MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { p(s(x)) -> x , p(0()) -> 0() , le(s(x), s(y)) -> le(x, y) , le(s(x), 0()) -> false() , le(0(), y) -> true() , average(x, y) -> if(le(x, 0()), le(y, 0()), le(y, s(0())), le(y, s(s(0()))), x, y) , if(true(), b1, b2, b3, x, y) -> if2(b1, b2, b3, x, y) , if(false(), b1, b2, b3, x, y) -> average(p(x), s(y)) , if2(true(), b2, b3, x, y) -> 0() , if2(false(), b2, b3, x, y) -> if3(b2, b3, x, y) , if3(true(), b3, x, y) -> 0() , if3(false(), b3, x, y) -> if4(b3, x, y) , if4(true(), x, y) -> s(0()) , if4(false(), x, y) -> average(s(x), p(p(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) '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: { p^#(s(x)) -> c_1(x) , p^#(0()) -> c_2() , le^#(s(x), s(y)) -> c_3(le^#(x, y)) , le^#(s(x), 0()) -> c_4() , le^#(0(), y) -> c_5() , average^#(x, y) -> c_6(if^#(le(x, 0()), le(y, 0()), le(y, s(0())), le(y, s(s(0()))), x, y)) , if^#(true(), b1, b2, b3, x, y) -> c_7(if2^#(b1, b2, b3, x, y)) , if^#(false(), b1, b2, b3, x, y) -> c_8(average^#(p(x), s(y))) , if2^#(true(), b2, b3, x, y) -> c_9() , if2^#(false(), b2, b3, x, y) -> c_10(if3^#(b2, b3, x, y)) , if3^#(true(), b3, x, y) -> c_11() , if3^#(false(), b3, x, y) -> c_12(if4^#(b3, x, y)) , if4^#(true(), x, y) -> c_13() , if4^#(false(), x, y) -> c_14(average^#(s(x), p(p(y)))) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { p^#(s(x)) -> c_1(x) , p^#(0()) -> c_2() , le^#(s(x), s(y)) -> c_3(le^#(x, y)) , le^#(s(x), 0()) -> c_4() , le^#(0(), y) -> c_5() , average^#(x, y) -> c_6(if^#(le(x, 0()), le(y, 0()), le(y, s(0())), le(y, s(s(0()))), x, y)) , if^#(true(), b1, b2, b3, x, y) -> c_7(if2^#(b1, b2, b3, x, y)) , if^#(false(), b1, b2, b3, x, y) -> c_8(average^#(p(x), s(y))) , if2^#(true(), b2, b3, x, y) -> c_9() , if2^#(false(), b2, b3, x, y) -> c_10(if3^#(b2, b3, x, y)) , if3^#(true(), b3, x, y) -> c_11() , if3^#(false(), b3, x, y) -> c_12(if4^#(b3, x, y)) , if4^#(true(), x, y) -> c_13() , if4^#(false(), x, y) -> c_14(average^#(s(x), p(p(y)))) } Strict Trs: { p(s(x)) -> x , p(0()) -> 0() , le(s(x), s(y)) -> le(x, y) , le(s(x), 0()) -> false() , le(0(), y) -> true() , average(x, y) -> if(le(x, 0()), le(y, 0()), le(y, s(0())), le(y, s(s(0()))), x, y) , if(true(), b1, b2, b3, x, y) -> if2(b1, b2, b3, x, y) , if(false(), b1, b2, b3, x, y) -> average(p(x), s(y)) , if2(true(), b2, b3, x, y) -> 0() , if2(false(), b2, b3, x, y) -> if3(b2, b3, x, y) , if3(true(), b3, x, y) -> 0() , if3(false(), b3, x, y) -> if4(b3, x, y) , if4(true(), x, y) -> s(0()) , if4(false(), x, y) -> average(s(x), p(p(y))) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {2,4,5,9,11,13} by applications of Pre({2,4,5,9,11,13}) = {1,3,7,10,12}. Here rules are labeled as follows: DPs: { 1: p^#(s(x)) -> c_1(x) , 2: p^#(0()) -> c_2() , 3: le^#(s(x), s(y)) -> c_3(le^#(x, y)) , 4: le^#(s(x), 0()) -> c_4() , 5: le^#(0(), y) -> c_5() , 6: average^#(x, y) -> c_6(if^#(le(x, 0()), le(y, 0()), le(y, s(0())), le(y, s(s(0()))), x, y)) , 7: if^#(true(), b1, b2, b3, x, y) -> c_7(if2^#(b1, b2, b3, x, y)) , 8: if^#(false(), b1, b2, b3, x, y) -> c_8(average^#(p(x), s(y))) , 9: if2^#(true(), b2, b3, x, y) -> c_9() , 10: if2^#(false(), b2, b3, x, y) -> c_10(if3^#(b2, b3, x, y)) , 11: if3^#(true(), b3, x, y) -> c_11() , 12: if3^#(false(), b3, x, y) -> c_12(if4^#(b3, x, y)) , 13: if4^#(true(), x, y) -> c_13() , 14: if4^#(false(), x, y) -> c_14(average^#(s(x), p(p(y)))) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { p^#(s(x)) -> c_1(x) , le^#(s(x), s(y)) -> c_3(le^#(x, y)) , average^#(x, y) -> c_6(if^#(le(x, 0()), le(y, 0()), le(y, s(0())), le(y, s(s(0()))), x, y)) , if^#(true(), b1, b2, b3, x, y) -> c_7(if2^#(b1, b2, b3, x, y)) , if^#(false(), b1, b2, b3, x, y) -> c_8(average^#(p(x), s(y))) , if2^#(false(), b2, b3, x, y) -> c_10(if3^#(b2, b3, x, y)) , if3^#(false(), b3, x, y) -> c_12(if4^#(b3, x, y)) , if4^#(false(), x, y) -> c_14(average^#(s(x), p(p(y)))) } Strict Trs: { p(s(x)) -> x , p(0()) -> 0() , le(s(x), s(y)) -> le(x, y) , le(s(x), 0()) -> false() , le(0(), y) -> true() , average(x, y) -> if(le(x, 0()), le(y, 0()), le(y, s(0())), le(y, s(s(0()))), x, y) , if(true(), b1, b2, b3, x, y) -> if2(b1, b2, b3, x, y) , if(false(), b1, b2, b3, x, y) -> average(p(x), s(y)) , if2(true(), b2, b3, x, y) -> 0() , if2(false(), b2, b3, x, y) -> if3(b2, b3, x, y) , if3(true(), b3, x, y) -> 0() , if3(false(), b3, x, y) -> if4(b3, x, y) , if4(true(), x, y) -> s(0()) , if4(false(), x, y) -> average(s(x), p(p(y))) } Weak DPs: { p^#(0()) -> c_2() , le^#(s(x), 0()) -> c_4() , le^#(0(), y) -> c_5() , if2^#(true(), b2, b3, x, y) -> c_9() , if3^#(true(), b3, x, y) -> c_11() , if4^#(true(), x, y) -> c_13() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..