MAYBE 824.31/297.04 MAYBE 824.31/297.04 824.31/297.04 We are left with following problem, upon which TcT provides the 824.31/297.04 certificate MAYBE. 824.31/297.04 824.31/297.04 Strict Trs: 824.31/297.04 { min(x, 0()) -> 0() 824.31/297.04 , min(0(), y) -> 0() 824.31/297.04 , min(s(x), s(y)) -> s(min(x, y)) 824.31/297.04 , max(x, 0()) -> x 824.31/297.04 , max(0(), y) -> y 824.31/297.04 , max(s(x), s(y)) -> s(max(x, y)) 824.31/297.04 , p(s(x)) -> x 824.31/297.04 , f(x, y, 0()) -> max(x, y) 824.31/297.04 , f(x, 0(), z) -> max(x, z) 824.31/297.04 , f(0(), y, z) -> max(y, z) 824.31/297.04 , f(s(x), s(y), s(z)) -> 824.31/297.04 f(max(s(x), max(s(y), s(z))), 824.31/297.04 p(min(s(x), max(s(y), s(z)))), 824.31/297.04 min(s(x), min(s(y), s(z)))) } 824.31/297.04 Obligation: 824.31/297.04 runtime complexity 824.31/297.04 Answer: 824.31/297.04 MAYBE 824.31/297.04 824.31/297.04 None of the processors succeeded. 824.31/297.04 824.31/297.04 Details of failed attempt(s): 824.31/297.04 ----------------------------- 824.31/297.04 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 824.31/297.04 following reason: 824.31/297.04 824.31/297.04 Computation stopped due to timeout after 297.0 seconds. 824.31/297.04 824.31/297.04 2) 'Best' failed due to the following reason: 824.31/297.04 824.31/297.04 None of the processors succeeded. 824.31/297.04 824.31/297.04 Details of failed attempt(s): 824.31/297.04 ----------------------------- 824.31/297.04 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 824.31/297.04 seconds)' failed due to the following reason: 824.31/297.04 824.31/297.04 Computation stopped due to timeout after 148.0 seconds. 824.31/297.04 824.31/297.04 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 824.31/297.04 failed due to the following reason: 824.31/297.04 824.31/297.04 None of the processors succeeded. 824.31/297.04 824.31/297.04 Details of failed attempt(s): 824.31/297.04 ----------------------------- 824.31/297.04 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 824.31/297.04 failed due to the following reason: 824.31/297.04 824.31/297.04 match-boundness of the problem could not be verified. 824.31/297.04 824.31/297.04 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 824.31/297.04 failed due to the following reason: 824.31/297.04 824.31/297.04 match-boundness of the problem could not be verified. 824.31/297.04 824.31/297.04 824.31/297.04 3) 'Best' failed due to the following reason: 824.31/297.04 824.31/297.04 None of the processors succeeded. 824.31/297.04 824.31/297.04 Details of failed attempt(s): 824.31/297.04 ----------------------------- 824.31/297.04 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 824.31/297.04 following reason: 824.31/297.04 824.31/297.04 The processor is inapplicable, reason: 824.31/297.04 Processor only applicable for innermost runtime complexity analysis 824.31/297.04 824.31/297.04 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 824.31/297.04 to the following reason: 824.31/297.04 824.31/297.04 The processor is inapplicable, reason: 824.31/297.04 Processor only applicable for innermost runtime complexity analysis 824.31/297.04 824.31/297.04 824.31/297.04 824.31/297.04 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 824.31/297.04 the following reason: 824.31/297.04 824.31/297.04 We add the following weak dependency pairs: 824.31/297.04 824.31/297.04 Strict DPs: 824.31/297.04 { min^#(x, 0()) -> c_1() 824.31/297.04 , min^#(0(), y) -> c_2() 824.31/297.04 , min^#(s(x), s(y)) -> c_3(min^#(x, y)) 824.31/297.04 , max^#(x, 0()) -> c_4(x) 824.31/297.04 , max^#(0(), y) -> c_5(y) 824.31/297.04 , max^#(s(x), s(y)) -> c_6(max^#(x, y)) 824.31/297.04 , p^#(s(x)) -> c_7(x) 824.31/297.04 , f^#(x, y, 0()) -> c_8(max^#(x, y)) 824.31/297.04 , f^#(x, 0(), z) -> c_9(max^#(x, z)) 824.31/297.04 , f^#(0(), y, z) -> c_10(max^#(y, z)) 824.31/297.04 , f^#(s(x), s(y), s(z)) -> 824.31/297.04 c_11(f^#(max(s(x), max(s(y), s(z))), 824.31/297.04 p(min(s(x), max(s(y), s(z)))), 824.31/297.04 min(s(x), min(s(y), s(z))))) } 824.31/297.04 824.31/297.04 and mark the set of starting terms. 