Problem Strategy outermost added 08 ExIntrod GM04

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Strategy outermost added 08 ExIntrod GM04

stdout:

MAYBE

Problem:
nats() -> adx(zeros())
zeros() -> cons(0(),zeros())
incr(cons(X,Y)) -> cons(s(X),incr(Y))
adx(cons(X,Y)) -> incr(cons(X,adx(Y)))
hd(cons(X,Y)) -> X
tl(cons(X,Y)) -> Y

Proof:
Complexity Transformation Processor:
  strict:
   nats() -> adx(zeros())
   zeros() -> cons(0(),zeros())
   incr(cons(X,Y)) -> cons(s(X),incr(Y))
   adx(cons(X,Y)) -> incr(cons(X,adx(Y)))
   hd(cons(X,Y)) -> X
   tl(cons(X,Y)) -> Y
  weak:

  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [tl](x0) = x0,

     [hd](x0) = x0,

     [s](x0) = x0,

     [incr](x0) = x0 + 3,

     [cons](x0, x1) = x0 + x1 + 9,

     [0] = 8,

     [adx](x0) = x0 + 5,

     [zeros] = 8,

     [nats] = 0
    orientation:
     nats() = 0 >= 13 = adx(zeros())

     zeros() = 8 >= 25 = cons(0(),zeros())

     incr(cons(X,Y)) = X + Y + 12 >= X + Y + 12 = cons(s(X),incr(Y))

     adx(cons(X,Y)) = X + Y + 14 >= X + Y + 17 = incr(cons(X,adx(Y)))

     hd(cons(X,Y)) = X + Y + 9 >= X = X

     tl(cons(X,Y)) = X + Y + 9 >= Y = Y
    problem:
     strict:
      nats() -> adx(zeros())
      zeros() -> cons(0(),zeros())
      incr(cons(X,Y)) -> cons(s(X),incr(Y))
      adx(cons(X,Y)) -> incr(cons(X,adx(Y)))
     weak:
      hd(cons(X,Y)) -> X
      tl(cons(X,Y)) -> Y
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [tl](x0) = x0,

       [hd](x0) = x0,

       [s](x0) = x0 + 6,

       [incr](x0) = x0 + 11,

       [cons](x0, x1) = x0 + x1,

       [0] = 0,

       [adx](x0) = x0 + 136,

       [zeros] = 32,

       [nats] = 169
      orientation:
       nats() = 169 >= 168 = adx(zeros())

       zeros() = 32 >= 32 = cons(0(),zeros())

       incr(cons(X,Y)) = X + Y + 11 >= X + Y + 17 = cons(s(X),incr(Y))

       adx(cons(X,Y)) = X + Y + 136 >= X + Y + 147 = incr(cons(X,adx(Y)))

       hd(cons(X,Y)) = X + Y >= X = X

       tl(cons(X,Y)) = X + Y >= Y = Y
      problem:
       strict:
        zeros() -> cons(0(),zeros())
        incr(cons(X,Y)) -> cons(s(X),incr(Y))
        adx(cons(X,Y)) -> incr(cons(X,adx(Y)))
       weak:
        nats() -> adx(zeros())
        hd(cons(X,Y)) -> X
        tl(cons(X,Y)) -> Y
      Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Strategy outermost added 08 ExIntrod GM04

stdout:

MAYBE
Warning when parsing problem:

Unsupported strategy 'OUTERMOST'

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Strategy outermost added 08 ExIntrod GM04

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  nats() -> adx(zeros())
     , zeros() -> cons(0(), zeros())
     , incr(cons(X, Y)) -> cons(s(X), incr(Y))
     , adx(cons(X, Y)) -> incr(cons(X, adx(Y)))
     , hd(cons(X, Y)) -> X
     , tl(cons(X, Y)) -> Y}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Strategy outermost added 08 ExIntrod GM04

stdout:

MAYBE
Warning when parsing problem:

Unsupported strategy 'OUTERMOST'

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Strategy outermost added 08 ExIntrod GM04

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  nats() -> adx(zeros())
     , zeros() -> cons(0(), zeros())
     , incr(cons(X, Y)) -> cons(s(X), incr(Y))
     , adx(cons(X, Y)) -> incr(cons(X, adx(Y)))
     , hd(cons(X, Y)) -> X
     , tl(cons(X, Y)) -> Y}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds