/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            concat(cons(u,v),y) -> cons(u,concat(v,y))
            concat(leaf(),y) -> y
            if1(b,false(),u,v) -> if2(b,u,v)
            if1(b,true(),u,v) -> false()
            if2(false(),u,v) -> less_leaves(concat(left(u),right(u)),concat(left(v),right(v)))
            if2(true(),u,v) -> true()
            isLeaf(cons(u,v)) -> false()
            isLeaf(leaf()) -> true()
            left(cons(u,v)) -> u
            less_leaves(u,v) -> if1(isLeaf(u),isLeaf(v),u,v)
            right(cons(u,v)) -> v
        - Signature:
            {concat/2,if1/4,if2/3,isLeaf/1,left/1,less_leaves/2,right/1} / {cons/2,false/0,leaf/0,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {concat,if1,if2,isLeaf,left,less_leaves
            ,right} and constructors {cons,false,leaf,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            concat(cons(u,v),y) -> cons(u,concat(v,y))
            concat(leaf(),y) -> y
            if1(b,false(),u,v) -> if2(b,u,v)
            if1(b,true(),u,v) -> false()
            if2(false(),u,v) -> less_leaves(concat(left(u),right(u)),concat(left(v),right(v)))
            if2(true(),u,v) -> true()
            isLeaf(cons(u,v)) -> false()
            isLeaf(leaf()) -> true()
            left(cons(u,v)) -> u
            less_leaves(u,v) -> if1(isLeaf(u),isLeaf(v),u,v)
            right(cons(u,v)) -> v
        - Signature:
            {concat/2,if1/4,if2/3,isLeaf/1,left/1,less_leaves/2,right/1} / {cons/2,false/0,leaf/0,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {concat,if1,if2,isLeaf,left,less_leaves
            ,right} and constructors {cons,false,leaf,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            concat(cons(u,v),y) -> cons(u,concat(v,y))
            concat(leaf(),y) -> y
            if1(b,false(),u,v) -> if2(b,u,v)
            if1(b,true(),u,v) -> false()
            if2(false(),u,v) -> less_leaves(concat(left(u),right(u)),concat(left(v),right(v)))
            if2(true(),u,v) -> true()
            isLeaf(cons(u,v)) -> false()
            isLeaf(leaf()) -> true()
            left(cons(u,v)) -> u
            less_leaves(u,v) -> if1(isLeaf(u),isLeaf(v),u,v)
            right(cons(u,v)) -> v
        - Signature:
            {concat/2,if1/4,if2/3,isLeaf/1,left/1,less_leaves/2,right/1} / {cons/2,false/0,leaf/0,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {concat,if1,if2,isLeaf,left,less_leaves
            ,right} and constructors {cons,false,leaf,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          concat(y,z){y -> cons(x,y)} =
            concat(cons(x,y),z) ->^+ cons(x,concat(y,z))
              = C[concat(y,z) = concat(y,z){}]

WORST_CASE(Omega(n^1),?)