* Step 1: Sum WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            U11(tt(),N) -> activate(N)
            U21(tt(),M,N) -> s(plus(activate(N),activate(M)))
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__isNat(X)) -> isNat(X)
            activate(n__plus(X1,X2)) -> plus(X1,X2)
            activate(n__s(X)) -> s(X)
            and(tt(),X) -> activate(X)
            isNat(X) -> n__isNat(X)
            isNat(n__0()) -> tt()
            isNat(n__plus(V1,V2)) -> and(isNat(activate(V1)),n__isNat(activate(V2)))
            isNat(n__s(V1)) -> isNat(activate(V1))
            plus(N,0()) -> U11(isNat(N),N)
            plus(N,s(M)) -> U21(and(isNat(M),n__isNat(N)),M,N)
            plus(X1,X2) -> n__plus(X1,X2)
            s(X) -> n__s(X)
        - Signature:
            {0/0,U11/2,U21/3,activate/1,and/2,isNat/1,plus/2,s/1} / {n__0/0,n__isNat/1,n__plus/2,n__s/1,tt/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {0,U11,U21,activate,and,isNat,plus
            ,s} and constructors {n__0,n__isNat,n__plus,n__s,tt}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: InnermostRuleRemoval WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            U11(tt(),N) -> activate(N)
            U21(tt(),M,N) -> s(plus(activate(N),activate(M)))
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__isNat(X)) -> isNat(X)
            activate(n__plus(X1,X2)) -> plus(X1,X2)
            activate(n__s(X)) -> s(X)
            and(tt(),X) -> activate(X)
            isNat(X) -> n__isNat(X)
            isNat(n__0()) -> tt()
            isNat(n__plus(V1,V2)) -> and(isNat(activate(V1)),n__isNat(activate(V2)))
            isNat(n__s(V1)) -> isNat(activate(V1))
            plus(N,0()) -> U11(isNat(N),N)
            plus(N,s(M)) -> U21(and(isNat(M),n__isNat(N)),M,N)
            plus(X1,X2) -> n__plus(X1,X2)
            s(X) -> n__s(X)
        - Signature:
            {0/0,U11/2,U21/3,activate/1,and/2,isNat/1,plus/2,s/1} / {n__0/0,n__isNat/1,n__plus/2,n__s/1,tt/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {0,U11,U21,activate,and,isNat,plus
            ,s} and constructors {n__0,n__isNat,n__plus,n__s,tt}
    + Applied Processor:
        InnermostRuleRemoval
    + Details:
        Arguments of following rules are not normal-forms.
          plus(N,0()) -> U11(isNat(N),N)
          plus(N,s(M)) -> U21(and(isNat(M),n__isNat(N)),M,N)
        All above mentioned rules can be savely removed.
* Step 3: Bounds WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            0() -> n__0()
            U11(tt(),N) -> activate(N)
            U21(tt(),M,N) -> s(plus(activate(N),activate(M)))
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__isNat(X)) -> isNat(X)
            activate(n__plus(X1,X2)) -> plus(X1,X2)
            activate(n__s(X)) -> s(X)
            and(tt(),X) -> activate(X)
            isNat(X) -> n__isNat(X)
            isNat(n__0()) -> tt()
            isNat(n__plus(V1,V2)) -> and(isNat(activate(V1)),n__isNat(activate(V2)))
            isNat(n__s(V1)) -> isNat(activate(V1))
            plus(X1,X2) -> n__plus(X1,X2)
            s(X) -> n__s(X)
        - Signature:
            {0/0,U11/2,U21/3,activate/1,and/2,isNat/1,plus/2,s/1} / {n__0/0,n__isNat/1,n__plus/2,n__s/1,tt/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {0,U11,U21,activate,and,isNat,plus
            ,s} and constructors {n__0,n__isNat,n__plus,n__s,tt}
    + Applied Processor:
        Bounds {initialAutomaton = perSymbol, enrichment = match}
    + Details:
        The problem is match-bounded by 5.
        The enriched problem is compatible with follwoing automaton.
          0_0() -> 1
          0_1() -> 2
          0_1() -> 4
          0_1() -> 5
          0_1() -> 19
          0_1() -> 20
          0_1() -> 23
          0_1() -> 24
          U11_0(7,7) -> 2
          U11_0(7,8) -> 2
          U11_0(7,9) -> 2
          U11_0(7,10) -> 2
          U11_0(7,13) -> 2
          U11_0(8,7) -> 2
          U11_0(8,8) -> 2
          U11_0(8,9) -> 2
          U11_0(8,10) -> 2
          U11_0(8,13) -> 2
          U11_0(9,7) -> 2
          U11_0(9,8) -> 2
          U11_0(9,9) -> 2
          U11_0(9,10) -> 2
          U11_0(9,13) -> 2
          U11_0(10,7) -> 2
          U11_0(10,8) -> 2
          U11_0(10,9) -> 2
          U11_0(10,10) -> 2
          U11_0(10,13) -> 2
          U11_0(13,7) -> 2
          U11_0(13,8) -> 2
          U11_0(13,9) -> 2
          U11_0(13,10) -> 2
          U11_0(13,13) -> 2
          U21_0(7,7,7) -> 3
          U21_0(7,7,8) -> 3
          U21_0(7,7,9) -> 3
          U21_0(7,7,10) -> 3
          U21_0(7,7,13) -> 3
          U21_0(7,8,7) -> 3
          U21_0(7,8,8) -> 3
          U21_0(7,8,9) -> 3
          U21_0(7,8,10) -> 3
          U21_0(7,8,13) -> 3
          U21_0(7,9,7) -> 3
