MAYBE 818.17/297.04 MAYBE 818.17/297.04 818.17/297.04 We are left with following problem, upon which TcT provides the 818.17/297.04 certificate MAYBE. 818.17/297.04 818.17/297.04 Strict Trs: 818.17/297.04 { eq(0(), 0()) -> true() 818.17/297.04 , eq(0(), s(x)) -> false() 818.17/297.04 , eq(s(x), 0()) -> false() 818.17/297.04 , eq(s(x), s(y)) -> eq(x, y) 818.17/297.04 , le(0(), y) -> true() 818.17/297.04 , le(s(x), 0()) -> false() 818.17/297.04 , le(s(x), s(y)) -> le(x, y) 818.17/297.04 , app(nil(), y) -> y 818.17/297.04 , app(add(n, x), y) -> add(n, app(x, y)) 818.17/297.04 , min(add(n, nil())) -> n 818.17/297.04 , min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x))) 818.17/297.04 , if_min(true(), add(n, add(m, x))) -> min(add(n, x)) 818.17/297.04 , if_min(false(), add(n, add(m, x))) -> min(add(m, x)) 818.17/297.04 , rm(n, nil()) -> nil() 818.17/297.04 , rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) 818.17/297.04 , if_rm(true(), n, add(m, x)) -> rm(n, x) 818.17/297.04 , if_rm(false(), n, add(m, x)) -> add(m, rm(n, x)) 818.17/297.04 , minsort(nil(), nil()) -> nil() 818.17/297.04 , minsort(add(n, x), y) -> 818.17/297.04 if_minsort(eq(n, min(add(n, x))), add(n, x), y) 818.17/297.04 , if_minsort(true(), add(n, x), y) -> 818.17/297.04 add(n, minsort(app(rm(n, x), y), nil())) 818.17/297.04 , if_minsort(false(), add(n, x), y) -> minsort(x, add(n, y)) } 818.17/297.04 Obligation: 818.17/297.04 runtime complexity 818.17/297.04 Answer: 818.17/297.04 MAYBE 818.17/297.04 818.17/297.04 None of the processors succeeded. 818.17/297.04 818.17/297.04 Details of failed attempt(s): 818.17/297.04 ----------------------------- 818.17/297.04 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 818.17/297.04 following reason: 818.17/297.04 818.17/297.04 Computation stopped due to timeout after 297.0 seconds. 818.17/297.04 818.17/297.04 2) 'Best' failed due to the following reason: 818.17/297.04 818.17/297.04 None of the processors succeeded. 818.17/297.04 818.17/297.04 Details of failed attempt(s): 818.17/297.04 ----------------------------- 818.17/297.04 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 818.17/297.04 seconds)' failed due to the following reason: 818.17/297.04 818.17/297.04 Computation stopped due to timeout after 148.0 seconds. 818.17/297.04 818.17/297.04 2) 'Best' failed due to the following reason: 818.17/297.04 818.17/297.04 None of the processors succeeded. 818.17/297.04 818.17/297.04 Details of failed attempt(s): 818.17/297.04 ----------------------------- 818.17/297.04 1) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 818.17/297.04 to the following reason: 818.17/297.04 818.17/297.04 The processor is inapplicable, reason: 818.17/297.04 Processor only applicable for innermost runtime complexity analysis 818.17/297.04 818.17/297.04 2) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 818.17/297.04 following reason: 818.17/297.04 818.17/297.04 The processor is inapplicable, reason: 818.17/297.04 Processor only applicable for innermost runtime complexity analysis 818.17/297.04 818.17/297.04 818.17/297.04 3) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 818.17/297.04 failed due to the following reason: 818.17/297.04 818.17/297.04 None of the processors succeeded. 818.17/297.04 818.17/297.04 Details of failed attempt(s): 818.17/297.04 ----------------------------- 818.17/297.04 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 818.17/297.04 failed due to the following reason: 818.17/297.04 818.17/297.04 match-boundness of the problem could not be verified. 818.17/297.04 818.17/297.04 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 818.17/297.04 failed due to the following reason: 818.17/297.04 818.17/297.04 match-boundness of the problem could not be verified. 818.17/297.04 818.17/297.04 818.17/297.04 818.17/297.04 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 818.17/297.04 the following reason: 818.17/297.04 818.17/297.04 We add the following weak dependency pairs: 818.17/297.04 818.17/297.04 Strict DPs: 818.17/297.04 { eq^#(0(), 0()) -> c_1() 818.17/297.04 , eq^#(0(), s(x)) -> c_2() 818.17/297.04 , eq^#(s(x), 0()) -> c_3() 818.17/297.04 , eq^#(s(x), s(y)) -> c_4(eq^#(x, y)) 818.17/297.04 , le^#(0(), y) -> c_5() 818.17/297.04 , le^#(s(x), 0()) -> c_6() 818.17/297.04 , le^#(s(x), s(y)) -> c_7(le^#(x, y)) 818.17/297.04 , app^#(nil(), y) -> c_8(y) 818.17/297.04 , app^#(add(n, x), y) -> c_9(n, app^#(x, y)) 818.17/297.04 , min^#(add(n, nil())) -> c_10(n) 818.17/297.04 , min^#(add(n, add(m, x))) -> 818.17/297.04 c_11(if_min^#(le(n, m), add(n, add(m, x)))) 818.17/297.04 , if_min^#(true(), add(n, add(m, x))) -> c_12(min^#(add(n, x))) 818.17/297.04 , if_min^#(false(), add(n, add(m, x))) -> c_13(min^#(add(m, x))) 818.17/297.04 , rm^#(n, nil()) -> c_14() 818.17/297.04 , rm^#(n, add(m, x)) -> c_15(if_rm^#(eq(n, m), n, add(m, x))) 818.17/297.04 , if_rm^#(true(), n, add(m, x)) -> c_16(rm^#(n, x)) 818.17/297.04 , if_rm^#(false(), n, add(m, x)) -> c_17(m, rm^#(n, x)) 818.17/297.04 , minsort^#(nil(), nil()) -> c_18() 818.17/297.04 , minsort^#(add(n, x), y) -> 818.17/297.04 c_19(if_minsort^#(eq(n, min(add(n, x))), add(n, x), y)) 818.17/297.04 , if_minsort^#(true(), add(n, x), y) -> 818.17/297.04 c_20(n, minsort^#(app(rm(n, x), y), nil())) 818.17/297.04 , if_minsort^#(false(), add(n, x), y) -> 818.17/297.04 c_21(minsort^#(x, add(n, y))) } 818.17/297.04 818.17/297.04 and mark the set of starting terms. 818.17/297.04 818.17/297.04 We are left with following problem, upon which TcT provides the 818.17/297.04 certificate MAYBE. 818.17/297.04 818.17/297.04 Strict DPs: 818.17/297.04 { eq^#(0(), 0()) -> c_1() 818.17/297.04 , eq^#(0(), s(x)) -> c_2() 818.17/297.04 , eq^#(s(x), 0()) -> c_3() 818.17/297.04 , eq^#(s(x), s(y)) -> c_4(eq^#(x, y)) 818.17/297.04 , le^#(0(), y) -> c_5() 818.17/297.04 , le^#(s(x), 0()) -> c_6() 818.17/297.04 , le^#(s(x), s(y)) -> c_7(le^#(x, y)) 818.17/297.04 , app^#(nil(), y) -> c_8(y) 818.17/297.04 , app^#(add(n, x), y) -> c_9(n, app^#(x, y)) 818.17/297.04 , min^#(add(n, nil())) -> c_10(n) 818.17/297.04 , min^#(add(n, add(m, x))) -> 818.17/297.04 c_11(if_min^#(le(n, m), add(n, add(m, x)))) 818.17/297.04 , if_min^#(true(), add(n, add(m, x))) -> c_12(min^#(add(n, x))) 818.17/297.04 , if_min^#(false(), add(n, add(m, x))) -> c_13(min^#(add(m, x))) 818.17/297.04 , rm^#(n, nil()) -> c_14() 818.17/297.04 , rm^#(n, add(m, x)) -> c_15(if_rm^#(eq(n, m), n, add(m, x))) 818.17/297.04 , if_rm^#(true(), n, add(m, x)) -> c_16(rm^#(n, x)) 818.17/297.04 , if_rm^#(false(), n, add(m, x)) -> c_17(m, rm^#(n, x)) 818.17/297.04 , minsort^#(nil(), nil()) -> c_18() 818.17/297.04 , minsort^#(add(n, x), y) -> 818.17/297.04 c_19(if_minsort^#(eq(n, min(add(n, x))), add(n, x), y)) 818.17/297.04 , if_minsort^#(true(), add(n, x), y) -> 818.17/297.04 c_20(n, minsort^#(app(rm(n, x), y), nil())) 818.17/297.04 , if_minsort^#(false(), add(n, x), y) -> 818.17/297.04 c_21(minsort^#(x, add(n, y))) } 818.17/297.04 Strict Trs: 818.17/297.04 { eq(0(), 0()) -> true() 818.17/297.04 , eq(0(), s(x)) -> false() 818.17/297.04 , eq(s(x), 0()) -> false() 818.17/297.04 , eq(s(x), s(y)) -> eq(x, y) 818.17/297.04 , le(0(), y) -> true() 818.17/297.04 , le(s(x), 0()) -> false() 818.17/297.04 , le(s(x), s(y)) -> le(x, y) 818.17/297.04 , app(nil(), y) -> y 818.17/297.04 , app(add(n, x), y) -> add(n, app(x, y)) 818.17/297.04 , min(add(n, nil())) -> n 818.17/297.04 , min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x))) 818.17/297.04 , if_min(true(), add(n, add(m, x))) -> min(add(n, x)) 818.17/297.04 , if_min(false(), add(n, add(m, x))) -> min(add(m, x)) 818.17/297.04 , rm(n, nil()) -> nil() 818.17/297.04 , rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) 818.17/297.04 , if_rm(true(), n, add(m, x)) -> rm(n, x) 818.17/297.04 , if_rm(false(), n, add(m, x)) -> add(m, rm(n, x)) 818.17/297.04 , minsort(nil(), nil()) -> nil() 818.17/297.04 , minsort(add(n, x), y) -> 818.17/297.04 if_minsort(eq(n, min(add(n, x))), add(n, x), y) 818.17/297.04 , if_minsort(true(), add(n, x), y) -> 818.17/297.04 add(n, minsort(app(rm(n, x), y), nil())) 818.17/297.04 , if_minsort(false(), add(n, x), y) -> minsort(x, add(n, y)) } 818.17/297.04 Obligation: 818.17/297.04 runtime complexity 818.17/297.04 Answer: 818.17/297.04 MAYBE 818.17/297.04 818.17/297.04 We estimate the number of application of {1,2,3,5,6,14,18} by 818.17/297.04 applications of Pre({1,2,3,5,6,14,18}) = {4,7,8,9,10,16,17,20}. 818.17/297.04 Here rules are labeled as follows: 818.17/297.04 818.17/297.04 DPs: 818.17/297.04 { 1: eq^#(0(), 0()) -> c_1() 818.17/297.04 , 2: eq^#(0(), s(x)) -> c_2() 818.17/297.04 , 3: eq^#(s(x), 0()) -> c_3() 818.17/297.04 , 4: eq^#(s(x), s(y)) -> c_4(eq^#(x, y)) 818.17/297.04 , 5: le^#(0(), y) -> c_5() 818.17/297.04 , 6: le^#(s(x), 0()) -> c_6() 818.17/297.04 , 7: le^#(s(x), s(y)) -> c_7(le^#(x, y)) 818.17/297.04 , 8: app^#(nil(), y) -> c_8(y) 818.17/297.04 , 9: app^#(add(n, x), y) -> c_9(n, app^#(x, y)) 818.17/297.04 , 10: min^#(add(n, nil())) -> c_10(n) 818.17/297.04 , 11: min^#(add(n, add(m, x))) -> 818.17/297.04 c_11(if_min^#(le(n, m), add(n, add(m, x)))) 818.17/297.04 , 12: if_min^#(true(), add(n, add(m, x))) -> c_12(min^#(add(n, x))) 818.17/297.04 , 13: if_min^#(false(), add(n, add(m, x))) -> 818.17/297.04 c_13(min^#(add(m, x))) 818.17/297.04 , 14: rm^#(n, nil()) -> c_14() 818.17/297.04 , 15: rm^#(n, add(m, x)) -> c_15(if_rm^#(eq(n, m), n, add(m, x))) 818.17/297.04 , 16: if_rm^#(true(), n, add(m, x)) -> c_16(rm^#(n, x)) 818.17/297.04 , 17: if_rm^#(false(), n, add(m, x)) -> c_17(m, rm^#(n, x)) 818.17/297.04 , 18: minsort^#(nil(), nil()) -> c_18() 818.17/297.04 , 19: minsort^#(add(n, x), y) -> 818.17/297.04 c_19(if_minsort^#(eq(n, min(add(n, x))), add(n, x), y)) 818.17/297.04 , 20: if_minsort^#(true(), add(n, x), y) -> 818.17/297.04 c_20(n, minsort^#(app(rm(n, x), y), nil())) 818.17/297.04 , 21: if_minsort^#(false(), add(n, x), y) -> 818.17/297.04 c_21(minsort^#(x, add(n, y))) } 818.17/297.04 818.17/297.04 We are left with following problem, upon which TcT provides the 818.17/297.04 certificate MAYBE. 