/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 
  cons2 : [o * o] --> o 
  from : [o] --> o 
  mark : [o] --> o 
  negrecip : [o] --> o 
  nil : [] --> o 
  ok : [o] --> o 
  pi : [o] --> o 
  plus : [o * o] --> o 
  posrecip : [o] --> o 
  proper : [o] --> o 
  rcons : [o * o] --> o 
  rnil : [] --> o 
  s : [o] --> o 
  square : [o] --> o 
  times : [o * o] --> o 
  top : [o] --> o 

  active(from(X)) => mark(cons(X, from(s(X)))) 
  active(2ndspos(0, X)) => mark(rnil) 
  active(2ndspos(s(X), cons(Y, Z))) => mark(2ndspos(s(X), cons2(Y, Z))) 
  active(2ndspos(s(X), cons2(Y, cons(Z, U)))) => mark(rcons(posrecip(Z), 2ndsneg(X, U))) 
  active(2ndsneg(0, X)) => mark(rnil) 
  active(2ndsneg(s(X), cons(Y, Z))) => mark(2ndsneg(s(X), cons2(Y, Z))) 
  active(2ndsneg(s(X), cons2(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)) 
  active(s(X)) => s(active(X)) 
  active(posrecip(X)) => posrecip(active(X)) 
  active(negrecip(X)) => negrecip(active(X)) 
  active(cons(X, Y)) => cons(active(X), Y) 
  active(cons2(X, Y)) => cons2(X, active(Y)) 
  active(rcons(X, Y)) => rcons(active(X), Y) 
  active(rcons(X, Y)) => rcons(X, active(Y)) 
  active(from(X)) => from(active(X)) 
  active(2ndspos(X, Y)) => 2ndspos(active(X), Y) 
  active(2ndspos(X, Y)) => 2ndspos(X, active(Y)) 
  active(2ndsneg(X, Y)) => 2ndsneg(active(X), Y) 
  active(2ndsneg(X, Y)) => 2ndsneg(X, active(Y)) 
  active(pi(X)) => pi(active(X)) 
  active(plus(X, Y)) => plus(active(X), Y) 
  active(plus(X, Y)) => plus(X, active(Y)) 
  active(times(X, Y)) => times(active(X), Y) 
  active(times(X, Y)) => times(X, active(Y)) 
  active(square(X)) => square(active(X)) 
  s(mark(X)) => mark(s(X)) 
  posrecip(mark(X)) => mark(posrecip(X)) 
  negrecip(mark(X)) => mark(negrecip(X)) 
  cons(mark(X), Y) => mark(cons(X, Y)) 
  cons2(X, mark(Y)) => mark(cons2(X, Y)) 
  rcons(mark(X), Y) => mark(rcons(X, Y)) 
  rcons(X, mark(Y)) => mark(rcons(X, Y)) 
  from(mark(X)) => mark(from(X)) 
  2ndspos(mark(X), Y) => mark(2ndspos(X, Y)) 
  2ndspos(X, mark(Y)) => mark(2ndspos(X, Y)) 
  2ndsneg(mark(X), Y) => mark(2ndsneg(X, Y)) 
  2ndsneg(X, mark(Y)) => mark(2ndsneg(X, Y)) 
  pi(mark(X)) => mark(pi(X)) 
  plus(mark(X), Y) => mark(plus(X, Y)) 
  plus(X, mark(Y)) => mark(plus(X, Y)) 
  times(mark(X), Y) => mark(times(X, Y)) 
  times(X, mark(Y)) => mark(times(X, Y)) 
  square(mark(X)) => mark(square(X)) 
  proper(0) => ok(0) 
  proper(s(X)) => s(proper(X)) 
  proper(posrecip(X)) => posrecip(proper(X)) 
  proper(negrecip(X)) => negrecip(proper(X)) 
  proper(nil) => ok(nil) 
  proper(cons(X, Y)) => cons(proper(X), proper(Y)) 
  proper(cons2(X, Y)) => cons2(proper(X), proper(Y)) 
  proper(rnil) => ok(rnil) 
  proper(rcons(X, Y)) => rcons(proper(X), proper(Y)) 
  proper(from(X)) => from(proper(X)) 
  proper(2ndspos(X, Y)) => 2ndspos(proper(X), proper(Y)) 
  proper(2ndsneg(X, Y)) => 2ndsneg(proper(X), proper(Y)) 
  proper(pi(X)) => pi(proper(X)) 
  proper(plus(X, Y)) => plus(proper(X), proper(Y)) 
  proper(times(X, Y)) => times(proper(X), proper(Y)) 
  proper(square(X)) => square(proper(X)) 
  s(ok(X)) => ok(s(X)) 
  posrecip(ok(X)) => ok(posrecip(X)) 
  negrecip(ok(X)) => ok(negrecip(X)) 
  cons(ok(X), ok(Y)) => ok(cons(X, Y)) 
  cons2(ok(X), ok(Y)) => ok(cons2(X, Y)) 
  rcons(ok(X), ok(Y)) => ok(rcons(X, Y)) 
  from(ok(X)) => ok(from(X)) 
  2ndspos(ok(X), ok(Y)) => ok(2ndspos(X, Y)) 
  2ndsneg(ok(X), ok(Y)) => ok(2ndsneg(X, Y)) 
  pi(ok(X)) => ok(pi(X)) 
  plus(ok(X), ok(Y)) => ok(plus(X, Y)) 
  times(ok(X), ok(Y)) => ok(times(X, Y)) 
  square(ok(X)) => ok(square(X)) 
  top(mark(X)) => top(proper(X)) 
  top(ok(X)) => top(active(X))