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


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MAYBE
We consider the system theBenchmark.

We are asked to determine termination of the following first-order TRS.

  0 : [] --> o 
  01 : [] --> o 
  active : [o] --> o 
  cons : [o * o] --> o 
  dbl : [o] --> o 
  dbl1 : [o] --> o 
  dbls : [o] --> o 
  from : [o] --> o 
  indx : [o * o] --> o 
  mark : [o] --> o 
  nil : [] --> o 
  ok : [o] --> o 
  proper : [o] --> o 
  quote : [o] --> o 
  s : [o] --> o 
  s1 : [o] --> o 
  sel : [o * o] --> o 
  sel1 : [o * o] --> o 
  top : [o] --> o 

  active(dbl(0)) => mark(0) 
  active(dbl(s(X))) => mark(s(s(dbl(X)))) 
  active(dbls(nil)) => mark(nil) 
  active(dbls(cons(X, Y))) => mark(cons(dbl(X), dbls(Y))) 
  active(sel(0, cons(X, Y))) => mark(X) 
  active(sel(s(X), cons(Y, Z))) => mark(sel(X, Z)) 
  active(indx(nil, X)) => mark(nil) 
  active(indx(cons(X, Y), Z)) => mark(cons(sel(X, Z), indx(Y, Z))) 
  active(from(X)) => mark(cons(X, from(s(X)))) 
  active(dbl1(0)) => mark(01) 
  active(dbl1(s(X))) => mark(s1(s1(dbl1(X)))) 
  active(sel1(0, cons(X, Y))) => mark(X) 
  active(sel1(s(X), cons(Y, Z))) => mark(sel1(X, Z)) 
  active(quote(0)) => mark(01) 
  active(quote(s(X))) => mark(s1(quote(X))) 
  active(quote(dbl(X))) => mark(dbl1(X)) 
  active(quote(sel(X, Y))) => mark(sel1(X, Y)) 
  active(dbl(X)) => dbl(active(X)) 
  active(dbls(X)) => dbls(active(X)) 
  active(sel(X, Y)) => sel(active(X), Y) 
  active(sel(X, Y)) => sel(X, active(Y)) 
  active(indx(X, Y)) => indx(active(X), Y) 
  active(dbl1(X)) => dbl1(active(X)) 
  active(s1(X)) => s1(active(X)) 
  active(sel1(X, Y)) => sel1(active(X), Y) 
  active(sel1(X, Y)) => sel1(X, active(Y)) 
  active(quote(X)) => quote(active(X)) 
  dbl(mark(X)) => mark(dbl(X)) 
  dbls(mark(X)) => mark(dbls(X)) 
  sel(mark(X), Y) => mark(sel(X, Y)) 
  sel(X, mark(Y)) => mark(sel(X, Y)) 
  indx(mark(X), Y) => mark(indx(X, Y)) 
  dbl1(mark(X)) => mark(dbl1(X)) 
  s1(mark(X)) => mark(s1(X)) 
  sel1(mark(X), Y) => mark(sel1(X, Y)) 
  sel1(X, mark(Y)) => mark(sel1(X, Y)) 
  quote(mark(X)) => mark(quote(X)) 
  proper(dbl(X)) => dbl(proper(X)) 
  proper(0) => ok(0) 
  proper(s(X)) => s(proper(X)) 
  proper(dbls(X)) => dbls(proper(X)) 
  proper(nil) => ok(nil) 
  proper(cons(X, Y)) => cons(proper(X), proper(Y)) 
  proper(sel(X, Y)) => sel(proper(X), proper(Y)) 
  proper(indx(X, Y)) => indx(proper(X), proper(Y)) 
  proper(from(X)) => from(proper(X)) 
  proper(dbl1(X)) => dbl1(proper(X)) 
  proper(01) => ok(01) 
  proper(s1(X)) => s1(proper(X)) 
  proper(sel1(X, Y)) => sel1(proper(X), proper(Y)) 
  proper(quote(X)) => quote(proper(X)) 
  dbl(ok(X)) => ok(dbl(X)) 
  s(ok(X)) => ok(s(X)) 
  dbls(ok(X)) => ok(dbls(X)) 
  cons(ok(X), ok(Y)) => ok(cons(X, Y)) 
  sel(ok(X), ok(Y)) => ok(sel(X, Y)) 
  indx(ok(X), ok(Y)) => ok(indx(X, Y)) 
  from(ok(X)) => ok(from(X)) 
  dbl1(ok(X)) => ok(dbl1(X)) 
  s1(ok(X)) => ok(s1(X)) 
  sel1(ok(X), ok(Y)) => ok(sel1(X, Y)) 
  quote(ok(X)) => ok(quote(X)) 
  top(mark(X)) => top(proper(X)) 
  top(ok(X)) => top(active(X))