MAYBE

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

Strict Trs:
  { 0(#()) -> #()
  , +(x, #()) -> x
  , +(x, +(y, z)) -> +(+(x, y), z)
  , +(0(x), 0(y)) -> 0(+(x, y))
  , +(0(x), 1(y)) -> 1(+(x, y))
  , +(#(), x) -> x
  , +(1(x), 0(y)) -> 1(+(x, y))
  , +(1(x), 1(y)) -> 0(+(+(x, y), 1(#())))
  , -(x, #()) -> x
  , -(0(x), 0(y)) -> 0(-(x, y))
  , -(0(x), 1(y)) -> 1(-(-(x, y), 1(#())))
  , -(#(), x) -> #()
  , -(1(x), 0(y)) -> 1(-(x, y))
  , -(1(x), 1(y)) -> 0(-(x, y))
  , not(false()) -> true()
  , not(true()) -> false()
  , and(x, false()) -> false()
  , and(x, true()) -> x
  , if(false(), x, y) -> y
  , if(true(), x, y) -> x
  , ge(x, #()) -> true()
  , ge(0(x), 0(y)) -> ge(x, y)
  , ge(0(x), 1(y)) -> not(ge(y, x))
  , ge(#(), 0(x)) -> ge(#(), x)
  , ge(#(), 1(x)) -> false()
  , ge(1(x), 0(y)) -> ge(x, y)
  , ge(1(x), 1(y)) -> ge(x, y)
  , val(l(x)) -> x
  , val(n(x, y, z)) -> x
  , min(l(x)) -> x
  , min(n(x, y, z)) -> min(y)
  , max(l(x)) -> x
  , max(n(x, y, z)) -> max(z)
  , bs(l(x)) -> true()
  , bs(n(x, y, z)) ->
    and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
  , size(l(x)) -> 1(#())
  , size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#()))
  , wb(l(x)) -> true()
  , wb(n(x, y, z)) ->
    and(if(ge(size(y), size(z)),
           ge(1(#()), -(size(y), size(z))),
           ge(1(#()), -(size(z), size(y)))),
        and(wb(y), wb(z))) }
Obligation:
  runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) 'WithProblem (timeout of 60 seconds)' failed due to the
   following reason:
   
   Computation stopped due to timeout after 60.0 seconds.

2) 'Best' failed due to the following reason:
   
   None of the processors succeeded.
   
   Details of failed attempt(s):
   -----------------------------
   1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)'
      failed due to the following reason:
      
      Computation stopped due to timeout after 30.0 seconds.
   
   2) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed
      due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'Bounds with minimal-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
   
   3) 'Best' failed due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
         to the following reason:
         
         The processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
      2) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
         following reason:
         
         The processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
   

3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { 0^#(#()) -> c_1()
     , +^#(x, #()) -> c_2(x)
     , +^#(x, +(y, z)) -> c_3(+^#(+(x, y), z))
     , +^#(0(x), 0(y)) -> c_4(0^#(+(x, y)))
     , +^#(0(x), 1(y)) -> c_5(+^#(x, y))
     , +^#(#(), x) -> c_6(x)
     , +^#(1(x), 0(y)) -> c_7(+^#(x, y))
     , +^#(1(x), 1(y)) -> c_8(0^#(+(+(x, y), 1(#()))))
     , -^#(x, #()) -> c_9(x)
     , -^#(0(x), 0(y)) -> c_10(0^#(-(x, y)))
     , -^#(0(x), 1(y)) -> c_11(-^#(-(x, y), 1(#())))
     , -^#(#(), x) -> c_12()
     , -^#(1(x), 0(y)) -> c_13(-^#(x, y))
     , -^#(1(x), 1(y)) -> c_14(0^#(-(x, y)))
     , not^#(false()) -> c_15()
     , not^#(true()) -> c_16()
     , and^#(x, false()) -> c_17()
     , and^#(x, true()) -> c_18(x)
     , if^#(false(), x, y) -> c_19(y)
     , if^#(true(), x, y) -> c_20(x)
     , ge^#(x, #()) -> c_21()
     , ge^#(0(x), 0(y)) -> c_22(ge^#(x, y))
     , ge^#(0(x), 1(y)) -> c_23(not^#(ge(y, x)))
     , ge^#(#(), 0(x)) -> c_24(ge^#(#(), x))
     , ge^#(#(), 1(x)) -> c_25()
     , ge^#(1(x), 0(y)) -> c_26(ge^#(x, y))
     , ge^#(1(x), 1(y)) -> c_27(ge^#(x, y))
     , val^#(l(x)) -> c_28(x)
     , val^#(n(x, y, z)) -> c_29(x)
     , min^#(l(x)) -> c_30(x)
     , min^#(n(x, y, z)) -> c_31(min^#(y))
     , max^#(l(x)) -> c_32(x)
     , max^#(n(x, y, z)) -> c_33(max^#(z))
     , bs^#(l(x)) -> c_34()
     , bs^#(n(x, y, z)) ->
       c_35(and^#(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z))))
     , size^#(l(x)) -> c_36()
     , size^#(n(x, y, z)) -> c_37(+^#(+(size(x), size(y)), 1(#())))
     , wb^#(l(x)) -> c_38()
     , wb^#(n(x, y, z)) ->
       c_39(and^#(if(ge(size(y), size(z)),
                     ge(1(#()), -(size(y), size(z))),
                     ge(1(#()), -(size(z), size(y)))),
                  and(wb(y), wb(z)))) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { 0^#(#()) -> c_1()
     , +^#(x, #()) -> c_2(x)
     , +^#(x, +(y, z)) -> c_3(+^#(+(x, y), z))
     , +^#(0(x), 0(y)) -> c_4(0^#(+(x, y)))
     , +^#(0(x), 1(y)) -> c_5(+^#(x, y))
     , +^#(#(), x) -> c_6(x)
     , +^#(1(x), 0(y)) -> c_7(+^#(x, y))
     , +^#(1(x), 1(y)) -> c_8(0^#(+(+(x, y), 1(#()))))
     , -^#(x, #()) -> c_9(x)
     , -^#(0(x), 0(y)) -> c_10(0^#(-(x, y)))
     , -^#(0(x), 1(y)) -> c_11(-^#(-(x, y), 1(#())))
     , -^#(#(), x) -> c_12()
     , -^#(1(x), 0(y)) -> c_13(-^#(x, y))
     , -^#(1(x), 1(y)) -> c_14(0^#(-(x, y)))
     , not^#(false()) -> c_15()
     , not^#(true()) -> c_16()
     , and^#(x, false()) -> c_17()
     , and^#(x, true()) -> c_18(x)
     , if^#(false(), x, y) -> c_19(y)
     , if^#(true(), x, y) -> c_20(x)
     , ge^#(x, #()) -> c_21()
