*** 1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        =(x,y) -> xor(x,xor(y,true()))
        implies(x,y) -> xor(and(x,y),xor(x,true()))
        not(x) -> xor(x,true())
        or(x,y) -> xor(and(x,y),xor(x,y))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {=/2,implies/2,not/1,or/2} / {and/2,true/0,xor/2}
      Obligation:
        Innermost
        basic terms: {=,implies,not,or}/{and,true,xor}
    Applied Processor:
      DependencyPairs {dpKind_ = DT}
    Proof:
      We add the following dependency tuples:
      
      Strict DPs
        =#(x,y) -> c_1()
        implies#(x,y) -> c_2()
        not#(x) -> c_3()
        or#(x,y) -> c_4()
      Weak DPs
        
      
      and mark the set of starting terms.
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        =#(x,y) -> c_1()
        implies#(x,y) -> c_2()
        not#(x) -> c_3()
        or#(x,y) -> c_4()
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        =(x,y) -> xor(x,xor(y,true()))
        implies(x,y) -> xor(and(x,y),xor(x,true()))
        not(x) -> xor(x,true())
        or(x,y) -> xor(and(x,y),xor(x,y))
      Signature:
        {=/2,implies/2,not/1,or/2,=#/2,implies#/2,not#/1,or#/2} / {and/2,true/0,xor/2,c_1/0,c_2/0,c_3/0,c_4/0}
      Obligation:
        Innermost
        basic terms: {=#,implies#,not#,or#}/{and,true,xor}
    Applied Processor:
      UsableRules
    Proof:
      We replace rewrite rules by usable rules:
        =#(x,y) -> c_1()
        implies#(x,y) -> c_2()
        not#(x) -> c_3()
        or#(x,y) -> c_4()
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        =#(x,y) -> c_1()
        implies#(x,y) -> c_2()
        not#(x) -> c_3()
        or#(x,y) -> c_4()
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {=/2,implies/2,not/1,or/2,=#/2,implies#/2,not#/1,or#/2} / {and/2,true/0,xor/2,c_1/0,c_2/0,c_3/0,c_4/0}
      Obligation:
        Innermost
        basic terms: {=#,implies#,not#,or#}/{and,true,xor}
    Applied Processor:
      Trivial
    Proof:
      Consider the dependency graph
        1:S:=#(x,y) -> c_1()
           
        
        2:S:implies#(x,y) -> c_2()
           
        
        3:S:not#(x) -> c_3()
           
        
        4:S:or#(x,y) -> 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,implies/2,not/1,or/2,=#/2,implies#/2,not#/1,or#/2} / {and/2,true/0,xor/2,c_1/0,c_2/0,c_3/0,c_4/0}
      Obligation:
        Innermost
        basic terms: {=#,implies#,not#,or#}/{and,true,xor}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).