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


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MAYBE

Problem:
 sub(0(),0()) -> 0()
 sub(s(x),0()) -> s(x)
 sub(0(),s(x)) -> 0()
 sub(s(x),s(y)) -> sub(x,y)
 zero(nil()) -> zero2(0(),nil())
 zero(cons(x,xs)) -> zero2(sub(x,x),cons(x,xs))
 zero2(0(),nil()) -> nil()
 zero2(0(),cons(x,xs)) -> cons(sub(x,x),zero(xs))
 zero2(s(y),nil()) -> zero(nil())
 zero2(s(y),cons(x,xs)) -> zero(cons(x,xs))

Proof:
 DP Processor:
  DPs:
   sub#(s(x),s(y)) -> sub#(x,y)
   zero#(nil()) -> zero2#(0(),nil())
   zero#(cons(x,xs)) -> sub#(x,x)
   zero#(cons(x,xs)) -> zero2#(sub(x,x),cons(x,xs))
   zero2#(0(),cons(x,xs)) -> zero#(xs)
   zero2#(0(),cons(x,xs)) -> sub#(x,x)
   zero2#(s(y),nil()) -> zero#(nil())
   zero2#(s(y),cons(x,xs)) -> zero#(cons(x,xs))
  TRS:
   sub(0(),0()) -> 0()
   sub(s(x),0()) -> s(x)
   sub(0(),s(x)) -> 0()
   sub(s(x),s(y)) -> sub(x,y)
   zero(nil()) -> zero2(0(),nil())
   zero(cons(x,xs)) -> zero2(sub(x,x),cons(x,xs))
   zero2(0(),nil()) -> nil()
   zero2(0(),cons(x,xs)) -> cons(sub(x,x),zero(xs))
   zero2(s(y),nil()) -> zero(nil())
   zero2(s(y),cons(x,xs)) -> zero(cons(x,xs))
  EDG Processor:
   DPs:
    sub#(s(x),s(y)) -> sub#(x,y)
    zero#(nil()) -> zero2#(0(),nil())
    zero#(cons(x,xs)) -> sub#(x,x)
    zero#(cons(x,xs)) -> zero2#(sub(x,x),cons(x,xs))
    zero2#(0(),cons(x,xs)) -> zero#(xs)
    zero2#(0(),cons(x,xs)) -> sub#(x,x)
    zero2#(s(y),nil()) -> zero#(nil())
    zero2#(s(y),cons(x,xs)) -> zero#(cons(x,xs))
   TRS:
    sub(0(),0()) -> 0()
    sub(s(x),0()) -> s(x)
    sub(0(),s(x)) -> 0()
    sub(s(x),s(y)) -> sub(x,y)
    zero(nil()) -> zero2(0(),nil())
    zero(cons(x,xs)) -> zero2(sub(x,x),cons(x,xs))
    zero2(0(),nil()) -> nil()
    zero2(0(),cons(x,xs)) -> cons(sub(x,x),zero(xs))
    zero2(s(y),nil()) -> zero(nil())
    zero2(s(y),cons(x,xs)) -> zero(cons(x,xs))
   graph:
    zero2#(s(y),cons(x,xs)) -> zero#(cons(x,xs)) ->
    zero#(cons(x,xs)) -> sub#(x,x)
    zero2#(s(y),cons(x,xs)) -> zero#(cons(x,xs)) ->
    zero#(cons(x,xs)) -> zero2#(sub(x,x),cons(x,xs))
    zero2#(s(y),nil()) -> zero#(nil()) ->
    zero#(nil()) -> zero2#(0(),nil())
    zero2#(0(),cons(x,xs)) -> zero#(xs) ->
    zero#(nil()) -> zero2#(0(),nil())
    zero2#(0(),cons(x,xs)) -> zero#(xs) ->
    zero#(cons(x,xs)) -> sub#(x,x)
    zero2#(0(),cons(x,xs)) -> zero#(xs) ->
    zero#(cons(x,xs)) -> zero2#(sub(x,x),cons(x,xs))
    zero2#(0(),cons(x,xs)) -> sub#(x,x) ->
    sub#(s(x),s(y)) -> sub#(x,y)
    zero#(cons(x,xs)) -> zero2#(sub(x,x),cons(x,xs)) ->
    zero2#(0(),cons(x,xs)) -> zero#(xs)
    zero#(cons(x,xs)) -> zero2#(sub(x,x),cons(x,xs)) ->
    zero2#(0(),cons(x,xs)) -> sub#(x,x)
    zero#(cons(x,xs)) -> zero2#(sub(x,x),cons(x,xs)) ->
    zero2#(s(y),cons(x,xs)) -> zero#(cons(x,xs))
    zero#(cons(x,xs)) -> sub#(x,x) -> sub#(s(x),s(y)) -> sub#(x,y)
    sub#(s(x),s(y)) -> sub#(x,y) -> sub#(s(x),s(y)) -> sub#(x,y)
   SCC Processor:
    #sccs: 2
    #rules: 4
    #arcs: 12/64
    DPs:
     zero2#(s(y),cons(x,xs)) -> zero#(cons(x,xs))
     zero#(cons(x,xs)) -> zero2#(sub(x,x),cons(x,xs))
     zero2#(0(),cons(x,xs)) -> zero#(xs)
    TRS:
     sub(0(),0()) -> 0()
     sub(s(x),0()) -> s(x)
     sub(0(),s(x)) -> 0()
     sub(s(x),s(y)) -> sub(x,y)
     zero(nil()) -> zero2(0(),nil())
     zero(cons(x,xs)) -> zero2(sub(x,x),cons(x,xs))
     zero2(0(),nil()) -> nil()
     zero2(0(),cons(x,xs)) -> cons(sub(x,x),zero(xs))
     zero2(s(y),nil()) -> zero(nil())
     zero2(s(y),cons(x,xs)) -> zero(cons(x,xs))
    Subterm Criterion Processor:
     simple projection:
      pi(zero#) = 0
      pi(zero2#) = 1
     problem:
      DPs:
       zero2#(s(y),cons(x,xs)) -> zero#(cons(x,xs))
       zero#(cons(x,xs)) -> zero2#(sub(x,x),cons(x,xs))
      TRS:
       sub(0(),0()) -> 0()
       sub(s(x),0()) -> s(x)
       sub(0(),s(x)) -> 0()
       sub(s(x),s(y)) -> sub(x,y)
       zero(nil()) -> zero2(0(),nil())
       zero(cons(x,xs)) -> zero2(sub(x,x),cons(x,xs))
       zero2(0(),nil()) -> nil()
       zero2(0(),cons(x,xs)) -> cons(sub(x,x),zero(xs))
       zero2(s(y),nil()) -> zero(nil())
       zero2(s(y),cons(x,xs)) -> zero(cons(x,xs))
     Open
    
