MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { isLeaf(leaf()) -> true() , isLeaf(cons(u, v)) -> false() , left(cons(u, v)) -> u , right(cons(u, v)) -> v , concat(leaf(), y) -> y , concat(cons(u, v), y) -> cons(u, concat(v, y)) , less_leaves(u, v) -> if1(isLeaf(u), isLeaf(v), u, v) , if1(b, true(), u, v) -> false() , if1(b, false(), u, v) -> if2(b, u, v) , if2(true(), u, v) -> true() , if2(false(), u, v) -> less_leaves(concat(left(u), right(u)), concat(left(v), right(v))) } 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: { isLeaf^#(leaf()) -> c_1() , isLeaf^#(cons(u, v)) -> c_2() , left^#(cons(u, v)) -> c_3(u) , right^#(cons(u, v)) -> c_4(v) , concat^#(leaf(), y) -> c_5(y) , concat^#(cons(u, v), y) -> c_6(u, concat^#(v, y)) , less_leaves^#(u, v) -> c_7(if1^#(isLeaf(u), isLeaf(v), u, v)) , if1^#(b, true(), u, v) -> c_8() , if1^#(b, false(), u, v) -> c_9(if2^#(b, u, v)) , if2^#(true(), u, v) -> c_10() , if2^#(false(), u, v) -> c_11(less_leaves^#(concat(left(u), right(u)), concat(left(v), right(v)))) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { isLeaf^#(leaf()) -> c_1() , isLeaf^#(cons(u, v)) -> c_2() , left^#(cons(u, v)) -> c_3(u) , right^#(cons(u, v)) -> c_4(v) , concat^#(leaf(), y) -> c_5(y) , concat^#(cons(u, v), y) -> c_6(u, concat^#(v, y)) , less_leaves^#(u, v) -> c_7(if1^#(isLeaf(u), isLeaf(v), u, v)) , if1^#(b, true(), u, v) -> c_8() , if1^#(b, false(), u, v) -> c_9(if2^#(b, u, v)) , if2^#(true(), u, v) -> c_10() , if2^#(false(), u, v) -> c_11(less_leaves^#(concat(left(u), right(u)), concat(left(v), right(v)))) } Strict Trs: { isLeaf(leaf()) -> true() , isLeaf(cons(u, v)) -> false() , left(cons(u, v)) -> u , right(cons(u, v)) -> v , concat(leaf(), y) -> y , concat(cons(u, v), y) -> cons(u, concat(v, y)) , less_leaves(u, v) -> if1(isLeaf(u), isLeaf(v), u, v) , if1(b, true(), u, v) -> false() , if1(b, false(), u, v) -> if2(b, u, v) , if2(true(), u, v) -> true() , if2(false(), u, v) -> less_leaves(concat(left(u), right(u)), concat(left(v), right(v))) } Obligation: runtime complexity Answer: MAYBE We estimate the number of application of {1,2,8,10} by applications of Pre({1,2,8,10}) = {3,4,5,6,7,9}. Here rules are labeled as follows: DPs: { 1: isLeaf^#(leaf()) -> c_1() , 2: isLeaf^#(cons(u, v)) -> c_2() , 3: left^#(cons(u, v)) -> c_3(u) , 4: right^#(cons(u, v)) -> c_4(v) , 5: concat^#(leaf(), y) -> c_5(y) , 6: concat^#(cons(u, v), y) -> c_6(u, concat^#(v, y)) , 7: less_leaves^#(u, v) -> c_7(if1^#(isLeaf(u), isLeaf(v), u, v)) , 8: if1^#(b, true(), u, v) -> c_8() , 9: if1^#(b, false(), u, v) -> c_9(if2^#(b, u, v)) , 10: if2^#(true(), u, v) -> c_10() , 11: if2^#(false(), u, v) -> c_11(less_leaves^#(concat(left(u), right(u)), concat(left(v), right(v)))) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { left^#(cons(u, v)) -> c_3(u) , right^#(cons(u, v)) -> c_4(v) , concat^#(leaf(), y) -> c_5(y) , concat^#(cons(u, v), y) -> c_6(u, concat^#(v, y)) , less_leaves^#(u, v) -> c_7(if1^#(isLeaf(u), isLeaf(v), u, v)) , if1^#(b, false(), u, v) -> c_9(if2^#(b, u, v)) , if2^#(false(), u, v) -> c_11(less_leaves^#(concat(left(u), right(u)), concat(left(v), right(v)))) } Strict Trs: { isLeaf(leaf()) -> true() , isLeaf(cons(u, v)) -> false() , left(cons(u, v)) -> u , right(cons(u, v)) -> v , concat(leaf(), y) -> y , concat(cons(u, v), y) -> cons(u, concat(v, y)) , less_leaves(u, v) -> if1(isLeaf(u), isLeaf(v), u, v) , if1(b, true(), u, v) -> false() , if1(b, false(), u, v) -> if2(b, u, v) , if2(true(), u, v) -> true() , if2(false(), u, v) -> less_leaves(concat(left(u), right(u)), concat(left(v), right(v))) } Weak DPs: { isLeaf^#(leaf()) -> c_1() , isLeaf^#(cons(u, v)) -> c_2() , if1^#(b, true(), u, v) -> c_8() , if2^#(true(), u, v) -> c_10() } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..