MAYBE 810.16/297.03 MAYBE 810.16/297.03 810.16/297.03 We are left with following problem, upon which TcT provides the 810.16/297.03 certificate MAYBE. 810.16/297.03 810.16/297.03 Strict Trs: 810.16/297.03 { min(x, 0()) -> 0() 810.16/297.03 , min(0(), y) -> 0() 810.16/297.03 , min(s(x), s(y)) -> s(min(x, y)) 810.16/297.03 , max(x, 0()) -> x 810.16/297.03 , max(0(), y) -> y 810.16/297.03 , max(s(x), s(y)) -> s(max(x, y)) 810.16/297.03 , twice(0()) -> 0() 810.16/297.03 , twice(s(x)) -> s(s(twice(x))) 810.16/297.03 , -(x, 0()) -> x 810.16/297.03 , -(s(x), s(y)) -> -(x, y) 810.16/297.03 , p(s(x)) -> x 810.16/297.03 , f(s(x), s(y)) -> 810.16/297.03 f(-(max(s(x), s(y)), min(s(x), s(y))), p(twice(min(x, y)))) } 810.16/297.03 Obligation: 810.16/297.03 runtime complexity 810.16/297.03 Answer: 810.16/297.03 MAYBE 810.16/297.03 810.16/297.03 None of the processors succeeded. 810.16/297.03 810.16/297.03 Details of failed attempt(s): 810.16/297.03 ----------------------------- 810.16/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 810.16/297.03 following reason: 810.16/297.03 810.16/297.03 Computation stopped due to timeout after 297.0 seconds. 810.16/297.03 810.16/297.03 2) 'Best' failed due to the following reason: 810.16/297.03 810.16/297.03 None of the processors succeeded. 810.16/297.03 810.16/297.03 Details of failed attempt(s): 810.16/297.03 ----------------------------- 810.16/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 810.16/297.03 seconds)' failed due to the following reason: 810.16/297.03 810.16/297.03 Computation stopped due to timeout after 148.0 seconds. 810.16/297.03 810.16/297.03 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 810.16/297.03 failed due to the following reason: 810.16/297.03 810.16/297.03 None of the processors succeeded. 810.16/297.03 810.16/297.03 Details of failed attempt(s): 810.16/297.03 ----------------------------- 810.16/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 810.16/297.03 failed due to the following reason: 810.16/297.03 810.16/297.03 match-boundness of the problem could not be verified. 810.16/297.03 810.16/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 810.16/297.03 failed due to the following reason: 810.16/297.03 810.16/297.03 match-boundness of the problem could not be verified. 810.16/297.03 810.16/297.03 810.16/297.03 3) 'Best' failed due to the following reason: 810.16/297.03 810.16/297.03 None of the processors succeeded. 810.16/297.03 810.16/297.03 Details of failed attempt(s): 810.16/297.03 ----------------------------- 810.16/297.03 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 810.16/297.03 following reason: 810.16/297.03 810.16/297.03 The processor is inapplicable, reason: 810.16/297.03 Processor only applicable for innermost runtime complexity analysis 810.16/297.03 810.16/297.03 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 810.16/297.03 to the following reason: 810.16/297.03 810.16/297.03 The processor is inapplicable, reason: 810.16/297.03 Processor only applicable for innermost runtime complexity analysis 810.16/297.03 810.16/297.03 810.16/297.03 810.16/297.03 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 810.16/297.03 the following reason: 810.16/297.03 810.16/297.03 We add the following weak dependency pairs: 810.16/297.03 810.16/297.03 Strict DPs: 810.16/297.03 { min^#(x, 0()) -> c_1() 810.16/297.03 , min^#(0(), y) -> c_2() 810.16/297.03 , min^#(s(x), s(y)) -> c_3(min^#(x, y)) 810.16/297.03 , max^#(x, 0()) -> c_4(x) 810.16/297.03 , max^#(0(), y) -> c_5(y) 810.16/297.03 , max^#(s(x), s(y)) -> c_6(max^#(x, y)) 810.16/297.03 , twice^#(0()) -> c_7() 810.16/297.03 , twice^#(s(x)) -> c_8(twice^#(x)) 810.16/297.03 , -^#(x, 0()) -> c_9(x) 810.16/297.03 , -^#(s(x), s(y)) -> c_10(-^#(x, y)) 810.16/297.03 , p^#(s(x)) -> c_11(x) 810.16/297.03 , f^#(s(x), s(y)) -> 810.16/297.03 c_12(f^#(-(max(s(x), s(y)), min(s(x), s(y))), 810.16/297.03 p(twice(min(x, y))))) } 810.16/297.03 810.16/297.03 and mark the set of starting terms. 