let R be the TRS under consideration a(_1) -> b(_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 = b(_1) b(b(c(_2))) -> a(c(c(c(a(a(_2)))))) is in R let l'0 be the left-hand side of this rule theta0 = {_1/b(c(_2))} is a mgu of r0|p0 and l'0 ==> a(b(c(_1))) -> a(c(c(c(a(a(_1)))))) is in EU_R^1 let r1 be the right-hand side of this rule p1 = epsilon is a position in r1 we have r1|p1 = a(c(c(c(a(a(_1)))))) a(_2) -> _2 is in R let l'1 be the left-hand side of this rule theta1 = {_2/c(c(c(a(a(_1)))))} is a mgu of r1|p1 and l'1 ==> a(b(c(_1))) -> a(a(_1)) is in EU_R^2 let r2 be the right-hand side of this rule p2 = epsilon is a position in r2 we have r2|p2 = a(a(_1)) a(_2) -> b(_2) is in R let l'2 be the left-hand side of this rule theta2 = {_2/a(_1)} is a mgu of r2|p2 and l'2 ==> a(b(c(_1))) -> b(a(_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 = a(_1) a(_2) -> b(_2) is in R let l'3 be the left-hand side of this rule theta3 = {_1/_2} is a mgu of r3|p3 and l'3 ==> a(b(c(_1))) -> b(b(_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 = b(b(_1)) b(b(c(_2))) -> a(c(c(c(a(a(_2)))))) is in R let l'4 be the left-hand side of this rule theta4 = {_1/c(_2)} is a mgu of r4|p4 and l'4 ==> a(b(c(c(_1)))) -> a(c(c(c(a(a(_1)))))) is in EU_R^5 let r5 be the right-hand side of this rule p5 = epsilon is a position in r5 we have r5|p5 = a(c(c(c(a(a(_1)))))) a(_2) -> _2 is in R let l'5 be the left-hand side of this rule theta5 = {_2/c(c(c(a(a(_1)))))} is a mgu of r5|p5 and l'5 ==> a(b(c(c(_1)))) -> a(a(_1)) is in EU_R^6 let r6 be the right-hand side of this rule p6 = epsilon is a position in r6 we have r6|p6 = a(a(_1)) a(_2) -> b(_2) is in R let l'6 be the left-hand side of this rule theta6 = {_2/a(_1)} is a mgu of r6|p6 and l'6 ==> a(b(c(c(_1)))) -> b(a(_1)) is in EU_R^7 let r7 be the right-hand side of this rule p7 = 0 is a position in r7 we have r7|p7 = a(_1) a(_2) -> b(_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 ==> a(b(c(c(_1)))) -> b(b(_1)) is in EU_R^8 let r8 be the right-hand side of this rule p8 = epsilon is a position in r8 we have r8|p8 = b(b(_1)) b(b(c(_2))) -> a(c(c(c(a(a(_2)))))) is in R let l'8 be the left-hand side of this rule theta8 = {_1/c(_2)} is a mgu of r8|p8 and l'8 ==> a(b(c(c(c(_1))))) -> a(c(c(c(a(a(_1)))))) is in EU_R^9 let r9 be the right-hand side of this rule p9 = epsilon is a position in r9 we have r9|p9 = a(c(c(c(a(a(_1)))))) a(_2) -> _2 is in R let l'9 be the left-hand side of this rule theta9 = {_2/c(c(c(a(a(_1)))))} is a mgu of r9|p9 and l'9 ==> a(b(c(c(c(_1))))) -> a(a(_1)) is in EU_R^10 let r10 be the right-hand side of this rule p10 = 0 is a position in r10 we have r10|p10 = a(_1) a(_2) -> b(_2) is in R let l'10 be the left-hand side of this rule theta10 = {_1/_2} is a mgu of r10|p10 and l'10 ==> a(b(c(c(c(_1))))) -> a(b(_1)) is in EU_R^11 let r11 be the right-hand side of this rule p11 = 0.0 is a position in r11 we have r11|p11 = _1 a(_2) -> b(_2) is in R let l'11 be the left-hand side of this rule theta11 = {_1/a(_2)} is a mgu of r11|p11 and l'11 ==> a(b(c(c(c(a(_1)))))) -> a(b(b(_1))) is in EU_R^12 let r12 be the right-hand side of this rule p12 = 0 is a position in r12 we have r12|p12 = b(b(_1)) b(b(c(_2))) -> a(c(c(c(a(a(_2)))))) is in R let l'12 be the left-hand side of this rule theta12 = {_1/c(_2)} is a mgu of r12|p12 and l'12 ==> a(b(c(c(c(a(c(_1))))))) -> a(a(c(c(c(a(a(_1))))))) is in EU_R^13 let r13 be the right-hand side of this rule p13 = 0 is a position in r13 we have r13|p13 = a(c(c(c(a(a(_1)))))) a(_2) -> b(_2) is in R let l'13 be the left-hand side of this rule theta13 = {_2/c(c(c(a(a(_1)))))} is a mgu of r13|p13 and l'13 ==> a(b(c(c(c(a(c(_1))))))) -> a(b(c(c(c(a(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(a(_1)) a(_2) -> b(_2) is in R let l'14 be the left-hand side of this rule theta14 = {_2/a(_1)} is a mgu of r14|p14 and l'14 ==> a(b(c(c(c(a(c(_1))))))) -> a(b(c(c(c(b(a(_1))))))) is in EU_R^15 let r15 be the right-hand side of this rule p15 = 0.0.0.0.0.0 is a position in r15 we have r15|p15 = a(_1) a(_2) -> b(_2) is in R let l'15 be the left-hand side of this rule theta15 = {_1/_2} is a mgu of r15|p15 and l'15 ==> a(b(c(c(c(a(c(_1))))))) -> a(b(c(c(c(b(b(_1))))))) is in EU_R^16 let r16 be the right-hand side of this rule p16 = 0.0.0.0.0 is a position in r16 we have r16|p16 = b(b(_1)) b(b(c(_2))) -> a(c(c(c(a(a(_2)))))) is in R let l'16 be the left-hand side of this rule theta16 = {_1/c(_2)} is a mgu of r16|p16 and l'16 ==> a(b(c(c(c(a(c(c(_1)))))))) -> a(b(c(c(c(a(c(c(c(a(a(_1))))))))))) is in EU_R^17 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(a(a(_1)))} we have r|p = a(b(c(c(c(a(c(c(c(a(a(_1))))))))))) and theta'(theta(l)) = theta(r|p) so, theta(l) = a(b(c(c(c(a(c(c(_1)))))))) is non-terminating w.r.t. R Termination disproved by the forward process proof stopped at iteration i=17, depth k=7 8902 rule(s) generated