     , ge^#(0(x), 0(y)) -> c_22(ge^#(x, y))
     , ge^#(0(x), 1(y)) -> c_23(not^#(ge(y, x)))
     , ge^#(#(), 0(x)) -> c_24(ge^#(#(), x))
     , ge^#(#(), 1(x)) -> c_25()
     , ge^#(1(x), 0(y)) -> c_26(ge^#(x, y))
     , ge^#(1(x), 1(y)) -> c_27(ge^#(x, y))
     , val^#(l(x)) -> c_28(x)
     , val^#(n(x, y, z)) -> c_29(x)
     , min^#(l(x)) -> c_30(x)
     , min^#(n(x, y, z)) -> c_31(min^#(y))
     , max^#(l(x)) -> c_32(x)
     , max^#(n(x, y, z)) -> c_33(max^#(z))
     , bs^#(l(x)) -> c_34()
     , bs^#(n(x, y, z)) ->
       c_35(and^#(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z))))
     , size^#(l(x)) -> c_36()
     , size^#(n(x, y, z)) -> c_37(+^#(+(size(x), size(y)), 1(#())))
     , wb^#(l(x)) -> c_38()
     , wb^#(n(x, y, z)) ->
       c_39(and^#(if(ge(size(y), size(z)),
                     ge(1(#()), -(size(y), size(z))),
                     ge(1(#()), -(size(z), size(y)))),
                  and(wb(y), wb(z)))) }
   Strict Trs:
     { 0(#()) -> #()
     , +(x, #()) -> x
     , +(x, +(y, z)) -> +(+(x, y), z)
     , +(0(x), 0(y)) -> 0(+(x, y))
     , +(0(x), 1(y)) -> 1(+(x, y))
     , +(#(), x) -> x
     , +(1(x), 0(y)) -> 1(+(x, y))
     , +(1(x), 1(y)) -> 0(+(+(x, y), 1(#())))
     , -(x, #()) -> x
     , -(0(x), 0(y)) -> 0(-(x, y))
     , -(0(x), 1(y)) -> 1(-(-(x, y), 1(#())))
     , -(#(), x) -> #()
     , -(1(x), 0(y)) -> 1(-(x, y))
     , -(1(x), 1(y)) -> 0(-(x, y))
     , not(false()) -> true()
     , not(true()) -> false()
     , and(x, false()) -> false()
     , and(x, true()) -> x
     , if(false(), x, y) -> y
     , if(true(), x, y) -> x
     , ge(x, #()) -> true()
     , ge(0(x), 0(y)) -> ge(x, y)
     , ge(0(x), 1(y)) -> not(ge(y, x))
     , ge(#(), 0(x)) -> ge(#(), x)
     , ge(#(), 1(x)) -> false()
     , ge(1(x), 0(y)) -> ge(x, y)
     , ge(1(x), 1(y)) -> ge(x, y)
     , val(l(x)) -> x
     , val(n(x, y, z)) -> x
     , min(l(x)) -> x
     , min(n(x, y, z)) -> min(y)
     , max(l(x)) -> x
     , max(n(x, y, z)) -> max(z)
     , bs(l(x)) -> true()
     , bs(n(x, y, z)) ->
       and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
     , size(l(x)) -> 1(#())
     , size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#()))
     , wb(l(x)) -> true()
     , wb(n(x, y, z)) ->
       and(if(ge(size(y), size(z)),
              ge(1(#()), -(size(y), size(z))),
              ge(1(#()), -(size(z), size(y)))),
           and(wb(y), wb(z))) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of
   {1,12,15,16,17,21,25,34,36,38} by applications of
   Pre({1,12,15,16,17,21,25,34,36,38}) =
   {2,4,6,8,9,10,11,13,14,18,19,20,22,23,24,26,27,28,29,30,32,35,39}.
   Here rules are labeled as follows:
   
