WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            DIFF(z0,z1) -> c7(IF(leq(z0,z1),0(),s(diff(p(z0),z1))),LEQ(z0,z1))
            DIFF(z0,z1) -> c8(IF(leq(z0,z1),0(),s(diff(p(z0),z1))),DIFF(p(z0),z1),P(z0))
            IF(false(),z0,z1) -> c6()
            IF(true(),z0,z1) -> c5()
            LEQ(0(),z0) -> c2()
            LEQ(s(z0),0()) -> c3()
            LEQ(s(z0),s(z1)) -> c4(LEQ(z0,z1))
            P(0()) -> c()
            P(s(z0)) -> c1()
        - Weak TRS:
            diff(z0,z1) -> if(leq(z0,z1),0(),s(diff(p(z0),z1)))
            if(false(),z0,z1) -> z1
            if(true(),z0,z1) -> z0
            leq(0(),z0) -> true()
            leq(s(z0),0()) -> false()
            leq(s(z0),s(z1)) -> leq(z0,z1)
            p(0()) -> 0()
            p(s(z0)) -> z0
        - Signature:
            {DIFF/2,IF/3,LEQ/2,P/1,diff/2,if/3,leq/2,p/1} / {0/0,c/0,c1/0,c2/0,c3/0,c4/1,c5/0,c6/0,c7/2,c8/3,false/0,s/1
            ,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {DIFF,IF,LEQ,P,diff,if,leq,p} and constructors {0,c,c1,c2
            ,c3,c4,c5,c6,c7,c8,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            DIFF(z0,z1) -> c7(IF(leq(z0,z1),0(),s(diff(p(z0),z1))),LEQ(z0,z1))
            DIFF(z0,z1) -> c8(IF(leq(z0,z1),0(),s(diff(p(z0),z1))),DIFF(p(z0),z1),P(z0))
            IF(false(),z0,z1) -> c6()
            IF(true(),z0,z1) -> c5()
            LEQ(0(),z0) -> c2()
            LEQ(s(z0),0()) -> c3()
            LEQ(s(z0),s(z1)) -> c4(LEQ(z0,z1))
            P(0()) -> c()
            P(s(z0)) -> c1()
        - Weak TRS:
            diff(z0,z1) -> if(leq(z0,z1),0(),s(diff(p(z0),z1)))
            if(false(),z0,z1) -> z1
            if(true(),z0,z1) -> z0
            leq(0(),z0) -> true()
            leq(s(z0),0()) -> false()
            leq(s(z0),s(z1)) -> leq(z0,z1)
            p(0()) -> 0()
            p(s(z0)) -> z0
        - Signature:
            {DIFF/2,IF/3,LEQ/2,P/1,diff/2,if/3,leq/2,p/1} / {0/0,c/0,c1/0,c2/0,c3/0,c4/1,c5/0,c6/0,c7/2,c8/3,false/0,s/1
            ,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {DIFF,IF,LEQ,P,diff,if,leq,p} and constructors {0,c,c1,c2
            ,c3,c4,c5,c6,c7,c8,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            DIFF(z0,z1) -> c7(IF(leq(z0,z1),0(),s(diff(p(z0),z1))),LEQ(z0,z1))
            DIFF(z0,z1) -> c8(IF(leq(z0,z1),0(),s(diff(p(z0),z1))),DIFF(p(z0),z1),P(z0))
            IF(false(),z0,z1) -> c6()
            IF(true(),z0,z1) -> c5()
            LEQ(0(),z0) -> c2()
            LEQ(s(z0),0()) -> c3()
            LEQ(s(z0),s(z1)) -> c4(LEQ(z0,z1))
            P(0()) -> c()
            P(s(z0)) -> c1()
        - Weak TRS:
            diff(z0,z1) -> if(leq(z0,z1),0(),s(diff(p(z0),z1)))
            if(false(),z0,z1) -> z1
            if(true(),z0,z1) -> z0
            leq(0(),z0) -> true()
            leq(s(z0),0()) -> false()
            leq(s(z0),s(z1)) -> leq(z0,z1)
            p(0()) -> 0()
            p(s(z0)) -> z0
        - Signature:
            {DIFF/2,IF/3,LEQ/2,P/1,diff/2,if/3,leq/2,p/1} / {0/0,c/0,c1/0,c2/0,c3/0,c4/1,c5/0,c6/0,c7/2,c8/3,false/0,s/1
            ,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {DIFF,IF,LEQ,P,diff,if,leq,p} and constructors {0,c,c1,c2
            ,c3,c4,c5,c6,c7,c8,false,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          LEQ(x,y){x -> s(x),y -> s(y)} =
            LEQ(s(x),s(y)) ->^+ c4(LEQ(x,y))
              = C[LEQ(x,y) = LEQ(x,y){}]

WORST_CASE(Omega(n^1),?)