/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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


YES

Problem:
 merge(nil(),y) -> y
 merge(x,nil()) -> x
 merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
 ++(nil(),y) -> y
 ++(.(x,y),z) -> .(x,++(y,z))
 if(true(),x,y) -> x
 if(false(),x,y) -> x

Proof:
 DP Processor:
  DPs:
   merge#(.(x,y),.(u,v)) -> merge#(.(x,y),v)
   merge#(.(x,y),.(u,v)) -> merge#(y,.(u,v))
   merge#(.(x,y),.(u,v)) -> if#(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
   ++#(.(x,y),z) -> ++#(y,z)
  TRS:
   merge(nil(),y) -> y
   merge(x,nil()) -> x
   merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
   ++(nil(),y) -> y
   ++(.(x,y),z) -> .(x,++(y,z))
   if(true(),x,y) -> x
   if(false(),x,y) -> x
  TDG Processor:
   DPs:
    merge#(.(x,y),.(u,v)) -> merge#(.(x,y),v)
    merge#(.(x,y),.(u,v)) -> merge#(y,.(u,v))
    merge#(.(x,y),.(u,v)) -> if#(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
    ++#(.(x,y),z) -> ++#(y,z)
   TRS:
    merge(nil(),y) -> y
    merge(x,nil()) -> x
    merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
    ++(nil(),y) -> y
    ++(.(x,y),z) -> .(x,++(y,z))
    if(true(),x,y) -> x
    if(false(),x,y) -> x
   graph:
    ++#(.(x,y),z) -> ++#(y,z) -> ++#(.(x,y),z) -> ++#(y,z)
    merge#(.(x,y),.(u,v)) -> merge#(.(x,y),v) ->
    merge#(.(x,y),.(u,v)) -> if#(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
    merge#(.(x,y),.(u,v)) -> merge#(.(x,y),v) ->
    merge#(.(x,y),.(u,v)) -> merge#(y,.(u,v))
    merge#(.(x,y),.(u,v)) -> merge#(.(x,y),v) ->
    merge#(.(x,y),.(u,v)) -> merge#(.(x,y),v)
    merge#(.(x,y),.(u,v)) -> merge#(y,.(u,v)) ->
    merge#(.(x,y),.(u,v)) -> if#(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
    merge#(.(x,y),.(u,v)) -> merge#(y,.(u,v)) ->
    merge#(.(x,y),.(u,v)) -> merge#(y,.(u,v))
    merge#(.(x,y),.(u,v)) -> merge#(y,.(u,v)) -> merge#(.(x,y),.(u,v)) -> merge#(.(x,y),v)
   SCC Processor:
    #sccs: 2
    #rules: 3
    #arcs: 7/16
    DPs:
     merge#(.(x,y),.(u,v)) -> merge#(.(x,y),v)
     merge#(.(x,y),.(u,v)) -> merge#(y,.(u,v))
    TRS:
     merge(nil(),y) -> y
     merge(x,nil()) -> x
     merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
     ++(nil(),y) -> y
     ++(.(x,y),z) -> .(x,++(y,z))
     if(true(),x,y) -> x
     if(false(),x,y) -> x
    Subterm Criterion Processor:
     simple projection:
      pi(merge#) = 0
     problem:
      DPs:
       merge#(.(x,y),.(u,v)) -> merge#(.(x,y),v)
      TRS:
       merge(nil(),y) -> y
       merge(x,nil()) -> x
       merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
       ++(nil(),y) -> y
       ++(.(x,y),z) -> .(x,++(y,z))
       if(true(),x,y) -> x
       if(false(),x,y) -> x
     Subterm Criterion Processor:
      simple projection:
       pi(merge#) = 1
      problem:
       DPs:
        
       TRS:
        merge(nil(),y) -> y
        merge(x,nil()) -> x
        merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
        ++(nil(),y) -> y
        ++(.(x,y),z) -> .(x,++(y,z))
        if(true(),x,y) -> x
        if(false(),x,y) -> x
      Qed
    
    DPs:
     ++#(.(x,y),z) -> ++#(y,z)
    TRS:
     merge(nil(),y) -> y
     merge(x,nil()) -> x
     merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
     ++(nil(),y) -> y
     ++(.(x,y),z) -> .(x,++(y,z))
     if(true(),x,y) -> x
     if(false(),x,y) -> x
    Subterm Criterion Processor:
     simple projection:
      pi(++#) = 0
     problem:
      DPs:
       
      TRS:
       merge(nil(),y) -> y
       merge(x,nil()) -> x
       merge(.(x,y),.(u,v)) -> if(<(x,u),.(x,merge(y,.(u,v))),.(u,merge(.(x,y),v)))
       ++(nil(),y) -> y
       ++(.(x,y),z) -> .(x,++(y,z))
       if(true(),x,y) -> x
       if(false(),x,y) -> x
     Qed