     DPs:
       { 1: 0^#(#()) -> c_1()
       , 2: +^#(x, #()) -> c_2(x)
       , 3: +^#(x, +(y, z)) -> c_3(+^#(+(x, y), z))
       , 4: +^#(0(x), 0(y)) -> c_4(0^#(+(x, y)))
       , 5: +^#(0(x), 1(y)) -> c_5(+^#(x, y))
       , 6: +^#(#(), x) -> c_6(x)
       , 7: +^#(1(x), 0(y)) -> c_7(+^#(x, y))
       , 8: +^#(1(x), 1(y)) -> c_8(0^#(+(+(x, y), 1(#()))))
       , 9: -^#(x, #()) -> c_9(x)
       , 10: -^#(0(x), 0(y)) -> c_10(0^#(-(x, y)))
       , 11: -^#(0(x), 1(y)) -> c_11(-^#(-(x, y), 1(#())))
       , 12: -^#(#(), x) -> c_12()
       , 13: -^#(1(x), 0(y)) -> c_13(-^#(x, y))
       , 14: -^#(1(x), 1(y)) -> c_14(0^#(-(x, y)))
       , 15: not^#(false()) -> c_15()
       , 16: not^#(true()) -> c_16()
       , 17: and^#(x, false()) -> c_17()
       , 18: and^#(x, true()) -> c_18(x)
       , 19: if^#(false(), x, y) -> c_19(y)
       , 20: if^#(true(), x, y) -> c_20(x)
       , 21: ge^#(x, #()) -> c_21()
       , 22: ge^#(0(x), 0(y)) -> c_22(ge^#(x, y))
       , 23: ge^#(0(x), 1(y)) -> c_23(not^#(ge(y, x)))
       , 24: ge^#(#(), 0(x)) -> c_24(ge^#(#(), x))
       , 25: ge^#(#(), 1(x)) -> c_25()
       , 26: ge^#(1(x), 0(y)) -> c_26(ge^#(x, y))
       , 27: ge^#(1(x), 1(y)) -> c_27(ge^#(x, y))
       , 28: val^#(l(x)) -> c_28(x)
       , 29: val^#(n(x, y, z)) -> c_29(x)
       , 30: min^#(l(x)) -> c_30(x)
       , 31: min^#(n(x, y, z)) -> c_31(min^#(y))
       , 32: max^#(l(x)) -> c_32(x)
       , 33: max^#(n(x, y, z)) -> c_33(max^#(z))
       , 34: bs^#(l(x)) -> c_34()
       , 35: bs^#(n(x, y, z)) ->
             c_35(and^#(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z))))
       , 36: size^#(l(x)) -> c_36()
       , 37: size^#(n(x, y, z)) -> c_37(+^#(+(size(x), size(y)), 1(#())))
       , 38: wb^#(l(x)) -> c_38()
       , 39: wb^#(n(x, y, z)) ->
             c_39(and^#(if(ge(size(y), size(z)),
                           ge(1(#()), -(size(y), size(z))),
                           ge(1(#()), -(size(z), size(y)))),
                        and(wb(y), wb(z)))) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { +^#(x, #()) -> c_2(x)
     , +^#(x, +(y, z)) -> c_3(+^#(+(x, y), z))
     , +^#(0(x), 0(y)) -> c_4(0^#(+(x, y)))
     , +^#(0(x), 1(y)) -> c_5(+^#(x, y))
     , +^#(#(), x) -> c_6(x)
     , +^#(1(x), 0(y)) -> c_7(+^#(x, y))
     , +^#(1(x), 1(y)) -> c_8(0^#(+(+(x, y), 1(#()))))
     , -^#(x, #()) -> c_9(x)
     , -^#(0(x), 0(y)) -> c_10(0^#(-(x, y)))
     , -^#(0(x), 1(y)) -> c_11(-^#(-(x, y), 1(#())))
     , -^#(1(x), 0(y)) -> c_13(-^#(x, y))
     , -^#(1(x), 1(y)) -> c_14(0^#(-(x, y)))
     , and^#(x, true()) -> c_18(x)
     , if^#(false(), x, y) -> c_19(y)
     , if^#(true(), x, y) -> c_20(x)
     , ge^#(0(x), 0(y)) -> c_22(ge^#(x, y))
     , ge^#(0(x), 1(y)) -> c_23(not^#(ge(y, x)))
