MAYBE
* Step 1: DependencyPairs MAYBE
    + Considered Problem:
        - Strict TRS:
            if(false(),x,b,y,z) -> loop(x,b,times(b,y),s(z))
            if(true(),x,b,y,z) -> z
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            log(x,0()) -> baseError()
            log(x,s(0())) -> baseError()
            log(0(),s(s(b))) -> logZeroError()
            log(s(x),s(s(b))) -> loop(s(x),s(s(b)),s(0()),0())
            loop(x,s(s(b)),s(y),z) -> if(le(x,s(y)),x,s(s(b)),s(y),z)
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
            times(0(),y) -> 0()
            times(s(x),y) -> plus(y,times(x,y))
        - Signature:
            {if/5,le/2,log/2,loop/4,plus/2,times/2} / {0/0,baseError/0,false/0,logZeroError/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if,le,log,loop,plus,times} and constructors {0,baseError
            ,false,logZeroError,s,true}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          if#(false(),x,b,y,z) -> c_1(loop#(x,b,times(b,y),s(z)),times#(b,y))
          if#(true(),x,b,y,z) -> c_2()
          le#(0(),y) -> c_3()
          le#(s(x),0()) -> c_4()
          le#(s(x),s(y)) -> c_5(le#(x,y))
          log#(x,0()) -> c_6()
          log#(x,s(0())) -> c_7()
          log#(0(),s(s(b))) -> c_8()
          log#(s(x),s(s(b))) -> c_9(loop#(s(x),s(s(b)),s(0()),0()))
          loop#(x,s(s(b)),s(y),z) -> c_10(if#(le(x,s(y)),x,s(s(b)),s(y),z),le#(x,s(y)))
          plus#(0(),y) -> c_11()
          plus#(s(x),y) -> c_12(plus#(x,y))
          times#(0(),y) -> c_13()
          times#(s(x),y) -> c_14(plus#(y,times(x,y)),times#(x,y))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 2: UsableRules MAYBE
    + Considered Problem:
        - Strict DPs:
            if#(false(),x,b,y,z) -> c_1(loop#(x,b,times(b,y),s(z)),times#(b,y))
            if#(true(),x,b,y,z) -> c_2()
            le#(0(),y) -> c_3()
            le#(s(x),0()) -> c_4()
            le#(s(x),s(y)) -> c_5(le#(x,y))
            log#(x,0()) -> c_6()
            log#(x,s(0())) -> c_7()
            log#(0(),s(s(b))) -> c_8()
            log#(s(x),s(s(b))) -> c_9(loop#(s(x),s(s(b)),s(0()),0()))
            loop#(x,s(s(b)),s(y),z) -> c_10(if#(le(x,s(y)),x,s(s(b)),s(y),z),le#(x,s(y)))
            plus#(0(),y) -> c_11()
            plus#(s(x),y) -> c_12(plus#(x,y))
            times#(0(),y) -> c_13()
            times#(s(x),y) -> c_14(plus#(y,times(x,y)),times#(x,y))
        - Weak TRS:
            if(false(),x,b,y,z) -> loop(x,b,times(b,y),s(z))
            if(true(),x,b,y,z) -> z
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            log(x,0()) -> baseError()
            log(x,s(0())) -> baseError()
            log(0(),s(s(b))) -> logZeroError()
            log(s(x),s(s(b))) -> loop(s(x),s(s(b)),s(0()),0())
            loop(x,s(s(b)),s(y),z) -> if(le(x,s(y)),x,s(s(b)),s(y),z)
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
            times(0(),y) -> 0()
            times(s(x),y) -> plus(y,times(x,y))
        - Signature:
            {if/5,le/2,log/2,loop/4,plus/2,times/2,if#/5,le#/2,log#/2,loop#/4,plus#/2,times#/2} / {0/0,baseError/0
            ,false/0,logZeroError/0,s/1,true/0,c_1/2,c_2/0,c_3/0,c_4/0,c_5/1,c_6/0,c_7/0,c_8/0,c_9/1,c_10/2,c_11/0
            ,c_12/1,c_13/0,c_14/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if#,le#,log#,loop#,plus#,times#} and constructors {0
            ,baseError,false,logZeroError,s,true}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          le(0(),y) -> true()
          le(s(x),0()) -> false()
          le(s(x),s(y)) -> le(x,y)
          plus(0(),y) -> y
          plus(s(x),y) -> s(plus(x,y))
          times(0(),y) -> 0()
          times(s(x),y) -> plus(y,times(x,y))
          if#(false(),x,b,y,z) -> c_1(loop#(x,b,times(b,y),s(z)),times#(b,y))
          if#(true(),x,b,y,z) -> c_2()
          le#(0(),y) -> c_3()
          le#(s(x),0()) -> c_4()
          le#(s(x),s(y)) -> c_5(le#(x,y))
          log#(x,0()) -> c_6()
          log#(x,s(0())) -> c_7()
          log#(0(),s(s(b))) -> c_8()
          log#(s(x),s(s(b))) -> c_9(loop#(s(x),s(s(b)),s(0()),0()))
          loop#(x,s(s(b)),s(y),z) -> c_10(if#(le(x,s(y)),x,s(s(b)),s(y),z),le#(x,s(y)))
