let R be the TRS under consideration
0(0(0(0(_1)))) -> 0(1(0(1(_1)))) is in elim_R(R)
let r0 be the right-hand side of this rule
p0 = 0.0.0 is a position in r0
we have r0|p0 = 1(_1)
1(0(0(1(_2)))) -> 0(0(1(0(_2)))) is in R
let l'0 be the left-hand side of this rule
theta0 = {_1/0(0(1(_2)))} is a mgu of r0|p0 and l'0
==> 0(0(0(0(0(0(1(_1))))))) -> 0(1(0(0(0(1(0(_1))))))) is in EU_R^1
let r1 be the right-hand side of this rule
p1 = 0.0.0.0.0 is a position in r1
we have r1|p1 = 1(0(_1))
1(0(0(1(_2)))) -> 0(0(1(0(_2)))) is in R
let l'1 be the left-hand side of this rule
theta1 = {_1/0(1(_2))} is a mgu of r1|p1 and l'1
==> 0(0(0(0(0(0(1(0(1(_1))))))))) -> 0(1(0(0(0(0(0(1(0(_1))))))))) is in EU_R^2
let r2 be the right-hand side of this rule
p2 = 0.0.0 is a position in r2
we have r2|p2 = 0(0(0(0(1(0(_1))))))
0(0(0(0(_2)))) -> 0(1(0(1(_2)))) is in R
let l'2 be the left-hand side of this rule
theta2 = {_2/1(0(_1))} is a mgu of r2|p2 and l'2
==> 0(0(0(0(0(0(1(0(1(_1))))))))) -> 0(1(0(0(1(0(1(1(0(_1))))))))) is in EU_R^3
let r3 be the right-hand side of this rule
p3 = 0 is a position in r3
we have r3|p3 = 1(0(0(1(0(1(1(0(_1))))))))
1(0(0(1(_2)))) -> 0(0(1(0(_2)))) is in R
let l'3 be the left-hand side of this rule
theta3 = {_2/0(1(1(0(_1))))} is a mgu of r3|p3 and l'3
==> 0(0(0(0(0(0(1(0(1(_1))))))))) -> 0(0(0(1(0(0(1(1(0(_1))))))))) is in EU_R^4
let r4 be the right-hand side of this rule
p4 = 0.0.0 is a position in r4
we have r4|p4 = 1(0(0(1(1(0(_1))))))
1(0(0(1(_2)))) -> 0(0(1(0(_2)))) is in R
let l'4 be the left-hand side of this rule
theta4 = {_2/1(0(_1))} is a mgu of r4|p4 and l'4
==> 0(0(0(0(0(0(1(0(1(_1))))))))) -> 0(0(0(0(0(1(0(1(0(_1))))))))) is in EU_R^5
let r5 be the right-hand side of this rule
p5 = 0.0.0.0.0.0.0 is a position in r5
we have r5|p5 = 1(0(_1))
1(0(0(1(_2)))) -> 0(0(1(0(_2)))) is in R
let l'5 be the left-hand side of this rule
theta5 = {_1/0(1(_2))} is a mgu of r5|p5 and l'5
==> 0(0(0(0(0(0(1(0(1(0(1(_1))))))))))) -> 0(0(0(0(0(1(0(0(0(1(0(_1))))))))))) is in EU_R^6
let r6 be the right-hand side of this rule
p6 = 0.0.0.0.0.0.0.0.0 is a position in r6
we have r6|p6 = 1(0(_1))
1(0(0(1(_2)))) -> 0(0(1(0(_2)))) is in R
let l'6 be the left-hand side of this rule
theta6 = {_1/0(1(_2))} is a mgu of r6|p6 and l'6
==> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) -> 0(0(0(0(0(1(0(0(0(0(0(1(0(_1))))))))))))) is in EU_R^7
let r7 be the right-hand side of this rule
p7 = 0.0.0.0.0.0.0 is a position in r7
we have r7|p7 = 0(0(0(0(1(0(_1))))))
0(0(0(0(_2)))) -> 0(1(0(1(_2)))) is in R
let l'7 be the left-hand side of this rule
theta7 = {_2/1(0(_1))} is a mgu of r7|p7 and l'7
==> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) -> 0(0(0(0(0(1(0(0(1(0(1(1(0(_1))))))))))))) is in EU_R^8
let r8 be the right-hand side of this rule
p8 = 0.0.0.0.0 is a position in r8
