MAYBE 833.66/297.03 MAYBE 833.66/297.03 833.66/297.03 We are left with following problem, upon which TcT provides the 833.66/297.03 certificate MAYBE. 833.66/297.03 833.66/297.03 Strict Trs: 833.66/297.03 { eq(0(), 0()) -> true() 833.66/297.03 , eq(0(), s(x)) -> false() 833.66/297.03 , eq(s(x), 0()) -> false() 833.66/297.03 , eq(s(x), s(y)) -> eq(x, y) 833.66/297.03 , or(true(), y) -> true() 833.66/297.03 , or(false(), y) -> y 833.66/297.03 , union(empty(), h) -> h 833.66/297.03 , union(edge(x, y, i), h) -> edge(x, y, union(i, h)) 833.66/297.03 , isEmpty(empty()) -> true() 833.66/297.03 , isEmpty(edge(x, y, i)) -> false() 833.66/297.03 , from(edge(x, y, i)) -> x 833.66/297.03 , to(edge(x, y, i)) -> y 833.66/297.03 , rest(empty()) -> empty() 833.66/297.03 , rest(edge(x, y, i)) -> i 833.66/297.03 , reach(x, y, i, h) -> 833.66/297.03 if1(eq(x, y), isEmpty(i), eq(x, from(i)), eq(y, to(i)), x, y, i, h) 833.66/297.03 , if1(true(), b1, b2, b3, x, y, i, h) -> true() 833.66/297.03 , if1(false(), b1, b2, b3, x, y, i, h) -> 833.66/297.03 if2(b1, b2, b3, x, y, i, h) 833.66/297.03 , if2(true(), b2, b3, x, y, i, h) -> false() 833.66/297.03 , if2(false(), b2, b3, x, y, i, h) -> if3(b2, b3, x, y, i, h) 833.66/297.03 , if3(true(), b3, x, y, i, h) -> if4(b3, x, y, i, h) 833.66/297.03 , if3(false(), b3, x, y, i, h) -> 833.66/297.03 reach(x, y, rest(i), edge(from(i), to(i), h)) 833.66/297.03 , if4(true(), x, y, i, h) -> true() 833.66/297.03 , if4(false(), x, y, i, h) -> 833.66/297.03 or(reach(x, y, rest(i), h), 833.66/297.03 reach(to(i), y, union(rest(i), h), empty())) } 833.66/297.03 Obligation: 833.66/297.03 runtime complexity 833.66/297.03 Answer: 833.66/297.03 MAYBE 833.66/297.03 833.66/297.03 None of the processors succeeded. 833.66/297.03 833.66/297.03 Details of failed attempt(s): 833.66/297.03 ----------------------------- 833.66/297.03 1) 'With Problem ... (timeout of 297 seconds)' failed due to the 833.66/297.03 following reason: 833.66/297.03 833.66/297.03 Computation stopped due to timeout after 297.0 seconds. 833.66/297.03 833.66/297.03 2) 'Best' failed due to the following reason: 833.66/297.03 833.66/297.03 None of the processors succeeded. 833.66/297.03 833.66/297.03 Details of failed attempt(s): 833.66/297.03 ----------------------------- 833.66/297.03 1) 'With Problem ... (timeout of 148 seconds) (timeout of 297 833.66/297.03 seconds)' failed due to the following reason: 833.66/297.03 833.66/297.03 Computation stopped due to timeout after 148.0 seconds. 833.66/297.03 833.66/297.03 2) 'Fastest (timeout of 24 seconds) (timeout of 297 seconds)' 833.66/297.03 failed due to the following reason: 833.66/297.03 833.66/297.03 None of the processors succeeded. 833.66/297.03 833.66/297.03 Details of failed attempt(s): 833.66/297.03 ----------------------------- 833.66/297.03 1) 'Bounds with minimal-enrichment and initial automaton 'match'' 833.66/297.03 failed due to the following reason: 833.66/297.03 833.66/297.03 match-boundness of the problem could not be verified. 833.66/297.03 833.66/297.03 2) 'Bounds with perSymbol-enrichment and initial automaton 'match'' 833.66/297.03 failed due to the following reason: 833.66/297.03 833.66/297.03 match-boundness of the problem could not be verified. 833.66/297.03 833.66/297.03 833.66/297.03 3) 'Best' failed due to the following reason: 833.66/297.03 833.66/297.03 None of the processors succeeded. 833.66/297.03 833.66/297.03 Details of failed attempt(s): 833.66/297.03 ----------------------------- 833.66/297.03 1) 'bsearch-popstar (timeout of 297 seconds)' failed due to the 833.66/297.03 following reason: 833.66/297.03 833.66/297.03 The processor is inapplicable, reason: 833.66/297.03 Processor only applicable for innermost runtime complexity analysis 833.66/297.03 833.66/297.03 2) 'Polynomial Path Order (PS) (timeout of 297 seconds)' failed due 833.66/297.03 to the following reason: 833.66/297.03 833.66/297.03 The processor is inapplicable, reason: 833.66/297.03 Processor only applicable for innermost runtime complexity analysis 833.66/297.03 833.66/297.03 833.66/297.03 833.66/297.03 3) 'Weak Dependency Pairs (timeout of 297 seconds)' failed due to 833.66/297.03 the following reason: 833.66/297.03 833.66/297.03 We add the following weak dependency pairs: 833.66/297.03 833.66/297.03 Strict DPs: 833.66/297.03 { eq^#(0(), 0()) -> c_1() 833.66/297.03 , eq^#(0(), s(x)) -> c_2() 833.66/297.03 , eq^#(s(x), 0()) -> c_3() 833.66/297.03 , eq^#(s(x), s(y)) -> c_4(eq^#(x, y)) 833.66/297.03 , or^#(true(), y) -> c_5() 833.66/297.03 , or^#(false(), y) -> c_6(y) 833.66/297.03 , union^#(empty(), h) -> c_7(h) 833.66/297.03 , union^#(edge(x, y, i), h) -> c_8(x, y, union^#(i, h)) 833.66/297.03 , isEmpty^#(empty()) -> c_9() 833.66/297.03 , isEmpty^#(edge(x, y, i)) -> c_10() 833.66/297.03 , from^#(edge(x, y, i)) -> c_11(x) 833.66/297.03 , to^#(edge(x, y, i)) -> c_12(y) 833.66/297.03 , rest^#(empty()) -> c_13() 833.66/297.03 , rest^#(edge(x, y, i)) -> c_14(i) 833.66/297.03 , reach^#(x, y, i, h) -> 833.66/297.03 c_15(if1^#(eq(x, y), 833.66/297.03 isEmpty(i), 833.66/297.03 eq(x, from(i)), 833.66/297.03 eq(y, to(i)), 833.66/297.03 x, 833.66/297.03 y, 833.66/297.03 i, 833.66/297.03 h)) 833.66/297.03 , if1^#(true(), b1, b2, b3, x, y, i, h) -> c_16() 833.66/297.03 , if1^#(false(), b1, b2, b3, x, y, i, h) -> 833.66/297.03 c_17(if2^#(b1, b2, b3, x, y, i, h)) 833.66/297.03 , if2^#(true(), b2, b3, x, y, i, h) -> c_18() 833.66/297.03 , if2^#(false(), b2, b3, x, y, i, h) -> 833.66/297.03 c_19(if3^#(b2, b3, x, y, i, h)) 833.66/297.03 , if3^#(true(), b3, x, y, i, h) -> c_20(if4^#(b3, x, y, i, h)) 833.66/297.03 , if3^#(false(), b3, x, y, i, h) -> 833.66/297.03 c_21(reach^#(x, y, rest(i), edge(from(i), to(i), h))) 833.66/297.03 , if4^#(true(), x, y, i, h) -> c_22() 833.66/297.03 , if4^#(false(), x, y, i, h) -> 833.66/297.03 c_23(or^#(reach(x, y, rest(i), h), 833.66/297.03 reach(to(i), y, union(rest(i), h), empty()))) } 833.66/297.03 833.66/297.03 and mark the set of starting terms. 833.66/297.03 833.66/297.03 We are left with following problem, upon which TcT provides the 833.66/297.03 certificate MAYBE. 833.66/297.03 833.66/297.03 Strict DPs: 833.66/297.03 { eq^#(0(), 0()) -> c_1() 833.66/297.03 , eq^#(0(), s(x)) -> c_2() 833.66/297.03 , eq^#(s(x), 0()) -> c_3() 833.66/297.03 , eq^#(s(x), s(y)) -> c_4(eq^#(x, y)) 833.66/297.03 , or^#(true(), y) -> c_5() 833.66/297.03 , or^#(false(), y) -> c_6(y) 833.66/297.03 , union^#(empty(), h) -> c_7(h) 833.66/297.03 , union^#(edge(x, y, i), h) -> c_8(x, y, union^#(i, h)) 833.66/297.03 , isEmpty^#(empty()) -> c_9() 833.66/297.03 , isEmpty^#(edge(x, y, i)) -> c_10() 833.66/297.03 , from^#(edge(x, y, i)) -> c_11(x) 833.66/297.03 , to^#(edge(x, y, i)) -> c_12(y) 833.66/297.03 , rest^#(empty()) -> c_13() 833.66/297.03 , rest^#(edge(x, y, i)) -> c_14(i) 833.66/297.03 , reach^#(x, y, i, h) -> 833.66/297.03 c_15(if1^#(eq(x, y), 833.66/297.03 isEmpty(i), 833.66/297.03 eq(x, from(i)), 833.66/297.03 eq(y, to(i)), 833.66/297.03 x, 833.66/297.03 y, 833.66/297.03 i, 833.66/297.03 h)) 833.66/297.03 , if1^#(true(), b1, b2, b3, x, y, i, h) -> c_16() 833.66/297.03 , if1^#(false(), b1, b2, b3, x, y, i, h) -> 833.66/297.03 c_17(if2^#(b1, b2, b3, x, y, i, h)) 833.66/297.03 , if2^#(true(), b2, b3, x, y, i, h) -> c_18() 833.66/297.03 , if2^#(false(), b2, b3, x, y, i, h) -> 833.66/297.03 c_19(if3^#(b2, b3, x, y, i, h)) 833.66/297.03 , if3^#(true(), b3, x, y, i, h) -> c_20(if4^#(b3, x, y, i, h)) 833.66/297.03 , if3^#(false(), b3, x, y, i, h) -> 833.66/297.03 c_21(reach^#(x, y, rest(i), edge(from(i), to(i), h))) 833.66/297.03 , if4^#(true(), x, y, i, h) -> c_22() 833.66/297.03 , if4^#(false(), x, y, i, h) -> 833.66/297.03 c_23(or^#(reach(x, y, rest(i), h), 833.66/297.03 reach(to(i), y, union(rest(i), h), empty()))) } 833.66/297.03 Strict Trs: 833.66/297.03 { eq(0(), 0()) -> true() 833.66/297.03 , eq(0(), s(x)) -> false() 833.66/297.03 , eq(s(x), 0()) -> false() 833.66/297.03 , eq(s(x), s(y)) -> eq(x, y) 833.66/297.03 , or(true(), y) -> true() 833.66/297.03 , or(false(), y) -> y 833.66/297.03 , union(empty(), h) -> h 833.66/297.03 , union(edge(x, y, i), h) -> edge(x, y, union(i, h)) 833.66/297.03 , isEmpty(empty()) -> true() 833.66/297.03 , isEmpty(edge(x, y, i)) -> false() 833.66/297.03 , from(edge(x, y, i)) -> x 833.66/297.03 , to(edge(x, y, i)) -> y 833.66/297.03 , rest(empty()) -> empty() 833.66/297.03 , rest(edge(x, y, i)) -> i 833.66/297.03 , reach(x, y, i, h) -> 833.66/297.03 if1(eq(x, y), isEmpty(i), eq(x, from(i)), eq(y, to(i)), x, y, i, h) 833.66/297.03 , if1(true(), b1, b2, b3, x, y, i, h) -> true() 833.66/297.03 , if1(false(), b1, b2, b3, x, y, i, h) -> 833.66/297.03 if2(b1, b2, b3, x, y, i, h) 833.66/297.03 , if2(true(), b2, b3, x, y, i, h) -> false() 833.66/297.03 , if2(false(), b2, b3, x, y, i, h) -> if3(b2, b3, x, y, i, h) 833.66/297.03 , if3(true(), b3, x, y, i, h) -> if4(b3, x, y, i, h) 833.66/297.03 , if3(false(), b3, x, y, i, h) -> 833.66/297.03 reach(x, y, rest(i), edge(from(i), to(i), h)) 833.66/297.03 , if4(true(), x, y, i, h) -> true() 833.66/297.03 , if4(false(), x, y, i, h) -> 833.66/297.03 or(reach(x, y, rest(i), h), 833.66/297.03 reach(to(i), y, union(rest(i), h), empty())) } 833.66/297.03 Obligation: 833.66/297.03 runtime complexity 833.66/297.03 Answer: 833.66/297.03 MAYBE 833.66/297.03 833.66/297.03 We estimate the number of application of {1,2,3,5,9,10,13,16,18,22} 833.66/297.03 by applications of Pre({1,2,3,5,9,10,13,16,18,22}) = 833.66/297.03 {4,6,7,8,11,12,14,15,17,20,23}. Here rules are labeled as follows: 833.66/297.03 833.66/297.03 DPs: 833.66/297.03 { 1: eq^#(0(), 0()) -> c_1() 833.66/297.03 , 2: eq^#(0(), s(x)) -> c_2() 833.66/297.03 , 3: eq^#(s(x), 0()) -> c_3() 833.66/297.03 , 4: eq^#(s(x), s(y)) -> c_4(eq^#(x, y)) 833.66/297.03 , 5: or^#(true(), y) -> c_5() 833.66/297.03 , 6: or^#(false(), y) -> c_6(y) 833.66/297.03 , 7: union^#(empty(), h) -> c_7(h) 833.66/297.03 , 8: union^#(edge(x, y, i), h) -> c_8(x, y, union^#(i, h)) 833.66/297.03 , 9: isEmpty^#(empty()) -> c_9() 833.66/297.03 , 10: isEmpty^#(edge(x, y, i)) -> c_10() 833.66/297.03 , 11: from^#(edge(x, y, i)) -> c_11(x) 833.66/297.03 , 12: to^#(edge(x, y, i)) -> c_12(y) 833.66/297.03 , 13: rest^#(empty()) -> c_13() 833.66/297.03 , 14: rest^#(edge(x, y, i)) -> c_14(i) 833.66/297.03 , 15: reach^#(x, y, i, h) -> 833.66/297.03 c_15(if1^#(eq(x, y), 833.66/297.03 isEmpty(i), 833.66/297.03 eq(x, from(i)), 833.66/297.03 eq(y, to(i)), 833.66/297.03 x, 833.66/297.03 y, 833.66/297.03 i, 833.66/297.03 h)) 833.66/297.03 , 16: if1^#(true(), b1, b2, b3, x, y, i, h) -> c_16() 833.66/297.03 , 17: if1^#(false(), b1, b2, b3, x, y, i, h) -> 833.66/297.03 c_17(if2^#(b1, b2, b3, x, y, i, h)) 833.66/297.03 , 18: if2^#(true(), b2, b3, x, y, i, h) -> c_18() 833.66/297.03 , 19: if2^#(false(), b2, b3, x, y, i, h) -> 833.66/297.03 c_19(if3^#(b2, b3, x, y, i, h)) 833.66/297.03 , 20: if3^#(true(), b3, x, y, i, h) -> c_20(if4^#(b3, x, y, i, h)) 833.66/297.03 , 21: if3^#(false(), b3, x, y, i, h) -> 833.66/297.03 c_21(reach^#(x, y, rest(i), edge(from(i), to(i), h))) 833.66/297.03 , 22: if4^#(true(), x, y, i, h) -> c_22() 833.66/297.03 , 23: if4^#(false(), x, y, i, h) -> 833.66/297.03 c_23(or^#(reach(x, y, rest(i), h), 833.66/297.03 reach(to(i), y, union(rest(i), h), empty()))) } 833.66/297.03 833.66/297.03 We are left with following problem, upon which TcT provides the 833.66/297.03 certificate MAYBE. 833.66/297.03 833.66/297.03 Strict DPs: 833.66/297.03 { eq^#(s(x), s(y)) -> c_4(eq^#(x, y)) 833.66/297.03 , or^#(false(), y) -> c_6(y) 833.66/297.03 , union^#(empty(), h) -> c_7(h) 833.66/297.03 , union^#(edge(x, y, i), h) -> c_8(x, y, union^#(i, h)) 833.66/297.03 , from^#(edge(x, y, i)) -> c_11(x) 833.66/297.03 , to^#(edge(x, y, i)) -> c_12(y) 833.66/297.03 , rest^#(edge(x, y, i)) -> c_14(i) 833.66/297.03 , reach^#(x, y, i, h) -> 833.66/297.03 c_15(if1^#(eq(x, y), 833.66/297.03 isEmpty(i), 833.66/297.03 eq(x, from(i)), 833.66/297.03 eq(y, to(i)), 833.66/297.03 x, 833.66/297.03 y, 833.66/297.03 i, 833.66/297.03 h)) 833.66/297.03 , if1^#(false(), b1, b2, b3, x, y, i, h) -> 833.66/297.03 c_17(if2^#(b1, b2, b3, x, y, i, h)) 833.66/297.03 , if2^#(false(), b2, b3, x, y, i, h) -> 833.66/297.03 c_19(if3^#(b2, b3, x, y, i, h)) 833.66/297.03 , if3^#(true(), b3, x, y, i, h) -> c_20(if4^#(b3, x, y, i, h)) 833.66/297.03 , if3^#(false(), b3, x, y, i, h) -> 833.66/297.03 c_21(reach^#(x, y, rest(i), edge(from(i), to(i), h))) 833.66/297.03 , if4^#(false(), x, y, i, h) -> 833.66/297.03 c_23(or^#(reach(x, y, rest(i), h), 833.66/297.03 reach(to(i), y, union(rest(i), h), empty()))) } 833.66/297.03 Strict Trs: 833.66/297.03 { eq(0(), 0()) -> true() 833.66/297.03 , eq(0(), s(x)) -> false() 833.66/297.03 , eq(s(x), 0()) -> false() 833.66/297.03 , eq(s(x), s(y)) -> eq(x, y) 833.66/297.03 , or(true(), y) -> true() 833.66/297.03 , or(false(), y) -> y 833.66/297.03 , union(empty(), h) -> h 833.66/297.03 , union(edge(x, y, i), h) -> edge(x, y, union(i, h)) 833.66/297.03 , isEmpty(empty()) -> true() 833.66/297.03 , isEmpty(edge(x, y, i)) -> false() 833.66/297.03 , from(edge(x, y, i)) -> x 833.66/297.03 , to(edge(x, y, i)) -> y 833.66/297.03 , rest(empty()) -> empty() 833.66/297.03 , rest(edge(x, y, i)) -> i 833.66/297.03 , reach(x, y, i, h) -> 833.66/297.03 if1(eq(x, y), isEmpty(i), eq(x, from(i)), eq(y, to(i)), x, y, i, h) 833.66/297.03 , if1(true(), b1, b2, b3, x, y, i, h) -> true() 833.66/297.03 , if1(false(), b1, b2, b3, x, y, i, h) -> 833.66/297.03 if2(b1, b2, b3, x, y, i, h) 833.66/297.03 , if2(true(), b2, b3, x, y, i, h) -> false() 833.66/297.03 , if2(false(), b2, b3, x, y, i, h) -> if3(b2, b3, x, y, i, h) 833.66/297.03 , if3(true(), b3, x, y, i, h) -> if4(b3, x, y, i, h) 833.66/297.03 , if3(false(), b3, x, y, i, h) -> 833.66/297.03 reach(x, y, rest(i), edge(from(i), to(i), h)) 833.66/297.03 , if4(true(), x, y, i, h) -> true() 833.66/297.03 , if4(false(), x, y, i, h) -> 833.66/297.03 or(reach(x, y, rest(i), h), 833.66/297.03 reach(to(i), y, union(rest(i), h), empty())) } 833.66/297.03 Weak DPs: 833.66/297.03 { eq^#(0(), 0()) -> c_1() 833.66/297.03 , eq^#(0(), s(x)) -> c_2() 833.66/297.03 , eq^#(s(x), 0()) -> c_3() 833.66/297.03 , or^#(true(), y) -> c_5() 833.66/297.03 , isEmpty^#(empty()) -> c_9() 833.66/297.03 , isEmpty^#(edge(x, y, i)) -> c_10() 833.66/297.03 , rest^#(empty()) -> c_13() 833.66/297.03 , if1^#(true(), b1, b2, b3, x, y, i, h) -> c_16() 833.66/297.03 , if2^#(true(), b2, b3, x, y, i, h) -> c_18() 833.66/297.03 , if4^#(true(), x, y, i, h) -> c_22() } 833.66/297.03 Obligation: 833.66/297.03 runtime complexity 833.66/297.03 Answer: 833.66/297.03 MAYBE 833.66/297.03 833.66/297.03 Empty strict component of the problem is NOT empty. 833.66/297.03 833.66/297.03 833.66/297.03 Arrrr.. 833.79/297.19 EOF