Problem Transformed CSR 04 Ex2 Luc03b C

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex2 Luc03b C

stdout:

MAYBE

Problem:
active(fst(0(),Z)) -> mark(nil())
active(fst(s(X),cons(Y,Z))) -> mark(cons(Y,fst(X,Z)))
active(from(X)) -> mark(cons(X,from(s(X))))
active(add(0(),X)) -> mark(X)
active(add(s(X),Y)) -> mark(s(add(X,Y)))
active(len(nil())) -> mark(0())
active(len(cons(X,Z))) -> mark(s(len(Z)))
active(cons(X1,X2)) -> cons(active(X1),X2)
active(fst(X1,X2)) -> fst(active(X1),X2)
active(fst(X1,X2)) -> fst(X1,active(X2))
active(from(X)) -> from(active(X))
active(add(X1,X2)) -> add(active(X1),X2)
active(add(X1,X2)) -> add(X1,active(X2))
active(len(X)) -> len(active(X))
cons(mark(X1),X2) -> mark(cons(X1,X2))
fst(mark(X1),X2) -> mark(fst(X1,X2))
fst(X1,mark(X2)) -> mark(fst(X1,X2))
from(mark(X)) -> mark(from(X))
add(mark(X1),X2) -> mark(add(X1,X2))
add(X1,mark(X2)) -> mark(add(X1,X2))
len(mark(X)) -> mark(len(X))
proper(0()) -> ok(0())
proper(s(X)) -> s(proper(X))
proper(nil()) -> ok(nil())
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(fst(X1,X2)) -> fst(proper(X1),proper(X2))
proper(from(X)) -> from(proper(X))
proper(add(X1,X2)) -> add(proper(X1),proper(X2))
proper(len(X)) -> len(proper(X))
s(ok(X)) -> ok(s(X))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
fst(ok(X1),ok(X2)) -> ok(fst(X1,X2))
from(ok(X)) -> ok(from(X))
add(ok(X1),ok(X2)) -> ok(add(X1,X2))
len(ok(X)) -> ok(len(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex2 Luc03b C

stdout:

MAYBE

Tool IRC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 Ex2 Luc03b C

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  active(fst(0(), Z)) -> mark(nil())
     , active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z)))
     , active(from(X)) -> mark(cons(X, from(s(X))))
     , active(add(0(), X)) -> mark(X)
     , active(add(s(X), Y)) -> mark(s(add(X, Y)))
     , active(len(nil())) -> mark(0())
     , active(len(cons(X, Z))) -> mark(s(len(Z)))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(fst(X1, X2)) -> fst(active(X1), X2)
     , active(fst(X1, X2)) -> fst(X1, active(X2))
     , active(from(X)) -> from(active(X))
     , active(add(X1, X2)) -> add(active(X1), X2)
     , active(add(X1, X2)) -> add(X1, active(X2))
     , active(len(X)) -> len(active(X))
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , fst(mark(X1), X2) -> mark(fst(X1, X2))
     , fst(X1, mark(X2)) -> mark(fst(X1, X2))
     , from(mark(X)) -> mark(from(X))
     , add(mark(X1), X2) -> mark(add(X1, X2))
     , add(X1, mark(X2)) -> mark(add(X1, X2))
     , len(mark(X)) -> mark(len(X))
     , proper(0()) -> ok(0())
     , proper(s(X)) -> s(proper(X))
     , proper(nil()) -> ok(nil())
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(fst(X1, X2)) -> fst(proper(X1), proper(X2))
     , proper(from(X)) -> from(proper(X))
     , proper(add(X1, X2)) -> add(proper(X1), proper(X2))
     , proper(len(X)) -> len(proper(X))
     , s(ok(X)) -> ok(s(X))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , fst(ok(X1), ok(X2)) -> ok(fst(X1, X2))
     , from(ok(X)) -> ok(from(X))
     , add(ok(X1), ok(X2)) -> ok(add(X1, X2))
     , len(ok(X)) -> ok(len(X))
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds

Tool RC1

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex2 Luc03b C

stdout:

MAYBE

Tool RC2

Execution Time	Unknown
Answer	TIMEOUT
Input	Transformed CSR 04 Ex2 Luc03b C

stdout:

TIMEOUT

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           TIMEOUT
Input Problem:    runtime-complexity with respect to
  Rules:
    {  active(fst(0(), Z)) -> mark(nil())
     , active(fst(s(X), cons(Y, Z))) -> mark(cons(Y, fst(X, Z)))
     , active(from(X)) -> mark(cons(X, from(s(X))))
     , active(add(0(), X)) -> mark(X)
     , active(add(s(X), Y)) -> mark(s(add(X, Y)))
     , active(len(nil())) -> mark(0())
     , active(len(cons(X, Z))) -> mark(s(len(Z)))
     , active(cons(X1, X2)) -> cons(active(X1), X2)
     , active(fst(X1, X2)) -> fst(active(X1), X2)
     , active(fst(X1, X2)) -> fst(X1, active(X2))
     , active(from(X)) -> from(active(X))
     , active(add(X1, X2)) -> add(active(X1), X2)
     , active(add(X1, X2)) -> add(X1, active(X2))
     , active(len(X)) -> len(active(X))
     , cons(mark(X1), X2) -> mark(cons(X1, X2))
     , fst(mark(X1), X2) -> mark(fst(X1, X2))
     , fst(X1, mark(X2)) -> mark(fst(X1, X2))
     , from(mark(X)) -> mark(from(X))
     , add(mark(X1), X2) -> mark(add(X1, X2))
     , add(X1, mark(X2)) -> mark(add(X1, X2))
     , len(mark(X)) -> mark(len(X))
     , proper(0()) -> ok(0())
     , proper(s(X)) -> s(proper(X))
     , proper(nil()) -> ok(nil())
     , proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
     , proper(fst(X1, X2)) -> fst(proper(X1), proper(X2))
     , proper(from(X)) -> from(proper(X))
     , proper(add(X1, X2)) -> add(proper(X1), proper(X2))
     , proper(len(X)) -> len(proper(X))
     , s(ok(X)) -> ok(s(X))
     , cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
     , fst(ok(X1), ok(X2)) -> ok(fst(X1, X2))
     , from(ok(X)) -> ok(from(X))
     , add(ok(X1), ok(X2)) -> ok(add(X1, X2))
     , len(ok(X)) -> ok(len(X))
     , top(mark(X)) -> top(proper(X))
     , top(ok(X)) -> top(active(X))}

Proof Output:
  Computation stopped due to timeout after 60.0 seconds