*** 1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        *(x,0()) -> 0()
        *(*(x,y),z) -> *(x,*(y,z))
        *(1(),y) -> y
        *(i(x),x) -> 1()
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {*/2} / {0/0,1/0,i/1}
      Obligation:
        Innermost
        basic terms: {*}/{0,1,i}
    Applied Processor:
      DependencyPairs {dpKind_ = DT}
    Proof:
      We add the following dependency tuples:
      
      Strict DPs
        *#(x,0()) -> c_1()
        *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
        *#(1(),y) -> c_3()
        *#(i(x),x) -> c_4()
      Weak DPs
        
      
      and mark the set of starting terms.
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        *#(x,0()) -> c_1()
        *#(*(x,y),z) -> c_2(*#(x,*(y,z)),*#(y,z))
        *#(1(),y) -> c_3()
        *#(i(x),x) -> c_4()
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        *(x,0()) -> 0()
        *(*(x,y),z) -> *(x,*(y,z))
        *(1(),y) -> y
        *(i(x),x) -> 1()
      Signature:
        {*/2,*#/2} / {0/0,1/0,i/1,c_1/0,c_2/2,c_3/0,c_4/0}
      Obligation:
        Innermost
        basic terms: {*#}/{0,1,i}
    Applied Processor:
      UsableRules
    Proof:
      We replace rewrite rules by usable rules:
        *#(x,0()) -> c_1()
        *#(1(),y) -> c_3()
        *#(i(x),x) -> c_4()
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        *#(x,0()) -> c_1()
        *#(1(),y) -> c_3()
        *#(i(x),x) -> c_4()
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {*/2,*#/2} / {0/0,1/0,i/1,c_1/0,c_2/2,c_3/0,c_4/0}
      Obligation:
        Innermost
        basic terms: {*#}/{0,1,i}
    Applied Processor:
      Trivial
    Proof:
      Consider the dependency graph
        1:S:*#(x,0()) -> c_1()
           
        
        2:S:*#(1(),y) -> c_3()
           
        
        3:S:*#(i(x),x) -> c_4()
           
        
      The dependency graph contains no loops, we remove all dependency pairs.
*** 1.1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {*/2,*#/2} / {0/0,1/0,i/1,c_1/0,c_2/2,c_3/0,c_4/0}
      Obligation:
        Innermost
        basic terms: {*#}/{0,1,i}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).