Tool CaT
stdout:
MAYBE
Problem:
test(x_0,y) -> True()
test(x_0,y) -> False()
append(l1_2,l2_1) -> match_0(l1_2,l2_1,l1_2)
match_0(l1_2,l2_1,Nil()) -> l2_1
match_0(l1_2,l2_1,Cons(x,l)) -> Cons(x,append(l,l2_1))
part(a_4,l_3) -> match_1(a_4,l_3,l_3)
match_1(a_4,l_3,Nil()) -> Pair(Nil(),Nil())
match_1(a_4,l_3,Cons(x,l')) -> match_2(x,l',a_4,l_3,part(a_4,l'))
match_2(x,l',a_4,l_3,Pair(l1,l2)) -> match_3(l1,l2,x,l',a_4,l_3,test(a_4,x))
match_3(l1,l2,x,l',a_4,l_3,False()) -> Pair(Cons(x,l1),l2)
match_3(l1,l2,x,l',a_4,l_3,True()) -> Pair(l1,Cons(x,l2))
quick(l_5) -> match_4(l_5,l_5)
match_4(l_5,Nil()) -> Nil()
match_4(l_5,Cons(a,l')) -> match_5(a,l',l_5,part(a,l'))
match_5(a,l',l_5,Pair(l1,l2)) -> append(quick(l1),Cons(a,quick(l2)))
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:
{ test(x_0, y) -> True()
, test(x_0, y) -> False()
, append(l1_2, l2_1) -> match_0(l1_2, l2_1, l1_2)
, match_0(l1_2, l2_1, Nil()) -> l2_1
, match_0(l1_2, l2_1, Cons(x, l)) -> Cons(x, append(l, l2_1))
, part(a_4, l_3) -> match_1(a_4, l_3, l_3)
, match_1(a_4, l_3, Nil()) -> Pair(Nil(), Nil())
, match_1(a_4, l_3, Cons(x, l')) ->
match_2(x, l', a_4, l_3, part(a_4, l'))
, match_2(x, l', a_4, l_3, Pair(l1, l2)) ->
match_3(l1, l2, x, l', a_4, l_3, test(a_4, x))
, match_3(l1, l2, x, l', a_4, l_3, False()) ->
Pair(Cons(x, l1), l2)
, match_3(l1, l2, x, l', a_4, l_3, True()) -> Pair(l1, Cons(x, l2))
, quick(l_5) -> match_4(l_5, l_5)
, match_4(l_5, Nil()) -> Nil()
, match_4(l_5, Cons(a, l')) -> match_5(a, l', l_5, part(a, l'))
, match_5(a, l', l_5, Pair(l1, l2)) ->
append(quick(l1), Cons(a, quick(l2)))}
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:
{ test(x_0, y) -> True()
, test(x_0, y) -> False()
, append(l1_2, l2_1) -> match_0(l1_2, l2_1, l1_2)
, match_0(l1_2, l2_1, Nil()) -> l2_1
, match_0(l1_2, l2_1, Cons(x, l)) -> Cons(x, append(l, l2_1))
, part(a_4, l_3) -> match_1(a_4, l_3, l_3)
, match_1(a_4, l_3, Nil()) -> Pair(Nil(), Nil())
, match_1(a_4, l_3, Cons(x, l')) ->
match_2(x, l', a_4, l_3, part(a_4, l'))
, match_2(x, l', a_4, l_3, Pair(l1, l2)) ->
match_3(l1, l2, x, l', a_4, l_3, test(a_4, x))
, match_3(l1, l2, x, l', a_4, l_3, False()) ->
Pair(Cons(x, l1), l2)
, match_3(l1, l2, x, l', a_4, l_3, True()) -> Pair(l1, Cons(x, l2))
, quick(l_5) -> match_4(l_5, l_5)
, match_4(l_5, Nil()) -> Nil()
, match_4(l_5, Cons(a, l')) -> match_5(a, l', l_5, part(a, l'))
, match_5(a, l', l_5, Pair(l1, l2)) ->
append(quick(l1), Cons(a, quick(l2)))}
Proof Output:
Computation stopped due to timeout after 60.0 seconds