/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(?,O(1))
* Step 1: Sum.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            f(g(h(a(),b()),c()),d()) -> if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'()))
            f(g(i(a(),b(),b'()),c()),d()) -> if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
        - Signature:
            {f/2} / {./2,a/0,b/0,b'/0,c/0,d/0,d'/0,e/0,g/2,h/2,i/3,if/3}
        - Obligation:
             runtime complexity wrt. defined symbols {f} and constructors {.,a,b,b',c,d,d',e,g,h,i,if}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: ToInnermost.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            f(g(h(a(),b()),c()),d()) -> if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'()))
            f(g(i(a(),b(),b'()),c()),d()) -> if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
        - Signature:
            {f/2} / {./2,a/0,b/0,b'/0,c/0,d/0,d'/0,e/0,g/2,h/2,i/3,if/3}
        - Obligation:
             runtime complexity wrt. defined symbols {f} and constructors {.,a,b,b',c,d,d',e,g,h,i,if}
    + Applied Processor:
        ToInnermost
    + Details:
        switch to innermost, as the system is overlay and right linear and does not contain weak rules
* Step 3: DependencyPairs.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            f(g(h(a(),b()),c()),d()) -> if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'()))
            f(g(i(a(),b(),b'()),c()),d()) -> if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
        - Signature:
            {f/2} / {./2,a/0,b/0,b'/0,c/0,d/0,d'/0,e/0,g/2,h/2,i/3,if/3}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f} and constructors {.,a,b,b',c,d,d',e,g,h,i,if}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          f#(g(h(a(),b()),c()),d()) -> c_1(f#(.(b(),g(h(a(),b()),c())),d()),f#(c(),d'()))
          f#(g(i(a(),b(),b'()),c()),d()) -> c_2(f#(.(b(),c()),d'()),f#(.(b'(),c()),d'()))
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 4: UsableRules.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            f#(g(h(a(),b()),c()),d()) -> c_1(f#(.(b(),g(h(a(),b()),c())),d()),f#(c(),d'()))
            f#(g(i(a(),b(),b'()),c()),d()) -> c_2(f#(.(b(),c()),d'()),f#(.(b'(),c()),d'()))
        - Weak TRS:
            f(g(h(a(),b()),c()),d()) -> if(e(),f(.(b(),g(h(a(),b()),c())),d()),f(c(),d'()))
            f(g(i(a(),b(),b'()),c()),d()) -> if(e(),f(.(b(),c()),d'()),f(.(b'(),c()),d'()))
        - Signature:
            {f/2,f#/2} / {./2,a/0,b/0,b'/0,c/0,d/0,d'/0,e/0,g/2,h/2,i/3,if/3,c_1/2,c_2/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#} and constructors {.,a,b,b',c,d,d',e,g,h,i,if}
    + Applied Processor:
        UsableRules
    + Details:
        We replace rewrite rules by usable rules:
          f#(g(h(a(),b()),c()),d()) -> c_1(f#(.(b(),g(h(a(),b()),c())),d()),f#(c(),d'()))
          f#(g(i(a(),b(),b'()),c()),d()) -> c_2(f#(.(b(),c()),d'()),f#(.(b'(),c()),d'()))
* Step 5: Trivial.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            f#(g(h(a(),b()),c()),d()) -> c_1(f#(.(b(),g(h(a(),b()),c())),d()),f#(c(),d'()))
            f#(g(i(a(),b(),b'()),c()),d()) -> c_2(f#(.(b(),c()),d'()),f#(.(b'(),c()),d'()))
        - Signature:
            {f/2,f#/2} / {./2,a/0,b/0,b'/0,c/0,d/0,d'/0,e/0,g/2,h/2,i/3,if/3,c_1/2,c_2/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#} and constructors {.,a,b,b',c,d,d',e,g,h,i,if}
    + Applied Processor:
        Trivial
    + Details:
        Consider the dependency graph
          1:S:f#(g(h(a(),b()),c()),d()) -> c_1(f#(.(b(),g(h(a(),b()),c())),d()),f#(c(),d'()))
             
          
          2:S:f#(g(i(a(),b(),b'()),c()),d()) -> c_2(f#(.(b(),c()),d'()),f#(.(b'(),c()),d'()))
             
          
        The dependency graph contains no loops, we remove all dependency pairs.
* Step 6: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        
        - Signature:
            {f/2,f#/2} / {./2,a/0,b/0,b'/0,c/0,d/0,d'/0,e/0,g/2,h/2,i/3,if/3,c_1/2,c_2/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f#} and constructors {.,a,b,b',c,d,d',e,g,h,i,if}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))