     , ge^#(#(), 0(x)) -> c_24(ge^#(#(), x))
     , ge^#(1(x), 0(y)) -> c_26(ge^#(x, y))
     , ge^#(1(x), 1(y)) -> c_27(ge^#(x, y))
     , val^#(l(x)) -> c_28(x)
     , val^#(n(x, y, z)) -> c_29(x)
     , min^#(l(x)) -> c_30(x)
     , min^#(n(x, y, z)) -> c_31(min^#(y))
     , max^#(l(x)) -> c_32(x)
     , max^#(n(x, y, z)) -> c_33(max^#(z))
     , bs^#(n(x, y, z)) ->
       c_35(and^#(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z))))
     , size^#(n(x, y, z)) -> c_37(+^#(+(size(x), size(y)), 1(#())))
     , wb^#(n(x, y, z)) ->
       c_39(and^#(if(ge(size(y), size(z)),
                     ge(1(#()), -(size(y), size(z))),
                     ge(1(#()), -(size(z), size(y)))),
                  and(wb(y), wb(z)))) }
   Strict Trs:
     { 0(#()) -> #()
     , +(x, #()) -> x
     , +(x, +(y, z)) -> +(+(x, y), z)
     , +(0(x), 0(y)) -> 0(+(x, y))
     , +(0(x), 1(y)) -> 1(+(x, y))
     , +(#(), x) -> x
     , +(1(x), 0(y)) -> 1(+(x, y))
     , +(1(x), 1(y)) -> 0(+(+(x, y), 1(#())))
     , -(x, #()) -> x
     , -(0(x), 0(y)) -> 0(-(x, y))
     , -(0(x), 1(y)) -> 1(-(-(x, y), 1(#())))
     , -(#(), x) -> #()
     , -(1(x), 0(y)) -> 1(-(x, y))
     , -(1(x), 1(y)) -> 0(-(x, y))
     , not(false()) -> true()
     , not(true()) -> false()
     , and(x, false()) -> false()
     , and(x, true()) -> x
     , if(false(), x, y) -> y
     , if(true(), x, y) -> x
     , ge(x, #()) -> true()
     , ge(0(x), 0(y)) -> ge(x, y)
     , ge(0(x), 1(y)) -> not(ge(y, x))
     , ge(#(), 0(x)) -> ge(#(), x)
     , ge(#(), 1(x)) -> false()
     , ge(1(x), 0(y)) -> ge(x, y)
     , ge(1(x), 1(y)) -> ge(x, y)
     , val(l(x)) -> x
     , val(n(x, y, z)) -> x
     , min(l(x)) -> x
     , min(n(x, y, z)) -> min(y)
     , max(l(x)) -> x
     , max(n(x, y, z)) -> max(z)
     , bs(l(x)) -> true()
     , bs(n(x, y, z)) ->
       and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
     , size(l(x)) -> 1(#())
     , size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#()))
     , wb(l(x)) -> true()
     , wb(n(x, y, z)) ->
       and(if(ge(size(y), size(z)),
              ge(1(#()), -(size(y), size(z))),
              ge(1(#()), -(size(z), size(y)))),
           and(wb(y), wb(z))) }
   Weak DPs:
     { 0^#(#()) -> c_1()
     , -^#(#(), x) -> c_12()
     , not^#(false()) -> c_15()
     , not^#(true()) -> c_16()
     , and^#(x, false()) -> c_17()
     , ge^#(x, #()) -> c_21()
     , ge^#(#(), 1(x)) -> c_25()
     , bs^#(l(x)) -> c_34()
     , size^#(l(x)) -> c_36()
     , wb^#(l(x)) -> c_38() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {3,7,9,12,17} by
   applications of Pre({3,7,9,12,17}) =
   {1,2,4,5,6,8,10,11,13,14,15,16,19,20,21,22,23,25,28}. Here rules
   are labeled as follows:
   
