MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { table() -> gen(s(0())) , gen(x) -> if1(le(x, 10()), x) , if1(false(), x) -> nil() , if1(true(), x) -> if2(x, x) , le(s(x), s(y)) -> le(x, y) , le(s(x), 0()) -> false() , le(0(), y) -> true() , 10() -> s(s(s(s(s(s(s(s(s(s(0())))))))))) , if2(x, y) -> if3(le(y, 10()), x, y) , if3(false(), x, y) -> gen(s(x)) , if3(true(), x, y) -> cons(entry(x, y, times(x, y)), if2(x, s(y))) , times(s(x), y) -> plus(y, times(x, y)) , times(0(), y) -> 0() , plus(s(x), y) -> s(plus(x, y)) , plus(0(), y) -> y } 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) '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 minimal-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' failed due to the following reason: match-boundness of the problem could not be verified. 3) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) '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 2) '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 3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed due to the following reason: We add the following weak dependency pairs: Strict DPs: { table^#() -> c_1(gen^#(s(0()))) , gen^#(x) -> c_2(if1^#(le(x, 10()), x)) , if1^#(false(), x) -> c_3() , if1^#(true(), x) -> c_4(if2^#(x, x)) , if2^#(x, y) -> c_9(if3^#(le(y, 10()), x, y)) , le^#(s(x), s(y)) -> c_5(le^#(x, y)) , le^#(s(x), 0()) -> c_6() , le^#(0(), y) -> c_7() , 10^#() -> c_8() , if3^#(false(), x, y) -> c_10(gen^#(s(x))) , if3^#(true(), x, y) -> c_11(x, y, times^#(x, y), if2^#(x, s(y))) , times^#(s(x), y) -> c_12(plus^#(y, times(x, y))) , times^#(0(), y) -> c_13() , plus^#(s(x), y) -> c_14(plus^#(x, y)) , plus^#(0(), y) -> c_15(y) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { table^#() -> c_1(gen^#(s(0()))) , gen^#(x) -> c_2(if1^#(le(x, 10()), x)) , if1^#(false(), x) -> c_3() , if1^#(true(), x) -> c_4(if2^#(x, x)) , if2^#(x, y) -> c_9(if3^#(le(y, 10()), x, y)) , le^#(s(x), s(y)) -> c_5(le^#(x, y)) , le^#(s(x), 0()) -> c_6() , le^#(0(), y) -> c_7() , 10^#() -> c_8() , if3^#(false(), x, y) -> c_10(gen^#(s(x))) , if3^#(true(), x, y) -> c_11(x, y, times^#(x, y), if2^#(x, s(y))) , times^#(s(x), y) -> c_12(plus^#(y, times(x, y))) , times^#(0(), y) -> c_13() , plus^#(s(x), y) -> c_14(plus^#(x, y)) , plus^#(0(), y) -> c_15(y) } Strict Trs: { table() -> gen(s(0())) , gen(x) -> if1(le(x, 10()), x) , if1(false(), x) -> nil() , if1(true(), x) -> if2(x, x) , le(s(x), s(y)) -> le(x, y) , le(s(x), 0()) -> false() , le(0(), y) -> true() , 10() -> s(s(s(s(s(s(s(s(s(s(0())))))))))) , if2(x, y) -> if3(le(y, 10()), x, y) , if3(false(), x, y) -> gen(s(x)) , if3(true(), x, y) -> cons(entry(x, y, times(x, y)), if2(x, s(y))) , times(s(x), y) -> plus(y, times(x, y)) , times(0(), y) -> 0() , plus(s(x), y) -> s(plus(x, y)) , plus(0(), y) -> y } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {3,7,8,9,13} by applications of Pre({3,7,8,9,13}) = {2,6,11,15}. Here rules are labeled as follows: DPs: { 1: table^#() -> c_1(gen^#(s(0()))) , 2: gen^#(x) -> c_2(if1^#(le(x, 10()), x)) , 3: if1^#(false(), x) -> c_3() , 4: if1^#(true(), x) -> c_4(if2^#(x, x)) , 5: if2^#(x, y) -> c_9(if3^#(le(y, 10()), x, y)) , 6: le^#(s(x), s(y)) -> c_5(le^#(x, y)) , 7: le^#(s(x), 0()) -> c_6() , 8: le^#(0(), y) -> c_7() , 9: 10^#() -> c_8() , 10: if3^#(false(), x, y) -> c_10(gen^#(s(x))) , 11: if3^#(true(), x, y) -> c_11(x, y, times^#(x, y), if2^#(x, s(y))) , 12: times^#(s(x), y) -> c_12(plus^#(y, times(x, y))) , 13: times^#(0(), y) -> c_13() , 14: plus^#(s(x), y) -> c_14(plus^#(x, y)) , 15: plus^#(0(), y) -> c_15(y) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { table^#() -> c_1(gen^#(s(0()))) , gen^#(x) -> c_2(if1^#(le(x, 10()), x)) , if1^#(true(), x) -> c_4(if2^#(x, x)) , if2^#(x, y) -> c_9(if3^#(le(y, 10()), x, y)) , le^#(s(x), s(y)) -> c_5(le^#(x, y)) , if3^#(false(), x, y) -> c_10(gen^#(s(x))) , if3^#(true(), x, y) -> c_11(x, y, times^#(x, y), if2^#(x, s(y))) , times^#(s(x), y) -> c_12(plus^#(y, times(x, y))) , plus^#(s(x), y) -> c_14(plus^#(x, y)) , plus^#(0(), y) -> c_15(y) } Strict Trs: { table() -> gen(s(0())) , gen(x) -> if1(le(x, 10()), x) , if1(false(), x) -> nil() , if1(true(), x) -> if2(x, x) , le(s(x), s(y)) -> le(x, y) , le(s(x), 0()) -> false() , le(0(), y) -> true() , 10() -> s(s(s(s(s(s(s(s(s(s(0())))))))))) , if2(x, y) -> if3(le(y, 10()), x, y) , if3(false(), x, y) -> gen(s(x)) , if3(true(), x, y) -> cons(entry(x, y, times(x, y)), if2(x, s(y))) , times(s(x), y) -> plus(y, times(x, y)) , times(0(), y) -> 0() , plus(s(x), y) -> s(plus(x, y)) , plus(0(), y) -> y } Weak DPs: { if1^#(false(), x) -> c_3() , le^#(s(x), 0()) -> c_6() , le^#(0(), y) -> c_7() , 10^#() -> c_8() , times^#(0(), y) -> c_13() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..