MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { D(t()) -> s(h()) , D(constant()) -> h() , D(b(x, y)) -> b(D(x), D(y)) , D(c(x, y)) -> b(c(y, D(x)), c(x, D(y))) , D(m(x, y)) -> m(D(x), D(y)) , D(opp(x)) -> opp(D(x)) , D(div(x, y)) -> m(div(D(x), y), div(c(x, D(y)), pow(y, 2()))) , D(pow(x, y)) -> b(c(c(y, pow(x, m(y, 1()))), D(x)), c(c(pow(x, y), ln(x)), D(y))) , D(ln(x)) -> div(D(x), x) , b(x, h()) -> x , b(s(x), s(y)) -> s(s(b(x, y))) , b(h(), x) -> x , b(b(x, y), z) -> b(x, b(y, z)) } Obligation: runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 60.0 seconds. 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)' failed due to the following reason: Computation stopped due to timeout after 30.0 seconds. 2) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'bsearch-popstar (timeout of 60 seconds)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 3) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { D^#(t()) -> c_1() , D^#(constant()) -> c_2() , D^#(b(x, y)) -> c_3(b^#(D(x), D(y))) , D^#(c(x, y)) -> c_4(b^#(c(y, D(x)), c(x, D(y)))) , D^#(m(x, y)) -> c_5(D^#(x), D^#(y)) , D^#(opp(x)) -> c_6(D^#(x)) , D^#(div(x, y)) -> c_7(D^#(x), y, x, D^#(y), y) , D^#(pow(x, y)) -> c_8(b^#(c(c(y, pow(x, m(y, 1()))), D(x)), c(c(pow(x, y), ln(x)), D(y)))) , D^#(ln(x)) -> c_9(D^#(x), x) , b^#(x, h()) -> c_10(x) , b^#(s(x), s(y)) -> c_11(b^#(x, y)) , b^#(h(), x) -> c_12(x) , b^#(b(x, y), z) -> c_13(b^#(x, b(y, z))) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { D^#(t()) -> c_1() , D^#(constant()) -> c_2() , D^#(b(x, y)) -> c_3(b^#(D(x), D(y))) , D^#(c(x, y)) -> c_4(b^#(c(y, D(x)), c(x, D(y)))) , D^#(m(x, y)) -> c_5(D^#(x), D^#(y)) , D^#(opp(x)) -> c_6(D^#(x)) , D^#(div(x, y)) -> c_7(D^#(x), y, x, D^#(y), y) , D^#(pow(x, y)) -> c_8(b^#(c(c(y, pow(x, m(y, 1()))), D(x)), c(c(pow(x, y), ln(x)), D(y)))) , D^#(ln(x)) -> c_9(D^#(x), x) , b^#(x, h()) -> c_10(x) , b^#(s(x), s(y)) -> c_11(b^#(x, y)) , b^#(h(), x) -> c_12(x) , b^#(b(x, y), z) -> c_13(b^#(x, b(y, z))) } Strict Trs: { D(t()) -> s(h()) , D(constant()) -> h() , D(b(x, y)) -> b(D(x), D(y)) , D(c(x, y)) -> b(c(y, D(x)), c(x, D(y))) , D(m(x, y)) -> m(D(x), D(y)) , D(opp(x)) -> opp(D(x)) , D(div(x, y)) -> m(div(D(x), y), div(c(x, D(y)), pow(y, 2()))) , D(pow(x, y)) -> b(c(c(y, pow(x, m(y, 1()))), D(x)), c(c(pow(x, y), ln(x)), D(y))) , D(ln(x)) -> div(D(x), x) , b(x, h()) -> x , b(s(x), s(y)) -> s(s(b(x, y))) , b(h(), x) -> x , b(b(x, y), z) -> b(x, b(y, z)) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {1,2,4,8} by applications of Pre({1,2,4,8}) = {5,6,7,9,10,12}. Here rules are labeled as follows: DPs: { 1: D^#(t()) -> c_1() , 2: D^#(constant()) -> c_2() , 3: D^#(b(x, y)) -> c_3(b^#(D(x), D(y))) , 4: D^#(c(x, y)) -> c_4(b^#(c(y, D(x)), c(x, D(y)))) , 5: D^#(m(x, y)) -> c_5(D^#(x), D^#(y)) , 6: D^#(opp(x)) -> c_6(D^#(x)) , 7: D^#(div(x, y)) -> c_7(D^#(x), y, x, D^#(y), y) , 8: D^#(pow(x, y)) -> c_8(b^#(c(c(y, pow(x, m(y, 1()))), D(x)), c(c(pow(x, y), ln(x)), D(y)))) , 9: D^#(ln(x)) -> c_9(D^#(x), x) , 10: b^#(x, h()) -> c_10(x) , 11: b^#(s(x), s(y)) -> c_11(b^#(x, y)) , 12: b^#(h(), x) -> c_12(x) , 13: b^#(b(x, y), z) -> c_13(b^#(x, b(y, z))) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { D^#(b(x, y)) -> c_3(b^#(D(x), D(y))) , D^#(m(x, y)) -> c_5(D^#(x), D^#(y)) , D^#(opp(x)) -> c_6(D^#(x)) , D^#(div(x, y)) -> c_7(D^#(x), y, x, D^#(y), y) , D^#(ln(x)) -> c_9(D^#(x), x) , b^#(x, h()) -> c_10(x) , b^#(s(x), s(y)) -> c_11(b^#(x, y)) , b^#(h(), x) -> c_12(x) , b^#(b(x, y), z) -> c_13(b^#(x, b(y, z))) } Strict Trs: { D(t()) -> s(h()) , D(constant()) -> h() , D(b(x, y)) -> b(D(x), D(y)) , D(c(x, y)) -> b(c(y, D(x)), c(x, D(y))) , D(m(x, y)) -> m(D(x), D(y)) , D(opp(x)) -> opp(D(x)) , D(div(x, y)) -> m(div(D(x), y), div(c(x, D(y)), pow(y, 2()))) , D(pow(x, y)) -> b(c(c(y, pow(x, m(y, 1()))), D(x)), c(c(pow(x, y), ln(x)), D(y))) , D(ln(x)) -> div(D(x), x) , b(x, h()) -> x , b(s(x), s(y)) -> s(s(b(x, y))) , b(h(), x) -> x , b(b(x, y), z) -> b(x, b(y, z)) } Weak DPs: { D^#(t()) -> c_1() , D^#(constant()) -> c_2() , D^#(c(x, y)) -> c_4(b^#(c(y, D(x)), c(x, D(y)))) , D^#(pow(x, y)) -> c_8(b^#(c(c(y, pow(x, m(y, 1()))), D(x)), c(c(pow(x, y), ln(x)), D(y)))) } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..