          plus#(0(),y) -> c_11()
          plus#(s(x),y) -> c_12(plus#(x,y))
          times#(0(),y) -> c_13()
          times#(s(x),y) -> c_14(plus#(y,times(x,y)),times#(x,y))
* Step 3: PredecessorEstimation MAYBE
    + Considered Problem:
        - Strict DPs:
            if#(false(),x,b,y,z) -> c_1(loop#(x,b,times(b,y),s(z)),times#(b,y))
            if#(true(),x,b,y,z) -> c_2()
            le#(0(),y) -> c_3()
            le#(s(x),0()) -> c_4()
            le#(s(x),s(y)) -> c_5(le#(x,y))
            log#(x,0()) -> c_6()
            log#(x,s(0())) -> c_7()
            log#(0(),s(s(b))) -> c_8()
            log#(s(x),s(s(b))) -> c_9(loop#(s(x),s(s(b)),s(0()),0()))
            loop#(x,s(s(b)),s(y),z) -> c_10(if#(le(x,s(y)),x,s(s(b)),s(y),z),le#(x,s(y)))
            plus#(0(),y) -> c_11()
            plus#(s(x),y) -> c_12(plus#(x,y))
            times#(0(),y) -> c_13()
            times#(s(x),y) -> c_14(plus#(y,times(x,y)),times#(x,y))
        - Weak TRS:
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
            times(0(),y) -> 0()
            times(s(x),y) -> plus(y,times(x,y))
        - Signature:
            {if/5,le/2,log/2,loop/4,plus/2,times/2,if#/5,le#/2,log#/2,loop#/4,plus#/2,times#/2} / {0/0,baseError/0
            ,false/0,logZeroError/0,s/1,true/0,c_1/2,c_2/0,c_3/0,c_4/0,c_5/1,c_6/0,c_7/0,c_8/0,c_9/1,c_10/2,c_11/0
            ,c_12/1,c_13/0,c_14/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if#,le#,log#,loop#,plus#,times#} and constructors {0
            ,baseError,false,logZeroError,s,true}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {2,3,4,6,7,8,11,13}
        by application of
          Pre({2,3,4,6,7,8,11,13}) = {1,5,10,12,14}.
        Here rules are labelled as follows:
          1: if#(false(),x,b,y,z) -> c_1(loop#(x,b,times(b,y),s(z)),times#(b,y))
          2: if#(true(),x,b,y,z) -> c_2()
          3: le#(0(),y) -> c_3()
          4: le#(s(x),0()) -> c_4()
          5: le#(s(x),s(y)) -> c_5(le#(x,y))
          6: log#(x,0()) -> c_6()
          7: log#(x,s(0())) -> c_7()
          8: log#(0(),s(s(b))) -> c_8()
          9: log#(s(x),s(s(b))) -> c_9(loop#(s(x),s(s(b)),s(0()),0()))
          10: loop#(x,s(s(b)),s(y),z) -> c_10(if#(le(x,s(y)),x,s(s(b)),s(y),z),le#(x,s(y)))
          11: plus#(0(),y) -> c_11()
          12: plus#(s(x),y) -> c_12(plus#(x,y))
          13: times#(0(),y) -> c_13()
          14: times#(s(x),y) -> c_14(plus#(y,times(x,y)),times#(x,y))
* Step 4: RemoveWeakSuffixes MAYBE
    + Considered Problem:
        - Strict DPs:
            if#(false(),x,b,y,z) -> c_1(loop#(x,b,times(b,y),s(z)),times#(b,y))
            le#(s(x),s(y)) -> c_5(le#(x,y))
            log#(s(x),s(s(b))) -> c_9(loop#(s(x),s(s(b)),s(0()),0()))
            loop#(x,s(s(b)),s(y),z) -> c_10(if#(le(x,s(y)),x,s(s(b)),s(y),z),le#(x,s(y)))
            plus#(s(x),y) -> c_12(plus#(x,y))
            times#(s(x),y) -> c_14(plus#(y,times(x,y)),times#(x,y))
        - Weak DPs:
            if#(true(),x,b,y,z) -> c_2()
            le#(0(),y) -> c_3()
            le#(s(x),0()) -> c_4()
            log#(x,0()) -> c_6()
            log#(x,s(0())) -> c_7()
            log#(0(),s(s(b))) -> c_8()
            plus#(0(),y) -> c_11()
            times#(0(),y) -> c_13()
        - Weak TRS:
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
            times(0(),y) -> 0()
            times(s(x),y) -> plus(y,times(x,y))
        - Signature:
            {if/5,le/2,log/2,loop/4,plus/2,times/2,if#/5,le#/2,log#/2,loop#/4,plus#/2,times#/2} / {0/0,baseError/0
            ,false/0,logZeroError/0,s/1,true/0,c_1/2,c_2/0,c_3/0,c_4/0,c_5/1,c_6/0,c_7/0,c_8/0,c_9/1,c_10/2,c_11/0
            ,c_12/1,c_13/0,c_14/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if#,le#,log#,loop#,plus#,times#} and constructors {0
            ,baseError,false,logZeroError,s,true}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:S:if#(false(),x,b,y,z) -> c_1(loop#(x,b,times(b,y),s(z)),times#(b,y))
             -->_2 times#(s(x),y) -> c_14(plus#(y,times(x,y)),times#(x,y)):6
             -->_1 loop#(x,s(s(b)),s(y),z) -> c_10(if#(le(x,s(y)),x,s(s(b)),s(y),z),le#(x,s(y))):4
             -->_2 times#(0(),y) -> c_13():14
          
          2:S:le#(s(x),s(y)) -> c_5(le#(x,y))
             -->_1 le#(s(x),0()) -> c_4():9
             -->_1 le#(0(),y) -> c_3():8
             -->_1 le#(s(x),s(y)) -> c_5(le#(x,y)):2
          
          3:S:log#(s(x),s(s(b))) -> c_9(loop#(s(x),s(s(b)),s(0()),0()))
             -->_1 loop#(x,s(s(b)),s(y),z) -> c_10(if#(le(x,s(y)),x,s(s(b)),s(y),z),le#(x,s(y))):4
          
          4:S:loop#(x,s(s(b)),s(y),z) -> c_10(if#(le(x,s(y)),x,s(s(b)),s(y),z),le#(x,s(y)))
             -->_2 le#(0(),y) -> c_3():8
             -->_1 if#(true(),x,b,y,z) -> c_2():7
             -->_2 le#(s(x),s(y)) -> c_5(le#(x,y)):2
             -->_1 if#(false(),x,b,y,z) -> c_1(loop#(x,b,times(b,y),s(z)),times#(b,y)):1
          
          5:S:plus#(s(x),y) -> c_12(plus#(x,y))
             -->_1 plus#(0(),y) -> c_11():13
             -->_1 plus#(s(x),y) -> c_12(plus#(x,y)):5
          
          6:S:times#(s(x),y) -> c_14(plus#(y,times(x,y)),times#(x,y))
             -->_2 times#(0(),y) -> c_13():14
             -->_1 plus#(0(),y) -> c_11():13
             -->_2 times#(s(x),y) -> c_14(plus#(y,times(x,y)),times#(x,y)):6
             -->_1 plus#(s(x),y) -> c_12(plus#(x,y)):5
          
          7:W:if#(true(),x,b,y,z) -> c_2()
             
          
          8:W:le#(0(),y) -> c_3()
             
          
          9:W:le#(s(x),0()) -> c_4()
             
          
          10:W:log#(x,0()) -> c_6()
             
          
          11:W:log#(x,s(0())) -> c_7()
             
          
          12:W:log#(0(),s(s(b))) -> c_8()
             
          
          13:W:plus#(0(),y) -> c_11()
             
          
          14:W:times#(0(),y) -> c_13()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          12: log#(0(),s(s(b))) -> c_8()
          11: log#(x,s(0())) -> c_7()
          10: log#(x,0()) -> c_6()
          9: le#(s(x),0()) -> c_4()
          7: if#(true(),x,b,y,z) -> c_2()
          8: le#(0(),y) -> c_3()
          13: plus#(0(),y) -> c_11()
          14: times#(0(),y) -> c_13()
* Step 5: RemoveHeads MAYBE
    + Considered Problem:
        - Strict DPs:
            if#(false(),x,b,y,z) -> c_1(loop#(x,b,times(b,y),s(z)),times#(b,y))
            le#(s(x),s(y)) -> c_5(le#(x,y))
            log#(s(x),s(s(b))) -> c_9(loop#(s(x),s(s(b)),s(0()),0()))
            loop#(x,s(s(b)),s(y),z) -> c_10(if#(le(x,s(y)),x,s(s(b)),s(y),z),le#(x,s(y)))
            plus#(s(x),y) -> c_12(plus#(x,y))
            times#(s(x),y) -> c_14(plus#(y,times(x,y)),times#(x,y))
        - Weak TRS:
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
            times(0(),y) -> 0()
            times(s(x),y) -> plus(y,times(x,y))
        - Signature:
            {if/5,le/2,log/2,loop/4,plus/2,times/2,if#/5,le#/2,log#/2,loop#/4,plus#/2,times#/2} / {0/0,baseError/0
            ,false/0,logZeroError/0,s/1,true/0,c_1/2,c_2/0,c_3/0,c_4/0,c_5/1,c_6/0,c_7/0,c_8/0,c_9/1,c_10/2,c_11/0
            ,c_12/1,c_13/0,c_14/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {if#,le#,log#,loop#,plus#,times#} and constructors {0
            ,baseError,false,logZeroError,s,true}
    + Applied Processor:
        RemoveHeads
    + Details:
        Consider the dependency graph
        
        1:S:if#(false(),x,b,y,z) -> c_1(loop#(x,b,times(b,y),s(z)),times#(b,y))
           -->_2 times#(s(x),y) -> c_14(plus#(y,times(x,y)),times#(x,y)):6
           -->_1 loop#(x,s(s(b)),s(y),z) -> c_10(if#(le(x,s(y)),x,s(s(b)),s(y),z),le#(x,s(y))):4
        
        2:S:le#(s(x),s(y)) -> c_5(le#(x,y))
           -->_1 le#(s(x),s(y)) -> c_5(le#(x,y)):2
        
        3:S:log#(s(x),s(s(b))) -> c_9(loop#(s(x),s(s(b)),s(0()),0()))
           -->_1 loop#(x,s(s(b)),s(y),z) -> c_10(if#(le(x,s(y)),x,s(s(b)),s(y),z),le#(x,s(y))):4
        
        4:S:loop#(x,s(s(b)),s(y),z) -> c_10(if#(le(x,s(y)),x,s(s(b)),s(y),z),le#(x,s(y)))
           -->_2 le#(s(x),s(y)) -> c_5(le#(x,y)):2
           -->_1 if#(false(),x,b,y,z) -> c_1(loop#(x,b,times(b,y),s(z)),times#(b,y)):1
        
        5:S:plus#(s(x),y) -> c_12(plus#(x,y))
           -->_1 plus#(s(x),y) -> c_12(plus#(x,y)):5
        
        6:S:times#(s(x),y) -> c_14(plus#(y,times(x,y)),times#(x,y))
           -->_2 times#(s(x),y) -> c_14(plus#(y,times(x,y)),times#(x,y)):6
           -->_1 plus#(s(x),y) -> c_12(plus#(x,y)):5
        
        
        Following roots of the dependency graph are removed, as the considered set of starting terms is closed under reduction with respect to these rules (modulo compound contexts).
        
        [(3,log#(s(x),s(s(b))) -> c_9(loop#(s(x),s(s(b)),s(0()),0())))]
* Step 6: Failure MAYBE
  + Considered Problem:
      - Strict DPs:
          if#(false(),x,b,y,z) -> c_1(loop#(x,b,times(b,y),s(z)),times#(b,y))
          le#(s(x),s(y)) -> c_5(le#(x,y))
          loop#(x,s(s(b)),s(y),z) -> c_10(if#(le(x,s(y)),x,s(s(b)),s(y),z),le#(x,s(y)))
          plus#(s(x),y) -> c_12(plus#(x,y))
          times#(s(x),y) -> c_14(plus#(y,times(x,y)),times#(x,y))
      - Weak TRS:
          le(0(),y) -> true()
          le(s(x),0()) -> false()
          le(s(x),s(y)) -> le(x,y)
          plus(0(),y) -> y
          plus(s(x),y) -> s(plus(x,y))
          times(0(),y) -> 0()
          times(s(x),y) -> plus(y,times(x,y))
      - Signature:
          {if/5,le/2,log/2,loop/4,plus/2,times/2,if#/5,le#/2,log#/2,loop#/4,plus#/2,times#/2} / {0/0,baseError/0
          ,false/0,logZeroError/0,s/1,true/0,c_1/2,c_2/0,c_3/0,c_4/0,c_5/1,c_6/0,c_7/0,c_8/0,c_9/1,c_10/2,c_11/0
          ,c_12/1,c_13/0,c_14/2}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {if#,le#,log#,loop#,plus#,times#} and constructors {0
          ,baseError,false,logZeroError,s,true}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE