MAYBE We are left with following problem, upon which TcT provides the certificate MAYBE. Strict Trs: { minus(x, 0()) -> x , minus(s(x), s(y)) -> minus(x, y) , double(0()) -> 0() , double(s(x)) -> s(s(double(x))) , plus(0(), y) -> y , plus(s(x), y) -> s(plus(x, y)) , plus(s(x), y) -> s(plus(minus(x, y), double(y))) , plus(s(x), y) -> plus(x, s(y)) } 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) '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: The weightgap principle applies (using the following nonconstant growth matrix-interpretation) The following argument positions are usable: Uargs(s) = {1}, Uargs(plus) = {1, 2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [minus](x1, x2) = [1] x1 + [0] [0] = [1] [s](x1) = [1] x1 + [0] [double](x1) = [0] [plus](x1, x2) = [1] x1 + [1] x2 + [0] The following symbols are considered usable {minus, double, plus} The order satisfies the following ordering constraints: [minus(x, 0())] = [1] x + [0] >= [1] x + [0] = [x] [minus(s(x), s(y))] = [1] x + [0] >= [1] x + [0] = [minus(x, y)] [double(0())] = [0] ? [1] = [0()] [double(s(x))] = [0] >= [0] = [s(s(double(x)))] [plus(0(), y)] = [1] y + [1] > [1] y + [0] = [y] [plus(s(x), y)] = [1] x + [1] y + [0] >= [1] x + [1] y + [0] = [s(plus(x, y))] [plus(s(x), y)] = [1] x + [1] y + [0] >= [1] x + [0] = [s(plus(minus(x, y), double(y)))] [plus(s(x), y)] = [1] x + [1] y + [0] >= [1] x + [1] y + [0] = [plus(x, s(y))] 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: { minus(x, 0()) -> x , minus(s(x), s(y)) -> minus(x, y) , double(0()) -> 0() , double(s(x)) -> s(s(double(x))) , plus(s(x), y) -> s(plus(x, y)) , plus(s(x), y) -> s(plus(minus(x, y), double(y))) , plus(s(x), y) -> plus(x, s(y)) } Weak Trs: { plus(0(), y) -> y } 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(plus) = {1, 2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [minus](x1, x2) = [1] x1 + [1] [0] = [5] [s](x1) = [1] x1 + [0] [double](x1) = [0] [plus](x1, x2) = [1] x1 + [1] x2 + [0] The following symbols are considered usable {minus, double, plus} The order satisfies the following ordering constraints: [minus(x, 0())] = [1] x + [1] > [1] x + [0] = [x] [minus(s(x), s(y))] = [1] x + [1] >= [1] x + [1] = [minus(x, y)] [double(0())] = [0] ? [5] = [0()] [double(s(x))] = [0] >= [0] = [s(s(double(x)))] [plus(0(), y)] = [1] y + [5] > [1] y + [0] = [y] [plus(s(x), y)] = [1] x + [1] y + [0] >= [1] x + [1] y + [0] = [s(plus(x, y))] [plus(s(x), y)] = [1] x + [1] y + [0] ? [1] x + [1] = [s(plus(minus(x, y), double(y)))] [plus(s(x), y)] = [1] x + [1] y + [0] >= [1] x + [1] y + [0] = [plus(x, s(y))] 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: { minus(s(x), s(y)) -> minus(x, y) , double(0()) -> 0() , double(s(x)) -> s(s(double(x))) , plus(s(x), y) -> s(plus(x, y)) , plus(s(x), y) -> s(plus(minus(x, y), double(y))) , plus(s(x), y) -> plus(x, s(y)) } Weak Trs: { minus(x, 0()) -> x , plus(0(), y) -> y } 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(plus) = {1, 2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [minus](x1, x2) = [1] x1 + [1] x2 + [0] [0] = [7] [s](x1) = [1] x1 + [4] [double](x1) = [0] [plus](x1, x2) = [1] x1 + [1] x2 + [0] The following symbols are considered usable {minus, double, plus} The order satisfies the following ordering constraints: [minus(x, 0())] = [1] x + [7] > [1] x + [0] = [x] [minus(s(x), s(y))] = [1] x + [1] y + [8] > [1] x + [1] y + [0] = [minus(x, y)] [double(0())] = [0] ? [7] = [0()] [double(s(x))] = [0] ? [8] = [s(s(double(x)))] [plus(0(), y)] = [1] y + [7] > [1] y + [0] = [y] [plus(s(x), y)] = [1] x + [1] y + [4] >= [1] x + [1] y + [4] = [s(plus(x, y))] [plus(s(x), y)] = [1] x + [1] y + [4] >= [1] x + [1] y + [4] = [s(plus(minus(x, y), double(y)))] [plus(s(x), y)] = [1] x + [1] y + [4] >= [1] x + [1] y + [4] = [plus(x, s(y))] 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: { double(0()) -> 0() , double(s(x)) -> s(s(double(x))) , plus(s(x), y) -> s(plus(x, y)) , plus(s(x), y) -> s(plus(minus(x, y), double(y))) , plus(s(x), y) -> plus(x, s(y)) } Weak Trs: { minus(x, 0()) -> x , minus(s(x), s(y)) -> minus(x, y) , plus(0(), y) -> y } 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(plus) = {1, 2} TcT has computed the following matrix interpretation satisfying not(EDA) and not(IDA(1)). [minus](x1, x2) = [1] x1 + [1] x2 + [2] [0] = [3] [s](x1) = [1] x1 + [2] [double](x1) = [4] [plus](x1, x2) = [1] x1 + [1] x2 + [2] The following symbols are considered usable {minus, double, plus} The order satisfies the following ordering constraints: [minus(x, 0())] = [1] x + [5] > [1] x + [0] = [x] [minus(s(x), s(y))] = [1] x + [1] y + [6] > [1] x + [1] y + [2] = [minus(x, y)] [double(0())] = [4] > [3] = [0()] [double(s(x))] = [4] ? [8] = [s(s(double(x)))] [plus(0(), y)] = [1] y + [5] > [1] y + [0] = [y] [plus(s(x), y)] = [1] x + [1] y + [4] >= [1] x + [1] y + [4] = [s(plus(x, y))] [plus(s(x), y)] = [1] x + [1] y + [4] ? [1] x + [1] y + [10] = [s(plus(minus(x, y), double(y)))] [plus(s(x), y)] = [1] x + [1] y + [4] >= [1] x + [1] y + [4] = [plus(x, s(y))] 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: { double(s(x)) -> s(s(double(x))) , plus(s(x), y) -> s(plus(x, y)) , plus(s(x), y) -> s(plus(minus(x, y), double(y))) , plus(s(x), y) -> plus(x, s(y)) } Weak Trs: { minus(x, 0()) -> x , minus(s(x), s(y)) -> minus(x, y) , double(0()) -> 0() , plus(0(), y) -> y } 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: 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. Arrrr..