          U21_0(7,9,8) -> 3
          U21_0(7,9,9) -> 3
          U21_0(7,9,10) -> 3
          U21_0(7,9,13) -> 3
          U21_0(7,10,7) -> 3
          U21_0(7,10,8) -> 3
          U21_0(7,10,9) -> 3
          U21_0(7,10,10) -> 3
          U21_0(7,10,13) -> 3
          U21_0(7,13,7) -> 3
          U21_0(7,13,8) -> 3
          U21_0(7,13,9) -> 3
          U21_0(7,13,10) -> 3
          U21_0(7,13,13) -> 3
          U21_0(8,7,7) -> 3
          U21_0(8,7,8) -> 3
          U21_0(8,7,9) -> 3
          U21_0(8,7,10) -> 3
          U21_0(8,7,13) -> 3
          U21_0(8,8,7) -> 3
          U21_0(8,8,8) -> 3
          U21_0(8,8,9) -> 3
          U21_0(8,8,10) -> 3
          U21_0(8,8,13) -> 3
          U21_0(8,9,7) -> 3
          U21_0(8,9,8) -> 3
          U21_0(8,9,9) -> 3
          U21_0(8,9,10) -> 3
          U21_0(8,9,13) -> 3
          U21_0(8,10,7) -> 3
          U21_0(8,10,8) -> 3
          U21_0(8,10,9) -> 3
          U21_0(8,10,10) -> 3
          U21_0(8,10,13) -> 3
          U21_0(8,13,7) -> 3
          U21_0(8,13,8) -> 3
          U21_0(8,13,9) -> 3
          U21_0(8,13,10) -> 3
          U21_0(8,13,13) -> 3
          U21_0(9,7,7) -> 3
          U21_0(9,7,8) -> 3
          U21_0(9,7,9) -> 3
          U21_0(9,7,10) -> 3
          U21_0(9,7,13) -> 3
          U21_0(9,8,7) -> 3
          U21_0(9,8,8) -> 3
          U21_0(9,8,9) -> 3
          U21_0(9,8,10) -> 3
          U21_0(9,8,13) -> 3
          U21_0(9,9,7) -> 3
          U21_0(9,9,8) -> 3
          U21_0(9,9,9) -> 3
          U21_0(9,9,10) -> 3
          U21_0(9,9,13) -> 3
          U21_0(9,10,7) -> 3
          U21_0(9,10,8) -> 3
          U21_0(9,10,9) -> 3
          U21_0(9,10,10) -> 3
          U21_0(9,10,13) -> 3
          U21_0(9,13,7) -> 3
          U21_0(9,13,8) -> 3
          U21_0(9,13,9) -> 3
          U21_0(9,13,10) -> 3
          U21_0(9,13,13) -> 3
          U21_0(10,7,7) -> 3
          U21_0(10,7,8) -> 3
          U21_0(10,7,9) -> 3
          U21_0(10,7,10) -> 3
          U21_0(10,7,13) -> 3
          U21_0(10,8,7) -> 3
          U21_0(10,8,8) -> 3
          U21_0(10,8,9) -> 3
          U21_0(10,8,10) -> 3
          U21_0(10,8,13) -> 3
          U21_0(10,9,7) -> 3
          U21_0(10,9,8) -> 3
          U21_0(10,9,9) -> 3
          U21_0(10,9,10) -> 3
          U21_0(10,9,13) -> 3
          U21_0(10,10,7) -> 3
          U21_0(10,10,8) -> 3
          U21_0(10,10,9) -> 3
          U21_0(10,10,10) -> 3
          U21_0(10,10,13) -> 3
          U21_0(10,13,7) -> 3
          U21_0(10,13,8) -> 3
          U21_0(10,13,9) -> 3
          U21_0(10,13,10) -> 3
          U21_0(10,13,13) -> 3
          U21_0(13,7,7) -> 3
          U21_0(13,7,8) -> 3
          U21_0(13,7,9) -> 3
          U21_0(13,7,10) -> 3
          U21_0(13,7,13) -> 3
          U21_0(13,8,7) -> 3
          U21_0(13,8,8) -> 3
          U21_0(13,8,9) -> 3
          U21_0(13,8,10) -> 3
          U21_0(13,8,13) -> 3
          U21_0(13,9,7) -> 3
          U21_0(13,9,8) -> 3
          U21_0(13,9,9) -> 3
          U21_0(13,9,10) -> 3
          U21_0(13,9,13) -> 3
          U21_0(13,10,7) -> 3
          U21_0(13,10,8) -> 3
          U21_0(13,10,9) -> 3
          U21_0(13,10,10) -> 3
          U21_0(13,10,13) -> 3
          U21_0(13,13,7) -> 3
          U21_0(13,13,8) -> 3
          U21_0(13,13,9) -> 3
          U21_0(13,13,10) -> 3
          U21_0(13,13,13) -> 3
          activate_0(7) -> 4
          activate_0(8) -> 4
          activate_0(9) -> 4
          activate_0(10) -> 4
          activate_0(13) -> 4
          activate_1(7) -> 2
          activate_1(7) -> 5
          activate_1(8) -> 2
          activate_1(8) -> 5
          activate_1(9) -> 2
          activate_1(9) -> 5
          activate_1(10) -> 2
          activate_1(10) -> 5
          activate_1(13) -> 2
          activate_1(13) -> 5
          activate_1(16) -> 21
          activate_1(16) -> 24
          activate_1(18) -> 21
          activate_1(18) -> 24
          activate_2(7) -> 19
          activate_2(7) -> 20
          activate_2(8) -> 20
          activate_2(9) -> 20
          activate_2(10) -> 20
          activate_2(13) -> 20
          activate_2(16) -> 2
          activate_2(16) -> 4
          activate_2(16) -> 5
          activate_2(16) -> 6
          activate_2(16) -> 15
          activate_2(16) -> 17
          activate_2(16) -> 20
          activate_2(16) -> 21
          activate_2(16) -> 24
          activate_2(18) -> 2
          activate_2(18) -> 4
          activate_2(18) -> 5
          activate_2(18) -> 6
          activate_2(18) -> 15
          activate_2(18) -> 17
          activate_2(18) -> 20
          activate_2(18) -> 21
          activate_2(18) -> 24
          activate_2(22) -> 2
          activate_2(22) -> 4
          activate_2(22) -> 5
          activate_2(22) -> 6
          activate_2(22) -> 15
          activate_2(22) -> 17
          activate_2(22) -> 20
          activate_2(22) -> 21
          activate_2(22) -> 24
          activate_3(7) -> 23
          activate_3(7) -> 24
          activate_3(8) -> 24
          activate_3(9) -> 24
          activate_3(10) -> 24
          activate_3(13) -> 24
          activate_3(18) -> 2
          activate_3(18) -> 4
          activate_3(18) -> 5
          activate_3(18) -> 6
          activate_3(18) -> 15
          activate_3(18) -> 17
          activate_3(18) -> 20
          activate_3(18) -> 21
          activate_3(18) -> 24
          activate_3(22) -> 2
          activate_3(22) -> 4
          activate_3(22) -> 5
          activate_3(22) -> 6
          activate_3(22) -> 15
          activate_3(22) -> 17
          activate_3(22) -> 20
          activate_3(22) -> 21
          activate_3(22) -> 24
          activate_4(22) -> 2
          activate_4(22) -> 4
          activate_4(22) -> 5
          activate_4(22) -> 6
          activate_4(22) -> 15
          activate_4(22) -> 17
          activate_4(22) -> 20
          activate_4(22) -> 21
          activate_4(22) -> 24
          and_0(7,7) -> 5
          and_0(7,8) -> 5
          and_0(7,9) -> 5
          and_0(7,10) -> 5
          and_0(7,13) -> 5
          and_0(8,7) -> 5
          and_0(8,8) -> 5
          and_0(8,9) -> 5
          and_0(8,10) -> 5
          and_0(8,13) -> 5
          and_0(9,7) -> 5
          and_0(9,8) -> 5
          and_0(9,9) -> 5
          and_0(9,10) -> 5
          and_0(9,13) -> 5
          and_0(10,7) -> 5
          and_0(10,8) -> 5
          and_0(10,9) -> 5
          and_0(10,10) -> 5
          and_0(10,13) -> 5
          and_0(13,7) -> 5
          and_0(13,8) -> 5
          and_0(13,9) -> 5
          and_0(13,10) -> 5
          and_0(13,13) -> 5
          and_1(15,16) -> 2
          and_1(15,16) -> 4
          and_1(15,16) -> 5
          and_1(15,16) -> 6
          and_1(15,16) -> 15
          and_1(15,16) -> 17
          and_1(15,16) -> 20
          and_1(20,16) -> 21
          and_1(20,16) -> 24
          and_2(17,18) -> 2
          and_2(17,18) -> 4
          and_2(17,18) -> 5
          and_2(17,18) -> 6
          and_2(17,18) -> 15
          and_2(17,18) -> 17
          and_2(17,18) -> 20
          and_2(20,18) -> 21
          and_2(20,18) -> 24
          and_3(21,22) -> 2
          and_3(21,22) -> 4
          and_3(21,22) -> 5
          and_3(21,22) -> 6
          and_3(21,22) -> 15
          and_3(21,22) -> 17
          and_3(21,22) -> 20
          and_3(21,22) -> 21
          and_3(21,22) -> 24
          isNat_0(7) -> 6
          isNat_0(8) -> 6
          isNat_0(9) -> 6
          isNat_0(10) -> 6
          isNat_0(13) -> 6
          isNat_1(5) -> 2
          isNat_1(5) -> 4
          isNat_1(5) -> 5
          isNat_1(5) -> 6
          isNat_1(5) -> 15
          isNat_1(5) -> 17
          isNat_1(5) -> 20
          isNat_1(5) -> 21
          isNat_1(5) -> 24
          isNat_1(7) -> 2
          isNat_1(7) -> 4
          isNat_1(7) -> 5
          isNat_1(7) -> 20
          isNat_1(7) -> 24
          isNat_1(8) -> 2
          isNat_1(8) -> 4
          isNat_1(8) -> 5
          isNat_1(8) -> 20
          isNat_1(8) -> 24
          isNat_1(9) -> 2
          isNat_1(9) -> 4
          isNat_1(9) -> 5
          isNat_1(9) -> 20
          isNat_1(9) -> 24
          isNat_1(10) -> 2
          isNat_1(10) -> 4
          isNat_1(10) -> 5
          isNat_1(10) -> 20
          isNat_1(10) -> 24
          isNat_1(13) -> 2
          isNat_1(13) -> 4
          isNat_1(13) -> 5
          isNat_1(13) -> 20
          isNat_1(13) -> 24
          isNat_2(5) -> 2
          isNat_2(5) -> 4
          isNat_2(5) -> 5
          isNat_2(5) -> 6
          isNat_2(5) -> 15
          isNat_2(5) -> 17
          isNat_2(5) -> 20
          isNat_2(5) -> 21
          isNat_2(5) -> 24
          isNat_2(19) -> 17
          isNat_2(20) -> 2
          isNat_2(20) -> 4
          isNat_2(20) -> 5
          isNat_2(20) -> 6
          isNat_2(20) -> 15
          isNat_2(20) -> 17
          isNat_2(20) -> 20
          isNat_2(20) -> 21
          isNat_2(20) -> 24
          isNat_3(20) -> 2
          isNat_3(20) -> 4
          isNat_3(20) -> 5
          isNat_3(20) -> 6
          isNat_3(20) -> 15
          isNat_3(20) -> 17
          isNat_3(20) -> 20
          isNat_3(20) -> 21
          isNat_3(20) -> 24
          isNat_3(23) -> 21
          isNat_3(24) -> 2
          isNat_3(24) -> 4
          isNat_3(24) -> 5
          isNat_3(24) -> 6
          isNat_3(24) -> 15
          isNat_3(24) -> 17
          isNat_3(24) -> 20
          isNat_3(24) -> 21
          isNat_3(24) -> 24
          isNat_4(24) -> 2
