let R be the TRS under consideration
0(0(0(0(_1)))) -> 0(1(1(1(_1)))) is in elim_R(R)
let l0 be the left-hand side of this rule
p0 = 0.0.0 is a position in l0
we have l0|p0 = 0(_1)
0(0(0(0(_2)))) -> 0(1(1(1(_2)))) is in R
let r'0 be the right-hand side of this rule
theta0 = {_1/1(1(1(_2)))} is a mgu of l0|p0 and r'0
==> 0(0(0(0(0(0(0(_1))))))) -> 0(1(1(1(1(1(1(_1))))))) is in EU_R^1
let l1 be the left-hand side of this rule
p1 = 0.0.0.0.0.0 is a position in l1
we have l1|p1 = 0(_1)
1(1(0(1(_2)))) -> 0(1(1(0(_2)))) is in R
let r'1 be the right-hand side of this rule
theta1 = {_1/1(1(0(_2)))} is a mgu of l1|p1 and r'1
==> 0(0(0(0(0(0(1(1(0(1(_1)))))))))) -> 0(1(1(1(1(1(1(1(1(0(_1)))))))))) is in EU_R^2
let l2 be the left-hand side of this rule
p2 = 0.0.0.0.0 is a position in l2
we have l2|p2 = 0(1(1(0(1(_1)))))
1(1(0(1(_2)))) -> 0(1(1(0(_2)))) is in R
let r'2 be the right-hand side of this rule
theta2 = {_2/1(_1)} is a mgu of l2|p2 and r'2
==> 0(0(0(0(0(1(1(0(1(1(_1)))))))))) -> 0(1(1(1(1(1(1(1(1(0(_1)))))))))) is in EU_R^3
let l3 be the left-hand side of this rule
p3 = 0.0.0.0 is a position in l3
we have l3|p3 = 0(1(1(0(1(1(_1))))))
1(1(0(1(_2)))) -> 0(1(1(0(_2)))) is in R
let r'3 be the right-hand side of this rule
theta3 = {_2/1(1(_1))} is a mgu of l3|p3 and r'3
==> 0(0(0(0(1(1(0(1(1(1(_1)))))))))) -> 0(1(1(1(1(1(1(1(1(0(_1)))))))))) is in EU_R^4
let l4 be the left-hand side of this rule
p4 = 0.0.0 is a position in l4
we have l4|p4 = 0(1(1(0(1(1(1(_1)))))))
1(1(0(1(_2)))) -> 0(1(1(0(_2)))) is in R
let r'4 be the right-hand side of this rule
theta4 = {_2/1(1(1(_1)))} is a mgu of l4|p4 and r'4
==> 0(0(0(1(1(0(1(1(1(1(_1)))))))))) -> 0(1(1(1(1(1(1(1(1(0(_1)))))))))) is in EU_R^5
let l5 be the left-hand side of this rule
p5 = 0.0.0.0.0 is a position in l5
we have l5|p5 = 0(1(1(1(1(_1)))))
0(0(0(0(_2)))) -> 0(1(1(1(_2)))) is in R
let r'5 be the right-hand side of this rule
theta5 = {_2/1(_1)} is a mgu of l5|p5 and r'5
==> 0(0(0(1(1(0(0(0(0(1(_1)))))))))) -> 0(1(1(1(1(1(1(1(1(0(_1)))))))))) is in EU_R^6
let l6 be the left-hand side of this rule
p6 = 0.0 is a position in l6
we have l6|p6 = 0(1(1(0(0(0(0(1(_1))))))))
1(1(0(1(_2)))) -> 0(1(1(0(_2)))) is in R
let r'6 be the right-hand side of this rule
theta6 = {_2/0(0(0(1(_1))))} is a mgu of l6|p6 and r'6
==> 0(0(1(1(0(1(0(0(0(1(_1)))))))))) -> 0(1(1(1(1(1(1(1(1(0(_1)))))))))) is in EU_R^7
let l7 be the left-hand side of this rule
p7 = 0 is a position in l7
we have l7|p7 = 0(1(1(0(1(0(0(0(1(_1)))))))))
1(1(0(1(_2)))) -> 0(1(1(0(_2)))) is in R
let r'7 be the right-hand side of this rule
theta7 = {_2/1(0(0(0(1(_1)))))} is a mgu of l7|p7 and r'7
==> 0(1(1(0(1(1(0(0(0(1(_1)))))))))) -> 0(1(1(1(1(1(1(1(1(0(_1)))))))))) is in EU_R^8
let l8 be the left-hand side of this rule
p8 = 0.0.0 is a position in l8
we have l8|p8 = 0(1(1(0(0(0(1(_1)))))))
1(1(0(1(_2)))) -> 0(1(1(0(_2)))) is in R
let r'8 be the right-hand side of this rule
theta8 = {_2/0(0(1(_1)))} is a mgu of l8|p8 and r'8
==> 0(1(1(1(1(0(1(0(0(1(_1)))))))))) -> 0(1(1(1(1(1(1(1(1(0(_1)))))))))) is in EU_R^9
let l9 be the left-hand side of this rule
p9 = 0.0.0.0.0.0.0.0 is a position in l9
we have l9|p9 = 0(1(_1))
1(1(0(1(_2)))) -> 0(1(1(0(_2)))) is in R
let r'9 be the right-hand side of this rule
theta9 = {_1/1(0(_2))} is a mgu of l9|p9 and r'9
==> 0(1(1(1(1(0(1(0(1(1(0(1(_1)))))))))))) -> 0(1(1(1(1(1(1(1(1(0(1(0(_1)))))))))))) is in EU_R^10
let l10 be the left-hand side of this rule
p10 = 0.0.0.0.0.0.0 is a position in l10
we have l10|p10 = 0(1(1(0(1(_1)))))
1(1(0(1(_2)))) -> 0(1(1(0(_2)))) is in R
