Confluence Competition

GCR Category

The GCR category is concerned with ground-confluence of many-sorted term rewrite systems (MSTRSs).


The input is a many-sorted first-order rewrite system without conditions, specified in the MSTRS format.

The question to be answered is whether the rewrite system is confluent on all well-sorted ground terms that can be built from the function symbols in the (SIG funlist) declaration. The first line of the output must be

In the first two cases, the output must be followed by justification that is understandable by a human expert.


  1. (VAR x)
      (a -> 0)
      (b -> 0)
      (c -> 0)
      (f 0 0 -> 1)
      a -> b
      f(b,b) -> f(a,a)
      f(x,a) -> f(a,a)
    The correct answer is NO and a possible output is
    The peak f(c,b) *<- f(c,a) ->* f(a,a) is not joinable since f(c,b) is not
    among the reducts { f(a,a), f(b,a), f(b,a), f(b,b) } of f(a,a).
  2. (SIG
       (0 -> Nat)
       (s Nat -> Nat)
       (eq Nat Nat -> Bool)
       (true -> Bool)
       (false -> Bool)
       eq(x,x) -> true
       eq(0,s(x)) -> false
       eq(s(x),0) -> false
       eq(s(x),s(y)) -> eq(x,y)
       eq(x,y) -> eq(y,x)
    The correct answer is YES and a possible output is
    Ground-confluence can be shown by rewriting induction, as explained in the
    FSCD 2016 paper of Takahito Aoto and Yoshihito Toyama.

Problem Selection

Problems are selected among those in COPS with the 'trs' or the 'mstrs' tag. The former are transformed into MSTRSs with a single sort, prior to passing them to competing tools.