WORST_CASE(?,O(1))
* Step 1: DependencyPairs WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            =(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} / {and/2,true/0,xor/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {=,implies,not,or} and constructors {and,true,xor}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        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.
* Step 2: UsableRules WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            =#(x,y) -> c_1()
            implies#(x,y) -> c_2()
            not#(x) -> c_3()
            or#(x,y) -> c_4()
        - Weak TRS:
            =(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 runtime complexity wrt. defined symbols {=#,implies#,not#,or#} and constructors {and,true,xor}
    + Applied Processor:
        UsableRules
    + Details:
        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()
* Step 3: Trivial WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            =#(x,y) -> c_1()
            implies#(x,y) -> c_2()
            not#(x) -> c_3()
            or#(x,y) -> c_4()
        - 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 runtime complexity wrt. defined symbols {=#,implies#,not#,or#} and constructors {and,true,xor}
    + Applied Processor:
        Trivial
    + Details:
        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.
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        
        - 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 runtime complexity wrt. defined symbols {=#,implies#,not#,or#} and constructors {and,true,xor}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))