/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/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 
  2ndsneg : [o * o] --> o 
  2ndspos : [o * o] --> o 
  active : [o] --> o 
  cons : [o * o] --> o 
  from : [o] --> o 
  mark : [o] --> o 
  negrecip : [o] --> o 
  pi : [o] --> o 
  plus : [o * o] --> o 
  posrecip : [o] --> o 
  rcons : [o * o] --> o 
  rnil : [] --> o 
  s : [o] --> o 
  square : [o] --> o 
  times : [o * o] --> o 

  active(from(X)) => mark(cons(X, from(s(X)))) 
  active(2ndspos(0, X)) => mark(rnil) 
  active(2ndspos(s(X), cons(Y, cons(Z, U)))) => mark(rcons(posrecip(Z), 2ndsneg(X, U))) 
  active(2ndsneg(0, X)) => mark(rnil) 
  active(2ndsneg(s(X), cons(Y, cons(Z, U)))) => mark(rcons(negrecip(Z), 2ndspos(X, U))) 
  active(pi(X)) => mark(2ndspos(X, from(0))) 
  active(plus(0, X)) => mark(X) 
  active(plus(s(X), Y)) => mark(s(plus(X, Y))) 
  active(times(0, X)) => mark(0) 
  active(times(s(X), Y)) => mark(plus(Y, times(X, Y))) 
  active(square(X)) => mark(times(X, X)) 
  mark(from(X)) => active(from(mark(X))) 
  mark(cons(X, Y)) => active(cons(mark(X), Y)) 
  mark(s(X)) => active(s(mark(X))) 
  mark(2ndspos(X, Y)) => active(2ndspos(mark(X), mark(Y))) 
  mark(0) => active(0) 
  mark(rnil) => active(rnil) 
  mark(rcons(X, Y)) => active(rcons(mark(X), mark(Y))) 
  mark(posrecip(X)) => active(posrecip(mark(X))) 
  mark(2ndsneg(X, Y)) => active(2ndsneg(mark(X), mark(Y))) 
  mark(negrecip(X)) => active(negrecip(mark(X))) 
  mark(pi(X)) => active(pi(mark(X))) 
  mark(plus(X, Y)) => active(plus(mark(X), mark(Y))) 
  mark(times(X, Y)) => active(times(mark(X), mark(Y))) 
  mark(square(X)) => active(square(mark(X))) 
  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) 
  2ndspos(mark(X), Y) => 2ndspos(X, Y) 
  2ndspos(X, mark(Y)) => 2ndspos(X, Y) 
  2ndspos(active(X), Y) => 2ndspos(X, Y) 
  2ndspos(X, active(Y)) => 2ndspos(X, Y) 
  rcons(mark(X), Y) => rcons(X, Y) 
  rcons(X, mark(Y)) => rcons(X, Y) 
  rcons(active(X), Y) => rcons(X, Y) 
  rcons(X, active(Y)) => rcons(X, Y) 
  posrecip(mark(X)) => posrecip(X) 
  posrecip(active(X)) => posrecip(X) 
  2ndsneg(mark(X), Y) => 2ndsneg(X, Y) 
  2ndsneg(X, mark(Y)) => 2ndsneg(X, Y) 
  2ndsneg(active(X), Y) => 2ndsneg(X, Y) 
  2ndsneg(X, active(Y)) => 2ndsneg(X, Y) 
  negrecip(mark(X)) => negrecip(X) 
  negrecip(active(X)) => negrecip(X) 
  pi(mark(X)) => pi(X) 
  pi(active(X)) => pi(X) 
  plus(mark(X), Y) => plus(X, Y) 
  plus(X, mark(Y)) => plus(X, Y) 
  plus(active(X), Y) => plus(X, Y) 
  plus(X, active(Y)) => plus(X, Y) 
  times(mark(X), Y) => times(X, Y) 
  times(X, mark(Y)) => times(X, Y) 
  times(active(X), Y) => times(X, Y) 
  times(X, active(Y)) => times(X, Y) 
  square(mark(X)) => square(X) 
  square(active(X)) => square(X)