let R be the TRS under consideration f(s(s(s(s(s(s(s(s(_1)))))))),_2,_2) -> f(id(s(s(s(s(s(s(s(s(_1))))))))),_2,_2) is in elim_R(R) let r0 be the right-hand side of this rule p0 = 0 is a position in r0 we have r0|p0 = id(s(s(s(s(s(s(s(s(_1))))))))) id(s(_3)) -> s(id(_3)) is in R let l'0 be the left-hand side of this rule theta0 = {_3/s(s(s(s(s(s(s(_1)))))))} is a mgu of r0|p0 and l'0 ==> f(s(s(s(s(s(s(s(s(_1)))))))),_2,_2) -> f(s(id(s(s(s(s(s(s(s(_1))))))))),_2,_2) is in EU_R^1 let r1 be the right-hand side of this rule p1 = 0.0 is a position in r1 we have r1|p1 = id(s(s(s(s(s(s(s(_1)))))))) id(s(_3)) -> s(id(_3)) is in R let l'1 be the left-hand side of this rule theta1 = {_3/s(s(s(s(s(s(_1))))))} is a mgu of r1|p1 and l'1 ==> f(s(s(s(s(s(s(s(s(_1)))))))),_2,_2) -> f(s(s(id(s(s(s(s(s(s(_1))))))))),_2,_2) 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 = id(s(s(s(s(s(s(_1))))))) id(s(_3)) -> s(id(_3)) is in R let l'2 be the left-hand side of this rule theta2 = {_3/s(s(s(s(s(_1)))))} is a mgu of r2|p2 and l'2 ==> f(s(s(s(s(s(s(s(s(_1)))))))),_2,_2) -> f(s(s(s(id(s(s(s(s(s(_1))))))))),_2,_2) is in EU_R^3 let r3 be the right-hand side of this rule p3 = 0.0.0.0 is a position in r3 we have r3|p3 = id(s(s(s(s(s(_1)))))) id(s(_3)) -> s(id(_3)) is in R let l'3 be the left-hand side of this rule theta3 = {_3/s(s(s(s(_1))))} is a mgu of r3|p3 and l'3 ==> f(s(s(s(s(s(s(s(s(_1)))))))),_2,_2) -> f(s(s(s(s(id(s(s(s(s(_1))))))))),_2,_2) is in EU_R^4 let r4 be the right-hand side of this rule p4 = 0.0.0.0.0 is a position in r4 we have r4|p4 = id(s(s(s(s(_1))))) id(s(_3)) -> s(id(_3)) is in R let l'4 be the left-hand side of this rule theta4 = {_3/s(s(s(_1)))} is a mgu of r4|p4 and l'4 ==> f(s(s(s(s(s(s(s(s(_1)))))))),_2,_2) -> f(s(s(s(s(s(id(s(s(s(_1))))))))),_2,_2) is in EU_R^5 let r5 be the right-hand side of this rule p5 = 0.0.0.0.0.0 is a position in r5 we have r5|p5 = id(s(s(s(_1)))) id(s(_3)) -> s(id(_3)) is in R let l'5 be the left-hand side of this rule theta5 = {_3/s(s(_1))} is a mgu of r5|p5 and l'5 ==> f(s(s(s(s(s(s(s(s(_1)))))))),_2,_2) -> f(s(s(s(s(s(s(id(s(s(_1))))))))),_2,_2) is in EU_R^6 let r6 be the right-hand side of this rule p6 = 0.0.0.0.0.0.0 is a position in r6 we have r6|p6 = id(s(s(_1))) id(s(_3)) -> s(id(_3)) is in R let l'6 be the left-hand side of this rule theta6 = {_3/s(_1)} is a mgu of r6|p6 and l'6 ==> f(s(s(s(s(s(s(s(s(_1)))))))),_2,_2) -> f(s(s(s(s(s(s(s(id(s(_1))))))))),_2,_2) is in EU_R^7 let r7 be the right-hand side of this rule p7 = 0.0.0.0.0.0.0.0 is a position in r7 we have r7|p7 = id(s(_1)) id(s(_3)) -> s(id(_3)) is in R let l'7 be the left-hand side of this rule theta7 = {_1/_3} is a mgu of r7|p7 and l'7 ==> f(s(s(s(s(s(s(s(s(_1)))))))),_2,_2) -> f(s(s(s(s(s(s(s(s(id(_1))))))))),_2,_2) is in EU_R^8 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/id(_1), _2/_2} we have r|p = f(s(s(s(s(s(s(s(s(id(_1))))))))),_2,_2) and theta'(theta(l)) = theta(r|p) so, theta(l) = f(s(s(s(s(s(s(s(s(_1)))))))),_2,_2) is non-terminating w.r.t. R Termination disproved by the forward process proof stopped at iteration i=8, depth k=10 17061 rule(s) generated