MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { fst(0(), Z) -> nil() , fst(s(X), cons(Y, Z)) -> cons(Y, fst(X, Z)) , from(X) -> cons(X, from(s(X))) , add(0(), X) -> X , add(s(X), Y) -> s(add(X, Y)) , len(nil()) -> 0() , len(cons(X, Z)) -> s(len(Z)) } Obligation: innermost 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) 'Best' failed due to the following reason: None of the processors succeeded. Details of failed attempt(s): ----------------------------- 1) '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(s) = {1}, Uargs(cons) = {2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [fst](x1, x2) = [1] x1 + [1] x2 + [0] [0] = [4] [nil] = [3] [s](x1) = [1] x1 + [0] [cons](x1, x2) = [1] x2 + [0] [from](x1) = [1] x1 + [0] [add](x1, x2) = [1] x2 + [0] [len](x1) = [0] The following symbols are considered usable {fst, from, add, len} The order satisfies the following ordering constraints: [fst(0(), Z)] = [1] Z + [4] > [3] = [nil()] [fst(s(X), cons(Y, Z))] = [1] Z + [1] X + [0] >= [1] Z + [1] X + [0] = [cons(Y, fst(X, Z))] [from(X)] = [1] X + [0] >= [1] X + [0] = [cons(X, from(s(X)))] [add(0(), X)] = [1] X + [0] >= [1] X + [0] = [X] [add(s(X), Y)] = [1] Y + [0] >= [1] Y + [0] = [s(add(X, Y))] [len(nil())] = [0] ? [4] = [0()] [len(cons(X, Z))] = [0] >= [0] = [s(len(Z))] 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: { fst(s(X), cons(Y, Z)) -> cons(Y, fst(X, Z)) , from(X) -> cons(X, from(s(X))) , add(0(), X) -> X , add(s(X), Y) -> s(add(X, Y)) , len(nil()) -> 0() , len(cons(X, Z)) -> s(len(Z)) } Weak Trs: { fst(0(), Z) -> nil() } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: Uargs(s) = {1}, Uargs(cons) = {2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [fst](x1, x2) = [1] x2 + [0] [0] = [4] [nil] = [0] [s](x1) = [1] x1 + [0] [cons](x1, x2) = [1] x2 + [0] [from](x1) = [1] x1 + [0] [add](x1, x2) = [1] x1 + [1] x2 + [0] [len](x1) = [0] The following symbols are considered usable {fst, from, add, len} The order satisfies the following ordering constraints: [fst(0(), Z)] = [1] Z + [0] >= [0] = [nil()] [fst(s(X), cons(Y, Z))] = [1] Z + [0] >= [1] Z + [0] = [cons(Y, fst(X, Z))] [from(X)] = [1] X + [0] >= [1] X + [0] = [cons(X, from(s(X)))] [add(0(), X)] = [1] X + [4] > [1] X + [0] = [X] [add(s(X), Y)] = [1] X + [1] Y + [0] >= [1] X + [1] Y + [0] = [s(add(X, Y))] [len(nil())] = [0] ? [4] = [0()] [len(cons(X, Z))] = [0] >= [0] = [s(len(Z))] 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: { fst(s(X), cons(Y, Z)) -> cons(Y, fst(X, Z)) , from(X) -> cons(X, from(s(X))) , add(s(X), Y) -> s(add(X, Y)) , len(nil()) -> 0() , len(cons(X, Z)) -> s(len(Z)) } Weak Trs: { fst(0(), Z) -> nil() , add(0(), X) -> X } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: Uargs(s) = {1}, Uargs(cons) = {2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [fst](x1, x2) = [1] x2 + [1] [0] = [0] [nil] = [1] [s](x1) = [1] x1 + [0] [cons](x1, x2) = [1] x2 + [0] [from](x1) = [1] x1 + [0] [add](x1, x2) = [1] x1 + [1] x2 + [0] [len](x1) = [1] x1 + [0] The following symbols are considered usable {fst, from, add, len} The order satisfies the following ordering constraints: [fst(0(), Z)] = [1] Z + [1] >= [1] = [nil()] [fst(s(X), cons(Y, Z))] = [1] Z + [1] >= [1] Z + [1] = [cons(Y, fst(X, Z))] [from(X)] = [1] X + [0] >= [1] X + [0] = [cons(X, from(s(X)))] [add(0(), X)] = [1] X + [0] >= [1] X + [0] = [X] [add(s(X), Y)] = [1] X + [1] Y + [0] >= [1] X + [1] Y + [0] = [s(add(X, Y))] [len(nil())] = [1] > [0] = [0()] [len(cons(X, Z))] = [1] Z + [0] >= [1] Z + [0] = [s(len(Z))] 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: { fst(s(X), cons(Y, Z)) -> cons(Y, fst(X, Z)) , from(X) -> cons(X, from(s(X))) , add(s(X), Y) -> s(add(X, Y)) , len(cons(X, Z)) -> s(len(Z)) } Weak Trs: { fst(0(), Z) -> nil() , add(0(), X) -> X , len(nil()) -> 0() } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: Uargs(s) = {1}, Uargs(cons) = {2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [fst](x1, x2) = [1] x1 + [1] x2 + [1] [0] = [3] [nil] = [4] [s](x1) = [1] x1 + [4] [cons](x1, x2) = [1] x2 + [0] [from](x1) = [0] [add](x1, x2) = [1] x2 + [4] [len](x1) = [1] x1 + [0] The following symbols are considered usable {fst, from, add, len} The order satisfies the following ordering constraints: [fst(0(), Z)] = [1] Z + [4] >= [4] = [nil()] [fst(s(X), cons(Y, Z))] = [1] Z + [1] X + [5] > [1] Z + [1] X + [1] = [cons(Y, fst(X, Z))] [from(X)] = [0] >= [0] = [cons(X, from(s(X)))] [add(0(), X)] = [1] X + [4] > [1] X + [0] = [X] [add(s(X), Y)] = [1] Y + [4] ? [1] Y + [8] = [s(add(X, Y))] [len(nil())] = [4] > [3] = [0()] [len(cons(X, Z))] = [1] Z + [0] ? [1] Z + [4] = [s(len(Z))] 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))) , add(s(X), Y) -> s(add(X, Y)) , len(cons(X, Z)) -> s(len(Z)) } Weak Trs: { fst(0(), Z) -> nil() , fst(s(X), cons(Y, Z)) -> cons(Y, fst(X, Z)) , add(0(), X) -> X , len(nil()) -> 0() } Obligation: innermost runtime complexity Answer: MAYBE The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: Uargs(s) = {1}, Uargs(cons) = {2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [fst](x1, x2) = [1] x1 + [1] x2 + [0] [0] = [0] [nil] = [0] [s](x1) = [1] x1 + [4] [cons](x1, x2) = [1] x2 + [5] [from](x1) = [0] [add](x1, x2) = [1] x2 + [0] [len](x1) = [1] x1 + [4] The following symbols are considered usable {fst, from, add, len} The order satisfies the following ordering constraints: [fst(0(), Z)] = [1] Z + [0] >= [0] = [nil()] [fst(s(X), cons(Y, Z))] = [1] Z + [1] X + [9] > [1] Z + [1] X + [5] = [cons(Y, fst(X, Z))] [from(X)] = [0] ? [5] = [cons(X, from(s(X)))] [add(0(), X)] = [1] X + [0] >= [1] X + [0] = [X] [add(s(X), Y)] = [1] Y + [0] ? [1] Y + [4] = [s(add(X, Y))] [len(nil())] = [4] > [0] = [0()] [len(cons(X, Z))] = [1] Z + [9] > [1] Z + [8] = [s(len(Z))] 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))) , add(s(X), Y) -> s(add(X, Y)) } Weak Trs: { fst(0(), Z) -> nil() , fst(s(X), cons(Y, Z)) -> cons(Y, fst(X, Z)) , add(0(), X) -> X , len(nil()) -> 0() , len(cons(X, Z)) -> s(len(Z)) } Obligation: innermost 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: The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: Uargs(s) = {1}, Uargs(cons) = {2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [fst](x1, x2) = [0 1] x2 + [0] [0 1] [0] [0] = [0] [0] [nil] = [0] [0] [s](x1) = [1 0] x1 + [0] [0 1] [1] [cons](x1, x2) = [1 0] x2 + [0] [0 1] [1] [from](x1) = [0] [0] [add](x1, x2) = [0 4] x1 + [1 0] x2 + [0] [0 1] [0 1] [0] [len](x1) = [0 1] x1 + [0] [0 1] [0] The following symbols are considered usable {fst, from, add, len} The order satisfies the following ordering constraints: [fst(0(), Z)] = [0 1] Z + [0] [0 1] [0] >= [0] [0] = [nil()] [fst(s(X), cons(Y, Z))] = [0 1] Z + [1] [0 1] [1] > [0 1] Z + [0] [0 1] [1] = [cons(Y, fst(X, Z))] [from(X)] = [0] [0] ? [0] [1] = [cons(X, from(s(X)))] [add(0(), X)] = [1 0] X + [0] [0 1] [0] >= [1 0] X + [0] [0 1] [0] = [X] [add(s(X), Y)] = [0 4] X + [1 0] Y + [4] [0 1] [0 1] [1] > [0 4] X + [1 0] Y + [0] [0 1] [0 1] [1] = [s(add(X, Y))] [len(nil())] = [0] [0] >= [0] [0] = [0()] [len(cons(X, Z))] = [0 1] Z + [1] [0 1] [1] > [0 1] Z + [0] [0 1] [1] = [s(len(Z))] 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: { fst(0(), Z) -> nil() , fst(s(X), cons(Y, Z)) -> cons(Y, fst(X, Z)) , add(0(), X) -> X , add(s(X), Y) -> s(add(X, Y)) , len(nil()) -> 0() , len(cons(X, Z)) -> s(len(Z)) } Obligation: innermost 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) '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) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due to the following reason: The input cannot be shown compatible 2) 'bsearch-popstar (timeout of 60 seconds)' failed due to the following reason: The input cannot be shown compatible 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 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. 2) 'WithProblem (timeout of 60 seconds)' failed due to the following reason: We add the following innermost weak dependency pairs: Strict DPs: { fst^#(0(), Z) -> c_1() , fst^#(s(X), cons(Y, Z)) -> c_2(fst^#(X, Z)) , from^#(X) -> c_3(from^#(s(X))) , add^#(0(), X) -> c_4() , add^#(s(X), Y) -> c_5(add^#(X, Y)) , len^#(nil()) -> c_6() , len^#(cons(X, Z)) -> c_7(len^#(Z)) } and mark the set of starting terms. We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { fst^#(0(), Z) -> c_1() , fst^#(s(X), cons(Y, Z)) -> c_2(fst^#(X, Z)) , from^#(X) -> c_3(from^#(s(X))) , add^#(0(), X) -> c_4() , add^#(s(X), Y) -> c_5(add^#(X, Y)) , len^#(nil()) -> c_6() , len^#(cons(X, Z)) -> c_7(len^#(Z)) } Strict Trs: { fst(0(), Z) -> nil() , fst(s(X), cons(Y, Z)) -> cons(Y, fst(X, Z)) , from(X) -> cons(X, from(s(X))) , add(0(), X) -> X , add(s(X), Y) -> s(add(X, Y)) , len(nil()) -> 0() , len(cons(X, Z)) -> s(len(Z)) } Obligation: innermost 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: { fst^#(0(), Z) -> c_1() , fst^#(s(X), cons(Y, Z)) -> c_2(fst^#(X, Z)) , from^#(X) -> c_3(from^#(s(X))) , add^#(0(), X) -> c_4() , add^#(s(X), Y) -> c_5(add^#(X, Y)) , len^#(nil()) -> c_6() , len^#(cons(X, Z)) -> c_7(len^#(Z)) } Obligation: innermost 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) = {1}, Uargs(c_5) = {1}, Uargs(c_7) = {1} TcT has computed the following constructor-restricted matrix interpretation. [0] = [0] [0] [nil] = [1] [1] [s](x1) = [1 