          isNat_4(24) -> 4
          isNat_4(24) -> 5
          isNat_4(24) -> 6
          isNat_4(24) -> 15
          isNat_4(24) -> 17
          isNat_4(24) -> 20
          isNat_4(24) -> 21
          isNat_4(24) -> 24
          n__0_0() -> 2
          n__0_0() -> 4
          n__0_0() -> 5
          n__0_0() -> 7
          n__0_0() -> 19
          n__0_0() -> 20
          n__0_0() -> 23
          n__0_0() -> 24
          n__0_1() -> 1
          n__0_2() -> 2
          n__0_2() -> 4
          n__0_2() -> 5
          n__0_2() -> 19
          n__0_2() -> 20
          n__0_2() -> 23
          n__0_2() -> 24
          n__isNat_0(7) -> 2
          n__isNat_0(7) -> 4
          n__isNat_0(7) -> 5
          n__isNat_0(7) -> 8
          n__isNat_0(7) -> 20
          n__isNat_0(7) -> 24
          n__isNat_0(8) -> 2
          n__isNat_0(8) -> 4
          n__isNat_0(8) -> 5
          n__isNat_0(8) -> 8
          n__isNat_0(8) -> 20
          n__isNat_0(8) -> 24
          n__isNat_0(9) -> 2
          n__isNat_0(9) -> 4
          n__isNat_0(9) -> 5
          n__isNat_0(9) -> 8
          n__isNat_0(9) -> 20
          n__isNat_0(9) -> 24
          n__isNat_0(10) -> 2
          n__isNat_0(10) -> 4
          n__isNat_0(10) -> 5
          n__isNat_0(10) -> 8
          n__isNat_0(10) -> 20
          n__isNat_0(10) -> 24
          n__isNat_0(13) -> 2
          n__isNat_0(13) -> 4
          n__isNat_0(13) -> 5
          n__isNat_0(13) -> 8
          n__isNat_0(13) -> 20
          n__isNat_0(13) -> 24
          n__isNat_1(5) -> 2
          n__isNat_1(5) -> 4
          n__isNat_1(5) -> 5
          n__isNat_1(5) -> 6
          n__isNat_1(5) -> 15
          n__isNat_1(5) -> 16
          n__isNat_1(5) -> 17
          n__isNat_1(5) -> 20
          n__isNat_1(5) -> 21
          n__isNat_1(5) -> 24
          n__isNat_1(7) -> 6
          n__isNat_1(8) -> 6
          n__isNat_1(9) -> 6
          n__isNat_1(10) -> 6
          n__isNat_1(13) -> 6
          n__isNat_2(5) -> 2
          n__isNat_2(5) -> 4
          n__isNat_2(5) -> 5
          n__isNat_2(5) -> 6
          n__isNat_2(5) -> 15
          n__isNat_2(5) -> 17
          n__isNat_2(5) -> 20
          n__isNat_2(5) -> 21
          n__isNat_2(5) -> 24
          n__isNat_2(7) -> 2
          n__isNat_2(7) -> 4
          n__isNat_2(7) -> 5
          n__isNat_2(7) -> 20
          n__isNat_2(7) -> 24
          n__isNat_2(8) -> 2
          n__isNat_2(8) -> 4
          n__isNat_2(8) -> 5
          n__isNat_2(8) -> 20
          n__isNat_2(8) -> 24
          n__isNat_2(9) -> 2
          n__isNat_2(9) -> 4
          n__isNat_2(9) -> 5
          n__isNat_2(9) -> 20
          n__isNat_2(9) -> 24
          n__isNat_2(10) -> 2
          n__isNat_2(10) -> 4
          n__isNat_2(10) -> 5
          n__isNat_2(10) -> 20
          n__isNat_2(10) -> 24
          n__isNat_2(13) -> 2
          n__isNat_2(13) -> 4
          n__isNat_2(13) -> 5
          n__isNat_2(13) -> 20
          n__isNat_2(13) -> 24
          n__isNat_2(20) -> 2
          n__isNat_2(20) -> 4
          n__isNat_2(20) -> 5
          n__isNat_2(20) -> 6
          n__isNat_2(20) -> 15
          n__isNat_2(20) -> 17
          n__isNat_2(20) -> 18
          n__isNat_2(20) -> 20
          n__isNat_2(20) -> 21
          n__isNat_2(20) -> 24
          n__isNat_3(5) -> 2
          n__isNat_3(5) -> 4
          n__isNat_3(5) -> 5
          n__isNat_3(5) -> 6
          n__isNat_3(5) -> 15
          n__isNat_3(5) -> 17
          n__isNat_3(5) -> 20
          n__isNat_3(5) -> 21
          n__isNat_3(5) -> 24
          n__isNat_3(19) -> 17
          n__isNat_3(20) -> 2
          n__isNat_3(20) -> 4
          n__isNat_3(20) -> 5
          n__isNat_3(20) -> 6
          n__isNat_3(20) -> 15
          n__isNat_3(20) -> 17
          n__isNat_3(20) -> 20
          n__isNat_3(20) -> 21
          n__isNat_3(20) -> 24
          n__isNat_3(24) -> 2
          n__isNat_3(24) -> 4
          n__isNat_3(24) -> 5
          n__isNat_3(24) -> 6
          n__isNat_3(24) -> 15
          n__isNat_3(24) -> 17
          n__isNat_3(24) -> 20
          n__isNat_3(24) -> 21
          n__isNat_3(24) -> 22
          n__isNat_3(24) -> 24
          n__isNat_4(20) -> 2
          n__isNat_4(20) -> 4
          n__isNat_4(20) -> 5
          n__isNat_4(20) -> 6
          n__isNat_4(20) -> 15
          n__isNat_4(20) -> 17
          n__isNat_4(20) -> 20
          n__isNat_4(20) -> 21
          n__isNat_4(20) -> 24
          n__isNat_4(23) -> 21
          n__isNat_4(24) -> 2
          n__isNat_4(24) -> 4
          n__isNat_4(24) -> 5
          n__isNat_4(24) -> 6
          n__isNat_4(24) -> 15
          n__isNat_4(24) -> 17
          n__isNat_4(24) -> 20
          n__isNat_4(24) -> 21
          n__isNat_4(24) -> 24
          n__isNat_5(24) -> 2
