tct-trs: Prelude.head: empty list
tct-trs: Prelude.head: empty list
tct-trs: Prelude.head: empty list
tct-trs: Prelude.head: empty list
WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            IF(false(),z0,z1,z2) -> c14()
            IF(true(),false(),z0,s(z1)) -> c15()
            IF(true(),true(),z0,z1) -> c16(LOGITER(z0,z1))
            INC(0()) -> c8()
            INC(s(z0)) -> c7(INC(z0))
            LE(0(),z0) -> c4()
            LE(s(z0),0()) -> c5()
            LE(s(z0),s(z1)) -> c6(LE(z0,z1))
            LOG(z0) -> c9(LOGITER(z0,0()))
            LOGITER(z0,z1) -> c10(IF(le(s(0()),z0),le(s(s(0())),z0),quot(z0,s(s(0()))),inc(z1)),LE(s(0()),z0))
            LOGITER(z0,z1) -> c11(IF(le(s(0()),z0),le(s(s(0())),z0),quot(z0,s(s(0()))),inc(z1)),LE(s(s(0())),z0))
            LOGITER(z0,z1) -> c12(IF(le(s(0()),z0),le(s(s(0())),z0),quot(z0,s(s(0()))),inc(z1)),QUOT(z0,s(s(0()))))
            LOGITER(z0,z1) -> c13(IF(le(s(0()),z0),le(s(s(0())),z0),quot(z0,s(s(0()))),inc(z1)),INC(z1))
            MINUS(z0,0()) -> c()
            MINUS(s(z0),s(z1)) -> c1(MINUS(z0,z1))
            QUOT(0(),s(z0)) -> c2()
            QUOT(s(z0),s(z1)) -> c3(QUOT(minus(z0,z1),s(z1)),MINUS(z0,z1))
        - Weak TRS:
            if(false(),z0,z1,z2) -> logZeroError()
            if(true(),false(),z0,s(z1)) -> z1
            if(true(),true(),z0,z1) -> logIter(z0,z1)
            inc(0()) -> s(0())
            inc(s(z0)) -> s(inc(z0))
            le(0(),z0) -> true()
            le(s(z0),0()) -> false()
            le(s(z0),s(z1)) -> le(z0,z1)
            log(z0) -> logIter(z0,0())
            logIter(z0,z1) -> if(le(s(0()),z0),le(s(s(0())),z0),quot(z0,s(s(0()))),inc(z1))
            minus(z0,0()) -> z0
            minus(s(z0),s(z1)) -> minus(z0,z1)
            quot(0(),s(z0)) -> 0()
            quot(s(z0),s(z1)) -> s(quot(minus(z0,z1),s(z1)))
        - Signature:
            {IF/4,INC/1,LE/2,LOG/1,LOGITER/2,MINUS/2,QUOT/2,if/4,inc/1,le/2,log/1,logIter/2,minus/2,quot/2} / {0/0,c/0
            ,c1/1,c10/2,c11/2,c12/2,c13/2,c14/0,c15/0,c16/1,c2/0,c3/2,c4/0,c5/0,c6/1,c7/1,c8/0,c9/1,false/0
            ,logZeroError/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {IF,INC,LE,LOG,LOGITER,MINUS,QUOT,if,inc,le,log,logIter
            ,minus,quot} and constructors {0,c,c1,c10,c11,c12,c13,c14,c15,c16,c2,c3,c4,c5,c6,c7,c8,c9,false,logZeroError
            ,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            IF(false(),z0,z1,z2) -> c14()
            IF(true(),false(),z0,s(z1)) -> c15()
            IF(true(),true(),z0,z1) -> c16(LOGITER(z0,z1))
            INC(0()) -> c8()
            INC(s(z0)) -> c7(INC(z0))
            LE(0(),z0) -> c4()
            LE(s(z0),0()) -> c5()
            LE(s(z0),s(z1)) -> c6(LE(z0,z1))
            LOG(z0) -> c9(LOGITER(z0,0()))
            LOGITER(z0,z1) -> c10(IF(le(s(0()),z0),le(s(s(0())),z0),quot(z0,s(s(0()))),inc(z1)),LE(s(0()),z0))
            LOGITER(z0,z1) -> c11(IF(le(s(0()),z0),le(s(s(0())),z0),quot(z0,s(s(0()))),inc(z1)),LE(s(s(0())),z0))
            LOGITER(z0,z1) -> c12(IF(le(s(0()),z0),le(s(s(0())),z0),quot(z0,s(s(0()))),inc(z1)),QUOT(z0,s(s(0()))))
            LOGITER(z0,z1) -> c13(IF(le(s(0()),z0),le(s(s(0())),z0),quot(z0,s(s(0()))),inc(z1)),INC(z1))
            MINUS(z0,0()) -> c()
            MINUS(s(z0),s(z1)) -> c1(MINUS(z0,z1))
            QUOT(0(),s(z0)) -> c2()
            QUOT(s(z0),s(z1)) -> c3(QUOT(minus(z0,z1),s(z1)),MINUS(z0,z1))
        - Weak TRS:
            if(false(),z0,z1,z2) -> logZeroError()