we have r8|p8 = 1(0(0(1(0(1(1(0(_1))))))))
1(0(0(1(_2)))) -> 0(0(1(0(_2)))) is in R
let l'8 be the left-hand side of this rule
theta8 = {_2/0(1(1(0(_1))))} is a mgu of r8|p8 and l'8
==> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) -> 0(0(0(0(0(0(0(1(0(0(1(1(0(_1))))))))))))) is in EU_R^9
let r9 be the right-hand side of this rule
p9 = 0.0.0 is a position in r9
we have r9|p9 = 0(0(0(0(1(0(0(1(1(0(_1))))))))))
0(0(0(0(_2)))) -> 0(1(0(1(_2)))) is in R
let l'9 be the left-hand side of this rule
theta9 = {_2/1(0(0(1(1(0(_1))))))} is a mgu of r9|p9 and l'9
==> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) -> 0(0(0(0(1(0(1(1(0(0(1(1(0(_1))))))))))))) is in EU_R^10
let r10 be the right-hand side of this rule
p10 = 0.0.0.0.0.0.0 is a position in r10
we have r10|p10 = 1(0(0(1(1(0(_1))))))
1(0(0(1(_2)))) -> 0(0(1(0(_2)))) is in R
let l'10 be the left-hand side of this rule
theta10 = {_2/1(0(_1))} is a mgu of r10|p10 and l'10
==> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) -> 0(0(0(0(1(0(1(0(0(1(0(1(0(_1))))))))))))) is in EU_R^11
let r11 be the right-hand side of this rule
p11 = 0.0.0.0.0.0 is a position in r11
we have r11|p11 = 1(0(0(1(0(1(0(_1)))))))
1(0(0(1(_2)))) -> 0(0(1(0(_2)))) is in R
let l'11 be the left-hand side of this rule
theta11 = {_2/0(1(0(_1)))} is a mgu of r11|p11 and l'11
==> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) -> 0(0(0(0(1(0(0(0(1(0(0(1(0(_1))))))))))))) is in EU_R^12
let r12 be the right-hand side of this rule
p12 = 0.0.0.0.0.0.0.0 is a position in r12
we have r12|p12 = 1(0(0(1(0(_1)))))
1(0(0(1(_2)))) -> 0(0(1(0(_2)))) is in R
let l'12 be the left-hand side of this rule
theta12 = {_2/0(_1)} is a mgu of r12|p12 and l'12
==> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) -> 0(0(0(0(1(0(0(0(0(0(1(0(0(_1))))))))))))) is in EU_R^13
let r13 be the right-hand side of this rule
p13 = 0.0.0.0.0.0 is a position in r13
we have r13|p13 = 0(0(0(0(1(0(0(_1)))))))
0(0(0(0(_2)))) -> 0(1(0(1(_2)))) is in R
let l'13 be the left-hand side of this rule
theta13 = {_2/1(0(0(_1)))} is a mgu of r13|p13 and l'13
==> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) -> 0(0(0(0(1(0(0(1(0(1(1(0(0(_1))))))))))))) is in EU_R^14
let r14 be the right-hand side of this rule
p14 = 0.0.0.0 is a position in r14
we have r14|p14 = 1(0(0(1(0(1(1(0(0(_1)))))))))
1(0(0(1(_2)))) -> 0(0(1(0(_2)))) is in R
let l'14 be the left-hand side of this rule
theta14 = {_2/0(1(1(0(0(_1)))))} is a mgu of r14|p14 and l'14
==> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) -> 0(0(0(0(0(0(1(0(0(1(1(0(0(_1))))))))))))) is in EU_R^15
let r15 be the right-hand side of this rule
p15 = 0.0 is a position in r15
we have r15|p15 = 0(0(0(0(1(0(0(1(1(0(0(_1)))))))))))
0(0(0(0(_2)))) -> 0(1(0(1(_2)))) is in R