          n__isNat_5(24) -> 4
          n__isNat_5(24) -> 5
          n__isNat_5(24) -> 6
          n__isNat_5(24) -> 15
          n__isNat_5(24) -> 17
          n__isNat_5(24) -> 20
          n__isNat_5(24) -> 21
          n__isNat_5(24) -> 24
          n__plus_0(7,7) -> 2
          n__plus_0(7,7) -> 4
          n__plus_0(7,7) -> 5
          n__plus_0(7,7) -> 9
          n__plus_0(7,7) -> 20
          n__plus_0(7,7) -> 24
          n__plus_0(7,8) -> 2
          n__plus_0(7,8) -> 4
          n__plus_0(7,8) -> 5
          n__plus_0(7,8) -> 9
          n__plus_0(7,8) -> 20
          n__plus_0(7,8) -> 24
          n__plus_0(7,9) -> 2
          n__plus_0(7,9) -> 4
          n__plus_0(7,9) -> 5
          n__plus_0(7,9) -> 9
          n__plus_0(7,9) -> 20
          n__plus_0(7,9) -> 24
          n__plus_0(7,10) -> 2
          n__plus_0(7,10) -> 4
          n__plus_0(7,10) -> 5
          n__plus_0(7,10) -> 9
          n__plus_0(7,10) -> 20
          n__plus_0(7,10) -> 24
          n__plus_0(7,13) -> 2
          n__plus_0(7,13) -> 4
          n__plus_0(7,13) -> 5
          n__plus_0(7,13) -> 9
          n__plus_0(7,13) -> 20
          n__plus_0(7,13) -> 24
          n__plus_0(8,7) -> 2
          n__plus_0(8,7) -> 4
          n__plus_0(8,7) -> 5
          n__plus_0(8,7) -> 9
          n__plus_0(8,7) -> 20
          n__plus_0(8,7) -> 24
          n__plus_0(8,8) -> 2
          n__plus_0(8,8) -> 4
          n__plus_0(8,8) -> 5
          n__plus_0(8,8) -> 9
          n__plus_0(8,8) -> 20
          n__plus_0(8,8) -> 24
          n__plus_0(8,9) -> 2
          n__plus_0(8,9) -> 4
          n__plus_0(8,9) -> 5
          n__plus_0(8,9) -> 9
          n__plus_0(8,9) -> 20
          n__plus_0(8,9) -> 24
          n__plus_0(8,10) -> 2
          n__plus_0(8,10) -> 4
          n__plus_0(8,10) -> 5
          n__plus_0(8,10) -> 9
          n__plus_0(8,10) -> 20
          n__plus_0(8,10) -> 24
          n__plus_0(8,13) -> 2
          n__plus_0(8,13) -> 4
          n__plus_0(8,13) -> 5
          n__plus_0(8,13) -> 9
          n__plus_0(8,13) -> 20
          n__plus_0(8,13) -> 24
          n__plus_0(9,7) -> 2
          n__plus_0(9,7) -> 4
          n__plus_0(9,7) -> 5
          n__plus_0(9,7) -> 9
          n__plus_0(9,7) -> 20
          n__plus_0(9,7) -> 24
          n__plus_0(9,8) -> 2
          n__plus_0(9,8) -> 4
          n__plus_0(9,8) -> 5
          n__plus_0(9,8) -> 9
          n__plus_0(9,8) -> 20
          n__plus_0(9,8) -> 24
          n__plus_0(9,9) -> 2
          n__plus_0(9,9) -> 4
          n__plus_0(9,9) -> 5
          n__plus_0(9,9) -> 9
          n__plus_0(9,9) -> 20
          n__plus_0(9,9) -> 24
          n__plus_0(9,10) -> 2
          n__plus_0(9,10) -> 4
          n__plus_0(9,10) -> 5
          n__plus_0(9,10) -> 9
          n__plus_0(9,10) -> 20
          n__plus_0(9,10) -> 24
          n__plus_0(9,13) -> 2
          n__plus_0(9,13) -> 4
          n__plus_0(9,13) -> 5
          n__plus_0(9,13) -> 9
          n__plus_0(9,13) -> 20
          n__plus_0(9,13) -> 24
          n__plus_0(10,7) -> 2
          n__plus_0(10,7) -> 4
          n__plus_0(10,7) -> 5
          n__plus_0(10,7) -> 9
          n__plus_0(10,7) -> 20
          n__plus_0(10,7) -> 24
          n__plus_0(10,8) -> 2
          n__plus_0(10,8) -> 4
          n__plus_0(10,8) -> 5
          n__plus_0(10,8) -> 9
          n__plus_0(10,8) -> 20
          n__plus_0(10,8) -> 24
          n__plus_0(10,9) -> 2
          n__plus_0(10,9) -> 4
          n__plus_0(10,9) -> 5
          n__plus_0(10,9) -> 9
          n__plus_0(10,9) -> 20
          n__plus_0(10,9) -> 24
          n__plus_0(10,10) -> 2
          n__plus_0(10,10) -> 4
          n__plus_0(10,10) -> 5
          n__plus_0(10,10) -> 9
          n__plus_0(10,10) -> 20
          n__plus_0(10,10) -> 24
          n__plus_0(10,13) -> 2
          n__plus_0(10,13) -> 4
          n__plus_0(10,13) -> 5
          n__plus_0(10,13) -> 9
          n__plus_0(10,13) -> 20
          n__plus_0(10,13) -> 24
          n__plus_0(13,7) -> 2
          n__plus_0(13,7) -> 4
          n__plus_0(13,7) -> 5
          n__plus_0(13,7) -> 9
          n__plus_0(13,7) -> 20
          n__plus_0(13,7) -> 24
          n__plus_0(13,8) -> 2
          n__plus_0(13,8) -> 4
          n__plus_0(13,8) -> 5
          n__plus_0(13,8) -> 9
          n__plus_0(13,8) -> 20
          n__plus_0(13,8) -> 24
          n__plus_0(13,9) -> 2
          n__plus_0(13,9) -> 4
          n__plus_0(13,9) -> 5
          n__plus_0(13,9) -> 9
          n__plus_0(13,9) -> 20
          n__plus_0(13,9) -> 24
          n__plus_0(13,10) -> 2
          n__plus_0(13,10) -> 4
          n__plus_0(13,10) -> 5
          n__plus_0(13,10) -> 9
          n__plus_0(13,10) -> 20
          n__plus_0(13,10) -> 24
          n__plus_0(13,13) -> 2
          n__plus_0(13,13) -> 4
          n__plus_0(13,13) -> 5
          n__plus_0(13,13) -> 9
          n__plus_0(13,13) -> 20
          n__plus_0(13,13) -> 24
          n__plus_1(7,7) -> 11
          n__plus_1(7,8) -> 11
          n__plus_1(7,9) -> 11
          n__plus_1(7,10) -> 11
          n__plus_1(7,13) -> 11
          n__plus_1(8,7) -> 11
          n__plus_1(8,8) -> 11
          n__plus_1(8,9) -> 11
          n__plus_1(8,10) -> 11
          n__plus_1(8,13) -> 11
          n__plus_1(9,7) -> 11
          n__plus_1(9,8) -> 11
          n__plus_1(9,9) -> 11
          n__plus_1(9,10) -> 11
          n__plus_1(9,13) -> 11
          n__plus_1(10,7) -> 11
          n__plus_1(10,8) -> 11
          n__plus_1(10,9) -> 11
          n__plus_1(10,10) -> 11
          n__plus_1(10,13) -> 11
          n__plus_1(13,7) -> 11
          n__plus_1(13,8) -> 11
          n__plus_1(13,9) -> 11
          n__plus_1(13,10) -> 11
          n__plus_1(13,13) -> 11
          n__plus_2(2,2) -> 14
          n__plus_2(7,7) -> 2
          n__plus_2(7,7) -> 4
          n__plus_2(7,7) -> 5
          n__plus_2(7,7) -> 20
          n__plus_2(7,7) -> 24
          n__plus_2(7,8) -> 2
          n__plus_2(7,8) -> 4
          n__plus_2(7,8) -> 5
          n__plus_2(7,8) -> 20
          n__plus_2(7,8) -> 24
          n__plus_2(7,9) -> 2
          n__plus_2(7,9) -> 4
          n__plus_2(7,9) -> 5
          n__plus_2(7,9) -> 20
          n__plus_2(7,9) -> 24
          n__plus_2(7,10) -> 2
          n__plus_2(7,10) -> 4
          n__plus_2(7,10) -> 5
          n__plus_2(7,10) -> 20
          n__plus_2(7,10) -> 24
          n__plus_2(7,13) -> 2
          n__plus_2(7,13) -> 4
          n__plus_2(7,13) -> 5
          n__plus_2(7,13) -> 20
          n__plus_2(7,13) -> 24
          n__plus_2(8,7) -> 2
          n__plus_2(8,7) -> 4
          n__plus_2(8,7) -> 5
          n__plus_2(8,7) -> 20
          n__plus_2(8,7) -> 24
          n__plus_2(8,8) -> 2
          n__plus_2(8,8) -> 4
          n__plus_2(8,8) -> 5
          n__plus_2(8,8) -> 20
          n__plus_2(8,8) -> 24
          n__plus_2(8,9) -> 2
          n__plus_2(8,9) -> 4
          n__plus_2(8,9) -> 5
          n__plus_2(8,9) -> 20
          n__plus_2(8,9) -> 24
          n__plus_2(8,10) -> 2
          n__plus_2(8,10) -> 4
          n__plus_2(8,10) -> 5
          n__plus_2(8,10) -> 20
          n__plus_2(8,10) -> 24
          n__plus_2(8,13) -> 2
          n__plus_2(8,13) -> 4
          n__plus_2(8,13) -> 5
          n__plus_2(8,13) -> 20
          n__plus_2(8,13) -> 24
          n__plus_2(9,7) -> 2
          n__plus_2(9,7) -> 4
          n__plus_2(9,7) -> 5
          n__plus_2(9,7) -> 20
          n__plus_2(9,7) -> 24
          n__plus_2(9,8) -> 2
          n__plus_2(9,8) -> 4
          n__plus_2(9,8) -> 5
          n__plus_2(9,8) -> 20
          n__plus_2(9,8) -> 24
          n__plus_2(9,9) -> 2
          n__plus_2(9,9) -> 4
          n__plus_2(9,9) -> 5
          n__plus_2(9,9) -> 20
          n__plus_2(9,9) -> 24
          n__plus_2(9,10) -> 2
          n__plus_2(9,10) -> 4
          n__plus_2(9,10) -> 5
          n__plus_2(9,10) -> 20
          n__plus_2(9,10) -> 24
          n__plus_2(9,13) -> 2
          n__plus_2(9,13) -> 4
          n__plus_2(9,13) -> 5
          n__plus_2(9,13) -> 20
          n__plus_2(9,13) -> 24
          n__plus_2(10,7) -> 2
          n__plus_2(10,7) -> 4
          n__plus_2(10,7) -> 5
          n__plus_2(10,7) -> 20
          n__plus_2(10,7) -> 24
          n__plus_2(10,8) -> 2
          n__plus_2(10,8) -> 4
          n__plus_2(10,8) -> 5
          n__plus_2(10,8) -> 20
          n__plus_2(10,8) -> 24
          n__plus_2(10,9) -> 2
          n__plus_2(10,9) -> 4
          n__plus_2(10,9) -> 5
          n__plus_2(10,9) -> 20
          n__plus_2(10,9) -> 24
          n__plus_2(10,10) -> 2
          n__plus_2(10,10) -> 4
          n__plus_2(10,10) -> 5
          n__plus_2(10,10) -> 20
          n__plus_2(10,10) -> 24
          n__plus_2(10,13) -> 2
          n__plus_2(10,13) -> 4
          n__plus_2(10,13) -> 5
          n__plus_2(10,13) -> 20
          n__plus_2(10,13) -> 24
          n__plus_2(13,7) -> 2
          n__plus_2(13,7) -> 4
          n__plus_2(13,7) -> 5
          n__plus_2(13,7) -> 20
          n__plus_2(13,7) -> 24
          n__plus_2(13,8) -> 2
          n__plus_2(13,8) -> 4
          n__plus_2(13,8) -> 5
          n__plus_2(13,8) -> 20
          n__plus_2(13,8) -> 24
          n__plus_2(13,9) -> 2
          n__plus_2(13,9) -> 4
          n__plus_2(13,9) -> 5
          n__plus_2(13,9) -> 20
          n__plus_2(13,9) -> 24
          n__plus_2(13,10) -> 2
          n__plus_2(13,10) -> 4
          n__plus_2(13,10) -> 5
          n__plus_2(13,10) -> 20
          n__plus_2(13,10) -> 24