let r'10 be the right-hand side of this rule
theta10 = {_2/1(_1)} is a mgu of l10|p10 and r'10
==> 0(1(1(1(1(0(1(1(1(0(1(1(_1)))))))))))) -> 0(1(1(1(1(1(1(1(1(0(1(0(_1)))))))))))) is in EU_R^11
let l11 be the left-hand side of this rule
p11 = 0.0.0.0.0 is a position in l11
we have l11|p11 = 0(1(1(1(0(1(1(_1)))))))
0(0(0(0(_2)))) -> 0(1(1(1(_2)))) is in R
let r'11 be the right-hand side of this rule
theta11 = {_2/0(1(1(_1)))} is a mgu of l11|p11 and r'11
==> 0(1(1(1(1(0(0(0(0(0(1(1(_1)))))))))))) -> 0(1(1(1(1(1(1(1(1(0(1(0(_1)))))))))))) is in EU_R^12
let l12 be the left-hand side of this rule
p12 = 0.0.0.0.0.0.0.0.0 is a position in l12
we have l12|p12 = 0(1(1(_1)))
1(1(0(1(_2)))) -> 0(1(1(0(_2)))) is in R
let r'12 be the right-hand side of this rule
theta12 = {_1/0(_2)} is a mgu of l12|p12 and r'12
==> 0(1(1(1(1(0(0(0(0(1(1(0(1(_1))))))))))))) -> 0(1(1(1(1(1(1(1(1(0(1(0(0(_1))))))))))))) is in EU_R^13
let l13 be the left-hand side of this rule
p13 = 0.0.0.0.0.0.0.0 is a position in l13
we have l13|p13 = 0(1(1(0(1(_1)))))
1(1(0(1(_2)))) -> 0(1(1(0(_2)))) is in R
let r'13 be the right-hand side of this rule
theta13 = {_2/1(_1)} is a mgu of l13|p13 and r'13
==> 0(1(1(1(1(0(0(0(1(1(0(1(1(_1))))))))))))) -> 0(1(1(1(1(1(1(1(1(0(1(0(0(_1))))))))))))) is in EU_R^14
let l14 be the left-hand side of this rule
p14 = 0.0.0.0.0.0.0 is a position in l14
we have l14|p14 = 0(1(1(0(1(1(_1))))))
1(1(0(1(_2)))) -> 0(1(1(0(_2)))) is in R
let r'14 be the right-hand side of this rule
theta14 = {_2/1(1(_1))} is a mgu of l14|p14 and r'14
==> 0(1(1(1(1(0(0(1(1(0(1(1(1(_1))))))))))))) -> 0(1(1(1(1(1(1(1(1(0(1(0(0(_1))))))))))))) is in EU_R^15
let l15 be the left-hand side of this rule
p15 = 0.0.0.0.0.0.0.0.0 is a position in l15
we have l15|p15 = 0(1(1(1(_1))))
0(0(0(0(_2)))) -> 0(1(1(1(_2)))) is in R
let r'15 be the right-hand side of this rule
theta15 = {_1/_2} is a mgu of l15|p15 and r'15
==> 0(1(1(1(1(0(0(1(1(0(0(0(0(_1))))))))))))) -> 0(1(1(1(1(1(1(1(1(0(1(0(0(_1))))))))))))) is in EU_R^16
let l16 be the left-hand side of this rule
p16 = 0.0.0.0.0.0 is a position in l16
we have l16|p16 = 0(1(1(0(0(0(0(_1)))))))
1(1(0(1(_2)))) -> 0(1(1(0(_2)))) is in R
let r'16 be the right-hand side of this rule
theta16 = {_2/0(0(0(_1)))} is a mgu of l16|p16 and r'16
==> 0(1(1(1(1(0(1(1(0(1(0(0(0(_1))))))))))))) -> 0(1(1(1(1(1(1(1(1(0(1(0(0(_1))))))))))))) is in EU_R^17
let l17 be the left-hand side of this rule
p17 = 0.0.0.0.0 is a position in l17
we have l17|p17 = 0(1(1(0(1(0(0(0(_1))))))))
1(1(0(1(_2)))) -> 0(1(1(0(_2)))) is in R
let r'17 be the right-hand side of this rule
theta17 = {_2/1(0(0(0(_1))))} is a mgu of l17|p17 and r'17
==> 0(1(1(1(1(1(1(0(1(1(0(0(0(_1))))))))))))) -> 0(1(1(1(1(1(1(1(1(0(1(0(0(_1))))))))))))) is in EU_R^18
let l18 be the left-hand side of this rule
p18 = 0.0.0.0.0.0.0 is a position in l18
we have l18|p18 = 0(1(1(0(0(0(_1))))))
1(1(0(1(_2)))) -> 0(1(1(0(_2)))) is in R
let r'18 be the right-hand side of this rule
theta18 = {_2/0(0(_1))} is a mgu of l18|p18 and r'18
==> 0(1(1(1(1(1(1(1(1(0(1(0(0(_1))))))))))))) -> 0(1(1(1(1(1(1(1(1(0(1(0(0(_1))))))))))))) is in EU_R^19
let l be the left-hand side and r be the right-hand side of this rule
let p = epsilon
let theta = {}
let theta' = {}
we have r|p = 0(1(1(1(1(1(1(1(1(0(1(0(0(_1))))))))))))) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = 0(1(1(1(1(1(1(1(1(0(1(0(0(_1))))))))))))) is non-terminating w.r.t. R
Termination disproved by the backward process
proof stopped at iteration i=19, depth k=13
4939 rule(s) generated