            if(true(),false(),z0,s(z1)) -> z1
            if(true(),true(),z0,z1) -> logIter(z0,z1)
            inc(0()) -> s(0())
            inc(s(z0)) -> s(inc(z0))
            le(0(),z0) -> true()
            le(s(z0),0()) -> false()
            le(s(z0),s(z1)) -> le(z0,z1)
            log(z0) -> logIter(z0,0())
            logIter(z0,z1) -> if(le(s(0()),z0),le(s(s(0())),z0),quot(z0,s(s(0()))),inc(z1))
            minus(z0,0()) -> z0
            minus(s(z0),s(z1)) -> minus(z0,z1)
            quot(0(),s(z0)) -> 0()
            quot(s(z0),s(z1)) -> s(quot(minus(z0,z1),s(z1)))
        - Signature:
            {IF/4,INC/1,LE/2,LOG/1,LOGITER/2,MINUS/2,QUOT/2,if/4,inc/1,le/2,log/1,logIter/2,minus/2,quot/2} / {0/0,c/0
            ,c1/1,c10/2,c11/2,c12/2,c13/2,c14/0,c15/0,c16/1,c2/0,c3/2,c4/0,c5/0,c6/1,c7/1,c8/0,c9/1,false/0
            ,logZeroError/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {IF,INC,LE,LOG,LOGITER,MINUS,QUOT,if,inc,le,log,logIter
            ,minus,quot} and constructors {0,c,c1,c10,c11,c12,c13,c14,c15,c16,c2,c3,c4,c5,c6,c7,c8,c9,false,logZeroError
            ,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            IF(false(),z0,z1,z2) -> c14()
            IF(true(),false(),z0,s(z1)) -> c15()
            IF(true(),true(),z0,z1) -> c16(LOGITER(z0,z1))
            INC(0()) -> c8()
            INC(s(z0)) -> c7(INC(z0))
            LE(0(),z0) -> c4()
            LE(s(z0),0()) -> c5()
            LE(s(z0),s(z1)) -> c6(LE(z0,z1))
            LOG(z0) -> c9(LOGITER(z0,0()))
            LOGITER(z0,z1) -> c10(IF(le(s(0()),z0),le(s(s(0())),z0),quot(z0,s(s(0()))),inc(z1)),LE(s(0()),z0))
            LOGITER(z0,z1) -> c11(IF(le(s(0()),z0),le(s(s(0())),z0),quot(z0,s(s(0()))),inc(z1)),LE(s(s(0())),z0))
            LOGITER(z0,z1) -> c12(IF(le(s(0()),z0),le(s(s(0())),z0),quot(z0,s(s(0()))),inc(z1)),QUOT(z0,s(s(0()))))
            LOGITER(z0,z1) -> c13(IF(le(s(0()),z0),le(s(s(0())),z0),quot(z0,s(s(0()))),inc(z1)),INC(z1))
            MINUS(z0,0()) -> c()
            MINUS(s(z0),s(z1)) -> c1(MINUS(z0,z1))
            QUOT(0(),s(z0)) -> c2()
            QUOT(s(z0),s(z1)) -> c3(QUOT(minus(z0,z1),s(z1)),MINUS(z0,z1))
        - Weak TRS:
            if(false(),z0,z1,z2) -> logZeroError()
            if(true(),false(),z0,s(z1)) -> z1
            if(true(),true(),z0,z1) -> logIter(z0,z1)
            inc(0()) -> s(0())
            inc(s(z0)) -> s(inc(z0))
            le(0(),z0) -> true()
            le(s(z0),0()) -> false()
            le(s(z0),s(z1)) -> le(z0,z1)
            log(z0) -> logIter(z0,0())
            logIter(z0,z1) -> if(le(s(0()),z0),le(s(s(0())),z0),quot(z0,s(s(0()))),inc(z1))
            minus(z0,0()) -> z0
            minus(s(z0),s(z1)) -> minus(z0,z1)
            quot(0(),s(z0)) -> 0()
            quot(s(z0),s(z1)) -> s(quot(minus(z0,z1),s(z1)))
        - Signature:
            {IF/4,INC/1,LE/2,LOG/1,LOGITER/2,MINUS/2,QUOT/2,if/4,inc/1,le/2,log/1,logIter/2,minus/2,quot/2} / {0/0,c/0
            ,c1/1,c10/2,c11/2,c12/2,c13/2,c14/0,c15/0,c16/1,c2/0,c3/2,c4/0,c5/0,c6/1,c7/1,c8/0,c9/1,false/0
            ,logZeroError/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {IF,INC,LE,LOG,LOGITER,MINUS,QUOT,if,inc,le,log,logIter
            ,minus,quot} and constructors {0,c,c1,c10,c11,c12,c13,c14,c15,c16,c2,c3,c4,c5,c6,c7,c8,c9,false,logZeroError
            ,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          INC(x){x -> s(x)} =
            INC(s(x)) ->^+ c7(INC(x))
              = C[INC(x) = INC(x){}]

WORST_CASE(Omega(n^1),?)