/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: app(app(minus(),x),0()) -> x app(app(minus(),app(s(),x)),app(s(),y)) -> app(app(minus(),x),y) app(app(quot(),0()),app(s(),y)) -> 0() app(app(quot(),app(s(),x)),app(s(),y)) -> app(s(),app(app(quot(),app(app(minus(),x),y)),app(s(),y))) app(app(plus(),0()),y) -> y app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y)) app(app(plus(),app(app(minus(),x),app(s(),0()))),app(app(minus(),y),app(s(),app(s(),z)))) -> app(app(plus(),app(app(minus(),y),app(s(),app(s(),z)))),app(app(minus(),x),app(s(),0()))) app(app(plus(),app(app(plus(),x),app(s(),0()))),app(app(plus(),y),app(s(),app(s(),z)))) -> app(app(plus(),app(app(plus(),y),app(s(),app(s(),z)))),app(app(plus(),x),app(s(),0()))) 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)) app(app(filter(),f),nil()) -> nil() app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs) app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs)) app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs) Proof: Extended Uncurrying Processor: application symbol: app symbol table: false ==> false0/0 true ==> true0/0 filter2 ==> filter20/0 filter21/1 filter22/2 filter23/3 filter24/4 filter ==> filter0/0 filter1/1 filter2/2 cons ==> cons0/0 cons1/1 cons2/2 nil ==> nil0/0 map ==> map0/0 map1/1 map2/2 plus ==> plus0/0 plus1/1 plus2/2 quot ==> quot0/0 quot1/1 quot2/2 s ==> s0/0 s1/1 0 ==> 00/0 minus ==> minus0/0 minus1/1 minus2/2 uncurry-rules: app(minus1(x5),x6) -> minus2(x5,x6) app(minus0(),x5) -> minus1(x5) app(s0(),x9) -> s1(x9) app(quot1(x11),x12) -> quot2(x11,x12) app(quot0(),x11) -> quot1(x11) app(plus1(x14),x15) -> plus2(x14,x15) app(plus0(),x14) -> plus1(x14) app(map1(x17),x18) -> map2(x17,x18) app(map0(),x17) -> map1(x17) app(cons1(x21),x22) -> cons2(x21,x22) app(cons0(),x21) -> cons1(x21) app(filter1(x24),x25) -> filter2(x24,x25) app(filter0(),x24) -> filter1(x24) app(filter23(x27,x28,x29),x30) -> filter24(x27,x28,x29,x30) app(filter22(x27,x28),x29) -> filter23(x27,x28,x29) app(filter21(x27),x28) -> filter22(x27,x28) app(filter20(),x27) -> filter21(x27) eta-rules: problem: minus2(x,00()) -> x minus2(s1(x),s1(y)) -> minus2(x,y) quot2(00(),s1(y)) -> 00() quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y))) plus2(00(),y) -> y plus2(s1(x),y) -> s1(plus2(x,y)) plus2(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus2(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(00()))) map2(f,nil0()) -> nil0() map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs)) filter2(f,nil0()) -> nil0() filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs) filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs)) filter24(false0(),f,x,xs) -> filter2(f,xs) app(minus1(x5),x6) -> minus2(x5,x6) app(minus0(),x5) -> minus1(x5) app(s0(),x9) -> s1(x9) app(quot1(x11),x12) -> quot2(x11,x12) app(quot0(),x11) -> quot1(x11) app(plus1(x14),x15) -> plus2(x14,x15) app(plus0(),x14) -> plus1(x14) app(map1(x17),x18) -> map2(x17,x18) app(map0(),x17) -> map1(x17) app(cons1(x21),x22) -> cons2(x21,x22) app(cons0(),x21) -> cons1(x21) app(filter1(x24),x25) -> filter2(x24,x25) app(filter0(),x24) -> filter1(x24) app(filter23(x27,x28,x29),x30) -> filter24(x27,x28,x29,x30) app(filter22(x27,x28),x29) -> filter23(x27,x28,x29) app(filter21(x27),x28) -> filter22(x27,x28) app(filter20(),x27) -> filter21(x27) DP Processor: DPs: minus{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y) quot{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y) quot{2,#}(s1(x),s1(y)) -> quot{2,#}(minus2(x,y),s1(y)) plus{2,#}(s1(x),y) -> plus{2,#}(x,y) plus{2,#}(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus{2,#}(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(00()))) map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) map{2,#}(f,cons2(x,xs)) -> app#(f,x) filter{2,#}(f,cons2(x,xs)) -> app#(f,x) filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs) filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs) filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs) app#(minus1(x5),x6) -> minus{2,#}(x5,x6) app#(quot1(x11),x12) -> quot{2,#}(x11,x12) app#(plus1(x14),x15) -> plus{2,#}(x14,x15) app#(map1(x17),x18) -> map{2,#}(x17,x18) app#(filter1(x24),x25) -> filter{2,#}(x24,x25) app#(filter23(x27,x28,x29),x30) -> filter2{4,#}(x27,x28,x29,x30) TRS: minus2(x,00()) -> x minus2(s1(x),s1(y)) -> minus2(x,y) quot2(00(),s1(y)) -> 00() quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y))) plus2(00(),y) -> y plus2(s1(x),y) -> s1(plus2(x,y)) plus2(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus2(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(00()))) map2(f,nil0()) -> nil0() map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs)) filter2(f,nil0()) -> nil0() filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs) filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs)) filter24(false0(),f,x,xs) -> filter2(f,xs) app(minus1(x5),x6) -> minus2(x5,x6) app(minus0(),x5) -> minus1(x5) app(s0(),x9) -> s1(x9) app(quot1(x11),x12) -> quot2(x11,x12) app(quot0(),x11) -> quot1(x11) app(plus1(x14),x15) -> plus2(x14,x15) app(plus0(),x14) -> plus1(x14) app(map1(x17),x18) -> map2(x17,x18) app(map0(),x17) -> map1(x17) app(cons1(x21),x22) -> cons2(x21,x22) app(cons0(),x21) -> cons1(x21) app(filter1(x24),x25) -> filter2(x24,x25) app(filter0(),x24) -> filter1(x24) app(filter23(x27,x28,x29),x30) -> filter24(x27,x28,x29,x30) app(filter22(x27,x28),x29) -> filter23(x27,x28,x29) app(filter21(x27),x28) -> filter22(x27,x28) app(filter20(),x27) -> filter21(x27) TDG Processor: DPs: minus{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y) quot{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y) quot{2,#}(s1(x),s1(y)) -> quot{2,#}(minus2(x,y),s1(y)) plus{2,#}(s1(x),y) -> plus{2,#}(x,y) plus{2,#}(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus{2,#}(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(00()))) map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) map{2,#}(f,cons2(x,xs)) -> app#(f,x) filter{2,#}(f,cons2(x,xs)) -> app#(f,x) filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs) filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs) filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs) app#(minus1(x5),x6) -> minus{2,#}(x5,x6) app#(quot1(x11),x12) -> quot{2,#}(x11,x12) app#(plus1(x14),x15) -> plus{2,#}(x14,x15) app#(map1(x17),x18) -> map{2,#}(x17,x18) app#(filter1(x24),x25) -> filter{2,#}(x24,x25) app#(filter23(x27,x28,x29),x30) -> filter2{4,#}(x27,x28,x29,x30) TRS: minus2(x,00()) -> x minus2(s1(x),s1(y)) -> minus2(x,y) quot2(00(),s1(y)) -> 00() quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y))) plus2(00(),y) -> y plus2(s1(x),y) -> s1(plus2(x,y)) plus2(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus2(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(00()))) map2(f,nil0()) -> nil0() map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs)) filter2(f,nil0()) -> nil0() filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs) filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs)) filter24(false0(),f,x,xs) -> filter2(f,xs) app(minus1(x5),x6) -> minus2(x5,x6) app(minus0(),x5) -> minus1(x5) app(s0(),x9) -> s1(x9) app(quot1(x11),x12) -> quot2(x11,x12) app(quot0(),x11) -> quot1(x11) app(plus1(x14),x15) -> plus2(x14,x15) app(plus0(),x14) -> plus1(x14) app(map1(x17),x18) -> map2(x17,x18) app(map0(),x17) -> map1(x17) app(cons1(x21),x22) -> cons2(x21,x22) app(cons0(),x21) -> cons1(x21) app(filter1(x24),x25) -> filter2(x24,x25) app(filter0(),x24) -> filter1(x24) app(filter23(x27,x28,x29),x30) -> filter24(x27,x28,x29,x30) app(filter22(x27,x28),x29) -> filter23(x27,x28,x29) app(filter21(x27),x28) -> filter22(x27,x28) app(filter20(),x27) -> filter21(x27) graph: filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs) -> filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs) filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs) -> filter{2,#}(f,cons2(x,xs)) -> app#(f,x) filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs) -> filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs) filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs) -> filter{2,#}(f,cons2(x,xs)) -> app#(f,x) filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs) -> filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs) filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs) -> filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs) filter{2,#}(f,cons2(x,xs)) -> app#(f,x) -> app#(filter23(x27,x28,x29),x30) -> filter2{4,#}(x27,x28,x29,x30) filter{2,#}(f,cons2(x,xs)) -> app#(f,x) -> app#(filter1(x24),x25) -> filter{2,#}(x24,x25) filter{2,#}(f,cons2(x,xs)) -> app#(f,x) -> app#(map1(x17),x18) -> map{2,#}(x17,x18) filter{2,#}(f,cons2(x,xs)) -> app#(f,x) -> app#(plus1(x14),x15) -> plus{2,#}(x14,x15) filter{2,#}(f,cons2(x,xs)) -> app#(f,x) -> app#(quot1(x11),x12) -> quot{2,#}(x11,x12) filter{2,#}(f,cons2(x,xs)) -> app#(f,x) -> app#(minus1(x5),x6) -> minus{2,#}(x5,x6) app#(filter23(x27,x28,x29),x30) -> filter2{4,#}(x27,x28,x29,x30) -> filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs) app#(filter23(x27,x28,x29),x30) -> filter2{4,#}(x27,x28,x29,x30) -> filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs) app#(filter1(x24),x25) -> filter{2,#}(x24,x25) -> filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs) app#(filter1(x24),x25) -> filter{2,#}(x24,x25) -> filter{2,#}(f,cons2(x,xs)) -> app#(f,x) app#(map1(x17),x18) -> map{2,#}(x17,x18) -> map{2,#}(f,cons2(x,xs)) -> app#(f,x) app#(map1(x17),x18) -> map{2,#}(x17,x18) -> map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) app#(plus1(x14),x15) -> plus{2,#}(x14,x15) -> plus{2,#}(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(00()))) app#(plus1(x14),x15) -> plus{2,#}(x14,x15) -> plus{2,#}(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(00()))) app#(plus1(x14),x15) -> plus{2,#}(x14,x15) -> plus{2,#}(s1(x),y) -> plus{2,#}(x,y) app#(quot1(x11),x12) -> quot{2,#}(x11,x12) -> quot{2,#}(s1(x),s1(y)) -> quot{2,#}(minus2(x,y),s1(y)) app#(quot1(x11),x12) -> quot{2,#}(x11,x12) -> quot{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y) app#(minus1(x5),x6) -> minus{2,#}(x5,x6) -> minus{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y) map{2,#}(f,cons2(x,xs)) -> app#(f,x) -> app#(filter23(x27,x28,x29),x30) -> filter2{4,#}(x27,x28,x29,x30) map{2,#}(f,cons2(x,xs)) -> app#(f,x) -> app#(filter1(x24),x25) -> filter{2,#}(x24,x25) map{2,#}(f,cons2(x,xs)) -> app#(f,x) -> app#(map1(x17),x18) -> map{2,#}(x17,x18) map{2,#}(f,cons2(x,xs)) -> app#(f,x) -> app#(plus1(x14),x15) -> plus{2,#}(x14,x15) map{2,#}(f,cons2(x,xs)) -> app#(f,x) -> app#(quot1(x11),x12) -> quot{2,#}(x11,x12) map{2,#}(f,cons2(x,xs)) -> app#(f,x) -> app#(minus1(x5),x6) -> minus{2,#}(x5,x6) map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) -> map{2,#}(f,cons2(x,xs)) -> app#(f,x) map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) -> map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) plus{2,#}(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(00()))) -> plus{2,#}(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(00()))) plus{2,#}(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(00()))) -> plus{2,#}(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus{2,#}(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(00()))) -> plus{2,#}(s1(x),y) -> plus{2,#}(x,y) plus{2,#}(s1(x),y) -> plus{2,#}(x,y) -> plus{2,#}(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(00()))) plus{2,#}(s1(x),y) -> plus{2,#}(x,y) -> plus{2,#}(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus{2,#}(s1(x),y) -> plus{2,#}(x,y) -> plus{2,#}(s1(x),y) -> plus{2,#}(x,y) plus{2,#}(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(00()))) -> plus{2,#}(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(00()))) plus{2,#}(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(00()))) -> plus{2,#}(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus{2,#}(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(00()))) -> plus{2,#}(s1(x),y) -> plus{2,#}(x,y) quot{2,#}(s1(x),s1(y)) -> quot{2,#}(minus2(x,y),s1(y)) -> quot{2,#}(s1(x),s1(y)) -> quot{2,#}(minus2(x,y),s1(y)) quot{2,#}(s1(x),s1(y)) -> quot{2,#}(minus2(x,y),s1(y)) -> quot{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y) quot{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y) -> minus{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y) minus{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y) -> minus{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y) SCC Processor: #sccs: 4 #rules: 14 #arcs: 45/324 DPs: filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs) filter{2,#}(f,cons2(x,xs)) -> app#(f,x) app#(map1(x17),x18) -> map{2,#}(x17,x18) map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) map{2,#}(f,cons2(x,xs)) -> app#(f,x) app#(filter1(x24),x25) -> filter{2,#}(x24,x25) filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs) filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs) app#(filter23(x27,x28,x29),x30) -> filter2{4,#}(x27,x28,x29,x30) TRS: minus2(x,00()) -> x minus2(s1(x),s1(y)) -> minus2(x,y) quot2(00(),s1(y)) -> 00() quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y))) plus2(00(),y) -> y plus2(s1(x),y) -> s1(plus2(x,y)) plus2(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus2(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(00()))) map2(f,nil0()) -> nil0() map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs)) filter2(f,nil0()) -> nil0() filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs) filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs)) filter24(false0(),f,x,xs) -> filter2(f,xs) app(minus1(x5),x6) -> minus2(x5,x6) app(minus0(),x5) -> minus1(x5) app(s0(),x9) -> s1(x9) app(quot1(x11),x12) -> quot2(x11,x12) app(quot0(),x11) -> quot1(x11) app(plus1(x14),x15) -> plus2(x14,x15) app(plus0(),x14) -> plus1(x14) app(map1(x17),x18) -> map2(x17,x18) app(map0(),x17) -> map1(x17) app(cons1(x21),x22) -> cons2(x21,x22) app(cons0(),x21) -> cons1(x21) app(filter1(x24),x25) -> filter2(x24,x25) app(filter0(),x24) -> filter1(x24) app(filter23(x27,x28,x29),x30) -> filter24(x27,x28,x29,x30) app(filter22(x27,x28),x29) -> filter23(x27,x28,x29) app(filter21(x27),x28) -> filter22(x27,x28) app(filter20(),x27) -> filter21(x27) Subterm Criterion Processor: simple projection: pi(map{2,#}) = 0 pi(app#) = 0 pi(filter{2,#}) = 0 pi(filter2{4,#}) = 1 problem: DPs: filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs) filter{2,#}(f,cons2(x,xs)) -> app#(f,x) map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) map{2,#}(f,cons2(x,xs)) -> app#(f,x) filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs) filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs) TRS: minus2(x,00()) -> x minus2(s1(x),s1(y)) -> minus2(x,y) quot2(00(),s1(y)) -> 00() quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y))) plus2(00(),y) -> y plus2(s1(x),y) -> s1(plus2(x,y)) plus2(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus2(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(00()))) map2(f,nil0()) -> nil0() map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs)) filter2(f,nil0()) -> nil0() filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs) filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs)) filter24(false0(),f,x,xs) -> filter2(f,xs) app(minus1(x5),x6) -> minus2(x5,x6) app(minus0(),x5) -> minus1(x5) app(s0(),x9) -> s1(x9) app(quot1(x11),x12) -> quot2(x11,x12) app(quot0(),x11) -> quot1(x11) app(plus1(x14),x15) -> plus2(x14,x15) app(plus0(),x14) -> plus1(x14) app(map1(x17),x18) -> map2(x17,x18) app(map0(),x17) -> map1(x17) app(cons1(x21),x22) -> cons2(x21,x22) app(cons0(),x21) -> cons1(x21) app(filter1(x24),x25) -> filter2(x24,x25) app(filter0(),x24) -> filter1(x24) app(filter23(x27,x28,x29),x30) -> filter24(x27,x28,x29,x30) app(filter22(x27,x28),x29) -> filter23(x27,x28,x29) app(filter21(x27),x28) -> filter22(x27,x28) app(filter20(),x27) -> filter21(x27) SCC