810.16/297.03 810.16/297.03 We are left with following problem, upon which TcT provides the 810.16/297.03 certificate MAYBE. 810.16/297.03 810.16/297.03 Strict DPs: 810.16/297.03 { min^#(x, 0()) -> c_1() 810.16/297.03 , min^#(0(), y) -> c_2() 810.16/297.03 , min^#(s(x), s(y)) -> c_3(min^#(x, y)) 810.16/297.03 , max^#(x, 0()) -> c_4(x) 810.16/297.03 , max^#(0(), y) -> c_5(y) 810.16/297.03 , max^#(s(x), s(y)) -> c_6(max^#(x, y)) 810.16/297.03 , twice^#(0()) -> c_7() 810.16/297.03 , twice^#(s(x)) -> c_8(twice^#(x)) 810.16/297.03 , -^#(x, 0()) -> c_9(x) 810.16/297.03 , -^#(s(x), s(y)) -> c_10(-^#(x, y)) 810.16/297.03 , p^#(s(x)) -> c_11(x) 810.16/297.03 , f^#(s(x), s(y)) -> 810.16/297.03 c_12(f^#(-(max(s(x), s(y)), min(s(x), s(y))), 810.16/297.03 p(twice(min(x, y))))) } 810.16/297.03 Strict Trs: 810.16/297.03 { min(x, 0()) -> 0() 810.16/297.03 , min(0(), y) -> 0() 810.16/297.03 , min(s(x), s(y)) -> s(min(x, y)) 810.16/297.03 , max(x, 0()) -> x 810.16/297.03 , max(0(), y) -> y 810.16/297.03 , max(s(x), s(y)) -> s(max(x, y)) 810.16/297.03 , twice(0()) -> 0() 810.16/297.03 , twice(s(x)) -> s(s(twice(x))) 810.16/297.03 , -(x, 0()) -> x 810.16/297.03 , -(s(x), s(y)) -> -(x, y) 810.16/297.03 , p(s(x)) -> x 810.16/297.03 , f(s(x), s(y)) -> 810.16/297.03 f(-(max(s(x), s(y)), min(s(x), s(y))), p(twice(min(x, y)))) } 810.16/297.03 Obligation: 810.16/297.03 runtime complexity 810.16/297.03 Answer: 810.16/297.03 MAYBE 810.16/297.03 810.16/297.03 We estimate the number of application of {1,2,7} by applications of 810.16/297.03 Pre({1,2,7}) = {3,4,5,8,9,11}. Here rules are labeled as follows: 810.16/297.03 810.16/297.03 DPs: 810.16/297.03 { 1: min^#(x, 0()) -> c_1() 810.16/297.03 , 2: min^#(0(), y) -> c_2() 810.16/297.03 , 3: min^#(s(x), s(y)) -> c_3(min^#(x, y)) 810.16/297.03 , 4: max^#(x, 0()) -> c_4(x) 810.16/297.03 , 5: max^#(0(), y) -> c_5(y) 810.16/297.03 , 6: max^#(s(x), s(y)) -> c_6(max^#(x, y)) 810.16/297.03 , 7: twice^#(0()) -> c_7() 810.16/297.03 , 8: twice^#(s(x)) -> c_8(twice^#(x)) 810.16/297.03 , 9: -^#(x, 0()) -> c_9(x) 810.16/297.03 , 10: -^#(s(x), s(y)) -> c_10(-^#(x, y)) 810.16/297.03 , 11: p^#(s(x)) -> c_11(x) 810.16/297.03 , 12: f^#(s(x), s(y)) -> 810.16/297.03 c_12(f^#(-(max(s(x), s(y)), min(s(x), s(y))), 810.16/297.03 p(twice(min(x, y))))) } 810.16/297.03 810.16/297.03 We are left with following problem, upon which TcT provides the 810.16/297.03 certificate MAYBE. 810.16/297.03 810.16/297.03 Strict DPs: 810.16/297.03 { min^#(s(x), s(y)) -> c_3(min^#(x, y)) 810.16/297.03 , max^#(x, 0()) -> c_4(x) 810.16/297.03 , max^#(0(), y) -> c_5(y) 810.16/297.03 , max^#(s(x), s(y)) -> c_6(max^#(x, y)) 810.16/297.03 , twice^#(s(x)) -> c_8(twice^#(x)) 810.16/297.03 , -^#(x, 0()) -> c_9(x) 810.16/297.03 , -^#(s(x), s(y)) -> c_10(-^#(x, y)) 810.16/297.03 , p^#(s(x)) -> c_11(x) 810.16/297.03 , f^#(s(x), s(y)) -> 810.16/297.03 c_12(f^#(-(max(s(x), s(y)), min(s(x), s(y))), 810.16/297.03 p(twice(min(x, y))))) } 810.16/297.03 Strict Trs: 810.16/297.03 { min(x, 0()) -> 0() 810.16/297.03 , min(0(), y) -> 0() 810.16/297.03 , min(s(x), s(y)) -> s(min(x, y)) 810.16/297.03 , max(x, 0()) -> x 810.16/297.03 , max(0(), y) -> y 810.16/297.03 , max(s(x), s(y)) -> s(max(x, y)) 810.16/297.03 , twice(0()) -> 0() 810.16/297.03 , twice(s(x)) -> s(s(twice(x))) 810.16/297.03 , -(x, 0()) -> x 810.16/297.03 , -(s(x), s(y)) -> -(x, y) 810.16/297.03 , p(s(x)) -> x 810.16/297.03 , f(s(x), s(y)) -> 810.16/297.03 f(-(max(s(x), s(y)), min(s(x), s(y))), p(twice(min(x, y)))) } 810.16/297.03 Weak DPs: 810.16/297.03 { min^#(x, 0()) -> c_1() 810.16/297.03 , min^#(0(), y) -> c_2() 810.16/297.03 , twice^#(0()) -> c_7() } 810.16/297.03 Obligation: 810.16/297.03 runtime complexity 810.16/297.03 Answer: 810.16/297.03 MAYBE 810.16/297.03 810.16/297.03 Empty strict component of the problem is NOT empty. 810.16/297.03 810.16/297.03 810.16/297.03 Arrrr.. 810.57/297.42 EOF