let R be the TRS under consideration b(_1) -> a(_1) is in elim_R(R) let l0 be the left-hand side of this rule p0 = 0 is a position in l0 we have l0|p0 = _1 a(b(_2)) -> b(a(c(b(c(_2))))) is in R let r'0 be the right-hand side of this rule theta0 = {_1/b(a(c(b(c(_2)))))} is a mgu of l0|p0 and r'0 ==> b(a(b(_1))) -> a(b(a(c(b(c(_1)))))) is in EU_R^1 let l1 be the left-hand side of this rule p1 = 0.0 is a position in l1 we have l1|p1 = b(_1) c(c(_2)) -> _2 is in R let r'1 be the right-hand side of this rule theta1 = {_2/b(_1)} is a mgu of l1|p1 and r'1 ==> b(a(c(c(b(_1))))) -> a(b(a(c(b(c(_1)))))) is in EU_R^2 let l2 be the left-hand side of this rule p2 = 0.0.0 is a position in l2 we have l2|p2 = c(b(_1)) a(_2) -> _2 is in R let r'2 be the right-hand side of this rule theta2 = {_2/c(b(_1))} is a mgu of l2|p2 and r'2 ==> b(a(c(a(c(b(_1)))))) -> a(b(a(c(b(c(_1)))))) is in EU_R^3 let l3 be the left-hand side of this rule p3 = 0.0.0 is a position in l3 we have l3|p3 = a(c(b(_1))) a(_2) -> _2 is in R let r'3 be the right-hand side of this rule theta3 = {_2/a(c(b(_1)))} is a mgu of l3|p3 and r'3 ==> b(a(c(a(a(c(b(_1))))))) -> a(b(a(c(b(c(_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 = a(a(c(b(_1)))) b(_2) -> a(_2) is in R let r'4 be the right-hand side of this rule theta4 = {_2/a(c(b(_1)))} is a mgu of l4|p4 and r'4 ==> b(a(c(b(a(c(b(_1))))))) -> a(b(a(c(b(c(_1)))))) is in EU_R^5 let l5 be the left-hand side of this rule p5 = 0.0.0 is a position in l5 we have l5|p5 = b(a(c(b(_1)))) a(b(_2)) -> b(a(c(b(c(_2))))) is in R let r'5 be the right-hand side of this rule theta5 = {_1/c(_2)} is a mgu of l5|p5 and r'5 ==> b(a(c(a(b(_1))))) -> a(b(a(c(b(c(c(_1))))))) is in EU_R^6 let l6 be the left-hand side of this rule p6 = 0.0.0 is a position in l6 we have l6|p6 = a(b(_1)) b(_2) -> a(_2) is in R let r'6 be the right-hand side of this rule theta6 = {_2/b(_1)} is a mgu of l6|p6 and r'6 ==> b(a(c(b(b(_1))))) -> a(b(a(c(b(c(c(_1))))))) is in EU_R^7 let l7 be the left-hand side of this rule p7 = 0.0.0.0 is a position in l7 we have l7|p7 = b(_1) c(c(_2)) -> _2 is in R let r'7 be the right-hand side of this rule theta7 = {_2/b(_1)} is a mgu of l7|p7 and r'7 ==> b(a(c(b(c(c(b(_1))))))) -> a(b(a(c(b(c(c(_1))))))) is in EU_R^8 let l8 be the left-hand side of this rule p8 = epsilon is a position in l8 we have l8|p8 = b(a(c(b(c(c(b(_1))))))) a(b(_2)) -> b(a(c(b(c(_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 ==> a(b(c(b(_1)))) -> a(b(a(c(b(c(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(b(_1)) a(_2) -> _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 ==> a(b(a(c(b(_1))))) -> a(b(a(c(b(c(c(_1))))))) is in EU_R^10 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/c(c(_1))} we have r|p = a(b(a(c(b(c(c(_1))))))) and theta'(theta(l)) = theta(r|p) so, theta(l) = a(b(a(c(b(_1))))) is non-terminating w.r.t. R Termination disproved by the backward process proof stopped at iteration i=10, depth k=7 12137 rule(s) generated