*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        f(+(x,y)) -> *(f(x),f(y))
        f(+(x,s(0()))) -> +(s(s(0())),f(x))
        f(0()) -> s(0())
        f(s(0())) -> *(s(s(0())),f(0()))
        f(s(0())) -> s(s(0()))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {f/1} / {*/2,+/2,0/0,s/1}
      Obligation:
        Innermost
        basic terms: {f}/{*,+,0,s}
    Applied Processor:
      Bounds {initialAutomaton = perSymbol, enrichment = match}
    Proof:
      The problem is match-bounded by 2.
      The enriched problem is compatible with follwoing automaton.
        *_0(1,1) -> 1
        *_0(1,2) -> 1
        *_0(1,3) -> 1
        *_0(1,5) -> 1
        *_0(2,1) -> 1
        *_0(2,2) -> 1
        *_0(2,3) -> 1
        *_0(2,5) -> 1
        *_0(3,1) -> 1
        *_0(3,2) -> 1
        *_0(3,3) -> 1
        *_0(3,5) -> 1
        *_0(5,1) -> 1
        *_0(5,2) -> 1
        *_0(5,3) -> 1
        *_0(5,5) -> 1
        *_1(6,7) -> 4
        *_1(7,7) -> 4
        *_1(7,7) -> 7
        *_1(8,11) -> 4
        *_1(8,11) -> 7
        +_0(1,1) -> 2
        +_0(1,2) -> 2
        +_0(1,3) -> 2
        +_0(1,5) -> 2
        +_0(2,1) -> 2
        +_0(2,2) -> 2
        +_0(2,3) -> 2
        +_0(2,5) -> 2
        +_0(3,1) -> 2
        +_0(3,2) -> 2
        +_0(3,3) -> 2
        +_0(3,5) -> 2
        +_0(5,1) -> 2
        +_0(5,2) -> 2
        +_0(5,3) -> 2
        +_0(5,5) -> 2
        +_1(8,7) -> 4
        +_1(8,7) -> 7
        0_0() -> 3
        0_1() -> 10
        0_2() -> 12
        f_0(1) -> 4
        f_0(2) -> 4
        f_0(3) -> 4
        f_0(5) -> 4
        f_1(1) -> 6
        f_1(1) -> 7
        f_1(2) -> 7
        f_1(3) -> 7
        f_1(5) -> 7
        f_1(10) -> 11
        s_0(1) -> 5
        s_0(2) -> 5
        s_0(3) -> 5
        s_0(5) -> 5
        s_1(9) -> 4
        s_1(9) -> 7
        s_1(9) -> 8
        s_1(10) -> 4
        s_1(10) -> 7
        s_1(10) -> 9
        s_2(12) -> 11
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        f(+(x,y)) -> *(f(x),f(y))
        f(+(x,s(0()))) -> +(s(s(0())),f(x))
        f(0()) -> s(0())
        f(s(0())) -> *(s(s(0())),f(0()))
        f(s(0())) -> s(s(0()))
      Signature:
        {f/1} / {*/2,+/2,0/0,s/1}
      Obligation:
        Innermost
        basic terms: {f}/{*,+,0,s}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).