/export/starexec/sandbox/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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 
  a : [] --> o 
  c : [] --> o 
  cons : [o * o] --> o 
  d : [] --> o 
  error : [] --> o 
  false : [] --> o 
  ge : [o * o] --> o 
  gen : [o * o * o] --> o 
  generate : [o * o] --> o 
  head : [o] --> o 
  if : [o * o * o * o] --> o 
  ifsum : [o * o * o * o] --> o 
  ifsum2 : [o * o * o] --> o 
  isNil : [o] --> o 
  isZero : [o] --> o 
  nil : [] --> o 
  p : [o] --> o 
  s : [o] --> o 
  sum : [o] --> o 
  sum2 : [o * o] --> o 
  tail : [o] --> o 
  times : [o * o] --> o 
  true : [] --> o 

  times(X, Y) => sum(generate(X, Y)) 
  generate(X, Y) => gen(X, Y, 0) 
  gen(X, Y, Z) => if(ge(Z, X), X, Y, Z) 
  if(true, X, Y, Z) => nil 
  if(false, X, Y, Z) => cons(Y, gen(X, Y, s(Z))) 
  sum(X) => sum2(X, 0) 
  sum2(X, Y) => ifsum(isNil(X), isZero(head(X)), X, Y) 
  ifsum(true, X, Y, Z) => Z 
  ifsum(false, X, Y, Z) => ifsum2(X, Y, Z) 
  ifsum2(true, X, Y) => sum2(tail(X), Y) 
  ifsum2(false, X, Y) => sum2(cons(p(head(X)), tail(X)), s(Y)) 
  isNil(nil) => true 
  isNil(cons(X, Y)) => false 
  tail(nil) => nil 
  tail(cons(X, Y)) => Y 
  head(cons(X, Y)) => X 
  head(nil) => error 
  isZero(0) => true 
  isZero(s(0)) => false 
  isZero(s(s(X))) => isZero(s(X)) 
  p(0) => s(s(0)) 
  p(s(0)) => 0 
  p(s(s(X))) => s(p(s(X))) 
  ge(X, 0) => true 
  ge(0, s(X)) => false 
  ge(s(X), s(Y)) => ge(X, Y) 
  a => c 
  a => d