/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.

  !plus : [o * o] --> o 
  0 : [] --> o 
  J1 : [o * o] --> o 
  J2 : [o * o * o] --> o 
  M : [o * o * o] --> o 
  P : [o * o * o] --> o 
  Q11 : [o * o] --> o 
  Q21 : [o * o * o] --> o 
  Q22 : [o * o * o] --> o 
  R1 : [o * o * o] --> o 
  R2 : [o * o * o * o] --> o 
  S : [o] --> o 
  a : [o] --> o 
  l : [o] --> o 
  o : [o] --> o 

  a(X) => X 
  o(X) => X 
  l(X) => X 
  S(X) => X 
  !plus(X, Y) => Y 
  !plus(X, Y) => X 
  P(X, Y, Z) => Z 
  P(X, Y, Z) => Y 
  P(X, Y, Z) => X 
  M(X, Y, Z) => Z 
  M(X, Y, Z) => Y 
  M(X, Y, Z) => X 
  J1(X, Y) => Y 
  J1(X, Y) => X 
  J2(X, Y, Z) => Z 
  J2(X, Y, Z) => Y 
  J2(X, Y, Z) => X 
  Q11(X, Y) => Y 
  Q11(X, Y) => X 
  Q21(X, Y, Z) => Z 
  Q21(X, Y, Z) => Y 
  Q21(X, Y, Z) => X 
  Q22(X, Y, Z) => Z 
  Q22(X, Y, Z) => Y 
  Q22(X, Y, Z) => X 
  R1(X, Y, Z) => Z 
  R1(X, Y, Z) => Y 
  R1(X, Y, Z) => X 
  R2(X, Y, Z, U) => U 
  R2(X, Y, Z, U) => Z 
  R2(X, Y, Z, U) => Y 
  R2(X, Y, Z, U) => X 
  P(0, 0, 0) => S(0) 
  !plus(X, S(Y)) => S(!plus(X, Y)) 
  a(l(X)) => l(a(a(X))) 
  l(o(X)) => o(l(l(X))) 
  o(X) => l(X) 
  l(X) => a(X) 
  a(S(X)) => S(l(X)) 
  a(!plus(X, Y)) => !plus(l(X), Y) 
  a(!plus(X, Y)) => !plus(X, l(Y)) 
  a(P(X, Y, Z)) => P(X, Y, l(Z)) 
  a(P(X, Y, Z)) => P(X, l(Y), Z) 
  a(P(X, Y, Z)) => P(l(X), Y, Z) 
  !plus(X, o(Y)) => o(!plus(X, Y)) 
  P(X, Y, o(Z)) => o(P(X, Y, Z)) 
  P(X, o(Y), Z) => o(P(X, Y, Z)) 
  P(o(X), Y, Z) => o(P(X, Y, Z)) 
  M(X, Y, l(Z)) => !plus(M(X, Y, Z), P(X, Y, Z)) 
  J2(X, l(Y), Z) => P(X, J2(X, Y, Z), 0) 
  J1(l(X), Y) => P(J1(X, Y), 0, 0) 
  a(S(X)) => o(X) 
  P(0, 0, S(X)) => o(M(0, 0, X)) 
  P(0, 0, P(X, Y, Z)) => o(M(X, Y, Z)) 
  P(X, S(Y), Z) => o(J2(X, Y, Z)) 
  P(S(X), 0, Y) => o(J1(X, Y)) 
  P(X, S(Y), S(Z)) => o(J2(X, Y, P(X, S(Y), Z))) 
  P(S(X), 0, S(Y)) => o(J1(X, P(S(X), 0, Y))) 
  a(P(X, Y, 0)) => Q22(X, a(Y), Y) 
  a(P(X, Y, 0)) => Q21(X, a(Y), X) 
  a(P(X, 0, 0)) => Q11(a(X), X) 
  Q22(X, o(Y), Z) => o(P(X, Y, Z)) 
  Q21(X, o(Y), Z) => o(P(X, Y, Z)) 
  Q11(o(X), Y) => o(P(X, 0, Y)) 
  a(P(X, Y, S(Z))) => R2(X, a(Y), Y, Z) 
  a(P(X, 0, S(Y))) => R1(a(X), X, Y) 
  R2(X, o(Y), Z, U) => o(P(X, Y, P(X, Z, U))) 
  R1(o(X), Y, Z) => o(P(X, 0, P(Y, 0, Z)))