818.17/297.04 818.17/297.04 Strict DPs: 818.17/297.04 { eq^#(s(x), s(y)) -> c_4(eq^#(x, y)) 818.17/297.04 , le^#(s(x), s(y)) -> c_7(le^#(x, y)) 818.17/297.04 , app^#(nil(), y) -> c_8(y) 818.17/297.04 , app^#(add(n, x), y) -> c_9(n, app^#(x, y)) 818.17/297.04 , min^#(add(n, nil())) -> c_10(n) 818.17/297.04 , min^#(add(n, add(m, x))) -> 818.17/297.04 c_11(if_min^#(le(n, m), add(n, add(m, x)))) 818.17/297.04 , if_min^#(true(), add(n, add(m, x))) -> c_12(min^#(add(n, x))) 818.17/297.04 , if_min^#(false(), add(n, add(m, x))) -> c_13(min^#(add(m, x))) 818.17/297.04 , rm^#(n, add(m, x)) -> c_15(if_rm^#(eq(n, m), n, add(m, x))) 818.17/297.04 , if_rm^#(true(), n, add(m, x)) -> c_16(rm^#(n, x)) 818.17/297.04 , if_rm^#(false(), n, add(m, x)) -> c_17(m, rm^#(n, x)) 818.17/297.04 , minsort^#(add(n, x), y) -> 818.17/297.04 c_19(if_minsort^#(eq(n, min(add(n, x))), add(n, x), y)) 818.17/297.04 , if_minsort^#(true(), add(n, x), y) -> 818.17/297.04 c_20(n, minsort^#(app(rm(n, x), y), nil())) 818.17/297.04 , if_minsort^#(false(), add(n, x), y) -> 818.17/297.04 c_21(minsort^#(x, add(n, y))) } 818.17/297.04 Strict Trs: 818.17/297.04 { eq(0(), 0()) -> true() 818.17/297.04 , eq(0(), s(x)) -> false() 818.17/297.04 , eq(s(x), 0()) -> false() 818.17/297.04 , eq(s(x), s(y)) -> eq(x, y) 818.17/297.04 , le(0(), y) -> true() 818.17/297.04 , le(s(x), 0()) -> false() 818.17/297.04 , le(s(x), s(y)) -> le(x, y) 818.17/297.04 , app(nil(), y) -> y 818.17/297.04 , app(add(n, x), y) -> add(n, app(x, y)) 818.17/297.04 , min(add(n, nil())) -> n 818.17/297.04 , min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x))) 818.17/297.04 , if_min(true(), add(n, add(m, x))) -> min(add(n, x)) 818.17/297.04 , if_min(false(), add(n, add(m, x))) -> min(add(m, x)) 818.17/297.04 , rm(n, nil()) -> nil() 818.17/297.04 , rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) 818.17/297.04 , if_rm(true(), n, add(m, x)) -> rm(n, x) 818.17/297.04 , if_rm(false(), n, add(m, x)) -> add(m, rm(n, x)) 818.17/297.04 , minsort(nil(), nil()) -> nil() 818.17/297.04 , minsort(add(n, x), y) -> 818.17/297.04 if_minsort(eq(n, min(add(n, x))), add(n, x), y) 818.17/297.04 , if_minsort(true(), add(n, x), y) -> 818.17/297.04 add(n, minsort(app(rm(n, x), y), nil())) 818.17/297.04 , if_minsort(false(), add(n, x), y) -> minsort(x, add(n, y)) } 818.17/297.04 Weak DPs: 818.17/297.04 { eq^#(0(), 0()) -> c_1() 818.17/297.04 , eq^#(0(), s(x)) -> c_2() 818.17/297.04 , eq^#(s(x), 0()) -> c_3() 818.17/297.04 , le^#(0(), y) -> c_5() 818.17/297.04 , le^#(s(x), 0()) -> c_6() 818.17/297.04 , rm^#(n, nil()) -> c_14() 818.17/297.04 , minsort^#(nil(), nil()) -> c_18() } 818.17/297.04 Obligation: 818.17/297.04 runtime complexity 818.17/297.04 Answer: 818.17/297.04 MAYBE 818.17/297.04 818.17/297.04 Empty strict component of the problem is NOT empty. 818.17/297.04 818.17/297.04 818.17/297.04 Arrrr.. 818.41/297.21 EOF