/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:
            eq(0(),0()) -> true()
            eq(0(),s(x)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            if_reach_1(false(),x,y,edge(u,v,i),h) -> reach(x,y,i,edge(u,v,h))
            if_reach_1(true(),x,y,edge(u,v,i),h) -> if_reach_2(eq(y,v),x,y,edge(u,v,i),h)
            if_reach_2(false(),x,y,edge(u,v,i),h) -> or(reach(x,y,i,h),reach(v,y,union(i,h),empty()))
            if_reach_2(true(),x,y,edge(u,v,i),h) -> true()
            or(false(),y) -> y
            or(true(),y) -> true()
            reach(x,y,edge(u,v,i),h) -> if_reach_1(eq(x,u),x,y,edge(u,v,i),h)
            reach(x,y,empty(),h) -> false()
            union(edge(x,y,i),h) -> edge(x,y,union(i,h))
            union(empty(),h) -> h
        - Signature:
            {eq/2,if_reach_1/5,if_reach_2/5,or/2,reach/4,union/2} / {0/0,edge/3,empty/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {eq,if_reach_1,if_reach_2,or,reach,union} and constructors {0,edge
            ,empty,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            eq(0(),0()) -> true()
            eq(0(),s(x)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            if_reach_1(false(),x,y,edge(u,v,i),h) -> reach(x,y,i,edge(u,v,h))
            if_reach_1(true(),x,y,edge(u,v,i),h) -> if_reach_2(eq(y,v),x,y,edge(u,v,i),h)
            if_reach_2(false(),x,y,edge(u,v,i),h) -> or(reach(x,y,i,h),reach(v,y,union(i,h),empty()))
            if_reach_2(true(),x,y,edge(u,v,i),h) -> true()
            or(false(),y) -> y
            or(true(),y) -> true()
            reach(x,y,edge(u,v,i),h) -> if_reach_1(eq(x,u),x,y,edge(u,v,i),h)
            reach(x,y,empty(),h) -> false()
            union(edge(x,y,i),h) -> edge(x,y,union(i,h))
            union(empty(),h) -> h
        - Signature:
            {eq/2,if_reach_1/5,if_reach_2/5,or/2,reach/4,union/2} / {0/0,edge/3,empty/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {eq,if_reach_1,if_reach_2,or,reach,union} and constructors {0,edge
            ,empty,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            eq(0(),0()) -> true()
            eq(0(),s(x)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            if_reach_1(false(),x,y,edge(u,v,i),h) -> reach(x,y,i,edge(u,v,h))
            if_reach_1(true(),x,y,edge(u,v,i),h) -> if_reach_2(eq(y,v),x,y,edge(u,v,i),h)
            if_reach_2(false(),x,y,edge(u,v,i),h) -> or(reach(x,y,i,h),reach(v,y,union(i,h),empty()))
            if_reach_2(true(),x,y,edge(u,v,i),h) -> true()
            or(false(),y) -> y
            or(true(),y) -> true()
            reach(x,y,edge(u,v,i),h) -> if_reach_1(eq(x,u),x,y,edge(u,v,i),h)
            reach(x,y,empty(),h) -> false()
            union(edge(x,y,i),h) -> edge(x,y,union(i,h))
            union(empty(),h) -> h
        - Signature:
            {eq/2,if_reach_1/5,if_reach_2/5,or/2,reach/4,union/2} / {0/0,edge/3,empty/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {eq,if_reach_1,if_reach_2,or,reach,union} and constructors {0,edge
            ,empty,false,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          eq(x,y){x -> s(x),y -> s(y)} =
            eq(s(x),s(y)) ->^+ eq(x,y)
              = C[eq(x,y) = eq(x,y){}]

WORST_CASE(Omega(n^1),?)