), y, union(rest(i), h), empty()))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds