MAYBE * Step 1: Failure MAYBE + Considered Problem: - Strict TRS: #less(@x,@y) -> #cklt(#compare(@x,@y)) merge(@l1,@l2) -> merge#1(@l1,@l2) merge#1(::(@x,@xs),@l2) -> merge#2(@l2,@x,@xs) merge#1(nil(),@l2) -> @l2 merge#2(::(@y,@ys),@x,@xs) -> merge#3(#less(@x,@y),@x,@xs,@y,@ys) merge#2(nil(),@x,@xs) -> ::(@x,@xs) merge#3(#false(),@x,@xs,@y,@ys) -> ::(@y,merge(::(@x,@xs),@ys)) merge#3(#true(),@x,@xs,@y,@ys) -> ::(@x,merge(@xs,::(@y,@ys))) mergesort(@l) -> mergesort#1(@l) mergesort#1(::(@x1,@xs)) -> mergesort#2(@xs,@x1) mergesort#1(nil()) -> nil() mergesort#2(::(@x2,@xs'),@x1) -> mergesort#3(msplit(::(@x1,::(@x2,@xs')))) mergesort#2(nil(),@x1) -> ::(@x1,nil()) mergesort#3(tuple#2(@l1,@l2)) -> merge(mergesort(@l1),mergesort(@l2)) msplit(@l) -> msplit#1(@l) msplit#1(::(@x1,@xs)) -> msplit#2(@xs,@x1) msplit#1(nil()) -> tuple#2(nil(),nil()) msplit#2(::(@x2,@xs'),@x1) -> msplit#3(msplit(@xs'),@x1,@x2) msplit#2(nil(),@x1) -> tuple#2(::(@x1,nil()),nil()) msplit#3(tuple#2(@l1,@l2),@x1,@x2) -> tuple#2(::(@x1,@l1),::(@x2,@l2)) - Weak TRS: #cklt(#EQ()) -> #false() #cklt(#GT()) -> #false() #cklt(#LT()) -> #true() #compare(#0(),#0()) -> #EQ() #compare(#0(),#neg(@y)) -> #GT() #compare(#0(),#pos(@y)) -> #LT() #compare(#0(),#s(@y)) -> #LT() #compare(#neg(@x),#0()) -> #LT() #compare(#neg(@x),#neg(@y)) -> #compare(@y,@x) #compare(#neg(@x),#pos(@y)) -> #LT() #compare(#pos(@x),#0()) -> #GT() #compare(#pos(@x),#neg(@y)) -> #GT() #compare(#pos(@x),#pos(@y)) -> #compare(@x,@y) #compare(#s(@x),#0()) -> #GT() #compare(#s(@x),#s(@y)) -> #compare(@x,@y) - Signature: {#cklt/1,#compare/2,#less/2,merge/2,merge#1/2,merge#2/3,merge#3/5,mergesort/1,mergesort#1/1,mergesort#2/2 ,mergesort#3/1,msplit/1,msplit#1/1,msplit#2/2,msplit#3/3} / {#0/0,#EQ/0,#GT/0,#LT/0,#false/0,#neg/1,#pos/1 ,#s/1,#true/0,::/2,nil/0,tuple#2/2} - Obligation: innermost runtime complexity wrt. defined symbols {#cklt,#compare,#less,merge,merge#1,merge#2,merge#3 ,mergesort,mergesort#1,mergesort#2,mergesort#3,msplit,msplit#1,msplit#2,msplit#3} and constructors {#0,#EQ ,#GT,#LT,#false,#neg,#pos,#s,#true,::,nil,tuple#2} + Applied Processor: NaturalPI {shape = Mixed 3, restrict = NoRestrict, uargs = UArgs, urules = URules, selector = Nothing} + Details: Incompatible MAYBE