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