0] x1 + [0] [0 0] [0] [cons](x1, x2) = [1 0] x2 + [0] [0 0] [0] [fst^#](x1, x2) = [0] [2] [c_1] = [1] [1] [c_2](x1) = [1 0] x1 + [2] [0 1] [0] [from^#](x1) = [1 1] x1 + [2] [1 1] [2] [c_3](x1) = [1 0] x1 + [2] [0 1] [2] [add^#](x1, x2) = [0 0] x1 + [2 2] x2 + [0] [2 2] [2 2] [2] [c_4] = [1] [1] [c_5](x1) = [1 0] x1 + [2] [0 1] [0] [len^#](x1) = [0 0] x1 + [1] [1 2] [1] [c_6] = [0] [0] [c_7](x1) = [1 0] x1 + [1] [0 1] [1] The following symbols are considered usable {fst^#, from^#, add^#, len^#} The order satisfies the following ordering constraints: [fst^#(0(), Z)] = [0] [2] ? [1] [1] = [c_1()] [fst^#(s(X), cons(Y, Z))] = [0] [2] ? [2] [2] = [c_2(fst^#(X, Z))] [from^#(X)] = [1 1] X + [2] [1 1] [2] ? [1 0] X + [4] [1 0] [4] = [c_3(from^#(s(X)))] [add^#(0(), X)] = [2 2] X + [0] [2 2] [2] ? [1] [1] = [c_4()] [add^#(s(X), Y)] = [0 0] X + [2 2] Y + [0] [2 0] [2 2] [2] ? [0 0] X + [2 2] Y + [2] [2 2] [2 2] [2] = [c_5(add^#(X, Y))] [len^#(nil())] = [1] [4] > [0] [0] = [c_6()] [len^#(cons(X, Z))] = [0 0] Z + [1] [1 0] [1] ? [0 0] Z + [2] [1 2] [2] = [c_7(len^#(Z))] 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: { fst^#(0(), Z) -> c_1() , fst^#(s(X), cons(Y, Z)) -> c_2(fst^#(X, Z)) , from^#(X) -> c_3(from^#(s(X))) , add^#(0(), X) -> c_4() , add^#(s(X), Y) -> c_5(add^#(X, Y)) , len^#(cons(X, Z)) -> c_7(len^#(Z)) } Weak DPs: { len^#(nil()) -> c_6() } Obligation: innermost runtime complexity Answer: MAYBE We estimate the number of application of {1,4} by applications of Pre({1,4}) = {2,5}. Here rules are labeled as follows: DPs: { 1: fst^#(0(), Z) -> c_1() , 2: fst^#(s(X), cons(Y, Z)) -> c_2(fst^#(X, Z)) , 3: from^#(X) -> c_3(from^#(s(X))) , 4: add^#(0(), X) -> c_4() , 5: add^#(s(X), Y) -> c_5(add^#(X, Y)) , 6: len^#(cons(X, Z)) -> c_7(len^#(Z)) , 7: len^#(nil()) -> c_6() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { fst^#(s(X), cons(Y, Z)) -> c_2(fst^#(X, Z)) , from^#(X) -> c_3(from^#(s(X))) , add^#(s(X), Y) -> c_5(add^#(X, Y)) , len^#(cons(X, Z)) -> c_7(len^#(Z)) } Weak DPs: { fst^#(0(), Z) -> c_1() , add^#(0(), X) -> c_4() , len^#(nil()) -> c_6() } Obligation: innermost runtime complexity Answer: MAYBE The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. { fst^#(0(), Z) -> c_1() , add^#(0(), X) -> c_4() , len^#(nil()) -> c_6() } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { fst^#(s(X), cons(Y, Z)) -> c_2(fst^#(X, Z)) , from^#(X) -> c_3(from^#(s(X))) , add^#(s(X), Y) -> c_5(add^#(X, Y)) , len^#(cons(X, Z)) -> c_7(len^#(Z)) } Obligation: innermost 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: We use the processor 'matrix interpretation of dimension 1' to orient following rules strictly. DPs: { 1: fst^#(s(X), cons(Y, Z)) -> c_2(fst^#(X, Z)) , 3: add^#(s(X), Y) -> c_5(add^#(X, Y)) } Sub-proof: ---------- The following argument positions are usable: Uargs(c_2) = {1}, Uargs(c_3) = {1}, Uargs(c_5) = {1}, Uargs(c_7) = {1} TcT has computed the following constructor-based matrix interpretation satisfying not(EDA). [fst](x1, x2) = [7] x1 + [7] x2 + [0] [0] = [0] [nil] = [0] [s](x1) = [1] x1 + [4] [cons](x1, x2) = [1] x1 + [1] x2 + [0] [from](x1) = [7] x1 + [0] [add](x1, x2) = [7] x1 + [7] x2 + [0] [len](x1) = [7] x1 + [0] [fst^#](x1, x2) = [2] x1 + [0] [c_1] = [0] [c_2](x1) = [1] x1 + [7] [from^#](x1) = [0] [c_3](x1) = [1] x1 + [0] [add^#](x1, x2) = [2] x1 + [7] x2 + [0] [c_4] = [0] [c_5](x1) = [1] x1 + [1] [len^#](x1) = [0] [c_6] = [0] [c_7](x1) = [1] x1 + [0] The following symbols are considered usable {fst^#, from^#, add^#, len^#} The order satisfies the following ordering constraints: [fst^#(s(X), cons(Y, Z))] = [2] X + [8] > [2] X + [7] = [c_2(fst^#(X, Z))] [from^#(X)] = [0] >= [0] = [c_3(from^#(s(X)))] [add^#(s(X), Y)] = [2] X + [7] Y + [8] > [2] X + [7] Y + [1] = [c_5(add^#(X, Y))] [len^#(cons(X, Z))] = [0] >= [0] = [c_7(len^#(Z))] 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(from^#(s(X))) , len^#(cons(X, Z)) -> c_7(len^#(Z)) } Weak DPs: { fst^#(s(X), cons(Y, Z)) -> c_2(fst^#(X, Z)) , add^#(s(X), Y) -> c_5(add^#(X, Y)) } Obligation: innermost runtime complexity Answer: MAYBE The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. { fst^#(s(X), cons(Y, Z)) -> c_2(fst^#(X, Z)) , add^#(s(X), Y) -> c_5(add^#(X, Y)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_3(from^#(s(X))) , len^#(cons(X, Z)) -> c_7(len^#(Z)) } Obligation: innermost runtime complexity Answer: MAYBE We use the processor 'matrix interpretation of dimension 1' to orient following rules strictly. DPs: { 2: len^#(cons(X, Z)) -> c_7(len^#(Z)) } Sub-proof: ---------- The following argument positions are usable: Uargs(c_3) = {1}, Uargs(c_7) = {1} TcT has computed the following constructor-based matrix interpretation satisfying not(EDA). [fst](x1, x2) = [7] x1 + [7] x2 + [0] [0] = [0] [nil] = [0] [s](x1) = [1] x1 + [4] [cons](x1, x2) = [1] x1 + [1] x2 + [2] [from](x1) = [7] x1 + [0] [add](x1, x2) = [7] x1 + [7] x2 + [0] [len](x1) = [7] x1 + [0] [fst^#](x1, x2) = [7] x1 + [7] x2 + [0] [c_1] = [0] [c_2](x1) = [7] x1 + [0] [from^#](x1) = [0] [c_3](x1) = [4] x1 + [0] [add^#](x1, x2) = [7] x1 + [7] x2 + [0] [c_4] = [0] [c_5](x1) = [7] x1 + [0] [len^#](x1) = [4] x1 + [0] [c_6] = [0] [c_7](x1) = [1] x1 + [1] The following symbols are considered usable {from^#, len^#} The order satisfies the following ordering constraints: [from^#(X)] = [0] >= [0] = [c_3(from^#(s(X)))] [len^#(cons(X, Z))] = [4] Z + [4] X + [8] > [4] Z + [1] = [c_7(len^#(Z))] 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(from^#(s(X))) } Weak DPs: { len^#(cons(X, Z)) -> c_7(len^#(Z)) } Obligation: innermost runtime complexity Answer: MAYBE The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. { len^#(cons(X, Z)) -> c_7(len^#(Z)) } We are left with following problem, upon which TcT provides the certificate MAYBE. Strict DPs: { from^#(X) -> c_3(from^#(s(X))) } Obligation: innermost 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 input cannot be shown compatible 2) 'Fastest (timeout of 5 seconds)' failed due to the following reason: Computation stopped due to timeout after 5.0 seconds. 3) 'Polynomial Path Order (PS)' failed due to the following reason: The input cannot be shown compatible Arrrr..