/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 
  active : [o] --> o 
  cons : [o * o] --> o 
  from : [o] --> o 
  mark : [o] --> o 
  minus : [o * o] --> o 
  nil : [] --> o 
  quot : [o * o] --> o 
  s : [o] --> o 
  sel : [o * o] --> o 
  zWquot : [o * o] --> o 

  active(from(X)) => mark(cons(X, from(s(X)))) 
  active(sel(0, cons(X, Y))) => mark(X) 
  active(sel(s(X), cons(Y, Z))) => mark(sel(X, Z)) 
  active(minus(X, 0)) => mark(0) 
  active(minus(s(X), s(Y))) => mark(minus(X, Y)) 
  active(quot(0, s(X))) => mark(0) 
  active(quot(s(X), s(Y))) => mark(s(quot(minus(X, Y), s(Y)))) 
  active(zWquot(X, nil)) => mark(nil) 
  active(zWquot(nil, X)) => mark(nil) 
  active(zWquot(cons(X, Y), cons(Z, U))) => mark(cons(quot(X, Z), zWquot(Y, U))) 
  mark(from(X)) => active(from(mark(X))) 
  mark(cons(X, Y)) => active(cons(mark(X), Y)) 
  mark(s(X)) => active(s(mark(X))) 
  mark(sel(X, Y)) => active(sel(mark(X), mark(Y))) 
  mark(0) => active(0) 
  mark(minus(X, Y)) => active(minus(mark(X), mark(Y))) 
  mark(quot(X, Y)) => active(quot(mark(X), mark(Y))) 
  mark(zWquot(X, Y)) => active(zWquot(mark(X), mark(Y))) 
  mark(nil) => active(nil) 
  from(mark(X)) => from(X) 
  from(active(X)) => from(X) 
  cons(mark(X), Y) => cons(X, Y) 
  cons(X, mark(Y)) => cons(X, Y) 
  cons(active(X), Y) => cons(X, Y) 
  cons(X, active(Y)) => cons(X, Y) 
  s(mark(X)) => s(X) 
  s(active(X)) => s(X) 
  sel(mark(X), Y) => sel(X, Y) 
  sel(X, mark(Y)) => sel(X, Y) 
  sel(active(X), Y) => sel(X, Y) 
  sel(X, active(Y)) => sel(X, Y) 
  minus(mark(X), Y) => minus(X, Y) 
  minus(X, mark(Y)) => minus(X, Y) 
  minus(active(X), Y) => minus(X, Y) 
  minus(X, active(Y)) => minus(X, Y) 
  quot(mark(X), Y) => quot(X, Y) 
  quot(X, mark(Y)) => quot(X, Y) 
  quot(active(X), Y) => quot(X, Y) 
  quot(X, active(Y)) => quot(X, Y) 
  zWquot(mark(X), Y) => zWquot(X, Y) 
  zWquot(X, mark(Y)) => zWquot(X, Y) 
  zWquot(active(X), Y) => zWquot(X, Y) 
  zWquot(X, active(Y)) => zWquot(X, Y)