     DPs:
       { 1: +^#(x, #()) -> c_2(x)
       , 2: +^#(x, +(y, z)) -> c_3(+^#(+(x, y), z))
       , 3: +^#(0(x), 0(y)) -> c_4(0^#(+(x, y)))
       , 4: +^#(0(x), 1(y)) -> c_5(+^#(x, y))
       , 5: +^#(#(), x) -> c_6(x)
       , 6: +^#(1(x), 0(y)) -> c_7(+^#(x, y))
       , 7: +^#(1(x), 1(y)) -> c_8(0^#(+(+(x, y), 1(#()))))
       , 8: -^#(x, #()) -> c_9(x)
       , 9: -^#(0(x), 0(y)) -> c_10(0^#(-(x, y)))
       , 10: -^#(0(x), 1(y)) -> c_11(-^#(-(x, y), 1(#())))
       , 11: -^#(1(x), 0(y)) -> c_13(-^#(x, y))
       , 12: -^#(1(x), 1(y)) -> c_14(0^#(-(x, y)))
       , 13: and^#(x, true()) -> c_18(x)
       , 14: if^#(false(), x, y) -> c_19(y)
       , 15: if^#(true(), x, y) -> c_20(x)
       , 16: ge^#(0(x), 0(y)) -> c_22(ge^#(x, y))
       , 17: ge^#(0(x), 1(y)) -> c_23(not^#(ge(y, x)))
       , 18: ge^#(#(), 0(x)) -> c_24(ge^#(#(), x))
       , 19: ge^#(1(x), 0(y)) -> c_26(ge^#(x, y))
       , 20: ge^#(1(x), 1(y)) -> c_27(ge^#(x, y))
       , 21: val^#(l(x)) -> c_28(x)
       , 22: val^#(n(x, y, z)) -> c_29(x)
       , 23: min^#(l(x)) -> c_30(x)
       , 24: min^#(n(x, y, z)) -> c_31(min^#(y))
       , 25: max^#(l(x)) -> c_32(x)
       , 26: max^#(n(x, y, z)) -> c_33(max^#(z))
       , 27: bs^#(n(x, y, z)) ->
             c_35(and^#(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z))))
       , 28: size^#(n(x, y, z)) -> c_37(+^#(+(size(x), size(y)), 1(#())))
       , 29: wb^#(n(x, y, z)) ->
             c_39(and^#(if(ge(size(y), size(z)),
                           ge(1(#()), -(size(y), size(z))),
                           ge(1(#()), -(size(z), size(y)))),
                        and(wb(y), wb(z))))
       , 30: 0^#(#()) -> c_1()
       , 31: -^#(#(), x) -> c_12()
       , 32: not^#(false()) -> c_15()
       , 33: not^#(true()) -> c_16()
       , 34: and^#(x, false()) -> c_17()
       , 35: ge^#(x, #()) -> c_21()
       , 36: ge^#(#(), 1(x)) -> c_25()
       , 37: bs^#(l(x)) -> c_34()
       , 38: size^#(l(x)) -> c_36()
       , 39: wb^#(l(x)) -> c_38() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { +^#(x, #()) -> c_2(x)
     , +^#(x, +(y, z)) -> c_3(+^#(+(x, y), z))
     , +^#(0(x), 1(y)) -> c_5(+^#(x, y))
     , +^#(#(), x) -> c_6(x)
     , +^#(1(x), 0(y)) -> c_7(+^#(x, y))
     , -^#(x, #()) -> c_9(x)
     , -^#(0(x), 1(y)) -> c_11(-^#(-(x, y), 1(#())))
     , -^#(1(x), 0(y)) -> c_13(-^#(x, y))
     , and^#(x, true()) -> c_18(x)
     , if^#(false(), x, y) -> c_19(y)
     , if^#(true(), x, y) -> c_20(x)
     , ge^#(0(x), 0(y)) -> c_22(ge^#(x, y))
     , ge^#(#(), 0(x)) -> c_24(ge^#(#(), x))
     , ge^#(1(x), 0(y)) -> c_26(ge^#(x, y))
     , ge^#(1(x), 1(y)) -> c_27(ge^#(x, y))