    DPs:
     sub#(s(x),s(y)) -> sub#(x,y)
    TRS:
     sub(0(),0()) -> 0()
     sub(s(x),0()) -> s(x)
     sub(0(),s(x)) -> 0()
     sub(s(x),s(y)) -> sub(x,y)
     zero(nil()) -> zero2(0(),nil())
     zero(cons(x,xs)) -> zero2(sub(x,x),cons(x,xs))
     zero2(0(),nil()) -> nil()
     zero2(0(),cons(x,xs)) -> cons(sub(x,x),zero(xs))
     zero2(s(y),nil()) -> zero(nil())
     zero2(s(y),cons(x,xs)) -> zero(cons(x,xs))
    Subterm Criterion Processor:
     simple projection:
      pi(sub#) = 0
     problem:
      DPs:
       
      TRS:
       sub(0(),0()) -> 0()
       sub(s(x),0()) -> s(x)
       sub(0(),s(x)) -> 0()
       sub(s(x),s(y)) -> sub(x,y)
       zero(nil()) -> zero2(0(),nil())
       zero(cons(x,xs)) -> zero2(sub(x,x),cons(x,xs))
       zero2(0(),nil()) -> nil()
       zero2(0(),cons(x,xs)) -> cons(sub(x,x),zero(xs))
       zero2(s(y),nil()) -> zero(nil())
       zero2(s(y),cons(x,xs)) -> zero(cons(x,xs))
     Qed