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


--------------------------------------------------------------------------------


MAYBE

Problem:
 a(x1) -> x1
 o(x1) -> x1
 l(x1) -> x1
 S(x1) -> x1
 +(x1,x2) -> x2
 +(x1,x2) -> x1
 P(x1,x2,x3,x4) -> x4
 P(x1,x2,x3,x4) -> x3
 P(x1,x2,x3,x4) -> x2
 P(x1,x2,x3,x4) -> x1
 M(x1,x2,x3,x4) -> x4
 M(x1,x2,x3,x4) -> x3
 M(x1,x2,x3,x4) -> x2
 M(x1,x2,x3,x4) -> x1
 J1(x1,x2) -> x2
 J1(x1,x2) -> x1
 J2(x1,x2,x3) -> x3
 J2(x1,x2,x3) -> x2
 J2(x1,x2,x3) -> x1
 J3(x1,x2,x3,x4) -> x4
 J3(x1,x2,x3,x4) -> x3
 J3(x1,x2,x3,x4) -> x2
 J3(x1,x2,x3,x4) -> 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
 Q31(x1,x2,x3,x4) -> x4
 Q31(x1,x2,x3,x4) -> x3
 Q31(x1,x2,x3,x4) -> x2
 Q31(x1,x2,x3,x4) -> x1
 Q32(x1,x2,x3,x4) -> x4
 Q32(x1,x2,x3,x4) -> x3
 Q32(x1,x2,x3,x4) -> x2
 Q32(x1,x2,x3,x4) -> x1
 Q33(x1,x2,x3,x4) -> x4
 Q33(x1,x2,x3,x4) -> x3
 Q33(x1,x2,x3,x4) -> x2
 Q33(x1,x2,x3,x4) -> 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
 R3(x1,x2,x3,x4,x5) -> x5
 R3(x1,x2,x3,x4,x5) -> x4
 R3(x1,x2,x3,x4,x5) -> x3
 R3(x1,x2,x3,x4,x5) -> x2
 R3(x1,x2,x3,x4,x5) -> x1
 P(0(),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,x4)) -> P(x1,x2,x3,l(x4))
 a(P(x1,x2,x3,x4)) -> P(x1,x2,l(x3),x4)
 a(P(x1,x2,x3,x4)) -> P(x1,l(x2),x3,x4)
 a(P(x1,x2,x3,x4)) -> P(l(x1),x2,x3,x4)
 +(x,o(y)) -> o(+(x,y))
 P(x1,x2,x3,o(x4)) -> o(P(x1,x2,x3,x4))
 P(x1,x2,o(x3),x4) -> o(P(x1,x2,x3,x4))
 P(x1,o(x2),x3,x4) -> o(P(x1,x2,x3,x4))
 P(o(x1),x2,x3,x4) -> o(P(x1,x2,x3,x4))
 M(x1,x2,x3,l(y)) -> +(M(x1,x2,x3,y),P(x1,x2,x3,y))
 J3(x1,x2,l(x3),y) -> P(x1,x2,J3(x1,x2,x3,y),0())
 J2(x1,l(x2),y) -> P(x1,J2(x1,x2,y),0(),0())
 J1(l(x1),y) -> P(J1(x1,y),0(),0(),0())
 a(S(x)) -> o(x)
 P(0(),0(),0(),S(y)) -> o(M(0(),0(),0(),y))
 P(0(),0(),0(),P(x1,x2,x3,y)) -> o(M(x1,x2,x3,y))
 P(x1,x2,S(x3),y) -> o(J3(x1,x2,x3,y))
 P(x1,S(x2),0(),y) -> o(J2(x1,x2,y))
 P(S(x1),0(),0(),y) -> o(J1(x1,y))
 P(x1,x2,S(x3),S(y)) -> o(J3(x1,x2,x3,P(x1,x2,S(x3),y)))
 P(x1,S(x2),0(),S(y)) -> o(J2(x1,x2,P(x1,S(x2),0(),y)))
 P(S(x1),0(),0(),S(y)) -> o(J1(x1,P(S(x1),0(),0(),y)))
 a(P(x1,x2,x3,0())) -> Q33(x1,x2,a(x3),x3)
 a(P(x1,x2,x3,0())) -> Q32(x1,x2,a(x3),x2)
 a(P(x1,x2,x3,0())) -> Q31(x1,x2,a(x3),x1)
 a(P(x1,x2,0(),0())) -> Q22(x1,a(x2),x2)
 a(P(x1,x2,0(),0())) -> Q21(x1,a(x2),x1)
 a(P(x1,0(),0(),0())) -> Q11(a(x1),x1)
 Q33(x1,x2,o(x3),y) -> o(P(x1,x2,x3,y))
 Q32(x1,x2,o(x3),y) -> o(P(x1,x2,x3,y))
 Q31(x1,x2,o(x3),y) -> o(P(x1,x2,x3,y))
 Q22(x1,o(x2),y) -> o(P(x1,x2,0(),y))
 Q21(x1,o(x2),y) -> o(P(x1,x2,0(),y))
 Q11(o(x1),y) -> o(P(x1,0(),0(),y))
 a(P(x1,x2,x3,S(y))) -> R3(x1,x2,a(x3),x3,y)
 a(P(x1,x2,0(),S(y))) -> R2(x1,a(x2),x2,y)
 a(P(x1,0(),0(),S(y))) -> R1(a(x1),x1,y)
 R3(x1,x2,o(x3),y,z) -> o(P(x1,x2,x3,P(x1,x2,y,z)))
 R2(x1,o(x2),y,z) -> o(P(x1,x2,0(),P(x1,y,0(),z)))
 R1(o(x1),y,z) -> o(P(x1,0(),0(),P(y,0(),0(),z)))

Proof:
 Open