TRS Stand 20472 pair #381712101

details

property	value
status	complete
benchmark	Ex1SimplyTyped.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n039.star.cs.uiowa.edu
space	AotoYamada_05

run statistics

property	value
solver	ttt2-1.17+nonreach
configuration	ttt2-1.17+nonreach
runtime (wallclock)	0.550933837891 seconds
cpu usage	0.973514759
max memory	2.00146944E8

stage attributes

key	value
output-size	8311
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 app(id(),x) -> x
 app(add(),0()) -> id()
 app(app(add(),app(s(),x)),y) -> app(s(),app(app(add(),x),y))
 app(app(map(),f),nil()) -> nil()
 app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))

Proof:
 Extended Uncurrying Processor:
  application symbol: app
  symbol table:
   cons ==> cons0/0 cons1/1 cons2/2
   nil ==> nil0/0
   map ==> map0/0 map1/1 map2/2
   s ==> s0/0 s1/1
   0 ==> 00/0
   add ==> add0/0 add1/1 add2/2
   id ==> id0/0 id1/1
   
  uncurry-rules:
   app(id0(),x5) -> id1(x5)
   app(add1(x7),x8) -> add2(x7,x8)
   app(add0(),x7) -> add1(x7)
   app(s0(),x11) -> s1(x11)
   app(map1(x13),x14) -> map2(x13,x14)
   app(map0(),x13) -> map1(x13)
   app(cons1(x17),x18) -> cons2(x17,x18)
   app(cons0(),x17) -> cons1(x17)
  eta-rules:
   app(app(add(),0()),x4) -> app(id(),x4)
  problem:
   id1(x) -> x
   add1(00()) -> id0()
   add2(s1(x),y) -> s1(add2(x,y))
   map2(f,nil0()) -> nil0()
   map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
   add2(00(),x4) -> id1(x4)
   app(id0(),x5) -> id1(x5)
   app(add1(x7),x8) -> add2(x7,x8)
   app(add0(),x7) -> add1(x7)
   app(s0(),x11) -> s1(x11)
   app(map1(x13),x14) -> map2(x13,x14)
   app(map0(),x13) -> map1(x13)
   app(cons1(x17),x18) -> cons2(x17,x18)
   app(cons0(),x17) -> cons1(x17)
  DP Processor:
   DPs:
    add{2,#}(s1(x),y) -> add{2,#}(x,y)
    map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
    map{2,#}(f,cons2(x,xs)) -> app#(f,x)
    add{2,#}(00(),x4) -> id{1,#}(x4)
    app#(id0(),x5) -> id{1,#}(x5)
    app#(add1(x7),x8) -> add{2,#}(x7,x8)
    app#(add0(),x7) -> add{1,#}(x7)
    app#(map1(x13),x14) -> map{2,#}(x13,x14)
   TRS:
    id1(x) -> x
    add1(00()) -> id0()
    add2(s1(x),y) -> s1(add2(x,y))
    map2(f,nil0()) -> nil0()
    map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
    add2(00(),x4) -> id1(x4)
    app(id0(),x5) -> id1(x5)
    app(add1(x7),x8) -> add2(x7,x8)
    app(add0(),x7) -> add1(x7)
    app(s0(),x11) -> s1(x11)
    app(map1(x13),x14) -> map2(x13,x14)
    app(map0(),x13) -> map1(x13)
    app(cons1(x17),x18) -> cons2(x17,x18)
    app(cons0(),x17) -> cons1(x17)
   TDG Processor:
    DPs:
     add{2,#}(s1(x),y) -> add{2,#}(x,y)
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     add{2,#}(00(),x4) -> id{1,#}(x4)
     app#(id0(),x5) -> id{1,#}(x5)
     app#(add1(x7),x8) -> add{2,#}(x7,x8)
     app#(add0(),x7) -> add{1,#}(x7)
     app#(map1(x13),x14) -> map{2,#}(x13,x14)
    TRS:
     id1(x) -> x
     add1(00()) -> id0()
     add2(s1(x),y) -> s1(add2(x,y))
     map2(f,nil0()) -> nil0()
     map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
     add2(00(),x4) -> id1(x4)
     app(id0(),x5) -> id1(x5)
     app(add1(x7),x8) -> add2(x7,x8)
     app(add0(),x7) -> add1(x7)
     app(s0(),x11) -> s1(x11)
     app(map1(x13),x14) -> map2(x13,x14)

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