Problem Secret 06 TRS times

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Secret 06 TRS times

stdout:

MAYBE

Problem:
inc(s(x)) -> s(inc(x))
inc(0()) -> s(0())
plus(x,y) -> ifPlus(eq(x,0()),minus(x,s(0())),x,inc(x))
ifPlus(false(),x,y,z) -> plus(x,z)
ifPlus(true(),x,y,z) -> y
minus(s(x),s(y)) -> minus(x,y)
minus(0(),x) -> 0()
minus(x,0()) -> x
minus(x,x) -> 0()
eq(s(x),s(y)) -> eq(x,y)
eq(0(),s(x)) -> false()
eq(s(x),0()) -> false()
eq(0(),0()) -> true()
eq(x,x) -> true()
times(x,y) -> timesIter(x,y,0())
timesIter(x,y,z) -> ifTimes(eq(x,0()),minus(x,s(0())),y,z,plus(y,z))
ifTimes(true(),x,y,z,u) -> z
ifTimes(false(),x,y,z,u) -> timesIter(x,y,u)
f() -> g()
f() -> h()

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Secret 06 TRS times

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Secret 06 TRS times

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  inc(s(x)) -> s(inc(x))
     , inc(0()) -> s(0())
     , plus(x, y) -> ifPlus(eq(x, 0()), minus(x, s(0())), x, inc(x))
     , ifPlus(false(), x, y, z) -> plus(x, z)
     , ifPlus(true(), x, y, z) -> y
     , minus(s(x), s(y)) -> minus(x, y)
     , minus(0(), x) -> 0()
     , minus(x, 0()) -> x
     , minus(x, x) -> 0()
     , eq(s(x), s(y)) -> eq(x, y)
     , eq(0(), s(x)) -> false()
     , eq(s(x), 0()) -> false()
     , eq(0(), 0()) -> true()
     , eq(x, x) -> true()
     , times(x, y) -> timesIter(x, y, 0())
     , timesIter(x, y, z) ->
       ifTimes(eq(x, 0()), minus(x, s(0())), y, z, plus(y, z))
     , ifTimes(true(), x, y, z, u) -> z
     , ifTimes(false(), x, y, z, u) -> timesIter(x, y, u)
     , f() -> g()
     , f() -> h()}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Secret 06 TRS times

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Secret 06 TRS times

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  inc(s(x)) -> s(inc(x))
     , inc(0()) -> s(0())
     , plus(x, y) -> ifPlus(eq(x, 0()), minus(x, s(0())), x, inc(x))
     , ifPlus(false(), x, y, z) -> plus(x, z)
     , ifPlus(true(), x, y, z) -> y
     , minus(s(x), s(y)) -> minus(x, y)
     , minus(0(), x) -> 0()
     , minus(x, 0()) -> x
     , minus(x, x) -> 0()
     , eq(s(x), s(y)) -> eq(x, y)
     , eq(0(), s(x)) -> false()
     , eq(s(x), 0()) -> false()
     , eq(0(), 0()) -> true()
     , eq(x, x) -> true()
     , times(x, y) -> timesIter(x, y, 0())
     , timesIter(x, y, z) ->
       ifTimes(eq(x, 0()), minus(x, s(0())), y, z, plus(y, z))
     , ifTimes(true(), x, y, z, u) -> z
     , ifTimes(false(), x, y, z, u) -> timesIter(x, y, u)
     , f() -> g()
     , f() -> h()}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds