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TRS Standard pair #487074037
details
property
value
status
complete
benchmark
list-sum-prod.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n187.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
0.582978 seconds
cpu usage
1.18968
user time
0.971588
system time
0.218089
max virtual memory
1658420.0
max residence set size
66516.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: +(x,0()) -> x +(0(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) *(x,0()) -> 0() *(0(),x) -> 0() *(s(x),s(y)) -> s(+(*(x,y),+(x,y))) sum(nil()) -> 0() sum(cons(x,l)) -> +(x,sum(l)) prod(nil()) -> s(0()) prod(cons(x,l)) -> *(x,prod(l)) Proof: DP Processor: DPs: +#(s(x),s(y)) -> +#(x,y) *#(s(x),s(y)) -> +#(x,y) *#(s(x),s(y)) -> *#(x,y) *#(s(x),s(y)) -> +#(*(x,y),+(x,y)) sum#(cons(x,l)) -> sum#(l) sum#(cons(x,l)) -> +#(x,sum(l)) prod#(cons(x,l)) -> prod#(l) prod#(cons(x,l)) -> *#(x,prod(l)) TRS: +(x,0()) -> x +(0(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) *(x,0()) -> 0() *(0(),x) -> 0() *(s(x),s(y)) -> s(+(*(x,y),+(x,y))) sum(nil()) -> 0() sum(cons(x,l)) -> +(x,sum(l)) prod(nil()) -> s(0()) prod(cons(x,l)) -> *(x,prod(l)) TDG Processor: DPs: +#(s(x),s(y)) -> +#(x,y) *#(s(x),s(y)) -> +#(x,y) *#(s(x),s(y)) -> *#(x,y) *#(s(x),s(y)) -> +#(*(x,y),+(x,y)) sum#(cons(x,l)) -> sum#(l) sum#(cons(x,l)) -> +#(x,sum(l)) prod#(cons(x,l)) -> prod#(l) prod#(cons(x,l)) -> *#(x,prod(l)) TRS: +(x,0()) -> x +(0(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) *(x,0()) -> 0() *(0(),x) -> 0() *(s(x),s(y)) -> s(+(*(x,y),+(x,y))) sum(nil()) -> 0() sum(cons(x,l)) -> +(x,sum(l)) prod(nil()) -> s(0()) prod(cons(x,l)) -> *(x,prod(l)) graph: prod#(cons(x,l)) -> prod#(l) -> prod#(cons(x,l)) -> *#(x,prod(l)) prod#(cons(x,l)) -> prod#(l) -> prod#(cons(x,l)) -> prod#(l) prod#(cons(x,l)) -> *#(x,prod(l)) -> *#(s(x),s(y)) -> +#(*(x,y),+(x,y)) prod#(cons(x,l)) -> *#(x,prod(l)) -> *#(s(x),s(y)) -> *#(x,y) prod#(cons(x,l)) -> *#(x,prod(l)) -> *#(s(x),s(y)) -> +#(x,y) sum#(cons(x,l)) -> sum#(l) -> sum#(cons(x,l)) -> +#(x,sum(l)) sum#(cons(x,l)) -> sum#(l) -> sum#(cons(x,l)) -> sum#(l) sum#(cons(x,l)) -> +#(x,sum(l)) -> +#(s(x),s(y)) -> +#(x,y) *#(s(x),s(y)) -> *#(x,y) -> *#(s(x),s(y)) -> +#(*(x,y),+(x,y)) *#(s(x),s(y)) -> *#(x,y) -> *#(s(x),s(y)) -> *#(x,y) *#(s(x),s(y)) -> *#(x,y) -> *#(s(x),s(y)) -> +#(x,y) *#(s(x),s(y)) -> +#(*(x,y),+(x,y)) -> +#(s(x),s(y)) -> +#(x,y) *#(s(x),s(y)) -> +#(x,y) -> +#(s(x),s(y)) -> +#(x,y) +#(s(x),s(y)) -> +#(x,y) -> +#(s(x),s(y)) -> +#(x,y) SCC Processor: #sccs: 4 #rules: 4 #arcs: 14/64 DPs: sum#(cons(x,l)) -> sum#(l) TRS: +(x,0()) -> x +(0(),x) -> x +(s(x),s(y)) -> s(s(+(x,y))) *(x,0()) -> 0() *(0(),x) -> 0() *(s(x),s(y)) -> s(+(*(x,y),+(x,y))) sum(nil()) -> 0() sum(cons(x,l)) -> +(x,sum(l)) prod(nil()) -> s(0()) prod(cons(x,l)) -> *(x,prod(l)) Subterm Criterion Processor: simple projection: pi(sum#) = 0 problem: DPs: TRS: +(x,0()) -> x +(0(),x) -> x +(s(x),s(y)) -> s(s(+(x,y)))
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