*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        compS_f#1(compS_f(x2),x1) -> compS_f#1(x2,S(x1))
        compS_f#1(id(),x3) -> S(x3)
        iter#3(0()) -> id()
        iter#3(S(x6)) -> compS_f(iter#3(x6))
        main(0()) -> 0()
        main(S(x9)) -> compS_f#1(iter#3(x9),0())
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {compS_f#1/2,iter#3/1,main/1} / {0/0,S/1,compS_f/1,id/0}
      Obligation:
        Innermost
        basic terms: {compS_f#1,iter#3,main}/{0,S,compS_f,id}
    Applied Processor:
      Bounds {initialAutomaton = minimal, enrichment = match}
    Proof:
      The problem is match-bounded by 2.
      The enriched problem is compatible with follwoing automaton.
        0_0() -> 2
        0_1() -> 1
        S_0(2) -> 2
        S_1(1) -> 1
        S_1(2) -> 1
        S_1(2) -> 3
        S_1(3) -> 1
        S_2(1) -> 1
        S_2(1) -> 5
        S_2(5) -> 1
        compS_f_0(2) -> 2
        compS_f_1(4) -> 1
        compS_f_1(4) -> 4
        compS_f#1_0(2,2) -> 1
        compS_f#1_1(2,1) -> 1
        compS_f#1_1(2,3) -> 1
        compS_f#1_1(4,1) -> 1
        compS_f#1_2(4,1) -> 1
        compS_f#1_2(4,5) -> 1
        id_0() -> 2
        id_1() -> 1
        id_1() -> 4
        iter#3_0(2) -> 1
        iter#3_1(2) -> 4
        main_0(2) -> 1
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        compS_f#1(compS_f(x2),x1) -> compS_f#1(x2,S(x1))
        compS_f#1(id(),x3) -> S(x3)
        iter#3(0()) -> id()
        iter#3(S(x6)) -> compS_f(iter#3(x6))
        main(0()) -> 0()
        main(S(x9)) -> compS_f#1(iter#3(x9),0())
      Signature:
        {compS_f#1/2,iter#3/1,main/1} / {0/0,S/1,compS_f/1,id/0}
      Obligation:
        Innermost
        basic terms: {compS_f#1,iter#3,main}/{0,S,compS_f,id}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).