          n__plus_2(13,13) -> 2
          n__plus_2(13,13) -> 4
          n__plus_2(13,13) -> 5
          n__plus_2(13,13) -> 20
          n__plus_2(13,13) -> 24
          n__s_0(7) -> 2
          n__s_0(7) -> 4
          n__s_0(7) -> 5
          n__s_0(7) -> 10
          n__s_0(7) -> 20
          n__s_0(7) -> 24
          n__s_0(8) -> 2
          n__s_0(8) -> 4
          n__s_0(8) -> 5
          n__s_0(8) -> 10
          n__s_0(8) -> 20
          n__s_0(8) -> 24
          n__s_0(9) -> 2
          n__s_0(9) -> 4
          n__s_0(9) -> 5
          n__s_0(9) -> 10
          n__s_0(9) -> 20
          n__s_0(9) -> 24
          n__s_0(10) -> 2
          n__s_0(10) -> 4
          n__s_0(10) -> 5
          n__s_0(10) -> 10
          n__s_0(10) -> 20
          n__s_0(10) -> 24
          n__s_0(13) -> 2
          n__s_0(13) -> 4
          n__s_0(13) -> 5
          n__s_0(13) -> 10
          n__s_0(13) -> 20
          n__s_0(13) -> 24
          n__s_1(7) -> 12
          n__s_1(8) -> 12
          n__s_1(9) -> 12
          n__s_1(10) -> 12
          n__s_1(13) -> 12
          n__s_2(7) -> 2
          n__s_2(7) -> 4
          n__s_2(7) -> 5
          n__s_2(7) -> 20
          n__s_2(7) -> 24
          n__s_2(8) -> 2
          n__s_2(8) -> 4
          n__s_2(8) -> 5
          n__s_2(8) -> 20
          n__s_2(8) -> 24
          n__s_2(9) -> 2
          n__s_2(9) -> 4
          n__s_2(9) -> 5
          n__s_2(9) -> 20
          n__s_2(9) -> 24
          n__s_2(10) -> 2
          n__s_2(10) -> 4
          n__s_2(10) -> 5
          n__s_2(10) -> 20
          n__s_2(10) -> 24
          n__s_2(13) -> 2
          n__s_2(13) -> 4
          n__s_2(13) -> 5
          n__s_2(13) -> 20
          n__s_2(13) -> 24
          n__s_2(14) -> 3
          plus_0(7,7) -> 11
          plus_0(7,8) -> 11
          plus_0(7,9) -> 11
          plus_0(7,10) -> 11
          plus_0(7,13) -> 11
          plus_0(8,7) -> 11
          plus_0(8,8) -> 11
          plus_0(8,9) -> 11
          plus_0(8,10) -> 11
          plus_0(8,13) -> 11
          plus_0(9,7) -> 11
          plus_0(9,8) -> 11
          plus_0(9,9) -> 11
          plus_0(9,10) -> 11
          plus_0(9,13) -> 11
          plus_0(10,7) -> 11
          plus_0(10,8) -> 11
          plus_0(10,9) -> 11
          plus_0(10,10) -> 11
          plus_0(10,13) -> 11
          plus_0(13,7) -> 11
          plus_0(13,8) -> 11
          plus_0(13,9) -> 11
          plus_0(13,10) -> 11
          plus_0(13,13) -> 11
          plus_1(2,2) -> 14
          plus_1(7,7) -> 2
          plus_1(7,7) -> 4
          plus_1(7,7) -> 5
          plus_1(7,7) -> 20
          plus_1(7,7) -> 24
          plus_1(7,8) -> 2
          plus_1(7,8) -> 4
          plus_1(7,8) -> 5
          plus_1(7,8) -> 20
          plus_1(7,8) -> 24
          plus_1(7,9) -> 2
          plus_1(7,9) -> 4
          plus_1(7,9) -> 5
          plus_1(7,9) -> 20
          plus_1(7,9) -> 24
          plus_1(7,10) -> 2
          plus_1(7,10) -> 4
          plus_1(7,10) -> 5
          plus_1(7,10) -> 20
          plus_1(7,10) -> 24
          plus_1(7,13) -> 2
          plus_1(7,13) -> 4
          plus_1(7,13) -> 5
          plus_1(7,13) -> 20
          plus_1(7,13) -> 24
          plus_1(8,7) -> 2
          plus_1(8,7) -> 4
          plus_1(8,7) -> 5
          plus_1(8,7) -> 20
          plus_1(8,7) -> 24
          plus_1(8,8) -> 2
          plus_1(8,8) -> 4
          plus_1(8,8) -> 5
          plus_1(8,8) -> 20
          plus_1(8,8) -> 24
          plus_1(8,9) -> 2
          plus_1(8,9) -> 4
          plus_1(8,9) -> 5
          plus_1(8,9) -> 20
          plus_1(8,9) -> 24
          plus_1(8,10) -> 2
          plus_1(8,10) -> 4
          plus_1(8,10) -> 5
          plus_1(8,10) -> 20
          plus_1(8,10) -> 24
          plus_1(8,13) -> 2
          plus_1(8,13) -> 4
          plus_1(8,13) -> 5
          plus_1(8,13) -> 20
          plus_1(8,13) -> 24
          plus_1(9,7) -> 2
          plus_1(9,7) -> 4
          plus_1(9,7) -> 5
          plus_1(9,7) -> 20
          plus_1(9,7) -> 24
          plus_1(9,8) -> 2
          plus_1(9,8) -> 4
          plus_1(9,8) -> 5
          plus_1(9,8) -> 20
          plus_1(9,8) -> 24
          plus_1(9,9) -> 2
          plus_1(9,9) -> 4
          plus_1(9,9) -> 5
          plus_1(9,9) -> 20
          plus_1(9,9) -> 24
          plus_1(9,10) -> 2
          plus_1(9,10) -> 4
          plus_1(9,10) -> 5
          plus_1(9,10) -> 20
          plus_1(9,10) -> 24
          plus_1(9,13) -> 2
          plus_1(9,13) -> 4
          plus_1(9,13) -> 5
          plus_1(9,13) -> 20
          plus_1(9,13) -> 24
          plus_1(10,7) -> 2
          plus_1(10,7) -> 4
          plus_1(10,7) -> 5
          plus_1(10,7) -> 20
          plus_1(10,7) -> 24
          plus_1(10,8) -> 2