Processor: #sccs: 2 #rules: 4 #arcs: 20/36 DPs: map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) TRS: minus2(x,00()) -> x minus2(s1(x),s1(y)) -> minus2(x,y) quot2(00(),s1(y)) -> 00() quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y))) plus2(00(),y) -> y plus2(s1(x),y) -> s1(plus2(x,y)) plus2(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus2(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(00()))) map2(f,nil0()) -> nil0() map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs)) filter2(f,nil0()) -> nil0() filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs) filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs)) filter24(false0(),f,x,xs) -> filter2(f,xs) app(minus1(x5),x6) -> minus2(x5,x6) app(minus0(),x5) -> minus1(x5) app(s0(),x9) -> s1(x9) app(quot1(x11),x12) -> quot2(x11,x12) app(quot0(),x11) -> quot1(x11) app(plus1(x14),x15) -> plus2(x14,x15) app(plus0(),x14) -> plus1(x14) app(map1(x17),x18) -> map2(x17,x18) app(map0(),x17) -> map1(x17) app(cons1(x21),x22) -> cons2(x21,x22) app(cons0(),x21) -> cons1(x21) app(filter1(x24),x25) -> filter2(x24,x25) app(filter0(),x24) -> filter1(x24) app(filter23(x27,x28,x29),x30) -> filter24(x27,x28,x29,x30) app(filter22(x27,x28),x29) -> filter23(x27,x28,x29) app(filter21(x27),x28) -> filter22(x27,x28) app(filter20(),x27) -> filter21(x27) Subterm Criterion Processor: simple projection: pi(map{2,#}) = 1 problem: DPs: TRS: minus2(x,00()) -> x minus2(s1(x),s1(y)) -> minus2(x,y) quot2(00(),s1(y)) -> 00() quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y))) plus2(00(),y) -> y plus2(s1(x),y) -> s1(plus2(x,y)) plus2(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus2(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(00()))) map2(f,nil0()) -> nil0() map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs)) filter2(f,nil0()) -> nil0() filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs) filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs)) filter24(false0(),f,x,xs) -> filter2(f,xs) app(minus1(x5),x6) -> minus2(x5,x6) app(minus0(),x5) -> minus1(x5) app(s0(),x9) -> s1(x9) app(quot1(x11),x12) -> quot2(x11,x12) app(quot0(),x11) -> quot1(x11) app(plus1(x14),x15) -> plus2(x14,x15) app(plus0(),x14) -> plus1(x14) app(map1(x17),x18) -> map2(x17,x18) app(map0(),x17) -> map1(x17) app(cons1(x21),x22) -> cons2(x21,x22) app(cons0(),x21) -> cons1(x21) app(filter1(x24),x25) -> filter2(x24,x25) app(filter0(),x24) -> filter1(x24) app(filter23(x27,x28,x29),x30) -> filter24(x27,x28,x29,x30) app(filter22(x27,x28),x29) -> filter23(x27,x28,x29) app(filter21(x27),x28) -> filter22(x27,x28) app(filter20(),x27) -> filter21(x27) Qed DPs: filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs) filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs) filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs) TRS: minus2(x,00()) -> x minus2(s1(x),s1(y)) -> minus2(x,y) quot2(00(),s1(y)) -> 00() quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y))) plus2(00(),y) -> y plus2(s1(x),y) -> s1(plus2(x,y)) plus2(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus2(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(00()))) map2(f,nil0()) -> nil0() map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs)) filter2(f,nil0()) -> nil0() filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs) filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs)) filter24(false0(),f,x,xs) -> filter2(f,xs) app(minus1(x5),x6) -> minus2(x5,x6) app(minus0(),x5) -> minus1(x5) app(s0(),x9) -> s1(x9) app(quot1(x11),x12) -> quot2(x11,x12) app(quot0(),x11) -> quot1(x11) app(plus1(x14),x15) -> plus2(x14,x15) app(plus0(),x14) -> plus1(x14) app(map1(x17),x18) -> map2(x17,x18) app(map0(),x17) -> map1(x17) app(cons1(x21),x22) -> cons2(x21,x22) app(cons0(),x21) -> cons1(x21) app(filter1(x24),x25) -> filter2(x24,x25) app(filter0(),x24) -> filter1(x24) app(filter23(x27,x28,x29),x30) -> filter24(x27,x28,x29,x30) app(filter22(x27,x28),x29) -> filter23(x27,x28,x29) app(filter21(x27),x28) -> filter22(x27,x28) app(filter20(),x27) -> filter21(x27) Subterm Criterion Processor: simple projection: pi(filter{2,#}) = 1 pi(filter2{4,#}) = 3 problem: DPs: filter2{4,#}(false0(),f,x,xs) -> filter{2,#}(f,xs) filter2{4,#}(true0(),f,x,xs) -> filter{2,#}(f,xs) TRS: minus2(x,00()) -> x minus2(s1(x),s1(y)) -> minus2(x,y) quot2(00(),s1(y)) -> 00() quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y))) plus2(00(),y) -> y plus2(s1(x),y) -> s1(plus2(x,y)) plus2(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus2(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(00()))) map2(f,nil0()) -> nil0() map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs)) filter2(f,nil0()) -> nil0() filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs) filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs)) filter24(false0(),f,x,xs) -> filter2(f,xs) app(minus1(x5),x6) -> minus2(x5,x6) app(minus0(),x5) -> minus1(x5) app(s0(),x9) -> s1(x9) app(quot1(x11),x12) -> quot2(x11,x12) app(quot0(),x11) -> quot1(x11) app(plus1(x14),x15) -> plus2(x14,x15) app(plus0(),x14) -> plus1(x14) app(map1(x17),x18) -> map2(x17,x18) app(map0(),x17) -> map1(x17) app(cons1(x21),x22) -> cons2(x21,x22) app(cons0(),x21) -> cons1(x21) app(filter1(x24),x25) -> filter2(x24,x25) app(filter0(),x24) -> filter1(x24) app(filter23(x27,x28,x29),x30) -> filter24(x27,x28,x29,x30) app(filter22(x27,x28),x29) -> filter23(x27,x28,x29) app(filter21(x27),x28) -> filter22(x27,x28) app(filter20(),x27) -> filter21(x27) SCC Processor: #sccs: 0 #rules: 0 #arcs: 4/4 DPs: plus{2,#}(s1(x),y) -> plus{2,#}(x,y) plus{2,#}(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus{2,#}(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(00()))) TRS: minus2(x,00()) -> x minus2(s1(x),s1(y)) -> minus2(x,y) quot2(00(),s1(y)) -> 00() quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y))) plus2(00(),y) -> y plus2(s1(x),y) -> s1(plus2(x,y)) plus2(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus2(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(00()))) map2(f,nil0()) -> nil0() map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs)) filter2(f,nil0()) -> nil0() filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs) filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs)) filter24(false0(),f,x,xs) -> filter2(f,xs) app(minus1(x5),x6) -> minus2(x5,x6) app(minus0(),x5) -> minus1(x5) app(s0(),x9) -> s1(x9) app(quot1(x11),x12) -> quot2(x11,x12) app(quot0(),x11) -> quot1(x11) app(plus1(x14),x15) -> plus2(x14,x15) app(plus0(),x14) -> plus1(x14) app(map1(x17),x18) -> map2(x17,x18) app(map0(),x17) -> map1(x17) app(cons1(x21),x22) -> cons2(x21,x22) app(cons0(),x21) -> cons1(x21) app(filter1(x24),x25) -> filter2(x24,x25) app(filter0(),x24) -> filter1(x24) app(filter23(x27,x28,x29),x30) -> filter24(x27,x28,x29,x30) app(filter22(x27,x28),x29) -> filter23(x27,x28,x29) app(filter21(x27),x28) -> filter22(x27,x28) app(filter20(),x27) -> filter21(x27) Subterm Criterion Processor: simple projection: pi(minus2) = [0,0] pi(filter23) = [1,1] pi(plus{2,#}) = [0,0,1,1] problem: DPs: plus{2,#}(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus{2,#}(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(00()))) TRS: minus2(x,00()) -> x minus2(s1(x),s1(y)) -> minus2(x,y) quot2(00(),s1(y)) -> 00() quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y))) plus2(00(),y) -> y plus2(s1(x),y) -> s1(plus2(x,y)) plus2(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus2(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(00()))) map2(f,nil0()) -> nil0() map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs)) filter2(f,nil0()) -> nil0() filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs) filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs)) filter24(false0(),f,x,xs) -> filter2(f,xs) app(minus1(x5),x6) -> minus2(x5,x6) app(minus0(),x5) -> minus1(x5) app(s0(),x9) -> s1(x9) app(quot1(x11),x12) -> quot2(x11,x12) app(quot0(),x11) -> quot1(x11) app(plus1(x14),x15) -> plus2(x14,x15) app(plus0(),x14) -> plus1(x14) app(map1(x17),x18) -> map2(x17,x18) app(map0(),x17) -> map1(x17) app(cons1(x21),x22) -> cons2(x21,x22) app(cons0(),x21) -> cons1(x21) app(filter1(x24),x25) -> filter2(x24,x25) app(filter0(),x24) -> filter1(x24) app(filter23(x27,x28,x29),x30) -> filter24(x27,x28,x29,x30) app(filter22(x27,x28),x29) -> filter23(x27,x28,x29) app(filter21(x27),x28) -> filter22(x27,x28) app(filter20(),x27) -> filter21(x27) Usable Rule Processor: DPs: plus{2,#}(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus{2,#}(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(00()))) TRS: minus2(s1(x),s1(y)) -> minus2(x,y) minus2(x,00()) -> x plus2(00(),y) -> y plus2(s1(x),y) -> s1(plus2(x,y)) plus2(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus2(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(00()))) Matrix Interpretation Processor: dim=4 usable rules: minus2(s1(x),s1(y)) -> minus2(x,y) minus2(x,00()) -> x plus2(00(),y) -> y plus2(s1(x),y) -> s1(plus2(x,y)) plus2(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus2(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(00()))) interpretation: [plus{2,#}](x0, x1) = [0 1 0 0]x0 + [0 0 0 1]x1, [1 0 0 0] [1 0 0 0] [0 1 0 1] [0 1 0 1] [plus2](x0, x1) = [0 0 1 0]x0 + [0 0 1 0]x1 [0 1 0 1] [0 1 0 1] , [1 0 0 0] [1] [0 0 0 1] [0] [s1](x0) = [0 0 1 0]x0 + [0] [0 1 0 0] [0], [0] [1] [00] = [0] [0], [1 0 0 0] [0 0 0 0] [0 1 0 1] [0 0 0 0] [minus2](x0, x1) = [0 0 1 0]x0 + [0 0 0 0]x1 [0 1 0 1] [1 0 0 0] orientation: plus{2,#}(minus2(x,s1(00())),minus2(y,s1(s1(z)))) = [0 1 0 1]x + [0 1 0 1]y + [1 0 0 0]z + [2] >= [0 1 0 1]x + [0 1 0 1]y + [1] = plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus{2,#}(plus2(x,s1(00())),plus2(y,s1(s1(z)))) = [0 1 0 1]x + [0 1 0 1]y + [0 1 0 1]z + [1] >= [0 1 0 1]x + [0 1 0 1]y + [0 1 0 1]z + [1] = plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(00()))) [1 0 0 0] [0 0 0 0] [1] [1 0 0 0] [0 0 0 0] [0 1 0 1] [0 0 0 0] [0] [0 1 0 1] [0 0 0 0] minus2(s1(x),s1(y)) = [0 0 1 0]x + [0 0 0 0]y + [0] >= [0 0 1 0]x + [0 0 0 0]y = minus2(x,y) [0 1 0 1] [1 0 0 0] [1] [0 1 0 1] [1 0 0 0] [1 0 0 0] [0 1 0 1] minus2(x,00()) = [0 0 1 0]x >= x = x [0 1 0 1] [1 0 0 0] [0] [0 1 0 1] [1] plus2(00(),y) = [0 0 1 0]y + [0] >= y = y [0 1 0 1] [1] [1 0 0 0] [1 0 0 0] [1] [1 0 0 0] [1 0 0 0] [1] [0 1 0 1] [0 1 0 1] [0] [0 1 0 1] [0 1 0 1] [0] plus2(s1(x),y) = [0 0 1 0]x + [0 0 1 0]y + [0] >= [0 0 1 0]x + [0 0 1 0]y + [0] = s1(plus2(x,y)) [0 1 0 1] [0 1 0 1] [0] [0 1 0 1] [0 1 0 1] [0] [1 0 0 0] [1 0 0 0] [0 0 0 0] [0] [1 0 0 0] [1 0 0 0] [0 0 0 0] [0] [0 2 0 2] [0 2 0 2] [1 0 0 0] [3] [0 2 0 2] [0 2 0 2] [1 0 0 0] [3] plus2(minus2(x,s1(00())),minus2(y,s1(s1(z)))) = [0 0 1 0]x + [0 0 1 0]y + [0 0 0 0]z + [0] >= [0 0 1 0]x + [0 0 1 0]y + [0 0 0 0]z + [0] = plus2(minus2(y,s1(s1(z))),minus2(x,s1(00()))) [0 2 0 2] [0 2 0 2] [1 0 0 0] [3] [0 2 0 2] [0 2 0 2] [1 0 0 0] [3] [1 0 0 0] [1 0 0 0] [1 0 0 0] [3] [1 0 0 0] [1 0 0 0] [1 0 0 0] [3] [0 2 0 2] [0 2 0 2] [0 2 0 2] [2] [0 2 0 2] [0 2 0 2] [0 2 0 2] [2] plus2(plus2(x,s1(00())),plus2(y,s1(s1(z)))) = [0 0 1 0]x + [0 0 1 0]y + [0 0 1 0]z + [0] >= [0 0 1 0]x + [0 0 1 0]y + [0 0 1 0]z + [0] = plus2(plus2(y,s1(s1(z))),plus2(x,s1(00()))) [0 2 0 2] [0 2 0 2] [0 2 0 2] [2] [0 2 0 2] [0 2 0 2] [0 2 0 2] [2] problem: DPs: plus{2,#}(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(00()))) TRS: minus2(s1(x),s1(y)) -> minus2(x,y) minus2(x,00()) -> x plus2(00(),y) -> y plus2(s1(x),y) -> s1(plus2(x,y)) plus2(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus2(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(00()))) Restore Modifier: DPs: plus{2,#}(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(00()))) TRS: minus2(x,00()) -> x minus2(s1(x),s1(y)) -> minus2(x,y) quot2(00(),s1(y)) -> 00() quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y))) plus2(00(),y) -> y plus2(s1(x),y) -> s1(plus2(x,y)) plus2(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus2(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(00()))) map2(f,nil0()) -> nil0() map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs)) filter2(f,nil0()) -> nil0() filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs) filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs)) filter24(false0(),f,x,xs) -> filter2(f,xs) app(minus1(x5),x6) -> minus2(x5,x6) app(minus0(),x5) -> minus1(x5) app(s0(),x9) -> s1(x9) app(quot1(x11),x12) -> quot2(x11,x12) app(quot0(),x11) -> quot1(x11) app(plus1(x14),x15) -> plus2(x14,x15) app(plus0(),x14) -> plus1(x14) app(map1(x17),x18) -> map2(x17,x18) app(map0(),x17) -> map1(x17) app(cons1(x21),x22) -> cons2(x21,x22) app(cons0(),x21) -> cons1(x21) app(filter1(x24),x25) -> filter2(x24,x25) app(filter0(),x24) -> filter1(x24) app(filter23(x27,x28,x29),x30) -> filter24(x27,x28,x29,x30) app(filter22(x27,x28),x29) -> filter23(x27,x28,x29) app(filter21(x27),x28) -> filter22(x27,x28) app(filter20(),x27) -> filter21(x27) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {2} transitions: false{0,0}() -> 1* minus{1,0}(10) -> 1* minus{1,0}(9) -> 1* minus{1,0}(11) -> 1* minus{1,0}(1) -> 1* minus{1,0}(8) -> 1* minus{0,0}() -> 1* s{0,0}() -> 1* quot{1,0}(10) -> 1* quot{1,0}(9) -> 1* quot{1,0}(11) -> 1* quot{1,0}(1) -> 1* quot{1,0}(8) -> 1* quot{0,0}() -> 1* plus{1,0}(10) -> 1* plus{1,0}(9) -> 1* plus{1,0}(11) -> 1* plus{1,0}(1) -> 1* plus{1,0}(8) -> 1* plus{0,0}() -> 1* map{1,0}(10) -> 1* map{1,0}(9) -> 1* map{1,0}(11) -> 1* map{1,0}(1) -> 1* map{1,0}(8) -> 1* map{0,0}() -> 1* cons{1,0}(10) -> 1* cons{1,0}(9) -> 1* cons{1,0}(11) -> 1* cons{1,0}(1) -> 1* cons{1,0}(8) -> 1* cons{0,0}() -> 1* filter{1,0}(10) -> 1* filter{1,0}(9) -> 1* filter{1,0}(11) -> 1* filter{1,0}(1) -> 1* filter{1,0}(8) -> 1* filter{0,0}() -> 1* filter2{3,0}(9,11,1) -> 1* filter2{3,0}(1,1,10) -> 1* filter2{3,0}(10,1,9) -> 1* filter2{3,0}(11,9,10) -> 1* filter2{3,0}(11,11,10) -> 1* filter2{3,0}(1,9,10) -> 1* filter2{3,0}(1,11,10) -> 1* filter2{3,0}(10,9,9) -> 1* filter2{3,0}(10,11,9) -> 1* filter2{3,0}(10,8,1) -> 1* filter2{3,0}(10,10,1) -> 1* filter2{3,0}(8,8,11) -> 1* filter2{3,0}(8,10,11) -> 1* filter2{3,0}(11,1,1) -> 1* filter2{3,0}(11,8,9) -> 1* filter2{3,0}(1,1,1) -> 1* filter2{3,0}(8,8,8) -> 1* filter2{3,0}(11,10,9) -> 1* filter2{3,0}(1,8,9) -> 1* filter2{3,0}(8,10,8) -> 1* filter2{3,0}(9,1,11) -> 1* filter2{3,0}(1,10,9) -> 1* filter2{3,0}(11,9,1) -> 1* filter2{3,0}(11,11,1) -> 1* filter2{3,0}(1,9,1) -> 1* filter2{3,0}(8,1,10) -> 1* filter2{3,0}(1,11,1) -> 1* filter2{3,0}(9,9,11) -> 1* filter2{3,0}(9,11,11) -> 1* filter2{3,0}(9,1,8) -> 1* filter2{3,0}(8,9,10) -> 1* filter2{3,0}(8,11,10) -> 1* filter2{3,0}(9,9,8) -> 1* filter2{3,0}(9,11,8) -> 1* filter2{3,0}(10,8,11) -> 1* filter2{3,0}(10,10,11) -> 1* filter2{3,0}(9,8,10) -> 1* filter2{3,0}(9,10,10) -> 1* filter2{3,0}(8,1,1) -> 1* filter2{3,0}(10,8,8) -> 1* filter2{3,0}(8,8,9) -> 1* filter2{3,0}(10,10,8) -> 1* filter2{3,0}(8,10,9) -> 1* filter2{3,0}(11,1,11) -> 1* filter2{3,0}(1,1,11) -> 1* filter2{3,0}(8,9,1) -> 1* filter2{3,0}(10,1,10) -> 1* filter2{3,0}(8,11,1) -> 1* filter2{3,0}(11,9,11) -> 1* filter2{3,0}(11,11,11) -> 1* filter2{3,0}(1,9,11) -> 1* filter2{3,0}(11,1,8) -> 1* filter2{3,0}(9,1,9) -> 1* filter2{3,0}(1,11,11) -> 1* filter2{3,0}(1,1,8) -> 1* filter2{3,0}(10,9,10) -> 1* filter2{3,0}(10,11,10) -> 1* filter2{3,0}(11,9,8) -> 1* filter2{3,0}(9,9,9) -> 1* filter2{3,0}(11,11,8) -> 1* filter2{3,0}(1,9,8) -> 1* filter2{3,0}(9,11,9) -> 1* filter2{3,0}(1,11,8) -> 1* filter2{3,0}(9,8,1) -> 1* filter2{3,0}(9,10,1) -> 1* filter2{3,0}(11,8,10) -> 1* filter2{3,0}(11,10,10) -> 1* filter2{3,0}(1,8,10) -> 1* filter2{3,0}(10,1,1) -> 1* filter2{3,0}(1,10,10) -> 1* filter2{3,0}(10,8,9) -> 1* filter2{3,0}(10,10,9) -> 1* filter2{3,0}(8,1,11) -> 1* filter2{3,0}(10,9,1) -> 1* filter2{3,0}(10,11,1) -> 1* filter2{3,0}(8,9,11) -> 1* filter2{3,0}(11,1,9) -> 1* filter2{3,0}(8,11,11) -> 1* filter2{3,0}(8,1,8) -> 1* filter2{3,0}(1,1,9) -> 1* filter2{3,0}(11,9,9) -> 1* filter2{3,0}(8,9,8) -> 1* filter2{3,0}(11,11,9) -> 1* filter2{3,0}(1,9,9) -> 1* filter2{3,0}(8,11,8) -> 1* filter2{3,0}(1,11,9) -> 1* filter2{3,0}(11,8,1) -> 1* filter2{3,0}(11,10,1) -> 1* filter2{3,0}(1,8,1) -> 1* filter2{3,0}(1,10,1) -> 1* filter2{3,0}(9,8,11) -> 1* filter2{3,0}(9,10,11) -> 1* filter2{3,0}(8,8,10) -> 1* filter2{3,0}(8,10,10) -> 1* filter2{3,0}(9,8,8) -> 1* filter2{3,0}(9,10,8) -> 1* filter2{3,0}(10,1,11) -> 1* filter2{3,0}(9,1,10) -> 1* filter2{3,0}(10,9,11) -> 1* filter2{3,0}(10,11,11) -> 1* filter2{3,0}(10,1,8) -> 1* filter2{3,0}(8,1,9) -> 1* filter2{3,0}(9,9,10) -> 1* filter2{3,0}(9,11,10) -> 1* filter2{3,0}(10,9,8) -> 1* filter2{3,0}(8,9,9) -> 1* filter2{3,0}(10,11,8) -> 1* filter2{3,0}(8,11,9) -> 1* filter2{3,0}(8,8,1) -> 1* filter2{3,0}(8,10,1) -> 1* filter2{3,0}(11,8,11) -> 1* filter2{3,0}(1,8,11) -> 1* filter2{3,0}(11,10,11) -> 1* filter2{3,0}(1,10,11) -> 1* filter2{3,0}(10,8,10) -> 1* filter2{3,0}(10,10,10) -> 1* filter2{3,0}(9,1,1) -> 1* filter2{3,0}(11,8,8) -> 1* filter2{3,0}(9,8,9) -> 1* filter2{3,0}(11,10,8) -> 1* filter2{3,0}(1,8,8) -> 1* filter2{3,0}(9,10,9) -> 1* filter2{3,0}(1,10,8) -> 1* filter2{3,0}(9,9,1) -> 1* filter2{3,0}(11,1,10) -> 1* filter2{2,0}(8,1) -> 1* filter2{2,0}(8,9) -> 1* filter2{2,0}(8,11) -> 1* filter2{2,0}(9,8) -> 1* filter2{2,0}(9,10) -> 1* filter2{2,0}(10,1) -> 1* filter2{2,0}(10,9) -> 1* filter2{2,0}(10,11) -> 1* filter2{2,0}(11,8) -> 1* filter2{2,0}(11,10) -> 1* filter2{2,0}(1,8) -> 1* filter2{2,0}(1,10) -> 1* filter2{2,0}(8,8) -> 1* filter2{2,0}(8,10) -> 1* filter2{2,0}(9,1) -> 1* filter2{2,0}(9,9) -> 1* filter2{2,0}(9,11) -> 1* filter2{2,0}(10,8) -> 1* filter2{2,0}(10,10) -> 1* filter2{2,0}(11,1) -> 1* filter2{2,0}(1,1) -> 1* filter2{2,0}(11,9) -> 1* filter2{2,0}(11,11) -> 1* filter2{2,0}(1,9) -> 1* filter2{2,0}(1,11) -> 1* filter2{1,0}(10) -> 1* filter2{1,0}(9) -> 1* filter2{1,0}(11) -> 1* filter2{1,0}(1) -> 1* filter2{1,0}(8) -> 1* filter2{0,0}() -> 1* plus{2,#,0}(11,4) -> 2* plus{2,#,0}(7,9) -> 2* plus{2,#,0}(7,11) -> 2* plus{2,#,0}(11,9) -> 2* plus{2,#,0}(11,11) -> 2* plus{2,#,0}(7,4) -> 2* plus{2,0}(8,1) -> 1* plus{2,0}(8,3) -> 4* plus{2,0}(8,9) -> 1* plus{2,0}(8,11) -> 1* plus{2,0}(9,6) -> 7* plus{2,0}(9,8) -> 9* plus{2,0}(9,10) -> 11* plus{2,0}(10,1) -> 1* plus{2,0}(10,3) -> 4* plus{2,0}(10,9) -> 1* plus{2,0}(10,11) -> 1* plus{2,0}(11,6) -> 7* plus{2,0}(11,8) -> 9* plus{2,0}(1,6) -> 7* plus{2,0}(11,10) -> 11* plus{2,0}(1,8) -> 9* plus{2,0}(1,10) -> 11* plus{2,0}(8,6) -> 7* plus{2,0}(8,8) -> 9* plus{2,0}(8,10) -> 11* plus{2,0}(9,1) -> 1* plus{2,0}(9,3) -> 4* plus{2,0}(9,9) -> 1* plus{2,0}(9,11) -> 1* plus{2,0}(10,6) -> 7* plus{2,0}(10,8) -> 9* plus{2,0}(10,10) -> 11* plus{2,0}(11,1) -> 1* plus{2,0}(11,3) -> 4* plus{2,0}(1,1) -> 1* plus{2,0}(1,3) -> 4* plus{2,0}(11,9) -> 1* plus{2,0}(11,11) -> 1* plus{2,0}(1,9) -> 1* plus{2,0}(1,11) -> 1* s{1,0}(10) -> 10* s{1,0}(5) -> 6* s{1,0}(7) -> 7* s{1,0}(9) -> 8* s{1,0}(4) -> 4* s{1,0}(11) -> 8* s{1,0}(1) -> 11,8 s{1,0}(8) -> 10* 0{0,0}() -> 1* minus{2,0}(8,1) -> 1* minus{2,0}(8,9) -> 1* minus{2,0}(8,11) -> 1* minus{2,0}(9,8) -> 1* minus{2,0}(9,10) -> 1* minus{2,0}(10,1) -> 1* minus{2,0}(10,9) -> 1* minus{2,0}(10,11) -> 1* minus{2,0}(11,8) -> 1* minus{2,0}(11,10) -> 1* minus{2,0}(1,8) -> 1* minus{2,0}(1,10) -> 1* minus{2,0}(8,8) -> 1* minus{2,0}(8,10) -> 1* minus{2,0}(9,1) -> 1* minus{2,0}(9,9) -> 1* minus{2,0}(9,11) -> 1* minus{2,0}(10,8) -> 1* minus{2,0}(10,10) -> 1* minus{2,0}(11,1) -> 1* minus{2,0}(1,1) -> 1* minus{2,0}(11,9) -> 1* minus{2,0}(11,11) -> 1* minus{2,0}(1,9) -> 1* minus{2,0}(1,11) -> 1* quot{2,0}(8,1) -> 1* quot{2,0}(8,9) -> 1* quot{2,0}(8,11) -> 1* quot{2,0}(9,8) -> 1* quot{2,0}(9,10) -> 1* quot{2,0}(10,1) -> 1* quot{2,0}(10,9) -> 1* quot{2,0}(10,11) -> 1* quot{2,0}(11,8) -> 1* quot{2,0}(11,10) -> 1* quot{2,0}(1,8) -> 1* quot{2,0}(1,10) -> 1* quot{2,0}(8,8) -> 1* quot{2,0}(8,10) -> 1* quot{2,0}(9,1) -> 1* quot{2,0}(9,9) -> 1* quot{2,0}(9,11) -> 1* quot{2,0}(10,8) -> 1* quot{2,0}(10,10) -> 1* quot{2,0}(11,1) -> 1* quot{2,0}(1,1) -> 1* quot{2,0}(11,9) -> 1* quot{2,0}(11,11) -> 1* quot{2,0}(1,9) -> 1* quot{2,0}(1,11) -> 1* map{2,0}(8,1) -> 1* map{2,0}(8,9) -> 1* map{2,0}(8,11) -> 1* map{2,0}(9,8) -> 1* map{2,0}(9,10) -> 1* map{2,0}(10,1) -> 1* map{2,0}(10,9) -> 1* map{2,0}(10,11) -> 1* map{2,0}(11,8) -> 1* map{2,0}(11,10) -> 1* map{2,0}(1,8) -> 1* map{2,0}(1,10) -> 1* map{2,0}(8,8) -> 1* map{2,0}(8,10) -> 1* map{2,0}(9,1) -> 1* map{2,0}(9,9) -> 1* map{2,0}(9,11) -> 1* map{2,0}(10,8) -> 1* map{2,0}(10,10) -> 1* map{2,0}(11,1) -> 1* map{2,0}(1,1) -> 1* map{2,0}(11,9) -> 1* map{2,0}(11,11) -> 1* map{2,0}(1,9) -> 1* map{2,0}(1,11) -> 1* nil{0,0}() -> 1* cons{2,0}(8,1) -> 1* cons{2,0}(8,9) -> 1* cons{2,0}(8,11) -> 1* cons{2,0}(9,8) -> 1* cons{2,0}(9,10) -> 1* cons{2,0}(10,1) -> 1* cons{2,0}(10,9) -> 1* cons{2,0}(10,11) -> 1* cons{2,0}(11,8) -> 1* cons{2,0}(11,10) -> 1* cons{2,0}(1,8) -> 1* cons{2,0}(1,10) -> 1* cons{2,0}(8,8) -> 1* cons{2,0}(8,10) -> 1* cons{2,0}(9,1) -> 1* cons{2,0}(9,9) -> 1* cons{2,0}(9,11) -> 1* cons{2,0}(10,8) -> 1* cons{2,0}(10,10) -> 1* cons{2,0}(11,1) -> 1* cons{2,0}(1,1) -> 1* cons{2,0}(11,9) -> 1* cons{2,0}(11,11) -> 1* cons{2,0}(1,9) -> 1* cons{2,0}(1,11) -> 1* app0(8,1) -> 1* app0(8,9) -> 1* app0(8,11) -> 1* app0(9,8) -> 1* app0(9,10) -> 1* app0(10,1) -> 1* app0(10,9) -> 1* app0(10,11) -> 1* app0(11,8) -> 1* app0(11,10) -> 1* app0(1,8) -> 1* app0(1,10) -> 1* app0(8,8) -> 1* app0(8,10) -> 1* app0(9,1) -> 1* app0(9,9) -> 1* app0(9,11) -> 1* app0(10,8) -> 1* app0(10,10) -> 1* app0(11,1) -> 1* app0(1,1) -> 1* app0(11,9) -> 1* app0(11,11) -> 1* app0(1,9) -> 1* app0(1,11) -> 1* filter{2,0}(8,1) -> 1* filter{2,0}(8,9) -> 1* filter{2,0}(8,11) -> 1* filter{2,0}(9,8) -> 1* filter{2,0}(9,10) -> 1* filter{2,0}(10,1) -> 1* filter{2,0}(10,9) -> 1* filter{2,0}(10,11) -> 1* filter{2,0}(11,8) -> 1* filter{2,0}(11,10) -> 1* filter{2,0}(1,8) -> 1* filter{2,0}(1,10) -> 1* filter{2,0}(8,8) -> 1* filter{2,0}(8,10) -> 1* filter{2,0}(9,1) -> 1* filter{2,0}(9,9) -> 1* filter{2,0}(9,11) -> 1* filter{2,0}(10,8) -> 1* filter{2,0}(10,10) -> 1* filter{2,0}(11,1) -> 1* filter{2,0}(1,1) -> 1* filter{2,0}(11,9) -> 1* filter{2,0}(11,11) -> 1* filter{2,0}(1,9) -> 1* filter{2,0}(1,11) -> 1* filter2{4,0}(8,1,9,11) -> 1* filter2{4,0}(9,11,1,11) -> 1* filter2{4,0}(11,11,8,10) -> 1* filter2{4,0}(8,11,1,8) -> 1* filter2{4,0}(1,9,8,10) -> 1* filter2{4,0}(9,9,10,11) -> 1* filter2{4,0}(8,9,8,1) -> 1* filter2{4,0}(11,9,11,8) -> 1* filter2{4,0}(1,11,8,10) -> 1* filter2{4,0}(10,8,11,10) -> 1* filter2{4,0}(8,9,10,8) -> 1* filter2{4,0}(9,8,1,10) -> 1* filter2{4,0}(9,1,1,9) -> 1* filter2{4,0}(9,11,10,11) -> 1* filter2{4,0}(8,11,8,1) -> 1* filter2{4,0}(11,11,11,8) -> 1* filter2{4,0}(1,9,11,8) -> 1* filter2{4,0}(11,1,8,8) -> 1* filter2{4,0}(11,8,8,9) -> 1* filter2{4,0}(10,10,11,10) -> 1* filter2{4,0}(8,11,10,8) -> 1* filter2{4,0}(9,10,1,10) -> 1* filter2{4,0}(11,8,1,1) -> 1* filter2{4,0}(1,11,11,8) -> 1* filter2{4,0}(11,10,8,9) -> 1* filter2{4,0}(1,8,8,9) -> 1* filter2{4,0}(1,1,8,8) -> 1* filter2{4,0}(8,9,9,11) -> 1* filter2{4,0}(11,10,1,1) -> 1* filter2{4,0}(9,8,10,10) -> 1* filter2{4,0}(9,1,10,9) -> 1* filter2{4,0}(1,8,1,1) -> 1* filter2{4,0}(1,10,8,9) -> 1* filter2{4,0}(8,11,9,11) -> 1* filter2{4,0}(1,10,1,1) -> 1* filter2{4,0}(9,10,10,10) -> 1* filter2{4,0}(9,8,11,1) -> 1* filter2{4,0}(9,9,1,9) -> 1* filter2{4,0}(11,9,8,8) -> 1* filter2{4,0}(9,10,11,1) -> 1* filter2{4,0}(8,8,9,10) -> 1* filter2{4,0}(8,1,9,9) -> 1* filter2{4,0}(9,11,1,9) -> 1* filter2{4,0}(11,11,8,8) -> 1* filter2{4,0}(1,9,8,8) -> 1* filter2{4,0}(8,10,9,10) -> 1* filter2{4,0}(11,8,11,11) -> 1* filter2{4,0}(8,8,10,1) -> 1* filter2{4,0}(9,9,10,9) -> 1* filter2{4,0}(10,8,1,11) -> 1* filter2{4,0}(10,1,1,10) -> 1* filter2{4,0}(1,11,8,8) -> 1* filter2{4,0}(9,8,1,8) -> 1* filter2{4,0}(11,10,11,11) -> 1* filter2{4,0}(1,8,11,11) -> 1* filter2{4,0}(10,10,9,1) -> 1* filter2{4,0}(9,11,10,9) -> 1* filter2{4,0}(8,10,10,1) -> 1* filter2{4,0}(10,10,1,11) -> 1* filter2{4,0}(9,10,1,8) -> 1* filter2{4,0}(1,10,11,11) -> 1* filter2{4,0}(10,8,10,11) -> 1* filter2{4,0}(10,1,10,10) -> 1* filter2{4,0}(8,1,11,10) -> 1* filter2{4,0}(9,8,8,1) -> 1* filter2{4,0}(8,9,9,9) -> 1* filter2{4,0}(9,8,10,8) -> 1* filter2{4,0}(10,10,10,11) -> 1* filter2{4,0}(9,10,8,1) -> 1* filter2{4,0}(8,11,9,9) -> 1* filter2{4,0}(11,9,11,10) -> 1* filter2{4,0}(10,1,11,1) -> 1* filter2{4,0}(9,10,10,8) -> 1* filter2{4,0}(10,9,1,10) -> 1* filter2{4,0}(11,11,11,10) -> 1* filter2{4,0}(1,9,11,10) -> 1* filter2{4,0}(9,8,9,11) -> 1* filter2{4,0}(9,1,9,10) -> 1* filter2{4,0}(10,11,1,10) -> 1* filter2{4,0}(8,8,9,8) -> 1* filter2{4,0}(1,11,11,10) -> 1* filter2{4,0}(9,10,9,11) -> 1* filter2{4,0}(10,9,10,10) -> 1* filter2{4,0}(9,1,10,1) -> 1* filter2{4,0}(11,1,1,11) -> 1* filter2{4,0}(8,10,9,8) -> 1* filter2{4,0}(10,8,1,9) -> 1* filter2{4,0}(10,1,1,8) -> 1* filter2{4,0}(10,11,10,10) -> 1* filter2{4,0}(1,1,1,11) -> 1* filter2{4,0}(8,8,8,11) -> 1* filter2{4,0}(8,1,8,10) -> 1* filter2{4,0}(10,9,11,1) -> 1* filter2{4,0}(10,10,1,9) -> 1* filter2{4,0}(8,10,8,11) -> 1* filter2{4,0}(11,1,10,11) -> 1* filter2{4,0}(10,11,11,1) -> 1* filter2{4,0}(10,1,8,1) -> 1* filter2{4,0}(8,1,9,1) -> 1* filter2{4,0}(9,9,9,10) -> 1* filter2{4,0}(10,1,10,8) -> 1* filter2{4,0}(10,8,10,9) -> 1* filter2{4,0}(8,8,11,9) -> 1* filter2{4,0}(8,1,11,8) -> 1* filter2{4,0}(1,1,10,11) -> 1* filter2{4,0}(9,11,9,10) -> 1* filter2{4,0}(11,9,9,1) -> 1* filter2{4,0}(10,10,10,9) -> 1* filter2{4,0}(9,9,10,1) -> 1* filter2{4,0}(11,9,1,11) -> 1* filter2{4,0}(8,10,11,9) -> 1* filter2{4,0}(10,9,1,8) -> 1* filter2{4,0}(11,11,9,1) -> 1* filter2{4,0}(1,9,9,1) -> 1* filter2{4,0}(9,11,10,1) -> 1* filter2{4,0}(10,1,9,11) -> 1* filter2{4,0}(11,11,1,11) -> 1* filter2{4,0}(1,9,1,11) -> 1* filter2{4,0}(8,9,8,10) -> 1* filter2{4,0}(9,8,9,9) -> 1* filter2{4,0}(9,1,9,8) -> 1* filter2{4,0}(10,11,1,8) -> 1* filter2{4,0}(1,11,9,1) -> 1* filter2{4,0}(1,11,1,11) -> 1* filter2{4,0}(8,11,8,10) -> 1* filter2{4,0}(11,9,10,11) -> 1* filter2{4,0}(10,9,8,1) -> 1* filter2{4,0}(9,10,9,9) -> 1* filter2{4,0}(10,9,10,8) -> 1* filter2{4,0}(11,8,1,10) -> 1* filter2{4,0}(11,1,1,9) -> 1* filter2{4,0}(8,9,11,8) -> 1* filter2{4,0}(11,11,10,11) -> 1* filter2{4,0}(1,9,10,11) -> 1* filter2{4,0}(10,11,8,1) -> 1* filter2{4,0}(9,1,8,11) -> 1* filter2{4,0}(10,11,10,8) -> 1* filter2{4,0}(11,10,1,10) -> 1* filter2{4,0}(8,11,11,8) -> 1* filter2{4,0}(1,8,1,10) -> 1* filter2{4,0}(1,1,1,9) -> 1* filter2{4,0}(8,8,8,9) -> 1* filter2{4,0}(8,1,8,8) -> 1* filter2{4,0}(1,11,10,11) -> 1* filter2{4,0}(8,8,1,1) -> 1* filter2{4,0}(10,9,9,11) -> 1* filter2{4,0}(1,10,1,10) -> 1* filter2{4,0}(8,10,8,9) -> 1* filter2{4,0}(11,8,10,10) -> 1* filter2{4,0}(11,1,10,9) -> 1* filter2{4,0}(9,1,11,9) -> 1* filter2{4,0}(9,9,9,8) -> 1* filter2{4,0}(8,10,1,1) -> 1* filter2{4,0}(10,11,9,11) -> 1* filter2{4,0}(11,10,10,10) -> 1* filter2{4,0}(1,8,10,10) -> 1* filter2{4,0}(1,1,10,9) -> 1* filter2{4,0}(9,11,9,8) -> 1* filter2{4,0}(11,8,11,1) -> 1* filter2{4,0}(11,9,1,9) -> 1* filter2{4,0}(1,10,10,10) -> 1* filter2{4,0}(9,9,8,11) -> 1* filter2{4,0}(11,10,11,1) -> 1* filter2{4,0}(1,8,11,1) -> 1* filter2{4,0}(10,8,9,10) -> 1* filter2{4,0}(10,1,9,9) -> 1* filter2{4,0}(11,11,1,9) -> 1* filter2{4,0}(1,9,1,9) -> 1* filter2{4,0}(8,9,8,8) -> 1* filter2{4,0}(9,11,8,11) -> 1* filter2{4,0}(1,10,11,1) -> 1* filter2{4,0}(10,10,9,10) -> 1* filter2{4,0}(1,11,1,9) -> 1* filter2{4,0}(8,11,8,8) -> 1* filter2{4,0}(11,9,10,9) -> 1* filter2{4,0}(10,8,10,1) -> 1* filter2{4,0}(9,9,11,9) -> 1* filter2{4,0}(8,8,11,11) -> 1* filter2{4,0}(11,8,1,8) -> 1* filter2{4,0}(11,11,10,9) -> 1* filter2{4,0}(10,10,10,1) -> 1* filter2{4,0}(1,9,10,9) -> 1* filter2{4,0}(9,11,11,9) -> 1* filter2{4,0}(9,8,8,10) -> 1* filter2{4,0}(9,1,8,9) -> 1* filter2{4,0}(8,10,11,11) -> 1* filter2{4,0}(11,10,1,8) -> 1* filter2{4,0}(1,8,1,8) -> 1* filter2{4,0}(9,1,1,1) -> 1* filter2{4,0}(1,11,10,9) -> 1* filter2{4,0}(9,10,8,10) -> 1* filter2{4,0}(11,8,8,1) -> 1* filter2{4,0}(10,1,11,10) -> 1* filter2{4,0}(9,8,9,1) -> 1* filter2{4,0}(10,9,9,9) -> 1* filter2{4,0}(1,10,1,8) -> 1* filter2{4,0}(11,8,10,8) -> 1* filter2{4,0}(9,8,11,8) -> 1* filter2{4,0}(11,10,8,1) -> 1* filter2{4,0}(1,8,8,1) -> 1* filter2{4,0}(10,11,9,9) -> 1* filter2{4,0}(11,10,10,8) -> 1* filter2{4,0}(1,8,10,8) -> 1* filter2{4,0}(9,10,11,8) -> 1* filter2{4,0}(8,9,11,10) -> 1* filter2{4,0}(1,10,8,1) -> 1* filter2{4,0}(11,1,9,10) -> 1* filter2{4,0}(11,8,9,11) -> 1* filter2{4,0}(1,10,10,8) -> 1* filter2{4,0}(9,9,8,9) -> 1* filter2{4,0}(8,11,11,10) -> 1* filter2{4,0}(10,8,9,8) -> 1* filter2{4,0}(9,9,1,1) -> 1* filter2{4,0}(11,10,9,11) -> 1* filter2{4,0}(1,8,9,11) -> 1* filter2{4,0}(1,1,9,10) -> 1* filter2{4,0}(9,11,8,9) -> 1* filter2{4,0}(11,1,10,1) -> 1* filter2{4,0}(10,10,9,8) -> 1* filter2{4,0}(9,1,11,11) -> 1* filter2{4,0}(9,11,1,1) -> 1* filter2{4,0}(1,10,9,11) -> 1* filter2{4,0}(8,1,1,11) -> 1* filter2{4,0}(1,1,10,1) -> 1* filter2{4,0}(10,8,8,11) -> 1* filter2{4,0}(10,1,8,10) -> 1* filter2{4,0}(9,8,8,8) -> 1* filter2{4,0}(10,10,8,11) -> 1* filter2{4,0}(11,9,9,10) -> 1* filter2{4,0}(10,1,9,1) -> 1* filter2{4,0}(9,10,8,8) -> 1* filter2{4,0}(8,1,10,11) -> 1* filter2{4,0}(10,8,11,9) -> 1* filter2{4,0}(10,1,11,8) -> 1* filter2{4,0}(11,11,9,10) -> 1* filter2{4,0}(1,9,9,10) -> 1* filter2{4,0}(11,9,10,1) -> 1* filter2{4,0}(10,10,11,9) -> 1* filter2{4,0}(9,9,11,11) -> 1* filter2{4,0}(8,9,9,1) -> 1* filter2{4,0}(1,11,9,10) -> 1* filter2{4,0}(8,9,1,11) -> 1* filter2{4,0}(11,11,10,1) -> 1* filter2{4,0}(1,9,10,1) -> 1* filter2{4,0}(10,9,8,10) -> 1* filter2{4,0}(9,11,11,11) -> 1* filter2{4,0}(8,11,9,1) -> 1* filter2{4,0}(11,8,9,9) -> 1* filter2{4,0}(11,1,9,8) -> 1* filter2{4,0}(8,11,1,11) -> 1* filter2{4,0}(1,11,10,1) -> 1* filter2{4,0}(10,11,8,10) -> 1* filter2{4,0}(11,10,9,9) -> 1* filter2{4,0}(1,8,9,9) -> 1* filter2{4,0}(1,1,9,8) -> 1* filter2{4,0}(8,9,10,11) -> 1* filter2{4,0}(10,9,11,8) -> 1* filter2{4,0}(9,8,11,10) -> 1* filter2{4,0}(11,1,8,11) -> 1* filter2{4,0}(1,10,9,9) -> 1* filter2{4,0}(8,8,1,10) -> 1* filter2{4,0}(8,1,1,9) -> 1* filter2{4,0}(8,11,10,11) -> 1* filter2{4,0}(10,11,11,8) -> 1* filter2{4,0}(10,1,8,8) -> 1* filter2{4,0}(10,8,8,9) -> 1* filter2{4,0}(9,10,11,10) -> 1* filter2{4,0}(1,1,8,11) -> 1* filter2{4,0}(8,10,1,10) -> 1* filter2{4,0}(10,8,1,1) -> 1* filter2{4,0}(10,10,8,9) -> 1* filter2{4,0}(11,1,11,9) -> 1* filter2{4,0}(11,9,9,8) -> 1* filter2{4,0}(10,10,1,1) -> 1* filter2{4,0}(8,8,10,10) -> 1* filter2{4,0}(8,1,10,9) -> 1* filter2{4,0}(1,1,11,9) -> 1* filter2{4,0}(11,11,9,8) -> 1* filter2{4,0}(1,9,9,8) -> 1* filter2{4,0}(8,10,10,10) -> 1* filter2{4,0}(8,8,11,1) -> 1* filter2{4,0}(11,9,8,11) -> 1* filter2{4,0}(1,11,9,8) -> 1* filter2{4,0}(8,9,1,9) -> 1* filter2{4,0}(10,9,8,8) -> 1* filter2{4,0}(8,10,11,1) -> 1* filter2{4,0}(11,11,8,11) -> 1* filter2{4,0}(8,11,1,9) -> 1* filter2{4,0}(1,9,8,11) -> 1* filter2{4,0}(10,11,8,8) -> 1* filter2{4,0}(11,9,11,9) -> 1* filter2{4,0}(1,11,8,11) -> 1* filter2{4,0}(10,8,11,11) -> 1* filter2{4,0}(8,9,10,9) -> 1* filter2{4,0}(9,8,1,11) -> 1* filter2{4,0}(9,1,1,10) -> 1* filter2{4,0}(11,11,11,9) -> 1* filter2{4,0}(1,9,11,9) -> 1* filter2{4,0}(11,8,8,10) -> 1* filter2{4,0}(11,1,8,9) -> 1* filter2{4,0}(8,8,1,8) -> 1* filter2{4,0}(10,10,11,11) -> 1* filter2{4,0}(9,10,9,1) -> 1* filter2{4,0}(8,11,10,9) -> 1* filter2{4,0}(9,10,1,11) -> 1* filter2{4,0}(11,1,1,1) -> 1* filter2{4,0}(1,11,11,9) -> 1* filter2{4,0}(11,10,8,10) -> 1* filter2{4,0}(8,10,1,8) -> 1* filter2{4,0}(1,8,8,10) -> 1* filter2{4,0}(1,1,8,9) -> 1* filter2{4,0}(11,8,9,1) -> 1* filter2{4,0}(9,8,10,11) -> 1* filter2{4,0}(9,1,10,10) -> 1* filter2{4,0}(1,1,1,1) -> 1* filter2{4,0}(8,8,8,1) -> 1* filter2{4,0}(11,8,11,8) -> 1* filter2{4,0}(1,10,8,10) -> 1* filter2{4,0}(8,8,10,8) -> 1* filter2{4,0}(1,8,9,1) -> 1* filter2{4,0}(9,10,10,11) -> 1* filter2{4,0}(8,10,8,1) -> 1* filter2{4,0}(11,10,11,8) -> 1* filter2{4,0}(1,8,11,8) -> 1* filter2{4,0}(9,1,11,1) -> 1* filter2{4,0}(10,9,11,10) -> 1* filter2{4,0}(8,10,10,8) -> 1* filter2{4,0}(9,9,1,10) -> 1* filter2{4,0}(1,10,11,8) -> 1* filter2{4,0}(11,9,8,9) -> 1* filter2{4,0}(10,11,11,10) -> 1* filter2{4,0}(8,8,9,11) -> 1* filter2{4,0}(8,1,9,10) -> 1* filter2{4,0}(9,11,1,10) -> 1* filter2{4,0}(11,9,1,1) -> 1* filter2{4,0}(11,11,8,9) -> 1* filter2{4,0}(1,9,8,9) -> 1* filter2{4,0}(8,10,9,11) -> 1* filter2{4,0}(11,1,11,11) -> 1* filter2{4,0}(11,11,1,1) -> 1* filter2{4,0}(9,9,10,10) -> 1* filter2{4,0}(1,9,1,1) -> 1* filter2{4,0}(8,1,10,1) -> 1* filter2{4,0}(10,1,1,11) -> 1* filter2{4,0}(1,11,8,9) -> 1* filter2{4,0}(9,8,1,9) -> 1* filter2{4,0}(9,1,1,8) -> 1* filter2{4,0}(1,1,11,11) -> 1* filter2{4,0}(9,11,10,10) -> 1* filter2{4,0}(1,11,1,1) -> 1* filter2{4,0}(11,8,8,8) -> 1* filter2{4,0}(9,9,11,1) -> 1* filter2{4,0}(9,10,1,9) -> 1* filter2{4,0}(11,10,8,8) -> 1* filter2{4,0}(1,8,8,8) -> 1* filter2{4,0}(10,1,10,11) -> 1* filter2{4,0}(9,11,11,1) -> 1* filter2{4,0}(9,1,8,1) -> 1* filter2{4,0}(8,9,9,10) -> 1* filter2{4,0}(9,1,10,8) -> 1* filter2{4,0}(9,8,10,9) -> 1* filter2{4,0}(1,10,8,8) -> 1* filter2{4,0}(8,11,9,10) -> 1* filter2{4,0}(11,9,11,11) -> 1* filter2{4,0}(10,9,9,1) -> 1* filter2{4,0}(9,10,10,9) -> 1* filter2{4,0}(8,9,10,1) -> 1* filter2{4,0}(10,9,1,11) -> 1* filter2{4,0}(9,9,1,8) -> 1* filter2{4,0}(11,11,11,11) -> 1* filter2{4,0}(1,9,11,11) -> 1* filter2{4,0}(10,11,9,1) -> 1* filter2{4,0}(8,11,10,1) -> 1* filter2{4,0}(9,1,9,11) -> 1* filter2{4,0}(10,11,1,11) -> 1* filter2{4,0}(8,8,9,9) -> 1* filter2{4,0}(8,1,9,8) -> 1* filter2{4,0}(9,11,1,8) -> 1* filter2{4,0}(1,11,11,11) -> 1* filter2{4,0}(10,9,10,11) -> 1* filter2{4,0}(9,9,8,1) -> 1* filter2{4,0}(8,10,9,9) -> 1* filter2{4,0}(11,8,11,10) -> 1* filter2{4,0}(9,9,10,8) -> 1* filter2{4,0}(10,8,1,10) -> 1* filter2{4,0}(10,1,1,9) -> 1* filter2{4,0}(10,11,10,11) -> 1* filter2{4,0}(9,11,8,1) -> 1* filter2{4,0}(8,1,8,11) -> 1* filter2{4,0}(11,10,11,10) -> 1* filter2{4,0}(1,8,11,10) -> 1* filter2{4,0}(9,11,10,8) -> 1* filter2{4,0}(10,10,1,10) -> 1* filter2{4,0}(1,10,11,10) -> 1* filter2{4,0}(9,9,9,11) -> 1* filter2{4,0}(10,8,10,10) -> 1* filter2{4,0}(10,1,10,9) -> 1* filter2{4,0}(8,1,11,9) -> 1* filter2{4,0}(8,9,9,8) -> 1* filter2{4,0}(9,11,9,11) -> 1* filter2{4,0}(10,10,10,10) -> 1* filter2{4,0}(8,11,9,8) -> 1* filter2{4,0}(10,8,11,1) -> 1* filter2{4,0}(10,9,1,9) -> 1* filter2{4,0}(8,9,8,11) -> 1* filter2{4,0}(10,10,11,1) -> 1* filter2{4,0}(9,8,9,10) -> 1* filter2{4,0}(9,1,9,9) -> 1* filter2{4,0}(10,11,1,9) -> 1* filter2{4,0}(8,11,8,11) -> 1* filter2{4,0}(9,10,9,10) -> 1* filter2{4,0}(9,8,10,1) -> 1* filter2{4,0}(10,9,10,9) -> 1* filter2{4,0}(8,9,11,9) -> 1* filter2{4,0}(11,1,1,10) -> 1* filter2{4,0}(11,8,1,11) -> 1* filter2{4,0}(10,8,1,8) -> 1* filter2{4,0}(11,10,9,1) -> 1* filter2{4,0}(10,11,10,9) -> 1* filter2{4,0}(9,10,10,1) -> 1* filter2{4,0}(8,11,11,9) -> 1* filter2{4,0}(11,10,1,11) -> 1* filter2{4,0}(1,8,1,11) -> 1* filter2{4,0}(1,1,1,10) -> 1* filter2{4,0}(8,8,8,10) -> 1* filter2{4,0}(8,1,8,9) -> 1* filter2{4,0}(10,10,1,8) -> 1* filter2{4,0}(1,10,9,1) -> 1* filter2{4,0}(8,1,1,1) -> 1* filter2{4,0}(1,10,1,11) -> 1* filter2{4,0}(8,10,8,10) -> 1* filter2{4,0}(11,1,10,10) -> 1* filter2{4,0}(11,8,10,11) -> 1* filter2{4,0}(9,1,11,10) -> 1* filter2{4,0}(10,8,8,1) -> 1* filter2{4,0}(8,8,9,1) -> 1* filter2{4,0}(9,9,9,9) -> 1* filter2{4,0}(10,8,10,8) -> 1* filter2{4,0}(8,8,11,8) -> 1* filter2{4,0}(11,10,10,11) -> 1* filter2{4,0}(1,8,10,11) -> 1* filter2{4,0}(1,1,10,10) -> 1* filter2{4,0}(10,10,8,1) -> 1* filter2{4,0}(9,11,9,9) -> 1* filter2{4,0}(11,1,11,1) -> 1* filter2{4,0}(10,10,10,8) -> 1* filter2{4,0}(8,10,11,8) -> 1* filter2{4,0}(11,9,1,10) -> 1* filter2{4,0}(1,10,10,11) -> 1* filter2{4,0}(1,1,11,1) -> 1* filter2{4,0}(10,8,9,11) -> 1* filter2{4,0}(10,1,9,10) -> 1* filter2{4,0}(11,11,1,10) -> 1* filter2{4,0}(1,9,1,10) -> 1* filter2{4,0}(8,9,8,9) -> 1* filter2{4,0}(9,8,9,8) -> 1* filter2{4,0}(8,9,1,1) -> 1* filter2{4,0}(10,10,9,11) -> 1* filter2{4,0}(1,11,1,10) -> 1* filter2{4,0}(8,11,8,9) -> 1* filter2{4,0}(11,9,10,10) -> 1* filter2{4,0}(10,1,10,1) -> 1* filter2{4,0}(9,10,9,8) -> 1* filter2{4,0}(8,1,11,11) -> 1* filter2{4,0}(8,11,1,1) -> 1* filter2{4,0}(11,8,1,9) -> 1* filter2{4,0}(11,1,1,8) -> 1* filter2{4,0}(11,11,10,10) -> 1* filter2{4,0}(1,9,10,10) -> 1* filter2{4,0}(9,8,8,11) -> 1* filter2{4,0}(9,1,8,10) -> 1* filter2{4,0}(11,9,11,1) -> 1* filter2{4,0}(11,10,1,9) -> 1* filter2{4,0}(1,8,1,9) -> 1* filter2{4,0}(1,1,1,8) -> 1* filter2{4,0}(8,8,8,8) -> 1* filter2{4,0}(1,11,10,10) -> 1* filter2{4,0}(9,10,8,11) -> 1* filter2{4,0}(1,9,11,1) -> 1* filter2{4,0}(11,11,11,1) -> 1* filter2{4,0}(11,1,8,1) -> 1* filter2{4,0}(9,1,9,1) -> 1* filter2{4,0}(10,9,9,10) -> 1* filter2{4,0}(1,10,1,9) -> 1* filter2{4,0}(8,10,8,8) -> 1* filter2{4,0}(11,1,10,8) -> 1* filter2{4,0}(11,8,10,9) -> 1* filter2{4,0}(9,8,11,9) -> 1* filter2{4,0}(9,1,11,8) -> 1* filter2{4,0}(1,11,11,1) -> 1* filter2{4,0}(1,1,8,1) -> 1* filter2{4,0}(10,11,9,10) -> 1* filter2{4,0}(11,10,10,9) -> 1* filter2{4,0}(1,1,10,8) -> 1* filter2{4,0}(1,8,10,9) -> 1* filter2{4,0}(10,9,10,1) -> 1* filter2{4,0}(9,10,11,9) -> 1* filter2{4,0}(8,9,11,11) -> 1* filter2{4,0}(11,9,1,8) -> 1* filter2{4,0}(11,1,9,11) -> 1* filter2{4,0}(10,11,10,1) -> 1* filter2{4,0}(1,10,10,9) -> 1* filter2{4,0}(9,9,8,10) -> 1* filter2{4,0}(8,11,11,11) -> 1* filter2{4,0}(10,8,9,9) -> 1* filter2{4,0}(10,1,9,8) -> 1* filter2{4,0}(11,11,1,8) -> 1* filter2{4,0}(1,9,1,8) -> 1* filter2{4,0}(1,1,9,11) -> 1* filter2{4,0}(9,11,8,10) -> 1* filter2{4,0}(11,9,8,1) -> 1* filter2{4,0}(10,10,9,9) -> 1* filter2{4,0}(1,11,1,8) -> 1* filter2{4,0}(11,9,10,8) -> 1* filter2{4,0}(9,9,11,8) -> 1* filter2{4,0}(8,8,11,10) -> 1* filter2{4,0}(11,11,8,1) -> 1* filter2{4,0}(1,9,8,1) -> 1* filter2{4,0}(10,1,8,11) -> 1* filter2{4,0}(11,11,10,8) -> 1* filter2{4,0}(1,9,10,8) -> 1* filter2{4,0}(9,11,11,8) -> 1* filter2{4,0}(9,1,8,8) -> 1* filter2{4,0}(9,8,8,9) -> 1* filter2{4,0}(8,10,11,10) -> 1* filter2{4,0}(1,11,8,1) -> 1* filter2{4,0}(9,8,1,1) -> 1* filter2{4,0}(11,9,9,11) -> 1* filter2{4,0}(1,11,10,8) -> 1* filter2{4,0}(9,10,8,9) -> 1* filter2{4,0}(10,1,11,9) -> 1* filter2{4,0}(10,9,9,8) -> 1* filter2{4,0}(9,10,1,1) -> 1* filter2{4,0}(11,11,9,11) -> 1* filter2{4,0}(1,9,9,11) -> 1* filter2{4,0}(10,11,9,8) -> 1* filter2{4,0}(1,11,9,11) -> 1* filter2{4,0}(10,9,8,11) -> 1* filter2{4,0}(11,8,9,10) -> 1* filter2{4,0}(11,1,9,9) -> 1* filter2{4,0}(9,9,8,8) -> 1* filter2{4,0}(10,11,8,11) -> 1* filter2{4,0}(11,10,9,10) -> 1* filter2{4,0}(1,8,9,10) -> 1* filter2{4,0}(1,1,9,9) -> 1* filter2{4,0}(9,11,8,8) -> 1* filter2{4,0}(11,8,10,1) -> 1* filter2{4,0}(10,9,11,9) -> 1* filter2{4,0}(9,8,11,11) -> 1* filter2{4,0}(8,8,1,11) -> 1* filter2{4,0}(1,10,9,10) -> 1* filter2{4,0}(8,1,1,10) -> 1* filter2{4,0}(11,10,10,1) -> 1* filter2{4,0}(1,8,10,1) -> 1* filter2{4,0}(10,11,11,9) -> 1* filter2{4,0}(10,8,8,10) -> 1* filter2{4,0}(10,1,8,9) -> 1* filter2{4,0}(9,10,11,11) -> 1* filter2{4,0}(8,10,9,1) -> 1* filter2{4,0}(8,10,1,11) -> 1* filter2{4,0}(10,1,1,1) -> 1* filter2{4,0}(1,10,10,1) -> 1* filter2{4,0}(10,10,8,10) -> 1* filter2{4,0}(11,1,11,10) -> 1* filter2{4,0}(11,9,9,9) -> 1* filter2{4,0}(10,8,9,1) -> 1* filter2{4,0}(8,8,10,11) -> 1* filter2{4,0}(8,1,10,10) -> 1* filter2{4,0}(10,8,11,8) -> 1* filter2{4,0}(1,1,11,10) -> 1* filter2{4,0}(11,11,9,9) -> 1* filter2{4,0}(1,9,9,9) -> 1* filter2{4,0}(8,10,10,11) -> 1* filter2{4,0}(10,10,11,8) -> 1* filter2{4,0}(8,1,11,1) -> 1* filter2{4,0}(9,9,11,10) -> 1* filter2{4,0}(1,11,9,9) -> 1* filter2{4,0}(8,9,1,10) -> 1* filter2{4,0}(10,9,8,9) -> 1* filter2{4,0}(9,11,11,10) -> 1* filter2{4,0}(11,8,9,8) -> 