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TRS Standard pair #487073082
details
property
value
status
complete
benchmark
thiemann17.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n179.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
4.78096 seconds
cpu usage
11.2781
user time
9.81489
system time
1.46324
max virtual memory
5822480.0
max residence set size
97676.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y)) sum(cons(0(),x),y) -> sum(x,y) sum(nil(),y) -> y empty(nil()) -> true() empty(cons(n,x)) -> false() tail(nil()) -> nil() tail(cons(n,x)) -> x head(cons(n,x)) -> n weight(x) -> if(empty(x),empty(tail(x)),x) if(true(),b,x) -> weight_undefined_error() if(false(),b,x) -> if2(b,x) if2(true(),x) -> head(x) if2(false(),x) -> weight(sum(x,cons(0(),tail(tail(x))))) Proof: DP Processor: DPs: sum#(cons(s(n),x),cons(m,y)) -> sum#(cons(n,x),cons(s(m),y)) sum#(cons(0(),x),y) -> sum#(x,y) weight#(x) -> tail#(x) weight#(x) -> empty#(tail(x)) weight#(x) -> empty#(x) weight#(x) -> if#(empty(x),empty(tail(x)),x) if#(false(),b,x) -> if2#(b,x) if2#(true(),x) -> head#(x) if2#(false(),x) -> tail#(x) if2#(false(),x) -> tail#(tail(x)) if2#(false(),x) -> sum#(x,cons(0(),tail(tail(x)))) if2#(false(),x) -> weight#(sum(x,cons(0(),tail(tail(x))))) TRS: sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y)) sum(cons(0(),x),y) -> sum(x,y) sum(nil(),y) -> y empty(nil()) -> true() empty(cons(n,x)) -> false() tail(nil()) -> nil() tail(cons(n,x)) -> x head(cons(n,x)) -> n weight(x) -> if(empty(x),empty(tail(x)),x) if(true(),b,x) -> weight_undefined_error() if(false(),b,x) -> if2(b,x) if2(true(),x) -> head(x) if2(false(),x) -> weight(sum(x,cons(0(),tail(tail(x))))) TDG Processor: DPs: sum#(cons(s(n),x),cons(m,y)) -> sum#(cons(n,x),cons(s(m),y)) sum#(cons(0(),x),y) -> sum#(x,y) weight#(x) -> tail#(x) weight#(x) -> empty#(tail(x)) weight#(x) -> empty#(x) weight#(x) -> if#(empty(x),empty(tail(x)),x) if#(false(),b,x) -> if2#(b,x) if2#(true(),x) -> head#(x) if2#(false(),x) -> tail#(x) if2#(false(),x) -> tail#(tail(x)) if2#(false(),x) -> sum#(x,cons(0(),tail(tail(x)))) if2#(false(),x) -> weight#(sum(x,cons(0(),tail(tail(x))))) TRS: sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y)) sum(cons(0(),x),y) -> sum(x,y) sum(nil(),y) -> y empty(nil()) -> true() empty(cons(n,x)) -> false() tail(nil()) -> nil() tail(cons(n,x)) -> x head(cons(n,x)) -> n weight(x) -> if(empty(x),empty(tail(x)),x) if(true(),b,x) -> weight_undefined_error() if(false(),b,x) -> if2(b,x) if2(true(),x) -> head(x) if2(false(),x) -> weight(sum(x,cons(0(),tail(tail(x))))) graph: if2#(false(),x) -> weight#(sum(x,cons(0(),tail(tail(x))))) -> weight#(x) -> if#(empty(x),empty(tail(x)),x) if2#(false(),x) -> weight#(sum(x,cons(0(),tail(tail(x))))) -> weight#(x) -> empty#(x) if2#(false(),x) -> weight#(sum(x,cons(0(),tail(tail(x))))) -> weight#(x) -> empty#(tail(x)) if2#(false(),x) -> weight#(sum(x,cons(0(),tail(tail(x))))) -> weight#(x) -> tail#(x) if2#(false(),x) -> sum#(x,cons(0(),tail(tail(x)))) -> sum#(cons(0(),x),y) -> sum#(x,y) if2#(false(),x) -> sum#(x,cons(0(),tail(tail(x)))) -> sum#(cons(s(n),x),cons(m,y)) -> sum#(cons(n,x),cons(s(m),y)) if#(false(),b,x) -> if2#(b,x) -> if2#(false(),x) -> weight#(sum(x,cons(0(),tail(tail(x))))) if#(false(),b,x) -> if2#(b,x) -> if2#(false(),x) -> sum#(x,cons(0(),tail(tail(x)))) if#(false(),b,x) -> if2#(b,x) -> if2#(false(),x) -> tail#(tail(x)) if#(false(),b,x) -> if2#(b,x) -> if2#(false(),x) -> tail#(x) if#(false(),b,x) -> if2#(b,x) -> if2#(true(),x) -> head#(x) weight#(x) -> if#(empty(x),empty(tail(x)),x) -> if#(false(),b,x) -> if2#(b,x) sum#(cons(0(),x),y) -> sum#(x,y) -> sum#(cons(0(),x),y) -> sum#(x,y) sum#(cons(0(),x),y) -> sum#(x,y) ->
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