MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { 2nd(cons1(X, cons(Y, Z))) -> Y , 2nd(cons(X, X1)) -> 2nd(cons1(X, X1)) , from(X) -> cons(X, from(s(X))) } 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: We add the following weak dependency pairs: Strict DPs: { 2nd^#(cons1(X, cons(Y, Z))) -> c_1(Y) , 2nd^#(cons(X, X1)) -> c_2(2nd^#(cons1(X, X1))) , from^#(X) -> c_3(X, from^#(s(X))) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { 2nd^#(cons1(X, cons(Y, Z))) -> c_1(Y) , 2nd^#(cons(X, X1)) -> c_2(2nd^#(cons1(X, X1))) , from^#(X) -> c_3(X, from^#(s(X))) } Strict Trs: { 2nd(cons1(X, cons(Y, Z))) -> Y , 2nd(cons(X, X1)) -> 2nd(cons1(X, X1)) , from(X) -> cons(X, from(s(X))) } Obligation: runtime complexity Answer: MAYBE No rule is usable, rules are removed from the input problem. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { 2nd^#(cons1(X, cons(Y, Z))) -> c_1(Y) , 2nd^#(cons(X, X1)) -> c_2(2nd^#(cons1(X, X1))) , from^#(X) -> c_3(X, from^#(s(X))) } Obligation: runtime complexity Answer: MAYBE The weightgap principle applies (using the following constant growth matrix-interpretation) The following argument positions are usable: Uargs(c_2) = {1}, Uargs(c_3) = {2} TcT has computed the following constructor-restricted matrix interpretation. [cons1](x1, x2) = [1 0] x1 + [0] [0 0] [2] [cons](x1, x2) = [1 0] x1 + [1 0] x2 + [0] [0 0] [0 0] [0] [s](x1) = [1 1] x1 + [2] [0 0] [2] [2nd^#](x1) = [0 2] x1 + [0] [0 0] [0] [c_1](x1) = [1] [0] [c_2](x1) = [1 0] x1 + [1] [0 1] [2] [from^#](x1) = [1 1] x1 + [2] [1 1] [2] [c_3](x1, x2) = [0 0] x1 + [1 0] x2 + [1] [1 2] [0 1] [1] The following symbols are considered usable {2nd^#, from^#} The order satisfies the following ordering constraints: [2nd^#(cons1(X, cons(Y, Z)))] = [4] [0] > [1] [0] = [c_1(Y)] [2nd^#(cons(X, X1))] = [0] [0] ? [5] [2] = [c_2(2nd^#(cons1(X, X1)))] [from^#(X)] = [1 1] X + [2] [1 1] [2] ? [1 1] X + [7] [2 3] [7] = [c_3(X, from^#(s(X)))] Further, it can be verified that all rules not oriented are covered by the weightgap condition. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { 2nd^#(cons(X, X1)) -> c_2(2nd^#(cons1(X, X1))) , from^#(X) -> c_3(X, from^#(s(X))) } Weak DPs: { 2nd^#(cons1(X, cons(Y, Z))) -> c_1(Y) } Obligation: runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'Inspecting Problem...' failed due to the following reason: We use the processor 'matrix interpretation of dimension 1' to orient following rules strictly. DPs: { 1: 2nd^#(cons(X, X1)) -> c_2(2nd^#(cons1(X, X1))) } Sub-proof: ---------- The following argument positions are usable: Uargs(c_2) = {1}, Uargs(c_3) = {2} TcT has computed the following constructor-based matrix interpretation satisfying not(EDA). [2nd](x1) = [7] x1 + [0] [cons1](x1, x2) = [0] [cons](x1, x2) = [1] x1 + [1] x2 + [1] [from](x1) = [7] x1 + [0] [s](x1) = [1] x1 + [4] [2nd^#](x1) = [1] x1 + [0] [c_1](x1) = [0] [c_2](x1) = [4] x1 + [0] [from^#](x1) = [0] [c_3](x1, x2) = [4] x2 + [0] The following symbols are considered usable {2nd^#, from^#} The order satisfies the following ordering constraints: [2nd^#(cons1(X, cons(Y, Z)))] = [0] >= [0] = [c_1(Y)] [2nd^#(cons(X, X1))] = [1] X + [1] X1 + [1] > [0] = [c_2(2nd^#(cons1(X, X1)))] [from^#(X)] = [0] >= [0] = [c_3(X, from^#(s(X)))] The strictly oriented rules are moved into the weak component. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_3(X, from^#(s(X))) } Weak DPs: { 2nd^#(cons1(X, cons(Y, Z))) -> c_1(Y) , 2nd^#(cons(X, X1)) -> c_2(2nd^#(cons1(X, X1))) } Obligation: runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'Fastest' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'Polynomial Path Order (PS)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 2) 'Fastest (timeout of 5 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) 'Polynomial Path Order (PS)' failed due to the following reason: The processor is inapplicable, reason: Processor only applicable for innermost runtime complexity analysis 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: The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: Uargs(cons) = {2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [2nd](x1) = [1] x1 + [0] [cons1](x1, x2) = [1] x1 + [1] x2 + [4] [cons](x1, x2) = [1] x1 + [1] x2 + [0] [from](x1) = [1] x1 + [0] [s](x1) = [0] The following symbols are considered usable {2nd, from} The order satisfies the following ordering constraints: [2nd(cons1(X, cons(Y, Z)))] = [1] X + [1] Y + [1] Z + [4] > [1] Y + [0] = [Y] [2nd(cons(X, X1))] = [1] X + [1] X1 + [0] ? [1] X + [1] X1 + [4] = [2nd(cons1(X, X1))] [from(X)] = [1] X + [0] >= [1] X + [0] = [cons(X, from(s(X)))] Further, it can be verified that all rules not oriented are covered by the weightgap condition. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { 2nd(cons(X, X1)) -> 2nd(cons1(X, X1)) , from(X) -> cons(X, from(s(X))) } Weak Trs: { 2nd(cons1(X, cons(Y, Z))) -> Y } Obligation: runtime complexity Answer: MAYBE The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: Uargs(cons) = {2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [2nd](x1) = [1] x1 + [4] [cons1](x1, x2) = [1] x1 + [1] x2 + [0] [cons](x1, x2) = [1] x1 + [1] x2 + [4] [from](x1) = [1] x1 + [0] [s](x1) = [0] The following symbols are considered usable {2nd, from} The order satisfies the following ordering constraints: [2nd(cons1(X, cons(Y, Z)))] = [1] X + [1] Y + [1] Z + [8] > [1] Y + [0] = [Y] [2nd(cons(X, X1))] = [1] X + [1] X1 + [8] > [1] X + [1] X1 + [4] = [2nd(cons1(X, X1))] [from(X)] = [1] X + [0] ? [1] X + [4] = [cons(X, from(s(X)))] Further, it can be verified that all rules not oriented are covered by the weightgap condition. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { from(X) -> cons(X, from(s(X))) } Weak Trs: { 2nd(cons1(X, cons(Y, Z))) -> Y , 2nd(cons(X, X1)) -> 2nd(cons1(X, X1)) } Obligation: runtime complexity Answer: MAYBE None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'Fastest' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) 'empty' failed due to the following reason: Empty strict component of the problem is NOT empty. 2) 'WithProblem' failed due to the following reason: Empty strict component of the problem is NOT empty. 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: { 2nd^#(cons1(X, cons(Y, Z))) -> c_1(Y) , 2nd^#(cons(X, X1)) -> c_2(2nd^#(cons1(X, X1))) , from^#(X) -> c_3(X, from^#(s(X))) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { 2nd^#(cons1(X, cons(Y, Z))) -> c_1(Y) , 2nd^#(cons(X, X1)) -> c_2(2nd^#(cons1(X, X1))) , from^#(X) -> c_3(X, from^#(s(X))) } Strict Trs: { 2nd(cons1(X, cons(Y, Z))) -> Y , 2nd(cons(X, X1)) -> 2nd(cons1(X, X1)) , from(X) -> cons(X, from(s(X))) } Obligation: runtime complexity Answer: MAYBE Empty strict component of the problem is NOT empty. Arrrr..