     , val^#(l(x)) -> c_28(x)
     , val^#(n(x, y, z)) -> c_29(x)
     , min^#(l(x)) -> c_30(x)
     , min^#(n(x, y, z)) -> c_31(min^#(y))
     , max^#(l(x)) -> c_32(x)
     , max^#(n(x, y, z)) -> c_33(max^#(z))
     , bs^#(n(x, y, z)) ->
       c_35(and^#(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z))))
     , size^#(n(x, y, z)) -> c_37(+^#(+(size(x), size(y)), 1(#())))
     , wb^#(n(x, y, z)) ->
       c_39(and^#(if(ge(size(y), size(z)),
                     ge(1(#()), -(size(y), size(z))),
                     ge(1(#()), -(size(z), size(y)))),
                  and(wb(y), wb(z)))) }
   Strict Trs:
     { 0(#()) -> #()
     , +(x, #()) -> x
     , +(x, +(y, z)) -> +(+(x, y), z)
     , +(0(x), 0(y)) -> 0(+(x, y))
     , +(0(x), 1(y)) -> 1(+(x, y))
     , +(#(), x) -> x
     , +(1(x), 0(y)) -> 1(+(x, y))
     , +(1(x), 1(y)) -> 0(+(+(x, y), 1(#())))
     , -(x, #()) -> x
     , -(0(x), 0(y)) -> 0(-(x, y))
     , -(0(x), 1(y)) -> 1(-(-(x, y), 1(#())))
     , -(#(), x) -> #()
     , -(1(x), 0(y)) -> 1(-(x, y))
     , -(1(x), 1(y)) -> 0(-(x, y))
     , not(false()) -> true()
     , not(true()) -> false()
     , and(x, false()) -> false()
     , and(x, true()) -> x
     , if(false(), x, y) -> y
     , if(true(), x, y) -> x
     , ge(x, #()) -> true()
     , ge(0(x), 0(y)) -> ge(x, y)
     , ge(0(x), 1(y)) -> not(ge(y, x))
     , ge(#(), 0(x)) -> ge(#(), x)
     , ge(#(), 1(x)) -> false()
     , ge(1(x), 0(y)) -> ge(x, y)
     , ge(1(x), 1(y)) -> ge(x, y)
     , val(l(x)) -> x
     , val(n(x, y, z)) -> x
     , min(l(x)) -> x
     , min(n(x, y, z)) -> min(y)
     , max(l(x)) -> x
     , max(n(x, y, z)) -> max(z)
     , bs(l(x)) -> true()
     , bs(n(x, y, z)) ->
       and(and(ge(x, max(y)), ge(min(z), x)), and(bs(y), bs(z)))
     , size(l(x)) -> 1(#())
     , size(n(x, y, z)) -> +(+(size(x), size(y)), 1(#()))
     , wb(l(x)) -> true()
     , wb(n(x, y, z)) ->
       and(if(ge(size(y), size(z)),
              ge(1(#()), -(size(y), size(z))),
              ge(1(#()), -(size(z), size(y)))),
           and(wb(y), wb(z))) }
   Weak DPs:
     { 0^#(#()) -> c_1()
     , +^#(0(x), 0(y)) -> c_4(0^#(+(x, y)))
     , +^#(1(x), 1(y)) -> c_8(0^#(+(+(x, y), 1(#()))))
     , -^#(0(x), 0(y)) -> c_10(0^#(-(x, y)))
     , -^#(#(), x) -> c_12()
     , -^#(1(x), 1(y)) -> c_14(0^#(-(x, y)))
     , not^#(false()) -> c_15()
     , not^#(true()) -> c_16()
     , and^#(x, false()) -> c_17()
     , ge^#(x, #()) -> c_21()
     , ge^#(0(x), 1(y)) -> c_23(not^#(ge(y, x)))
     , ge^#(#(), 1(x)) -> c_25()
     , bs^#(l(x)) -> c_34()
     , size^#(l(x)) -> c_36()
     , wb^#(l(x)) -> c_38() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..