/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 
  app : [o * o] --> o 
  cons : [o * o] --> o 
  empty : [o] --> o 
  f : [o * o] --> o 
  false : [] --> o 
  fstsplit : [o * o] --> o 
  head : [o] --> o 
  if!62201 : [o * o * o * o * o * o * o] --> o 
  if!62202 : [o * o * o * o * o * o * o] --> o 
  if!62203 : [o * o * o * o * o * o * o] --> o 
  if!62204 : [o * o * o * o * o * o * o] --> o 
  if!62205 : [o * o * o * o * o * o * o] --> o 
  if!62206 : [o * o * o * o * o * o * o] --> o 
  if!62207 : [o * o * o * o * o * o * o] --> o 
  if!62208 : [o * o * o * o * o * o * o] --> o 
  if!62209 : [o * o * o * o * o * o * o] --> o 
  length : [o] --> o 
  leq : [o * o] --> o 
  map!6220f : [o * o] --> o 
  nil : [] --> o 
  ring : [o * o * o * o * o * o] --> o 
  s : [o] --> o 
  sndsplit : [o * o] --> o 
  tail : [o] --> o 
  three : [] --> o 
  true : [] --> o 
  two : [] --> o 

  fstsplit(0, X) => nil 
  fstsplit(s(X), nil) => nil 
  fstsplit(s(X), cons(Y, Z)) => cons(Y, fstsplit(X, Z)) 
  sndsplit(0, X) => X 
  sndsplit(s(X), nil) => nil 
  sndsplit(s(X), cons(Y, Z)) => sndsplit(X, Z) 
  empty(nil) => true 
  empty(cons(X, Y)) => false 
  leq(0, X) => true 
  leq(s(X), 0) => false 
  leq(s(X), s(Y)) => leq(X, Y) 
  length(nil) => 0 
  length(cons(X, Y)) => s(length(Y)) 
  app(nil, X) => X 
  app(cons(X, Y), Z) => cons(X, app(Y, Z)) 
  map!6220f(X, nil) => nil 
  map!6220f(X, cons(Y, Z)) => app(f(X, Y), map!6220f(X, Z)) 
  head(cons(X, Y)) => X 
  tail(cons(X, Y)) => Y 
  ring(X, Y, Z, U, V, W) => if!62201(X, Y, Z, U, V, W, empty(fstsplit(W, X))) 
  if!62201(X, Y, Z, U, V, W, false) => ring(sndsplit(W, X), cons(fstsplit(W, X), Y), Z, U, V, W) 
  ring(X, Y, Z, U, V, W) => if!62202(X, Y, Z, U, V, W, leq(W, length(Z))) 
  if!62202(X, Y, Z, U, V, W, true) => if!62203(X, Y, Z, U, V, W, empty(fstsplit(W, Z))) 
  if!62203(X, Y, Z, U, V, W, false) => ring(X, Y, sndsplit(W, Z), cons(fstsplit(W, Z), U), V, W) 
  if!62202(X, Y, Z, U, V, W, false) => if!62204(X, Y, Z, U, V, W, empty(fstsplit(W, app(map!6220f(two, head(Y)), Z)))) 
  if!62204(X, Y, Z, U, V, W, false) => ring(X, tail(Y), sndsplit(W, app(map!6220f(two, head(Y)), Z)), cons(fstsplit(W, app(map!6220f(two, head(Y)), Z)), U), V, W) 
  ring(X, Y, Z, U, V, W) => if!62205(X, Y, Z, U, V, W, empty(map!6220f(two, head(Y)))) 
  if!62205(X, Y, Z, U, V, W, true) => ring(X, tail(Y), Z, U, V, W) 
  ring(X, Y, Z, U, V, W) => if!62206(X, Y, Z, U, V, W, leq(W, length(V))) 
  if!62206(X, Y, Z, U, V, W, true) => if!62207(X, Y, Z, U, V, W, empty(fstsplit(W, V))) 
  if!62207(X, Y, Z, U, V, W, false) => ring(X, Y, Z, U, sndsplit(W, V), W) 
  if!62206(X, Y, Z, U, V, W, false) => if!62208(X, Y, Z, U, V, W, empty(fstsplit(W, app(map!6220f(three, head(U)), V)))) 
  if!62208(X, Y, Z, U, V, W, false) => ring(X, Y, Z, tail(U), sndsplit(W, app(map!6220f(three, head(U)), V)), W) 
  ring(X, Y, Z, U, V, W) => if!62209(X, Y, Z, U, V, W, empty(map!6220f(three, head(U)))) 
  if!62209(X, Y, Z, U, V, W, true) => ring(X, Y, Z, tail(U), V, W)