Problem Various 04 08

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Various 04 08

stdout:

MAYBE

Problem:
f1(a(),x) -> g1(x,x)
f1(x,a()) -> g2(x,x)
f2(a(),x) -> g1(x,x)
f2(x,a()) -> g2(x,x)
g1(a(),x) -> h1(x)
g1(x,a()) -> h2(x)
g2(a(),x) -> h1(x)
g2(x,a()) -> h2(x)
h1(a()) -> i()
h2(a()) -> i()
e1(h1(w),h2(w),x,y,z,w) -> e2(x,x,y,z,z,w)
e1(x1,x1,x,y,z,a()) -> e5(x1,x,y,z)
e2(f1(w,w),x,y,z,f2(w,w),w) -> e3(x,y,x,y,y,z,y,z,x,y,z,w)
e2(x,x,y,z,z,a()) -> e6(x,y,z)
e2(i(),x,y,z,i(),a()) -> e6(x,y,z)
e3(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w) -> e4(x1,x1,x2,x2,x3,x3,x4,x4,x,y,z,w)
e3(x,y,x,y,y,z,y,z,x,y,z,a()) -> e6(x,y,z)
e4(g1(w,w),x1,g2(w,w),x1,g1(w,w),x1,g2(w,w),x1,x,y,z,w) -> e1(x1,x1,x,y,z,w)
e4(i(),x1,i(),x1,i(),x1,i(),x1,x,y,z,a()) -> e5(x1,x,y,z)
e4(x,x,x,x,x,x,x,x,x,x,x,a()) -> e6(x,x,x)
e5(i(),x,y,z) -> e6(x,y,z)

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Various 04 08

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Various 04 08

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  f1(a(), x) -> g1(x, x)
     , f1(x, a()) -> g2(x, x)
     , f2(a(), x) -> g1(x, x)
     , f2(x, a()) -> g2(x, x)
     , g1(a(), x) -> h1(x)
     , g1(x, a()) -> h2(x)
     , g2(a(), x) -> h1(x)
     , g2(x, a()) -> h2(x)
     , h1(a()) -> i()
     , h2(a()) -> i()
     , e1(h1(w), h2(w), x, y, z, w) -> e2(x, x, y, z, z, w)
     , e1(x1, x1, x, y, z, a()) -> e5(x1, x, y, z)
     , e2(f1(w, w), x, y, z, f2(w, w), w) ->
       e3(x, y, x, y, y, z, y, z, x, y, z, w)
     , e2(x, x, y, z, z, a()) -> e6(x, y, z)
     , e2(i(), x, y, z, i(), a()) -> e6(x, y, z)
     , e3(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z, w) ->
       e4(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z, w)
     , e3(x, y, x, y, y, z, y, z, x, y, z, a()) -> e6(x, y, z)
     , e4(g1(w, w),
          x1,
          g2(w, w),
          x1,
          g1(w, w),
          x1,
          g2(w, w),
          x1,
          x,
          y,
          z,
          w)
       -> e1(x1, x1, x, y, z, w)
     , e4(i(), x1, i(), x1, i(), x1, i(), x1, x, y, z, a()) ->
       e5(x1, x, y, z)
     , e4(x, x, x, x, x, x, x, x, x, x, x, a()) -> e6(x, x, x)
     , e5(i(), x, y, z) -> e6(x, y, z)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Various 04 08

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Various 04 08

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  f1(a(), x) -> g1(x, x)
     , f1(x, a()) -> g2(x, x)
     , f2(a(), x) -> g1(x, x)
     , f2(x, a()) -> g2(x, x)
     , g1(a(), x) -> h1(x)
     , g1(x, a()) -> h2(x)
     , g2(a(), x) -> h1(x)
     , g2(x, a()) -> h2(x)
     , h1(a()) -> i()
     , h2(a()) -> i()
     , e1(h1(w), h2(w), x, y, z, w) -> e2(x, x, y, z, z, w)
     , e1(x1, x1, x, y, z, a()) -> e5(x1, x, y, z)
     , e2(f1(w, w), x, y, z, f2(w, w), w) ->
       e3(x, y, x, y, y, z, y, z, x, y, z, w)
     , e2(x, x, y, z, z, a()) -> e6(x, y, z)
     , e2(i(), x, y, z, i(), a()) -> e6(x, y, z)
     , e3(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z, w) ->
       e4(x1, x1, x2, x2, x3, x3, x4, x4, x, y, z, w)
     , e3(x, y, x, y, y, z, y, z, x, y, z, a()) -> e6(x, y, z)
     , e4(g1(w, w),
          x1,
          g2(w, w),
          x1,
          g1(w, w),
          x1,
          g2(w, w),
          x1,
          x,
          y,
          z,
          w)
       -> e1(x1, x1, x, y, z, w)
     , e4(i(), x1, i(), x1, i(), x1, i(), x1, x, y, z, a()) ->
       e5(x1, x, y, z)
     , e4(x, x, x, x, x, x, x, x, x, x, x, a()) -> e6(x, x, x)
     , e5(i(), x, y, z) -> e6(x, y, z)}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds