MAYBE 540.13/297.12 MAYBE 540.13/297.12 540.13/297.12 We are left with following problem, upon which TcT provides the 540.13/297.12 certificate MAYBE. 540.13/297.12 540.13/297.12 Strict Trs: 540.13/297.12 { le(0(), y) -> true() 540.13/297.12 , le(s(x), 0()) -> false() 540.13/297.12 , le(s(x), s(y)) -> le(x, y) 540.13/297.12 , minus(x, 0()) -> x 540.13/297.12 , minus(0(), s(y)) -> 0() 540.13/297.12 , minus(s(x), s(y)) -> minus(x, y) 540.13/297.12 , plus(x, 0()) -> x 540.13/297.12 , plus(x, s(y)) -> s(plus(x, y)) 540.13/297.12 , mod(x, s(y)) -> help(x, s(y), 0()) 540.13/297.12 , mod(s(x), 0()) -> 0() 540.13/297.12 , help(x, s(y), c) -> if(le(c, x), x, s(y), c) 540.13/297.12 , if(true(), x, s(y), c) -> help(x, s(y), plus(c, s(y))) 540.13/297.12 , if(false(), x, s(y), c) -> minus(x, minus(c, s(y))) } 540.13/297.12 Obligation: 540.13/297.12 runtime complexity 540.13/297.12 Answer: 540.13/297.12 MAYBE 540.13/297.12 540.13/297.12 None of the processors succeeded. 540.13/297.12 540.13/297.12 Details of failed attempt(s): 540.13/297.12 ----------------------------- 540.13/297.12 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 540.13/297.12 following reason: 540.13/297.12 540.13/297.12 Computation stopped due to timeout after 297.0 seconds. 540.13/297.12 540.13/297.12 2) 'Best' failed due to the following reason: 540.13/297.12 540.13/297.12 None of the processors succeeded. 540.13/297.12 540.13/297.12 Details of failed attempt(s): 540.13/297.12 ----------------------------- 540.13/297.12 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 540.13/297.12 seconds)' failed due to the following reason: 540.13/297.12 540.13/297.12 None of the processors succeeded. 540.13/297.12 540.13/297.12 Details of failed attempt(s): 540.13/297.12 ----------------------------- 540.13/297.12 1) 'empty' failed due to the following reason: 540.13/297.12 540.13/297.12 Empty strict component of the problem is NOT empty. 540.13/297.12 540.13/297.12 2) 'With Problem ...' failed due to the following reason: 540.13/297.12 540.13/297.12 None of the processors succeeded. 540.13/297.12 540.13/297.12 Details of failed attempt(s): 540.13/297.12 ----------------------------- 540.13/297.12 1) 'empty' failed due to the following reason: 540.13/297.12 540.13/297.12 Empty strict component of the problem is NOT empty. 540.13/297.12 540.13/297.12 2) 'Fastest' failed due to the following reason: 540.13/297.12 540.13/297.12 None of the processors succeeded. 540.13/297.12 540.13/297.12 Details of failed attempt(s): 540.13/297.12 ----------------------------- 540.13/297.12 1) 'With Problem ...' failed due to the following reason: 540.13/297.12 540.13/297.12 None of the processors succeeded. 540.13/297.12 540.13/297.12 Details of failed attempt(s): 540.13/297.12 ----------------------------- 540.13/297.12 1) 'empty' failed due to the following reason: 540.13/297.12 540.13/297.12 Empty strict component of the problem is NOT empty. 540.13/297.12 540.13/297.12 2) 'With Problem ...' failed due to the following reason: 540.13/297.12 540.13/297.12 Empty strict component of the problem is NOT empty. 540.13/297.12 540.13/297.12 540.13/297.12 2) 'With Problem ...' failed due to the following reason: 540.13/297.12 540.13/297.12 None of the processors succeeded. 540.13/297.12 540.13/297.12 Details of failed attempt(s): 540.13/297.12 ----------------------------- 540.13/297.12 1) 'empty' failed due to the following reason: 540.13/297.12 540.13/297.12 Empty strict component of the problem is NOT empty. 540.13/297.12 540.13/297.12 2) 'With Problem ...' failed due to the following reason: 540.13/297.12 540.13/297.12 None of the processors succeeded. 540.13/297.12 540.13/297.12 Details of failed attempt(s): 540.13/297.12 ----------------------------- 540.13/297.12 1) 'empty' failed due to the following reason: 540.13/297.12 540.13/297.12 Empty strict component of the problem is NOT empty. 540.13/297.12 540.13/297.12 2) 'With Problem ...' failed due to the following reason: 540.13/297.12 540.13/297.12 None of the processors succeeded. 540.13/297.12 540.13/297.12 Details of failed attempt(s): 540.13/297.12 ----------------------------- 540.13/297.12 1) 'empty' failed due to the following reason: 540.13/297.12 540.13/297.12 Empty strict component of the problem is NOT empty. 540.13/297.12 540.13/297.12 2) 'With Problem ...' failed due to the following reason: 540.13/297.12 540.13/297.12 Empty strict component of the problem is NOT empty. 540.13/297.12 540.13/297.12 540.13/297.12 540.13/297.12 540.13/297.12 540.13/297.12 540.13/297.12 540.13/297.12 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 540.13/297.12 failed due to the following reason: 540.13/297.12 540.13/297.12 None of the processors succeeded. 540.13/297.12 540.13/297.12 Details of failed attempt(s): 540.13/297.12 ----------------------------- 540.13/297.12 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 540.13/297.12 failed due to the following reason: 540.13/297.12 540.13/297.12 match-boundness of the problem could not be verified. 540.13/297.12 540.13/297.12 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 540.13/297.12 failed due to the following reason: 540.13/297.12 540.13/297.12 match-boundness of the problem could not be verified. 540.13/297.12 540.13/297.12 540.13/297.12 3) 'Best' failed due to the following reason: 540.13/297.12 540.13/297.12 None of the processors succeeded. 540.13/297.12 540.13/297.12 Details of failed attempt(s): 540.13/297.12 ----------------------------- 540.13/297.12 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 540.13/297.12 following reason: 540.13/297.12 540.13/297.12 The processor is inapplicable, reason: 540.13/297.12 Processor only applicable for innermost runtime complexity analysis 540.13/297.12 540.13/297.12 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 540.13/297.12 to the following reason: 540.13/297.12 540.13/297.12 The processor is inapplicable, reason: 540.13/297.12 Processor only applicable for innermost runtime complexity analysis 540.13/297.12 540.13/297.12 540.13/297.12 540.13/297.12 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 540.13/297.12 the following reason: 540.13/297.12 540.13/297.12 We add the following weak dependency pairs: 540.13/297.12 540.13/297.12 Strict DPs: 540.13/297.12 { le^#(0(), y) -> c_1() 540.13/297.12 , le^#(s(x), 0()) -> c_2() 540.13/297.12 , le^#(s(x), s(y)) -> c_3(le^#(x, y)) 540.13/297.12 , minus^#(x, 0()) -> c_4(x) 540.13/297.12 , minus^#(0(), s(y)) -> c_5() 540.13/297.12 , minus^#(s(x), s(y)) -> c_6(minus^#(x, y)) 540.13/297.12 , plus^#(x, 0()) -> c_7(x) 540.13/297.12 , plus^#(x, s(y)) -> c_8(plus^#(x, y)) 540.13/297.12 , mod^#(x, s(y)) -> c_9(help^#(x, s(y), 0())) 540.13/297.12 , mod^#(s(x), 0()) -> c_10() 540.13/297.12 , help^#(x, s(y), c) -> c_11(if^#(le(c, x), x, s(y), c)) 540.13/297.12 , if^#(true(), x, s(y), c) -> c_12(help^#(x, s(y), plus(c, s(y)))) 540.13/297.12 , if^#(false(), x, s(y), c) -> c_13(minus^#(x, minus(c, s(y)))) } 540.13/297.12 540.13/297.12 and mark the set of starting terms. 540.13/297.12 540.13/297.12 We are left with following problem, upon which TcT provides the 540.13/297.12 certificate MAYBE. 