          plus_1(10,8) -> 4
          plus_1(10,8) -> 5
          plus_1(10,8) -> 20
          plus_1(10,8) -> 24
          plus_1(10,9) -> 2
          plus_1(10,9) -> 4
          plus_1(10,9) -> 5
          plus_1(10,9) -> 20
          plus_1(10,9) -> 24
          plus_1(10,10) -> 2
          plus_1(10,10) -> 4
          plus_1(10,10) -> 5
          plus_1(10,10) -> 20
          plus_1(10,10) -> 24
          plus_1(10,13) -> 2
          plus_1(10,13) -> 4
          plus_1(10,13) -> 5
          plus_1(10,13) -> 20
          plus_1(10,13) -> 24
          plus_1(13,7) -> 2
          plus_1(13,7) -> 4
          plus_1(13,7) -> 5
          plus_1(13,7) -> 20
          plus_1(13,7) -> 24
          plus_1(13,8) -> 2
          plus_1(13,8) -> 4
          plus_1(13,8) -> 5
          plus_1(13,8) -> 20
          plus_1(13,8) -> 24
          plus_1(13,9) -> 2
          plus_1(13,9) -> 4
          plus_1(13,9) -> 5
          plus_1(13,9) -> 20
          plus_1(13,9) -> 24
          plus_1(13,10) -> 2
          plus_1(13,10) -> 4
          plus_1(13,10) -> 5
          plus_1(13,10) -> 20
          plus_1(13,10) -> 24
          plus_1(13,13) -> 2
          plus_1(13,13) -> 4
          plus_1(13,13) -> 5
          plus_1(13,13) -> 20
          plus_1(13,13) -> 24
          s_0(7) -> 12
          s_0(8) -> 12
          s_0(9) -> 12
          s_0(10) -> 12
          s_0(13) -> 12
          s_1(7) -> 2
          s_1(7) -> 4
          s_1(7) -> 5
          s_1(7) -> 20
          s_1(7) -> 24
          s_1(8) -> 2
          s_1(8) -> 4
          s_1(8) -> 5
          s_1(8) -> 20
          s_1(8) -> 24
          s_1(9) -> 2
          s_1(9) -> 4
          s_1(9) -> 5
          s_1(9) -> 20
          s_1(9) -> 24
          s_1(10) -> 2
          s_1(10) -> 4
          s_1(10) -> 5
          s_1(10) -> 20
          s_1(10) -> 24
          s_1(13) -> 2
          s_1(13) -> 4
          s_1(13) -> 5
          s_1(13) -> 20
          s_1(13) -> 24
          s_1(14) -> 3
          tt_0() -> 2
          tt_0() -> 4
          tt_0() -> 5
          tt_0() -> 13
          tt_0() -> 20
          tt_0() -> 24
          tt_1() -> 2
          tt_1() -> 4
          tt_1() -> 5
          tt_1() -> 6
          tt_1() -> 15
          tt_1() -> 17
          tt_1() -> 20
          tt_1() -> 21
          tt_1() -> 24
          tt_2() -> 2
          tt_2() -> 4
          tt_2() -> 5
          tt_2() -> 6
          tt_2() -> 15
          tt_2() -> 17
          tt_2() -> 20
          tt_2() -> 21
          tt_2() -> 24
          tt_3() -> 2
          tt_3() -> 4
          tt_3() -> 5
          tt_3() -> 6
          tt_3() -> 15
          tt_3() -> 17
          tt_3() -> 20
          tt_3() -> 21
          tt_3() -> 24
          7 -> 2
          7 -> 4
          7 -> 5
          7 -> 19
          7 -> 20
          7 -> 23
          7 -> 24
          8 -> 2
          8 -> 4
          8 -> 5
          8 -> 20
          8 -> 24
          9 -> 2
          9 -> 4
          9 -> 5
          9 -> 20
          9 -> 24
          10 -> 2
          10 -> 4
          10 -> 5
          10 -> 20
          10 -> 24
          13 -> 2
          13 -> 4
          13 -> 5
          13 -> 20
          13 -> 24
          16 -> 2
          16 -> 4
          16 -> 5
          16 -> 6
          16 -> 15
          16 -> 17
          16 -> 20
          16 -> 21
          16 -> 24
          18 -> 2
          18 -> 4
          18 -> 5
          18 -> 6
          18 -> 15
          18 -> 17
          18 -> 20
          18 -> 21
          18 -> 24
          22 -> 2
          22 -> 4
          22 -> 5
          22 -> 6
          22 -> 15
          22 -> 17
          22 -> 20
          22 -> 21
          22 -> 24
* Step 4: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            0() -> n__0()
            U11(tt(),N) -> activate(N)
            U21(tt(),M,N) -> s(plus(activate(N),activate(M)))
            activate(X) -> X
            activate(n__0()) -> 0()
            activate(n__isNat(X)) -> isNat(X)
            activate(n__plus(X1,X2)) -> plus(X1,X2)
            activate(n__s(X)) -> s(X)
            and(tt(),X) -> activate(X)
            isNat(X) -> n__isNat(X)
            isNat(n__0()) -> tt()
            isNat(n__plus(V1,V2)) -> and(isNat(activate(V1)),n__isNat(activate(V2)))
            isNat(n__s(V1)) -> isNat(activate(V1))
            plus(X1,X2) -> n__plus(X1,X2)
            s(X) -> n__s(X)
        - Signature:
            {0/0,U11/2,U21/3,activate/1,and/2,isNat/1,plus/2,s/1} / {n__0/0,n__isNat/1,n__plus/2,n__s/1,tt/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {0,U11,U21,activate,and,isNat,plus
            ,s} and constructors {n__0,n__isNat,n__plus,n__s,tt}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))