1* filter2{4,0}(8,11,1,10) -> 1* filter2{4,0}(10,9,1,1) -> 1* filter2{4,0}(10,11,8,9) -> 1* filter2{4,0}(11,10,9,8) -> 1* filter2{4,0}(1,8,9,8) -> 1* filter2{4,0}(10,1,11,11) -> 1* filter2{4,0}(10,11,1,1) -> 1* filter2{4,0}(8,9,10,10) -> 1* filter2{4,0}(9,1,1,11) -> 1* filter2{4,0}(11,1,8,10) -> 1* filter2{4,0}(11,8,8,11) -> 1* filter2{4,0}(8,8,1,9) -> 1* filter2{4,0}(1,10,9,8) -> 1* filter2{4,0}(8,1,1,8) -> 1* filter2{4,0}(8,11,10,10) -> 1* filter2{4,0}(10,8,8,8) -> 1* filter2{4,0}(8,9,11,1) -> 1* filter2{4,0}(1,8,8,11) -> 1* filter2{4,0}(11,10,8,11) -> 1* filter2{4,0}(1,1,8,10) -> 1* filter2{4,0}(8,10,1,9) -> 1* filter2{4,0}(11,1,9,1) -> 1* filter2{4,0}(10,10,8,8) -> 1* filter2{4,0}(9,1,10,11) -> 1* filter2{4,0}(8,11,11,1) -> 1* filter2{4,0}(8,1,8,1) -> 1* filter2{4,0}(11,8,11,9) -> 1* filter2{4,0}(11,1,11,8) -> 1* filter2{4,0}(1,10,8,11) -> 1* filter2{4,0}(8,1,10,8) -> 1* filter2{4,0}(8,8,10,9) -> 1* filter2{4,0}(1,1,9,1) -> 1* filter2{4,0}(11,10,11,9) -> 1* filter2{4,0}(1,8,11,9) -> 1* filter2{4,0}(1,1,11,8) -> 1* filter2{4,0}(10,9,11,11) -> 1* filter2{4,0}(9,9,9,1) -> 1* filter2{4,0}(8,10,10,9) -> 1* filter2{4,0}(9,9,1,11) -> 1* filter2{4,0}(1,10,11,9) -> 1* filter2{4,0}(11,9,8,10) -> 1* filter2{4,0}(8,9,1,8) -> 1* filter2{4,0}(10,11,11,11) -> 1* filter2{4,0}(9,11,9,1) -> 1* true{0,0}() -> 1* 3 -> 4* 6 -> 7* 8 -> 9,1 9 -> 1* 10 -> 11,1 11 -> 1* problem: DPs: TRS: minus2(x,00()) -> x minus2(s1(x),s1(y)) -> minus2(x,y) quot2(00(),s1(y)) -> 00() quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y))) plus2(00(),y) -> y plus2(s1(x),y) -> s1(plus2(x,y)) plus2(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus2(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(00()))) map2(f,nil0()) -> nil0() map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs)) filter2(f,nil0()) -> nil0() filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs) filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs)) filter24(false0(),f,x,xs) -> filter2(f,xs) app(minus1(x5),x6) -> minus2(x5,x6) app(minus0(),x5) -> minus1(x5) app(s0(),x9) -> s1(x9) app(quot1(x11),x12) -> quot2(x11,x12) app(quot0(),x11) -> quot1(x11) app(plus1(x14),x15) -> plus2(x14,x15) app(plus0(),x14) -> plus1(x14) app(map1(x17),x18) -> map2(x17,x18) app(map0(),x17) -> map1(x17) app(cons1(x21),x22) -> cons2(x21,x22) app(cons0(),x21) -> cons1(x21) app(filter1(x24),x25) -> filter2(x24,x25) app(filter0(),x24) -> filter1(x24) app(filter23(x27,x28,x29),x30) -> filter24(x27,x28,x29,x30) app(filter22(x27,x28),x29) -> filter23(x27,x28,x29) app(filter21(x27),x28) -> filter22(x27,x28) app(filter20(),x27) -> filter21(x27) Qed DPs: quot{2,#}(s1(x),s1(y)) -> quot{2,#}(minus2(x,y),s1(y)) TRS: minus2(x,00()) -> x minus2(s1(x),s1(y)) -> minus2(x,y) quot2(00(),s1(y)) -> 00() quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y))) plus2(00(),y) -> y plus2(s1(x),y) -> s1(plus2(x,y)) plus2(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus2(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(00()))) map2(f,nil0()) -> nil0() map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs)) filter2(f,nil0()) -> nil0() filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs) filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs)) filter24(false0(),f,x,xs) -> filter2(f,xs) app(minus1(x5),x6) -> minus2(x5,x6) app(minus0(),x5) -> minus1(x5) app(s0(),x9) -> s1(x9) app(quot1(x11),x12) -> quot2(x11,x12) app(quot0(),x11) -> quot1(x11) app(plus1(x14),x15) -> plus2(x14,x15) app(plus0(),x14) -> plus1(x14) app(map1(x17),x18) -> map2(x17,x18) app(map0(),x17) -> map1(x17) app(cons1(x21),x22) -> cons2(x21,x22) app(cons0(),x21) -> cons1(x21) app(filter1(x24),x25) -> filter2(x24,x25) app(filter0(),x24) -> filter1(x24) app(filter23(x27,x28,x29),x30) -> filter24(x27,x28,x29,x30) app(filter22(x27,x28),x29) -> filter23(x27,x28,x29) app(filter21(x27),x28) -> filter22(x27,x28) app(filter20(),x27) -> filter21(x27) Subterm Criterion Processor: simple projection: pi(minus2) = 0 pi(quot{2,#}) = 0 problem: DPs: TRS: minus2(x,00()) -> x minus2(s1(x),s1(y)) -> minus2(x,y) quot2(00(),s1(y)) -> 00() quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y))) plus2(00(),y) -> y plus2(s1(x),y) -> s1(plus2(x,y)) plus2(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus2(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(00()))) map2(f,nil0()) -> nil0() map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs)) filter2(f,nil0()) -> nil0() filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs) filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs)) filter24(false0(),f,x,xs) -> filter2(f,xs) app(minus1(x5),x6) -> minus2(x5,x6) app(minus0(),x5) -> minus1(x5) app(s0(),x9) -> s1(x9) app(quot1(x11),x12) -> quot2(x11,x12) app(quot0(),x11) -> quot1(x11) app(plus1(x14),x15) -> plus2(x14,x15) app(plus0(),x14) -> plus1(x14) app(map1(x17),x18) -> map2(x17,x18) app(map0(),x17) -> map1(x17) app(cons1(x21),x22) -> cons2(x21,x22) app(cons0(),x21) -> cons1(x21) app(filter1(x24),x25) -> filter2(x24,x25) app(filter0(),x24) -> filter1(x24) app(filter23(x27,x28,x29),x30) -> filter24(x27,x28,x29,x30) app(filter22(x27,x28),x29) -> filter23(x27,x28,x29) app(filter21(x27),x28) -> filter22(x27,x28) app(filter20(),x27) -> filter21(x27) Qed DPs: minus{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y) TRS: minus2(x,00()) -> x minus2(s1(x),s1(y)) -> minus2(x,y) quot2(00(),s1(y)) -> 00() quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y))) plus2(00(),y) -> y plus2(s1(x),y) -> s1(plus2(x,y)) plus2(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus2(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(00()))) map2(f,nil0()) -> nil0() map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs)) filter2(f,nil0()) -> nil0() filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs) filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs)) filter24(false0(),f,x,xs) -> filter2(f,xs) app(minus1(x5),x6) -> minus2(x5,x6) app(minus0(),x5) -> minus1(x5) app(s0(),x9) -> s1(x9) app(quot1(x11),x12) -> quot2(x11,x12) app(quot0(),x11) -> quot1(x11) app(plus1(x14),x15) -> plus2(x14,x15) app(plus0(),x14) -> plus1(x14) app(map1(x17),x18) -> map2(x17,x18) app(map0(),x17) -> map1(x17) app(cons1(x21),x22) -> cons2(x21,x22) app(cons0(),x21) -> cons1(x21) app(filter1(x24),x25) -> filter2(x24,x25) app(filter0(),x24) -> filter1(x24) app(filter23(x27,x28,x29),x30) -> filter24(x27,x28,x29,x30) app(filter22(x27,x28),x29) -> filter23(x27,x28,x29) app(filter21(x27),x28) -> filter22(x27,x28) app(filter20(),x27) -> filter21(x27) Subterm Criterion Processor: simple projection: pi(minus{2,#}) = 0 problem: DPs: TRS: minus2(x,00()) -> x minus2(s1(x),s1(y)) -> minus2(x,y) quot2(00(),s1(y)) -> 00() quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y))) plus2(00(),y) -> y plus2(s1(x),y) -> s1(plus2(x,y)) plus2(minus2(x,s1(00())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(00()))) plus2(plus2(x,s1(00())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(00()))) map2(f,nil0()) -> nil0() map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs)) filter2(f,nil0()) -> nil0() filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs) filter24(true0(),f,x,xs) -> cons2(x,filter2(f,xs)) filter24(false0(),f,x,xs) -> filter2(f,xs) app(minus1(x5),x6) -> minus2(x5,x6) app(minus0(),x5) -> minus1(x5) app(s0(),x9) -> s1(x9) app(quot1(x11),x12) -> quot2(x11,x12) app(quot0(),x11) -> quot1(x11) app(plus1(x14),x15) -> plus2(x14,x15) app(plus0(),x14) -> plus1(x14) app(map1(x17),x18) -> map2(x17,x18) app(map0(),x17) -> map1(x17) app(cons1(x21),x22) -> cons2(x21,x22) app(cons0(),x21) -> cons1(x21) app(filter1(x24),x25) -> filter2(x24,x25) app(filter0(),x24) -> filter1(x24) app(filter23(x27,x28,x29),x30) -> filter24(x27,x28,x29,x30) app(filter22(x27,x28),x29) -> filter23(x27,x28,x29) app(filter21(x27),x28) -> filter22(x27,x28) app(filter20(),x27) -> filter21(x27) Qed