MAYBE

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { +(0(), y) -> y
  , +(s(x), y) -> s(+(x, y))
  , +(p(x), y) -> p(+(x, y))
  , minus(0()) -> 0()
  , minus(s(x)) -> p(minus(x))
  , minus(p(x)) -> s(minus(x))
  , *(0(), y) -> 0()
  , *(s(x), y) -> +(*(x, y), y)
  , *(p(x), y) -> +(*(x, y), minus(y)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following dependency tuples:

Strict DPs:
  { +^#(0(), y) -> c_1()
  , +^#(s(x), y) -> c_2(+^#(x, y))
  , +^#(p(x), y) -> c_3(+^#(x, y))
  , minus^#(0()) -> c_4()
  , minus^#(s(x)) -> c_5(minus^#(x))
  , minus^#(p(x)) -> c_6(minus^#(x))
  , *^#(0(), y) -> c_7()
  , *^#(s(x), y) -> c_8(+^#(*(x, y), y), *^#(x, y))
  , *^#(p(x), y) ->
    c_9(+^#(*(x, y), minus(y)), *^#(x, y), minus^#(y)) }

and mark the set of starting terms.

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { +^#(0(), y) -> c_1()
  , +^#(s(x), y) -> c_2(+^#(x, y))
  , +^#(p(x), y) -> c_3(+^#(x, y))
  , minus^#(0()) -> c_4()
  , minus^#(s(x)) -> c_5(minus^#(x))
  , minus^#(p(x)) -> c_6(minus^#(x))
  , *^#(0(), y) -> c_7()
  , *^#(s(x), y) -> c_8(+^#(*(x, y), y), *^#(x, y))
  , *^#(p(x), y) ->
    c_9(+^#(*(x, y), minus(y)), *^#(x, y), minus^#(y)) }
Weak Trs:
  { +(0(), y) -> y
  , +(s(x), y) -> s(+(x, y))
  , +(p(x), y) -> p(+(x, y))
  , minus(0()) -> 0()
  , minus(s(x)) -> p(minus(x))
  , minus(p(x)) -> s(minus(x))
  , *(0(), y) -> 0()
  , *(s(x), y) -> +(*(x, y), y)
  , *(p(x), y) -> +(*(x, y), minus(y)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We estimate the number of application of {1,4,7} by applications of
Pre({1,4,7}) = {2,3,5,6,8,9}. Here rules are labeled as follows:

  DPs:
    { 1: +^#(0(), y) -> c_1()
    , 2: +^#(s(x), y) -> c_2(+^#(x, y))
    , 3: +^#(p(x), y) -> c_3(+^#(x, y))
    , 4: minus^#(0()) -> c_4()
    , 5: minus^#(s(x)) -> c_5(minus^#(x))
    , 6: minus^#(p(x)) -> c_6(minus^#(x))
    , 7: *^#(0(), y) -> c_7()
    , 8: *^#(s(x), y) -> c_8(+^#(*(x, y), y), *^#(x, y))
    , 9: *^#(p(x), y) ->
         c_9(+^#(*(x, y), minus(y)), *^#(x, y), minus^#(y)) }

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { +^#(s(x), y) -> c_2(+^#(x, y))
  , +^#(p(x), y) -> c_3(+^#(x, y))
  , minus^#(s(x)) -> c_5(minus^#(x))
  , minus^#(p(x)) -> c_6(minus^#(x))
  , *^#(s(x), y) -> c_8(+^#(*(x, y), y), *^#(x, y))
  , *^#(p(x), y) ->
    c_9(+^#(*(x, y), minus(y)), *^#(x, y), minus^#(y)) }
Weak DPs:
  { +^#(0(), y) -> c_1()
  , minus^#(0()) -> c_4()
  , *^#(0(), y) -> c_7() }
Weak Trs:
  { +(0(), y) -> y
  , +(s(x), y) -> s(+(x, y))
  , +(p(x), y) -> p(+(x, y))
  , minus(0()) -> 0()
  , minus(s(x)) -> p(minus(x))
  , minus(p(x)) -> s(minus(x))
  , *(0(), y) -> 0()
  , *(s(x), y) -> +(*(x, y), y)
  , *(p(x), y) -> +(*(x, y), minus(y)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The following weak DPs constitute a sub-graph of the DG that is
closed under successors. The DPs are removed.

{ +^#(0(), y) -> c_1()
, minus^#(0()) -> c_4()
, *^#(0(), y) -> c_7() }

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { +^#(s(x), y) -> c_2(+^#(x, y))
  , +^#(p(x), y) -> c_3(+^#(x, y))
  , minus^#(s(x)) -> c_5(minus^#(x))
  , minus^#(p(x)) -> c_6(minus^#(x))
  , *^#(s(x), y) -> c_8(+^#(*(x, y), y), *^#(x, y))
  , *^#(p(x), y) ->
    c_9(+^#(*(x, y), minus(y)), *^#(x, y), minus^#(y)) }
Weak Trs:
  { +(0(), y) -> y
  , +(s(x), y) -> s(+(x, y))
  , +(p(x), y) -> p(+(x, y))
  , minus(0()) -> 0()
  , minus(s(x)) -> p(minus(x))
  , minus(p(x)) -> s(minus(x))
  , *(0(), y) -> 0()
  , *(s(x), y) -> +(*(x, y), y)
  , *(p(x), y) -> +(*(x, y), minus(y)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) 'matrices' failed due to the following reason:
   
   None of the processors succeeded.
   
   Details of failed attempt(s):
   -----------------------------
   1) 'matrix interpretation of dimension 4' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   2) 'matrix interpretation of dimension 3' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   3) 'matrix interpretation of dimension 3' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   4) 'matrix interpretation of dimension 2' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   5) 'matrix interpretation of dimension 2' failed due to the
      following reason:
      
      The input cannot be shown compatible
   
   6) 'matrix interpretation of dimension 1' failed due to the
      following reason:
      
      The input cannot be shown compatible
   

2) 'empty' failed due to the following reason:
   
   Empty strict component of the problem is NOT empty.


Arrrr..