540.13/297.12 540.13/297.12 Strict DPs: 540.13/297.12 { le^#(0(), y) -> c_1() 540.13/297.12 , le^#(s(x), 0()) -> c_2() 540.13/297.12 , le^#(s(x), s(y)) -> c_3(le^#(x, y)) 540.13/297.12 , minus^#(x, 0()) -> c_4(x) 540.13/297.12 , minus^#(0(), s(y)) -> c_5() 540.13/297.12 , minus^#(s(x), s(y)) -> c_6(minus^#(x, y)) 540.13/297.12 , plus^#(x, 0()) -> c_7(x) 540.13/297.12 , plus^#(x, s(y)) -> c_8(plus^#(x, y)) 540.13/297.12 , mod^#(x, s(y)) -> c_9(help^#(x, s(y), 0())) 540.13/297.12 , mod^#(s(x), 0()) -> c_10() 540.13/297.12 , help^#(x, s(y), c) -> c_11(if^#(le(c, x), x, s(y), c)) 540.13/297.12 , if^#(true(), x, s(y), c) -> c_12(help^#(x, s(y), plus(c, s(y)))) 540.13/297.12 , if^#(false(), x, s(y), c) -> c_13(minus^#(x, minus(c, s(y)))) } 540.13/297.12 Strict Trs: 540.13/297.12 { le(0(), y) -> true() 540.13/297.12 , le(s(x), 0()) -> false() 540.13/297.12 , le(s(x), s(y)) -> le(x, y) 540.13/297.12 , minus(x, 0()) -> x 540.13/297.12 , minus(0(), s(y)) -> 0() 540.13/297.12 , minus(s(x), s(y)) -> minus(x, y) 540.13/297.12 , plus(x, 0()) -> x 540.13/297.12 , plus(x, s(y)) -> s(plus(x, y)) 540.13/297.12 , mod(x, s(y)) -> help(x, s(y), 0()) 540.13/297.12 , mod(s(x), 0()) -> 0() 540.13/297.12 , help(x, s(y), c) -> if(le(c, x), x, s(y), c) 540.13/297.12 , if(true(), x, s(y), c) -> help(x, s(y), plus(c, s(y))) 540.13/297.12 , if(false(), x, s(y), c) -> minus(x, minus(c, s(y))) } 540.13/297.12 Obligation: 540.13/297.12 runtime complexity 540.13/297.12 Answer: 540.13/297.12 MAYBE 540.13/297.12 540.13/297.12 We estimate the number of application of {1,2,5,10} by applications 540.13/297.12 of Pre({1,2,5,10}) = {3,4,6,7,13}. Here rules are labeled as 540.13/297.12 follows: 540.13/297.12 540.13/297.12 DPs: 540.13/297.12 { 1: le^#(0(), y) -> c_1() 540.13/297.12 , 2: le^#(s(x), 0()) -> c_2() 540.13/297.12 , 3: le^#(s(x), s(y)) -> c_3(le^#(x, y)) 540.13/297.12 , 4: minus^#(x, 0()) -> c_4(x) 540.13/297.12 , 5: minus^#(0(), s(y)) -> c_5() 540.13/297.12 , 6: minus^#(s(x), s(y)) -> c_6(minus^#(x, y)) 540.13/297.12 , 7: plus^#(x, 0()) -> c_7(x) 540.13/297.12 , 8: plus^#(x, s(y)) -> c_8(plus^#(x, y)) 540.13/297.12 , 9: mod^#(x, s(y)) -> c_9(help^#(x, s(y), 0())) 540.13/297.12 , 10: mod^#(s(x), 0()) -> c_10() 540.13/297.12 , 11: help^#(x, s(y), c) -> c_11(if^#(le(c, x), x, s(y), c)) 540.13/297.12 , 12: if^#(true(), x, s(y), c) -> 540.13/297.12 c_12(help^#(x, s(y), plus(c, s(y)))) 540.13/297.12 , 13: if^#(false(), x, s(y), c) -> 540.13/297.12 c_13(minus^#(x, minus(c, s(y)))) } 540.13/297.12 540.13/297.12 We are left with following problem, upon which TcT provides the 540.13/297.12 certificate MAYBE. 540.13/297.12 540.13/297.12 Strict DPs: 540.13/297.12 { le^#(s(x), s(y)) -> c_3(le^#(x, y)) 540.13/297.12 , minus^#(x, 0()) -> c_4(x) 540.13/297.12 , minus^#(s(x), s(y)) -> c_6(minus^#(x, y)) 540.13/297.12 , plus^#(x, 0()) -> c_7(x) 540.13/297.12 , plus^#(x, s(y)) -> c_8(plus^#(x, y)) 540.13/297.12 , mod^#(x, s(y)) -> c_9(help^#(x, s(y), 0())) 540.13/297.12 , help^#(x, s(y), c) -> c_11(if^#(le(c, x), x, s(y), c)) 540.13/297.12 , if^#(true(), x, s(y), c) -> c_12(help^#(x, s(y), plus(c, s(y)))) 540.13/297.12 , if^#(false(), x, s(y), c) -> c_13(minus^#(x, minus(c, s(y)))) } 540.13/297.12 Strict Trs: 540.13/297.12 { le(0(), y) -> true() 540.13/297.12 , le(s(x), 0()) -> false() 540.13/297.12 , le(s(x), s(y)) -> le(x, y) 540.13/297.12 , minus(x, 0()) -> x 540.13/297.12 , minus(0(), s(y)) -> 0() 540.13/297.12 , minus(s(x), s(y)) -> minus(x, y) 540.13/297.12 , plus(x, 0()) -> x 540.13/297.12 , plus(x, s(y)) -> s(plus(x, y)) 540.13/297.12 , mod(x, s(y)) -> help(x, s(y), 0()) 540.13/297.12 , mod(s(x), 0()) -> 0() 540.13/297.12 , help(x, s(y), c) -> if(le(c, x), x, s(y), c) 540.13/297.12 , if(true(), x, s(y), c) -> help(x, s(y), plus(c, s(y))) 540.13/297.12 , if(false(), x, s(y), c) -> minus(x, minus(c, s(y))) } 540.13/297.12 Weak DPs: 540.13/297.12 { le^#(0(), y) -> c_1() 540.13/297.12 , le^#(s(x), 0()) -> c_2() 540.13/297.12 , minus^#(0(), s(y)) -> c_5() 540.13/297.12 , mod^#(s(x), 0()) -> c_10() } 540.13/297.12 Obligation: 540.13/297.12 runtime complexity 540.13/297.12 Answer: 540.13/297.12 MAYBE 540.13/297.12 540.13/297.12 Empty strict component of the problem is NOT empty. 540.13/297.12 540.13/297.12 540.13/297.12 Arrrr.. 540.33/297.39 EOF