/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 
  U11 : [o * o] --> o 
  active : [o] --> o 
  and : [o * o] --> o 
  cons : [o * o] --> o 
  isNat : [o] --> o 
  isNatIList : [o] --> o 
  isNatList : [o] --> o 
  length : [o] --> o 
  mark : [o] --> o 
  nil : [] --> o 
  ok : [o] --> o 
  proper : [o] --> o 
  s : [o] --> o 
  top : [o] --> o 
  tt : [] --> o 
  zeros : [] --> o 

  active(zeros) => mark(cons(0, zeros)) 
  active(U11(tt, X)) => mark(s(length(X))) 
  active(and(tt, X)) => mark(X) 
  active(isNat(0)) => mark(tt) 
  active(isNat(length(X))) => mark(isNatList(X)) 
  active(isNat(s(X))) => mark(isNat(X)) 
  active(isNatIList(X)) => mark(isNatList(X)) 
  active(isNatIList(zeros)) => mark(tt) 
  active(isNatIList(cons(X, Y))) => mark(and(isNat(X), isNatIList(Y))) 
  active(isNatList(nil)) => mark(tt) 
  active(isNatList(cons(X, Y))) => mark(and(isNat(X), isNatList(Y))) 
  active(length(nil)) => mark(0) 
  active(length(cons(X, Y))) => mark(U11(and(isNatList(Y), isNat(X)), Y)) 
  active(cons(X, Y)) => cons(active(X), Y) 
  active(U11(X, Y)) => U11(active(X), Y) 
  active(s(X)) => s(active(X)) 
  active(length(X)) => length(active(X)) 
  active(and(X, Y)) => and(active(X), Y) 
  cons(mark(X), Y) => mark(cons(X, Y)) 
  U11(mark(X), Y) => mark(U11(X, Y)) 
  s(mark(X)) => mark(s(X)) 
  length(mark(X)) => mark(length(X)) 
  and(mark(X), Y) => mark(and(X, Y)) 
  proper(zeros) => ok(zeros) 
  proper(cons(X, Y)) => cons(proper(X), proper(Y)) 
  proper(0) => ok(0) 
  proper(U11(X, Y)) => U11(proper(X), proper(Y)) 
  proper(tt) => ok(tt) 
  proper(s(X)) => s(proper(X)) 
  proper(length(X)) => length(proper(X)) 
  proper(and(X, Y)) => and(proper(X), proper(Y)) 
  proper(isNat(X)) => isNat(proper(X)) 
  proper(isNatList(X)) => isNatList(proper(X)) 
  proper(isNatIList(X)) => isNatIList(proper(X)) 
  proper(nil) => ok(nil) 
  cons(ok(X), ok(Y)) => ok(cons(X, Y)) 
  U11(ok(X), ok(Y)) => ok(U11(X, Y)) 
  s(ok(X)) => ok(s(X)) 
  length(ok(X)) => ok(length(X)) 
  and(ok(X), ok(Y)) => ok(and(X, Y)) 
  isNat(ok(X)) => ok(isNat(X)) 
  isNatList(ok(X)) => ok(isNatList(X)) 
  isNatIList(ok(X)) => ok(isNatIList(X)) 
  top(mark(X)) => top(proper(X)) 
  top(ok(X)) => top(active(X))