/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 
  and : [o * o] --> o 
  cond1 : [o * o * o] --> o 
  cond2 : [o * o * o] --> o 
  cond3 : [o * o * o] --> o 
  cond4 : [o * o * o] --> o 
  false : [] --> o 
  gr : [o * o] --> o 
  p : [o] --> o 
  s : [o] --> o 
  true : [] --> o 

  cond1(true, X, Y) => cond2(gr(X, Y), X, Y) 
  cond2(true, X, Y) => cond3(gr(X, 0), X, Y) 
  cond2(false, X, Y) => cond4(gr(Y, 0), X, Y) 
  cond3(true, X, Y) => cond3(gr(X, 0), p(X), Y) 
  cond3(false, X, Y) => cond1(and(gr(X, 0), gr(Y, 0)), X, Y) 
  cond4(true, X, Y) => cond4(gr(Y, 0), X, p(Y)) 
  cond4(false, X, Y) => cond1(and(gr(X, 0), gr(Y, 0)), X, Y) 
  gr(0, X) => false 
  gr(s(X), 0) => true 
  gr(s(X), s(Y)) => gr(X, Y) 
  and(true, true) => true 
  and(false, X) => false 
  and(X, false) => false 
  p(0) => 0 
  p(s(X)) => X