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


--------------------------------------------------------------------------------


MAYBE
We consider the system theBenchmark.

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

  0 : [] --> o 
  U11 : [o * o] --> o 
  U12 : [o] --> o 
  U21 : [o] --> o 
  U31 : [o * o] --> o 
  U41 : [o * o * o] --> o 
  U42 : [o * o * o] --> o 
  active : [o] --> o 
  isNat : [o] --> o 
  mark : [o] --> o 
  ok : [o] --> o 
  plus : [o * o] --> o 
  proper : [o] --> o 
  s : [o] --> o 
  top : [o] --> o 
  tt : [] --> o 

  active(U11(tt, X)) => mark(U12(isNat(X))) 
  active(U12(tt)) => mark(tt) 
  active(U21(tt)) => mark(tt) 
  active(U31(tt, X)) => mark(X) 
  active(U41(tt, X, Y)) => mark(U42(isNat(Y), X, Y)) 
  active(U42(tt, X, Y)) => mark(s(plus(Y, X))) 
  active(isNat(0)) => mark(tt) 
  active(isNat(plus(X, Y))) => mark(U11(isNat(X), Y)) 
  active(isNat(s(X))) => mark(U21(isNat(X))) 
  active(plus(X, 0)) => mark(U31(isNat(X), X)) 
  active(plus(X, s(Y))) => mark(U41(isNat(Y), Y, X)) 
  active(U11(X, Y)) => U11(active(X), Y) 
  active(U12(X)) => U12(active(X)) 
  active(U21(X)) => U21(active(X)) 
  active(U31(X, Y)) => U31(active(X), Y) 
  active(U41(X, Y, Z)) => U41(active(X), Y, Z) 
  active(U42(X, Y, Z)) => U42(active(X), Y, Z) 
  active(s(X)) => s(active(X)) 
  active(plus(X, Y)) => plus(active(X), Y) 
  active(plus(X, Y)) => plus(X, active(Y)) 
  U11(mark(X), Y) => mark(U11(X, Y)) 
  U12(mark(X)) => mark(U12(X)) 
  U21(mark(X)) => mark(U21(X)) 
  U31(mark(X), Y) => mark(U31(X, Y)) 
  U41(mark(X), Y, Z) => mark(U41(X, Y, Z)) 
  U42(mark(X), Y, Z) => mark(U42(X, Y, Z)) 
  s(mark(X)) => mark(s(X)) 
  plus(mark(X), Y) => mark(plus(X, Y)) 
  plus(X, mark(Y)) => mark(plus(X, Y)) 
  proper(U11(X, Y)) => U11(proper(X), proper(Y)) 
  proper(tt) => ok(tt) 
  proper(U12(X)) => U12(proper(X)) 
  proper(isNat(X)) => isNat(proper(X)) 
  proper(U21(X)) => U21(proper(X)) 
  proper(U31(X, Y)) => U31(proper(X), proper(Y)) 
  proper(U41(X, Y, Z)) => U41(proper(X), proper(Y), proper(Z)) 
  proper(U42(X, Y, Z)) => U42(proper(X), proper(Y), proper(Z)) 
  proper(s(X)) => s(proper(X)) 
  proper(plus(X, Y)) => plus(proper(X), proper(Y)) 
  proper(0) => ok(0) 
  U11(ok(X), ok(Y)) => ok(U11(X, Y)) 
  U12(ok(X)) => ok(U12(X)) 
  isNat(ok(X)) => ok(isNat(X)) 
  U21(ok(X)) => ok(U21(X)) 
  U31(ok(X), ok(Y)) => ok(U31(X, Y)) 
  U41(ok(X), ok(Y), ok(Z)) => ok(U41(X, Y, Z)) 
  U42(ok(X), ok(Y), ok(Z)) => ok(U42(X, Y, Z)) 
  s(ok(X)) => ok(s(X)) 
  plus(ok(X), ok(Y)) => ok(plus(X, Y)) 
  top(mark(X)) => top(proper(X)) 
  top(ok(X)) => top(active(X))