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


--------------------------------------------------------------------------------


WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__A() -> A()
            a__A() -> a__h(a__f(a__a()),a__f(a__b()))
            a__a() -> a()
            a__a() -> a__c()
            a__a() -> a__d()
            a__b() -> a__c()
            a__b() -> a__d()
            a__b() -> b()
            a__c() -> c()
            a__c() -> e()
            a__c() -> l()
            a__d() -> d()
            a__d() -> m()
            a__f(X) -> a__z(mark(X),X)
            a__f(X) -> f(X)
            a__g(X1,X2,X3) -> g(X1,X2,X3)
            a__g(d(),X,X) -> a__A()
            a__h(X,X) -> a__g(mark(X),mark(X),a__f(a__k()))
            a__h(X1,X2) -> h(X1,X2)
            a__k() -> k()
            a__k() -> l()
            a__k() -> m()
            a__z(X1,X2) -> z(X1,X2)
            a__z(e(),X) -> mark(X)
            mark(A()) -> a__A()
            mark(a()) -> a__a()
            mark(b()) -> a__b()
            mark(c()) -> a__c()
            mark(d()) -> a__d()
            mark(e()) -> e()
            mark(f(X)) -> a__f(mark(X))
            mark(g(X1,X2,X3)) -> a__g(mark(X1),mark(X2),mark(X3))
            mark(h(X1,X2)) -> a__h(mark(X1),mark(X2))
            mark(k()) -> a__k()
            mark(l()) -> l()
            mark(m()) -> m()
            mark(z(X1,X2)) -> a__z(mark(X1),X2)
        - Signature:
            {a__A/0,a__a/0,a__b/0,a__c/0,a__d/0,a__f/1,a__g/3,a__h/2,a__k/0,a__z/2,mark/1} / {A/0,a/0,b/0,c/0,d/0,e/0
            ,f/1,g/3,h/2,k/0,l/0,m/0,z/2}
        - Obligation:
             runtime complexity wrt. defined symbols {a__A,a__a,a__b,a__c,a__d,a__f,a__g,a__h,a__k,a__z
            ,mark} and constructors {A,a,b,c,d,e,f,g,h,k,l,m,z}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__A() -> A()
            a__A() -> a__h(a__f(a__a()),a__f(a__b()))
            a__a() -> a()
            a__a() -> a__c()
            a__a() -> a__d()
            a__b() -> a__c()
            a__b() -> a__d()
            a__b() -> b()
            a__c() -> c()
            a__c() -> e()
            a__c() -> l()
            a__d() -> d()
            a__d() -> m()
            a__f(X) -> a__z(mark(X),X)
            a__f(X) -> f(X)
            a__g(X1,X2,X3) -> g(X1,X2,X3)
            a__g(d(),X,X) -> a__A()
            a__h(X,X) -> a__g(mark(X),mark(X),a__f(a__k()))
            a__h(X1,X2) -> h(X1,X2)
            a__k() -> k()
            a__k() -> l()
            a__k() -> m()
            a__z(X1,X2) -> z(X1,X2)
            a__z(e(),X) -> mark(X)
            mark(A()) -> a__A()
            mark(a()) -> a__a()
            mark(b()) -> a__b()
            mark(c()) -> a__c()
            mark(d()) -> a__d()
            mark(e()) -> e()
            mark(f(X)) -> a__f(mark(X))
            mark(g(X1,X2,X3)) -> a__g(mark(X1),mark(X2),mark(X3))
            mark(h(X1,X2)) -> a__h(mark(X1),mark(X2))
            mark(k()) -> a__k()
            mark(l()) -> l()
            mark(m()) -> m()
            mark(z(X1,X2)) -> a__z(mark(X1),X2)
        - Signature:
            {a__A/0,a__a/0,a__b/0,a__c/0,a__d/0,a__f/1,a__g/3,a__h/2,a__k/0,a__z/2,mark/1} / {A/0,a/0,b/0,c/0,d/0,e/0
            ,f/1,g/3,h/2,k/0,l/0,m/0,z/2}
        - Obligation:
             runtime complexity wrt. defined symbols {a__A,a__a,a__b,a__c,a__d,a__f,a__g,a__h,a__k,a__z
            ,mark} and constructors {A,a,b,c,d,e,f,g,h,k,l,m,z}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__A() -> A()
            a__A() -> a__h(a__f(a__a()),a__f(a__b()))
            a__a() -> a()
            a__a() -> a__c()
            a__a() -> a__d()
            a__b() -> a__c()
            a__b() -> a__d()
            a__b() -> b()
            a__c() -> c()
            a__c() -> e()
            a__c() -> l()
            a__d() -> d()
            a__d() -> m()
            a__f(X) -> a__z(mark(X),X)
            a__f(X) -> f(X)
            a__g(X1,X2,X3) -> g(X1,X2,X3)
            a__g(d(),X,X) -> a__A()
            a__h(X,X) -> a__g(mark(X),mark(X),a__f(a__k()))
            a__h(X1,X2) -> h(X1,X2)
            a__k() -> k()
            a__k() -> l()
            a__k() -> m()
            a__z(X1,X2) -> z(X1,X2)
            a__z(e(),X) -> mark(X)
            mark(A()) -> a__A()
            mark(a()) -> a__a()
            mark(b()) -> a__b()
            mark(c()) -> a__c()
            mark(d()) -> a__d()
            mark(e()) -> e()
            mark(f(X)) -> a__f(mark(X))
            mark(g(X1,X2,X3)) -> a__g(mark(X1),mark(X2),mark(X3))
            mark(h(X1,X2)) -> a__h(mark(X1),mark(X2))
            mark(k()) -> a__k()
            mark(l()) -> l()
            mark(m()) -> m()
            mark(z(X1,X2)) -> a__z(mark(X1),X2)
        - Signature:
            {a__A/0,a__a/0,a__b/0,a__c/0,a__d/0,a__f/1,a__g/3,a__h/2,a__k/0,a__z/2,mark/1} / {A/0,a/0,b/0,c/0,d/0,e/0
            ,f/1,g/3,h/2,k/0,l/0,m/0,z/2}
        - Obligation:
             runtime complexity wrt. defined symbols {a__A,a__a,a__b,a__c,a__d,a__f,a__g,a__h,a__k,a__z
            ,mark} and constructors {A,a,b,c,d,e,f,g,h,k,l,m,z}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          mark(x){x -> f(x)} =
            mark(f(x)) ->^+ a__f(mark(x))
              = C[mark(x) = mark(x){}]

WORST_CASE(Omega(n^1),?)