/export/starexec/sandbox/solver/bin/starexec_run_tct_rc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            if(false(),x,b,y,z) -> loop(x,b,times(b,y),s(z))
            if(true(),x,b,y,z) -> z
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            log(x,0()) -> baseError()
            log(x,s(0())) -> baseError()
            log(0(),s(s(b))) -> logZeroError()
            log(s(x),s(s(b))) -> loop(s(x),s(s(b)),s(0()),0())
            loop(x,s(s(b)),s(y),z) -> if(le(x,s(y)),x,s(s(b)),s(y),z)
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
            times(0(),y) -> 0()
            times(s(x),y) -> plus(y,times(x,y))
        - Signature:
            {if/5,le/2,log/2,loop/4,plus/2,times/2} / {0/0,baseError/0,false/0,logZeroError/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {if,le,log,loop,plus,times} and constructors {0,baseError,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(),x,b,y,z) -> loop(x,b,times(b,y),s(z))
            if(true(),x,b,y,z) -> z
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            log(x,0()) -> baseError()
            log(x,s(0())) -> baseError()
            log(0(),s(s(b))) -> logZeroError()
            log(s(x),s(s(b))) -> loop(s(x),s(s(b)),s(0()),0())
            loop(x,s(s(b)),s(y),z) -> if(le(x,s(y)),x,s(s(b)),s(y),z)
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
            times(0(),y) -> 0()
            times(s(x),y) -> plus(y,times(x,y))
        - Signature:
            {if/5,le/2,log/2,loop/4,plus/2,times/2} / {0/0,baseError/0,false/0,logZeroError/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {if,le,log,loop,plus,times} and constructors {0,baseError,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(),x,b,y,z) -> loop(x,b,times(b,y),s(z))
            if(true(),x,b,y,z) -> z
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            log(x,0()) -> baseError()
            log(x,s(0())) -> baseError()
            log(0(),s(s(b))) -> logZeroError()
            log(s(x),s(s(b))) -> loop(s(x),s(s(b)),s(0()),0())
            loop(x,s(s(b)),s(y),z) -> if(le(x,s(y)),x,s(s(b)),s(y),z)
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
            times(0(),y) -> 0()
            times(s(x),y) -> plus(y,times(x,y))
        - Signature:
            {if/5,le/2,log/2,loop/4,plus/2,times/2} / {0/0,baseError/0,false/0,logZeroError/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {if,le,log,loop,plus,times} and constructors {0,baseError,false
            ,logZeroError,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          le(x,y){x -> s(x),y -> s(y)} =
            le(s(x),s(y)) ->^+ le(x,y)
              = C[le(x,y) = le(x,y){}]

WORST_CASE(Omega(n^1),?)