824.31/297.04 824.31/297.04 We are left with following problem, upon which TcT provides the 824.31/297.04 certificate MAYBE. 824.31/297.04 824.31/297.04 Strict DPs: 824.31/297.04 { min^#(x, 0()) -> c_1() 824.31/297.04 , min^#(0(), y) -> c_2() 824.31/297.04 , min^#(s(x), s(y)) -> c_3(min^#(x, y)) 824.31/297.04 , max^#(x, 0()) -> c_4(x) 824.31/297.04 , max^#(0(), y) -> c_5(y) 824.31/297.04 , max^#(s(x), s(y)) -> c_6(max^#(x, y)) 824.31/297.04 , p^#(s(x)) -> c_7(x) 824.31/297.04 , f^#(x, y, 0()) -> c_8(max^#(x, y)) 824.31/297.04 , f^#(x, 0(), z) -> c_9(max^#(x, z)) 824.31/297.04 , f^#(0(), y, z) -> c_10(max^#(y, z)) 824.31/297.04 , f^#(s(x), s(y), s(z)) -> 824.31/297.04 c_11(f^#(max(s(x), max(s(y), s(z))), 824.31/297.04 p(min(s(x), max(s(y), s(z)))), 824.31/297.04 min(s(x), min(s(y), s(z))))) } 824.31/297.04 Strict Trs: 824.31/297.04 { min(x, 0()) -> 0() 824.31/297.04 , min(0(), y) -> 0() 824.31/297.04 , min(s(x), s(y)) -> s(min(x, y)) 824.31/297.04 , max(x, 0()) -> x 824.31/297.04 , max(0(), y) -> y 824.31/297.04 , max(s(x), s(y)) -> s(max(x, y)) 824.31/297.04 , p(s(x)) -> x 824.31/297.04 , f(x, y, 0()) -> max(x, y) 824.31/297.04 , f(x, 0(), z) -> max(x, z) 824.31/297.04 , f(0(), y, z) -> max(y, z) 824.31/297.04 , f(s(x), s(y), s(z)) -> 824.31/297.04 f(max(s(x), max(s(y), s(z))), 824.31/297.04 p(min(s(x), max(s(y), s(z)))), 824.31/297.04 min(s(x), min(s(y), s(z)))) } 824.31/297.04 Obligation: 824.31/297.04 runtime complexity 824.31/297.04 Answer: 824.31/297.04 MAYBE 824.31/297.04 824.31/297.04 We estimate the number of application of {1,2} by applications of 824.31/297.04 Pre({1,2}) = {3,4,5,7}. Here rules are labeled as follows: 824.31/297.04 824.31/297.04 DPs: 824.31/297.04 { 1: min^#(x, 0()) -> c_1() 824.31/297.04 , 2: min^#(0(), y) -> c_2() 824.31/297.04 , 3: min^#(s(x), s(y)) -> c_3(min^#(x, y)) 824.31/297.04 , 4: max^#(x, 0()) -> c_4(x) 824.31/297.04 , 5: max^#(0(), y) -> c_5(y) 824.31/297.04 , 6: max^#(s(x), s(y)) -> c_6(max^#(x, y)) 824.31/297.04 , 7: p^#(s(x)) -> c_7(x) 824.31/297.04 , 8: f^#(x, y, 0()) -> c_8(max^#(x, y)) 824.31/297.04 , 9: f^#(x, 0(), z) -> c_9(max^#(x, z)) 824.31/297.04 , 10: f^#(0(), y, z) -> c_10(max^#(y, z)) 824.31/297.04 , 11: f^#(s(x), s(y), s(z)) -> 824.31/297.04 c_11(f^#(max(s(x), max(s(y), s(z))), 824.31/297.04 p(min(s(x), max(s(y), s(z)))), 824.31/297.04 min(s(x), min(s(y), s(z))))) } 824.31/297.04 824.31/297.04 We are left with following problem, upon which TcT provides the 824.31/297.04 certificate MAYBE. 824.31/297.04 824.31/297.04 Strict DPs: 824.31/297.04 { min^#(s(x), s(y)) -> c_3(min^#(x, y)) 824.31/297.04 , max^#(x, 0()) -> c_4(x) 824.31/297.04 , max^#(0(), y) -> c_5(y) 824.31/297.04 , max^#(s(x), s(y)) -> c_6(max^#(x, y)) 824.31/297.04 , p^#(s(x)) -> c_7(x) 824.31/297.04 , f^#(x, y, 0()) -> c_8(max^#(x, y)) 824.31/297.04 , f^#(x, 0(), z) -> c_9(max^#(x, z)) 824.31/297.04 , f^#(0(), y, z) -> c_10(max^#(y, z)) 824.31/297.04 , f^#(s(x), s(y), s(z)) -> 824.31/297.04 c_11(f^#(max(s(x), max(s(y), s(z))), 824.31/297.04 p(min(s(x), max(s(y), s(z)))), 824.31/297.04 min(s(x), min(s(y), s(z))))) } 824.31/297.04 Strict Trs: 824.31/297.04 { min(x, 0()) -> 0() 824.31/297.04 , min(0(), y) -> 0() 824.31/297.04 , min(s(x), s(y)) -> s(min(x, y)) 824.31/297.04 , max(x, 0()) -> x 824.31/297.04 , max(0(), y) -> y 824.31/297.04 , max(s(x), s(y)) -> s(max(x, y)) 824.31/297.04 , p(s(x)) -> x 824.31/297.04 , f(x, y, 0()) -> max(x, y) 824.31/297.04 , f(x, 0(), z) -> max(x, z) 824.31/297.04 , f(0(), y, z) -> max(y, z) 824.31/297.04 , f(s(x), s(y), s(z)) -> 824.31/297.04 f(max(s(x), max(s(y), s(z))), 824.31/297.04 p(min(s(x), max(s(y), s(z)))), 824.31/297.04 min(s(x), min(s(y), s(z)))) } 824.31/297.04 Weak DPs: 824.31/297.04 { min^#(x, 0()) -> c_1() 824.31/297.04 , min^#(0(), y) -> c_2() } 824.31/297.04 Obligation: 824.31/297.04 runtime complexity 824.31/297.04 Answer: 824.31/297.04 MAYBE 824.31/297.04 824.31/297.04 Empty strict component of the problem is NOT empty. 824.31/297.04 824.31/297.04 824.31/297.04 Arrrr.. 824.52/297.27 EOF