*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        r1(cons(x,k),a) -> r1(k,cons(x,a))
        r1(empty(),a) -> a
        rev(ls) -> r1(ls,empty())
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {r1/2,rev/1} / {cons/2,empty/0}
      Obligation:
        Full
        basic terms: {r1,rev}/{cons,empty}
    Applied Processor:
      ToInnermost
    Proof:
      switch to innermost, as the system is overlay and right linear and does not contain weak rules
*** 1.1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        r1(cons(x,k),a) -> r1(k,cons(x,a))
        r1(empty(),a) -> a
        rev(ls) -> r1(ls,empty())
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {r1/2,rev/1} / {cons/2,empty/0}
      Obligation:
        Innermost
        basic terms: {r1,rev}/{cons,empty}
    Applied Processor:
      Bounds {initialAutomaton = minimal, enrichment = match}
    Proof:
      The problem is match-bounded by 1.
      The enriched problem is compatible with follwoing automaton.
        cons_0(2,2) -> 1
        cons_0(2,2) -> 2
        cons_1(2,2) -> 1
        cons_1(2,2) -> 3
        cons_1(2,3) -> 1
        cons_1(2,3) -> 3
        empty_0() -> 1
        empty_0() -> 2
        empty_1() -> 1
        empty_1() -> 3
        r1_0(2,2) -> 1
        r1_1(2,3) -> 1
        rev_0(2) -> 1
        2 -> 1
        3 -> 1
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        r1(cons(x,k),a) -> r1(k,cons(x,a))
        r1(empty(),a) -> a
        rev(ls) -> r1(ls,empty())
      Signature:
        {r1/2,rev/1} / {cons/2,empty/0}
      Obligation:
        Innermost
        basic terms: {r1,rev}/{cons,empty}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).