*** 1 Progress [(O(1),O(n^1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: append(@l1,@l2) -> append#1(@l1,@l2) append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2)) append#1(nil(),@l2) -> @l2 appendAll(@l) -> appendAll#1(@l) appendAll#1(::(@l1,@ls)) -> append(@l1,appendAll(@ls)) appendAll#1(nil()) -> nil() appendAll2(@l) -> appendAll2#1(@l) appendAll2#1(::(@l1,@ls)) -> append(appendAll(@l1),appendAll2(@ls)) appendAll2#1(nil()) -> nil() appendAll3(@l) -> appendAll3#1(@l) appendAll3#1(::(@l1,@ls)) -> append(appendAll2(@l1),appendAll3(@ls)) appendAll3#1(nil()) -> nil() Weak DP Rules: Weak TRS Rules: Signature: {append/2,append#1/2,appendAll/1,appendAll#1/1,appendAll2/1,appendAll2#1/1,appendAll3/1,appendAll3#1/1} / {::/2,nil/0} Obligation: Innermost basic terms: {append,append#1,appendAll,appendAll#1,appendAll2,appendAll2#1,appendAll3,appendAll3#1}/{::,nil} Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} Proof: The problem is match-bounded by 4. The enriched problem is compatible with follwoing automaton. ::_0(2,2) -> 1 ::_0(2,2) -> 2 ::_0(2,2) -> 3 ::_1(2,1) -> 1 ::_1(2,3) -> 1 ::_1(2,3) -> 3 ::_1(2,4) -> 1 ::_1(2,4) -> 4 ::_2(2,7) -> 1 ::_2(2,7) -> 5 ::_2(2,7) -> 7 ::_3(2,8) -> 1 ::_3(2,8) -> 6 ::_3(2,8) -> 8 append_0(2,2) -> 1 append_1(2,2) -> 3 append_1(2,4) -> 1 append_1(2,4) -> 4 append_1(4,5) -> 1 append_1(4,5) -> 5 append_1(4,5) -> 7 append_1(5,6) -> 1 append_1(5,6) -> 6 append_1(5,6) -> 8 append_2(4,5) -> 7 append_3(7,6) -> 8 append#1_0(2,2) -> 1 append#1_1(2,2) -> 1 append#1_2(2,2) -> 3 append#1_2(2,4) -> 1 append#1_2(2,4) -> 4 append#1_2(4,5) -> 1 append#1_2(4,5) -> 5 append#1_2(4,5) -> 7 append#1_2(5,6) -> 1 append#1_2(5,6) -> 6 append#1_2(5,6) -> 8 append#1_3(4,5) -> 7 append#1_4(7,6) -> 8 appendAll_0(2) -> 1 appendAll_1(2) -> 1 appendAll_1(2) -> 4 appendAll#1_0(2) -> 1 appendAll#1_1(2) -> 1 appendAll#1_2(2) -> 1 appendAll#1_2(2) -> 4 appendAll2_0(2) -> 1 appendAll2_1(2) -> 1 appendAll2_1(2) -> 5 appendAll2_1(2) -> 7 appendAll2#1_0(2) -> 1 appendAll2#1_1(2) -> 1 appendAll2#1_2(2) -> 1 appendAll2#1_2(2) -> 5 appendAll2#1_2(2) -> 7 appendAll3_0(2) -> 1 appendAll3_1(2) -> 1 appendAll3_1(2) -> 6 appendAll3_1(2) -> 8 appendAll3#1_0(2) -> 1 appendAll3#1_1(2) -> 1 appendAll3#1_2(2) -> 1 appendAll3#1_2(2) -> 6 appendAll3#1_2(2) -> 8 nil_0() -> 1 nil_0() -> 2 nil_0() -> 3 nil_1() -> 1 nil_1() -> 4 nil_1() -> 5 nil_1() -> 6 nil_1() -> 7 nil_1() -> 8 2 -> 1 2 -> 3 4 -> 1 5 -> 1 5 -> 7 6 -> 1 6 -> 8 *** 1.1 Progress [(O(1),O(1))] *** Considered Problem: Strict DP Rules: Strict TRS Rules: Weak DP Rules: Weak TRS Rules: append(@l1,@l2) -> append#1(@l1,@l2) append#1(::(@x,@xs),@l2) -> ::(@x,append(@xs,@l2)) append#1(nil(),@l2) -> @l2 appendAll(@l) -> appendAll#1(@l) appendAll#1(::(@l1,@ls)) -> append(@l1,appendAll(@ls)) appendAll#1(nil()) -> nil() appendAll2(@l) -> appendAll2#1(@l) appendAll2#1(::(@l1,@ls)) -> append(appendAll(@l1),appendAll2(@ls)) appendAll2#1(nil()) -> nil() appendAll3(@l) -> appendAll3#1(@l) appendAll3#1(::(@l1,@ls)) -> append(appendAll2(@l1),appendAll3(@ls)) appendAll3#1(nil()) -> nil() Signature: {append/2,append#1/2,appendAll/1,appendAll#1/1,appendAll2/1,appendAll2#1/1,appendAll3/1,appendAll3#1/1} / {::/2,nil/0} Obligation: Innermost basic terms: {append,append#1,appendAll,appendAll#1,appendAll2,appendAll2#1,appendAll3,appendAll3#1}/{::,nil} Applied Processor: EmptyProcessor Proof: The problem is already closed. The intended complexity is O(1).