/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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NO

Problem:
 a(x1) -> x1
 o(x1) -> x1
 l(x1) -> x1
 S(x1) -> x1
 +(x1,x2) -> x2
 +(x1,x2) -> x1
 P(x1,x2,x3) -> x3
 P(x1,x2,x3) -> x2
 P(x1,x2,x3) -> x1
 M(x1,x2,x3) -> x3
 M(x1,x2,x3) -> x2
 M(x1,x2,x3) -> x1
 J1(x1,x2) -> x2
 J1(x1,x2) -> x1
 J2(x1,x2,x3) -> x3
 J2(x1,x2,x3) -> x2
 J2(x1,x2,x3) -> x1
 Q11(x1,x2) -> x2
 Q11(x1,x2) -> x1
 Q21(x1,x2,x3) -> x3
 Q21(x1,x2,x3) -> x2
 Q21(x1,x2,x3) -> x1
 Q22(x1,x2,x3) -> x3
 Q22(x1,x2,x3) -> x2
 Q22(x1,x2,x3) -> x1
 R1(x1,x2,x3) -> x3
 R1(x1,x2,x3) -> x2
 R1(x1,x2,x3) -> x1
 R2(x1,x2,x3,x4) -> x4
 R2(x1,x2,x3,x4) -> x3
 R2(x1,x2,x3,x4) -> x2
 R2(x1,x2,x3,x4) -> x1
 P(0(),0(),0()) -> S(0())
 +(x,S(y)) -> S(+(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(+(x,y)) -> +(l(x),y)
 a(+(x,y)) -> +(x,l(y))
 a(P(x1,x2,x3)) -> P(x1,x2,l(x3))
 a(P(x1,x2,x3)) -> P(x1,l(x2),x3)
 a(P(x1,x2,x3)) -> P(l(x1),x2,x3)
 +(x,o(y)) -> o(+(x,y))
 P(x1,x2,o(x3)) -> o(P(x1,x2,x3))
 P(x1,o(x2),x3) -> o(P(x1,x2,x3))
 P(o(x1),x2,x3) -> o(P(x1,x2,x3))
 M(x1,x2,l(y)) -> +(M(x1,x2,y),P(x1,x2,y))
 J2(x1,l(x2),y) -> P(x1,J2(x1,x2,y),0())
 J1(l(x1),y) -> P(J1(x1,y),0(),0())
 a(S(x)) -> o(x)
 P(0(),0(),S(y)) -> o(M(0(),0(),y))
 P(0(),0(),P(x1,x2,y)) -> o(M(x1,x2,y))
 P(x1,S(x2),y) -> o(J2(x1,x2,y))
 P(S(x1),0(),y) -> o(J1(x1,y))
 P(x1,S(x2),S(y)) -> o(J2(x1,x2,P(x1,S(x2),y)))
 P(S(x1),0(),S(y)) -> o(J1(x1,P(S(x1),0(),y)))
 a(P(x1,x2,0())) -> Q22(x1,a(x2),x2)
 a(P(x1,x2,0())) -> Q21(x1,a(x2),x1)
 a(P(x1,0(),0())) -> Q11(a(x1),x1)
 Q22(x1,o(x2),y) -> o(P(x1,x2,y))
 Q21(x1,o(x2),y) -> o(P(x1,x2,y))
 Q11(o(x1),y) -> o(P(x1,0(),y))
 a(P(x1,x2,S(y))) -> R2(x1,a(x2),x2,y)
 a(P(x1,0(),S(y))) -> R1(a(x1),x1,y)
 R2(x1,o(x2),y,z) -> o(P(x1,x2,P(x1,y,z)))
 R1(o(x1),y,z) -> o(P(x1,0(),P(y,0(),z)))

Proof:
 Unfolding Processor:
  loop length: 3
  terms:
   J2(S(l(x116028)),l(x116028),0())
   P(S(l(x116028)),J2(S(l(x116028)),x116028,0()),0())
   P(S(l(x116028)),S(l(x116028)),0())
  context: o([])
  substitution:
   x116028 -> x116028
  Qed