let R be the TRS under consideration c(c(_1)) -> a(_1) is in elim_R(R) let r0 be the right-hand side of this rule p0 = epsilon is a position in r0 we have r0|p0 = a(_1) a(b(_2)) -> c(a(_2)) is in R let l'0 be the left-hand side of this rule theta0 = {_1/b(_2)} is a mgu of r0|p0 and l'0 ==> c(c(b(_1))) -> c(a(_1)) is in EU_R^1 let r1 be the right-hand side of this rule p1 = 0 is a position in r1 we have r1|p1 = a(_1) a(b(_2)) -> c(a(_2)) is in R let l'1 be the left-hand side of this rule theta1 = {_1/b(_2)} is a mgu of r1|p1 and l'1 ==> c(c(b(b(_1)))) -> c(c(a(_1))) is in EU_R^2 let r2 be the right-hand side of this rule p2 = 0.0 is a position in r2 we have r2|p2 = a(_1) a(_2) -> _2 is in R let l'2 be the left-hand side of this rule theta2 = {_1/_2} is a mgu of r2|p2 and l'2 ==> c(c(b(b(_1)))) -> c(c(_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 = c(_1) c(c(_2)) -> b(b(c(b(a(_2))))) is in R let l'3 be the left-hand side of this rule theta3 = {_1/c(_2)} is a mgu of r3|p3 and l'3 ==> c(c(b(b(c(_1))))) -> a(_1) is in EU_R^4 let r4 be the right-hand side of this rule p4 = epsilon is a position in r4 we have r4|p4 = a(_1) a(b(_2)) -> c(a(_2)) is in R let l'4 be the left-hand side of this rule theta4 = {_1/b(_2)} is a mgu of r4|p4 and l'4 ==> c(c(b(b(c(b(_1)))))) -> c(a(_1)) is in EU_R^5 let l5 be the left-hand side of this rule p5 = 0.0 is a position in l5 we have l5|p5 = b(b(c(b(_1)))) c(c(_2)) -> b(b(c(b(a(_2))))) is in R let r'5 be the right-hand side of this rule theta5 = {_1/a(_2)} is a mgu of l5|p5 and r'5 ==> c(c(c(c(_1)))) -> c(a(a(_1))) is in EU_R^6 let r6 be the right-hand side of this rule p6 = 0.0 is a position in r6 we have r6|p6 = a(_1) a(b(_2)) -> c(a(_2)) is in R let l'6 be the left-hand side of this rule theta6 = {_1/b(_2)} is a mgu of r6|p6 and l'6 ==> c(c(c(c(b(_1))))) -> c(a(c(a(_1)))) is in EU_R^7 let r7 be the right-hand side of this rule p7 = 0.0.0 is a position in r7 we have r7|p7 = a(_1) a(_2) -> _2 is in R let l'7 be the left-hand side of this rule theta7 = {_1/_2} is a mgu of r7|p7 and l'7 ==> c(c(c(c(b(_1))))) -> c(a(c(_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 = c(b(_1)) a(_2) -> _2 is in R let r'8 be the right-hand side of this rule theta8 = {_2/c(b(_1))} is a mgu of l8|p8 and r'8 ==> c(c(c(a(c(b(_1)))))) -> c(a(c(_1))) is in EU_R^9 let l9 be the left-hand side of this rule p9 = 0.0 is a position in l9 we have l9|p9 = c(a(c(b(_1)))) a(b(_2)) -> c(a(_2)) is in R let r'9 be the right-hand side of this rule theta9 = {_2/c(b(_1))} is a mgu of l9|p9 and r'9 ==> c(c(a(b(c(b(_1)))))) -> c(a(c(_1))) is in EU_R^10 let l10 be the left-hand side of this rule p10 = 0 is a position in l10 we have l10|p10 = c(a(b(c(b(_1))))) a(b(_2)) -> c(a(_2)) is in R let r'10 be the right-hand side of this rule theta10 = {_2/b(c(b(_1)))} is a mgu of l10|p10 and r'10 ==> c(a(b(b(c(b(_1)))))) -> c(a(c(_1))) is in EU_R^11 let l11 be the left-hand side of this rule p11 = 0.0 is a position in l11 we have l11|p11 = b(b(c(b(_1)))) c(c(_2)) -> b(b(c(b(a(_2))))) is in R let r'11 be the right-hand side of this rule theta11 = {_1/a(_2)} is a mgu of l11|p11 and r'11 ==> c(a(c(c(_1)))) -> c(a(c(a(_1)))) is in EU_R^12 let r12 be the right-hand side of this rule p12 = 0.0.0 is a position in r12 we have r12|p12 = a(_1) a(b(_2)) -> c(a(_2)) is in R let l'12 be the left-hand side of this rule theta12 = {_1/b(_2)} is a mgu of r12|p12 and l'12 ==> c(a(c(c(b(_1))))) -> c(a(c(c(a(_1))))) is in EU_R^13 let r13 be the right-hand side of this rule p13 = 0.0.0.0 is a position in r13 we have r13|p13 = a(_1) a(b(_2)) -> c(a(_2)) is in R let l'13 be the left-hand side of this rule theta13 = {_1/b(_2)} is a mgu of r13|p13 and l'13 ==> c(a(c(c(b(b(_1)))))) -> c(a(c(c(c(a(_1)))))) is in EU_R^14 let r14 be the right-hand side of this rule p14 = 0.0.0.0.0 is a position in r14 we have r14|p14 = a(_1) a(_2) -> _2 is in R let l'14 be the left-hand side of this rule theta14 = {_1/_2} is a mgu of r14|p14 and l'14 ==> c(a(c(c(b(b(_1)))))) -> c(a(c(c(c(_1))))) is in EU_R^15 let r15 be the right-hand side of this rule p15 = 0.0.0.0 is a position in r15 we have r15|p15 = c(_1) c(c(_2)) -> b(b(c(b(a(_2))))) is in R let l'15 be the left-hand side of this rule theta15 = {_1/c(_2)} is a mgu of r15|p15 and l'15 ==> c(a(c(c(b(b(c(_1))))))) -> c(a(c(c(b(b(c(b(a(_1))))))))) is in EU_R^16 let l be the left-hand side and r be the right-hand side of this rule let p = epsilon let theta = {} let theta' = {_1/b(a(_1))} we have r|p = c(a(c(c(b(b(c(b(a(_1))))))))) and theta'(theta(l)) = theta(r|p) so, theta(l) = c(a(c(c(b(b(c(_1))))))) is non-terminating w.r.t. R Termination disproved by the forward+backward process proof stopped at iteration i=16, depth k=6 7083 rule(s) generated