TRS Standard pair #615297673

details

property	value
status	complete
benchmark	mapHard.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n058.star.cs.uiowa.edu
space	AProVE_06

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	1.29087805748 seconds
cpu usage	3.862491984
max memory	7.03909888E8

stage attributes

key	value
output-size	18481
starexec-result	"MAYBE"

output

/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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failure 'Failure("No result of SMT solver - maybe due to some flag of the solver? or the solver was not found in PATH?")' in subprocess 29277
YES

Problem:
 ap(ap(map(),f),xs) -> ap(ap(ap(if(),ap(isEmpty(),xs)),f),xs)
 ap(ap(ap(if(),true()),f),xs) -> nil()
 ap(ap(ap(if(),false()),f),xs) ->
 ap(ap(cons(),ap(f,ap(last(),xs))),ap(ap(map(),f),ap(dropLast(),xs)))
 ap(isEmpty(),nil()) -> true()
 ap(isEmpty(),ap(ap(cons(),x),xs)) -> false()
 ap(last(),ap(ap(cons(),x),nil())) -> x
 ap(last(),ap(ap(cons(),x),ap(ap(cons(),y),ys))) -> ap(last(),ap(ap(cons(),y),ys))
 ap(dropLast(),nil()) -> nil()
 ap(dropLast(),ap(ap(cons(),x),nil())) -> nil()
 ap(dropLast(),ap(ap(cons(),x),ap(ap(cons(),y),ys))) ->
 ap(ap(cons(),x),ap(dropLast(),ap(ap(cons(),y),ys)))

Proof:
 Extended Uncurrying Processor:
  application symbol: ap
  symbol table:
   dropLast ==> dropLast0/0 dropLast1/1
   last ==> last0/0 last1/1
   cons ==> cons0/0 cons1/1 cons2/2
   false ==> false0/0
   nil ==> nil0/0
   true ==> true0/0
   isEmpty ==> isEmpty0/0 isEmpty1/1
   if ==> if0/0 if1/1 if2/2 if3/3
   map ==> map0/0 map1/1 map2/2
   
  uncurry-rules:
   ap(map1(x5),x6) -> map2(x5,x6)
   ap(map0(),x5) -> map1(x5)
   ap(if2(x8,x9),x10) -> if3(x8,x9,x10)
   ap(if1(x8),x9) -> if2(x8,x9)
   ap(if0(),x8) -> if1(x8)
   ap(isEmpty0(),x12) -> isEmpty1(x12)
   ap(cons1(x17),x18) -> cons2(x17,x18)
   ap(cons0(),x17) -> cons1(x17)
   ap(last0(),x20) -> last1(x20)
   ap(dropLast0(),x22) -> dropLast1(x22)
  eta-rules:
   
  problem:
   map2(f,xs) -> if3(isEmpty1(xs),f,xs)
   if3(true0(),f,xs) -> nil0()
   if3(false0(),f,xs) -> cons2(ap(f,last1(xs)),map2(f,dropLast1(xs)))
   isEmpty1(nil0()) -> true0()
   isEmpty1(cons2(x,xs)) -> false0()
   last1(cons2(x,nil0())) -> x
   last1(cons2(x,cons2(y,ys))) -> last1(cons2(y,ys))
   dropLast1(nil0()) -> nil0()
   dropLast1(cons2(x,nil0())) -> nil0()
   dropLast1(cons2(x,cons2(y,ys))) -> cons2(x,dropLast1(cons2(y,ys)))
   ap(map1(x5),x6) -> map2(x5,x6)
   ap(map0(),x5) -> map1(x5)
   ap(if2(x8,x9),x10) -> if3(x8,x9,x10)
   ap(if1(x8),x9) -> if2(x8,x9)
   ap(if0(),x8) -> if1(x8)
   ap(isEmpty0(),x12) -> isEmpty1(x12)
   ap(cons1(x17),x18) -> cons2(x17,x18)
   ap(cons0(),x17) -> cons1(x17)
   ap(last0(),x20) -> last1(x20)
   ap(dropLast0(),x22) -> dropLast1(x22)
  DP Processor:
   DPs:
    map{2,#}(f,xs) -> isEmpty{1,#}(xs)
    map{2,#}(f,xs) -> if{3,#}(isEmpty1(xs),f,xs)
    if{3,#}(false0(),f,xs) -> dropLast{1,#}(xs)
    if{3,#}(false0(),f,xs) -> map{2,#}(f,dropLast1(xs))
    if{3,#}(false0(),f,xs) -> last{1,#}(xs)
    if{3,#}(false0(),f,xs) -> ap#(f,last1(xs))
    last{1,#}(cons2(x,cons2(y,ys))) -> last{1,#}(cons2(y,ys))
    dropLast{1,#}(cons2(x,cons2(y,ys))) -> dropLast{1,#}(cons2(y,ys))
    ap#(map1(x5),x6) -> map{2,#}(x5,x6)
    ap#(if2(x8,x9),x10) -> if{3,#}(x8,x9,x10)
    ap#(isEmpty0(),x12) -> isEmpty{1,#}(x12)
    ap#(last0(),x20) -> last{1,#}(x20)
    ap#(dropLast0(),x22) -> dropLast{1,#}(x22)
   TRS:
    map2(f,xs) -> if3(isEmpty1(xs),f,xs)
    if3(true0(),f,xs) -> nil0()
    if3(false0(),f,xs) -> cons2(ap(f,last1(xs)),map2(f,dropLast1(xs)))
    isEmpty1(nil0()) -> true0()
    isEmpty1(cons2(x,xs)) -> false0()
    last1(cons2(x,nil0())) -> x
    last1(cons2(x,cons2(y,ys))) -> last1(cons2(y,ys))
    dropLast1(nil0()) -> nil0()
    dropLast1(cons2(x,nil0())) -> nil0()
    dropLast1(cons2(x,cons2(y,ys))) -> cons2(x,dropLast1(cons2(y,ys)))
    ap(map1(x5),x6) -> map2(x5,x6)
    ap(map0(),x5) -> map1(x5)
    ap(if2(x8,x9),x10) -> if3(x8,x9,x10)

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