let l'15 be the left-hand side of this rule
theta15 = {_2/1(0(0(1(1(0(0(_1)))))))} is a mgu of r15|p15 and l'15
==> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) -> 0(0(0(1(0(1(1(0(0(1(1(0(0(_1))))))))))))) is in EU_R^16
let r16 be the right-hand side of this rule
p16 = 0.0.0.0.0.0 is a position in r16
we have r16|p16 = 1(0(0(1(1(0(0(_1)))))))
1(0(0(1(_2)))) -> 0(0(1(0(_2)))) is in R
let l'16 be the left-hand side of this rule
theta16 = {_2/1(0(0(_1)))} is a mgu of r16|p16 and l'16
==> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) -> 0(0(0(1(0(1(0(0(1(0(1(0(0(_1))))))))))))) is in EU_R^17
let r17 be the right-hand side of this rule
p17 = 0.0.0.0.0 is a position in r17
we have r17|p17 = 1(0(0(1(0(1(0(0(_1))))))))
1(0(0(1(_2)))) -> 0(0(1(0(_2)))) is in R
let l'17 be the left-hand side of this rule
theta17 = {_2/0(1(0(0(_1))))} is a mgu of r17|p17 and l'17
==> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) -> 0(0(0(1(0(0(0(1(0(0(1(0(0(_1))))))))))))) is in EU_R^18
let r18 be the right-hand side of this rule
p18 = 0.0.0.0.0.0.0 is a position in r18
we have r18|p18 = 1(0(0(1(0(0(_1))))))
1(0(0(1(_2)))) -> 0(0(1(0(_2)))) is in R
let l'18 be the left-hand side of this rule
theta18 = {_2/0(0(_1))} is a mgu of r18|p18 and l'18
==> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) -> 0(0(0(1(0(0(0(0(0(1(0(0(0(_1))))))))))))) is in EU_R^19
let r19 be the right-hand side of this rule
p19 = 0.0.0.0.0 is a position in r19
we have r19|p19 = 0(0(0(0(1(0(0(0(_1))))))))
0(0(0(0(_2)))) -> 0(1(0(1(_2)))) is in R
let l'19 be the left-hand side of this rule
theta19 = {_2/1(0(0(0(_1))))} is a mgu of r19|p19 and l'19
==> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) -> 0(0(0(1(0(0(1(0(1(1(0(0(0(_1))))))))))))) is in EU_R^20
let r20 be the right-hand side of this rule
p20 = 0.0.0 is a position in r20
we have r20|p20 = 1(0(0(1(0(1(1(0(0(0(_1))))))))))
1(0(0(1(_2)))) -> 0(0(1(0(_2)))) is in R
let l'20 be the left-hand side of this rule
theta20 = {_2/0(1(1(0(0(0(_1))))))} is a mgu of r20|p20 and l'20
==> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) -> 0(0(0(0(0(1(0(0(1(1(0(0(0(_1))))))))))))) is in EU_R^21
let r21 be the right-hand side of this rule
p21 = 0 is a position in r21
we have r21|p21 = 0(0(0(0(1(0(0(1(1(0(0(0(_1))))))))))))
0(0(0(0(_2)))) -> 0(1(0(1(_2)))) is in R
let l'21 be the left-hand side of this rule
theta21 = {_2/1(0(0(1(1(0(0(0(_1))))))))} is a mgu of r21|p21 and l'21
==> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) -> 0(0(1(0(1(1(0(0(1(1(0(0(0(_1))))))))))))) is in EU_R^22
let r22 be the right-hand side of this rule
p22 = 0.0.0.0.0 is a position in r22
we have r22|p22 = 1(0(0(1(1(0(0(0(_1))))))))
1(0(0(1(_2)))) -> 0(0(1(0(_2)))) is in R
let l'22 be the left-hand side of this rule
theta22 = {_2/1(0(0(0(_1))))} is a mgu of r22|p22 and l'22
==> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) -> 0(0(1(0(1(0(0(1(0(1(0(0(0(_1))))))))))))) is in EU_R^23
let r23 be the right-hand side of this rule
p23 = 0.0.0.0 is a position in r23
we have r23|p23 = 1(0(0(1(0(1(0(0(0(_1)))))))))
1(0(0(1(_2)))) -> 0(0(1(0(_2)))) is in R
let l'23 be the left-hand side of this rule
theta23 = {_2/0(1(0(0(0(_1)))))} is a mgu of r23|p23 and l'23
==> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) -> 0(0(1(0(0(0(1(0(0(1(0(0(0(_1))))))))))))) is in EU_R^24
let r24 be the right-hand side of this rule
p24 = 0.0.0.0.0.0 is a position in r24
we have r24|p24 = 1(0(0(1(0(0(0(_1)))))))
1(0(0(1(_2)))) -> 0(0(1(0(_2)))) is in R
let l'24 be the left-hand side of this rule
theta24 = {_2/0(0(0(_1)))} is a mgu of r24|p24 and l'24
==> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) -> 0(0(1(0(0(0(0(0(1(0(0(0(0(_1))))))))))))) is in EU_R^25
let r25 be the right-hand side of this rule
p25 = 0.0.0.0 is a position in r25
we have r25|p25 = 0(0(0(0(1(0(0(0(0(_1)))))))))
0(0(0(0(_2)))) -> 0(1(0(1(_2)))) is in R
let l'25 be the left-hand side of this rule
theta25 = {_2/1(0(0(0(0(_1)))))} is a mgu of r25|p25 and l'25
==> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) -> 0(0(1(0(0(1(0(1(1(0(0(0(0(_1))))))))))))) is in EU_R^26
let r26 be the right-hand side of this rule
p26 = 0.0 is a position in r26
we have r26|p26 = 1(0(0(1(0(1(1(0(0(0(0(_1)))))))))))
1(0(0(1(_2)))) -> 0(0(1(0(_2)))) is in R
let l'26 be the left-hand side of this rule
theta26 = {_2/0(1(1(0(0(0(0(_1)))))))} is a mgu of r26|p26 and l'26
==> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) -> 0(0(0(0(1(0(0(1(1(0(0(0(0(_1))))))))))))) is in EU_R^27
let r27 be the right-hand side of this rule
p27 = 0.0.0.0 is a position in r27
we have r27|p27 = 1(0(0(1(1(0(0(0(0(_1)))))))))
1(0(0(1(_2)))) -> 0(0(1(0(_2)))) is in R
let l'27 be the left-hand side of this rule
theta27 = {_2/1(0(0(0(0(_1)))))} is a mgu of r27|p27 and l'27
==> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) -> 0(0(0(0(0(0(1(0(1(0(0(0(0(_1))))))))))))) is in EU_R^28
let r28 be the right-hand side of this rule
p28 = 0.0.0.0.0.0.0.0.0 is a position in r28
we have r28|p28 = 0(0(0(0(_1))))
0(0(0(0(_2)))) -> 0(1(0(1(_2)))) is in R
let l'28 be the left-hand side of this rule
theta28 = {_1/_2} is a mgu of r28|p28 and l'28
==> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) -> 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) is in EU_R^29
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(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) and
theta'(theta(l)) = theta(r|p)
so, theta(l) = 0(0(0(0(0(0(1(0(1(0(1(0(1(_1))))))))))))) is non-terminating w.r.t. R
Termination disproved by the forward process
proof stopped at iteration i=29, depth k=13
4617 rule(s) generated