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TRS Standard pair #487069302
details
property
value
status
complete
benchmark
division.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n175.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
0.968833 seconds
cpu usage
2.62291
user time
1.9652
system time
0.657711
max virtual memory
3976800.0
max residence set size
69080.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: le(0(),Y) -> true() le(s(X),0()) -> false() le(s(X),s(Y)) -> le(X,Y) minus(0(),Y) -> 0() minus(s(X),Y) -> ifMinus(le(s(X),Y),s(X),Y) ifMinus(true(),s(X),Y) -> 0() ifMinus(false(),s(X),Y) -> s(minus(X,Y)) quot(0(),s(Y)) -> 0() quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y))) Proof: DP Processor: DPs: le#(s(X),s(Y)) -> le#(X,Y) minus#(s(X),Y) -> le#(s(X),Y) minus#(s(X),Y) -> ifMinus#(le(s(X),Y),s(X),Y) ifMinus#(false(),s(X),Y) -> minus#(X,Y) quot#(s(X),s(Y)) -> minus#(X,Y) quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y)) TRS: le(0(),Y) -> true() le(s(X),0()) -> false() le(s(X),s(Y)) -> le(X,Y) minus(0(),Y) -> 0() minus(s(X),Y) -> ifMinus(le(s(X),Y),s(X),Y) ifMinus(true(),s(X),Y) -> 0() ifMinus(false(),s(X),Y) -> s(minus(X,Y)) quot(0(),s(Y)) -> 0() quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y))) TDG Processor: DPs: le#(s(X),s(Y)) -> le#(X,Y) minus#(s(X),Y) -> le#(s(X),Y) minus#(s(X),Y) -> ifMinus#(le(s(X),Y),s(X),Y) ifMinus#(false(),s(X),Y) -> minus#(X,Y) quot#(s(X),s(Y)) -> minus#(X,Y) quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y)) TRS: le(0(),Y) -> true() le(s(X),0()) -> false() le(s(X),s(Y)) -> le(X,Y) minus(0(),Y) -> 0() minus(s(X),Y) -> ifMinus(le(s(X),Y),s(X),Y) ifMinus(true(),s(X),Y) -> 0() ifMinus(false(),s(X),Y) -> s(minus(X,Y)) quot(0(),s(Y)) -> 0() quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y))) graph: quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y)) -> quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y)) quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y)) -> quot#(s(X),s(Y)) -> minus#(X,Y) quot#(s(X),s(Y)) -> minus#(X,Y) -> minus#(s(X),Y) -> ifMinus#(le(s(X),Y),s(X),Y) quot#(s(X),s(Y)) -> minus#(X,Y) -> minus#(s(X),Y) -> le#(s(X),Y) ifMinus#(false(),s(X),Y) -> minus#(X,Y) -> minus#(s(X),Y) -> ifMinus#(le(s(X),Y),s(X),Y) ifMinus#(false(),s(X),Y) -> minus#(X,Y) -> minus#(s(X),Y) -> le#(s(X),Y) minus#(s(X),Y) -> ifMinus#(le(s(X),Y),s(X),Y) -> ifMinus#(false(),s(X),Y) -> minus#(X,Y) minus#(s(X),Y) -> le#(s(X),Y) -> le#(s(X),s(Y)) -> le#(X,Y) le#(s(X),s(Y)) -> le#(X,Y) -> le#(s(X),s(Y)) -> le#(X,Y) SCC Processor: #sccs: 3 #rules: 4 #arcs: 9/36 DPs: quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y)) TRS: le(0(),Y) -> true() le(s(X),0()) -> false() le(s(X),s(Y)) -> le(X,Y) minus(0(),Y) -> 0() minus(s(X),Y) -> ifMinus(le(s(X),Y),s(X),Y) ifMinus(true(),s(X),Y) -> 0() ifMinus(false(),s(X),Y) -> s(minus(X,Y)) quot(0(),s(Y)) -> 0() quot(s(X),s(Y)) -> s(quot(minus(X,Y),s(Y))) Usable Rule Processor: DPs: quot#(s(X),s(Y)) -> quot#(minus(X,Y),s(Y)) TRS: minus(0(),Y) -> 0() minus(s(X),Y) -> ifMinus(le(s(X),Y),s(X),Y) ifMinus(true(),s(X),Y) -> 0() ifMinus(false(),s(X),Y) -> s(minus(X,Y)) le(s(X),0()) -> false() le(s(X),s(Y)) -> le(X,Y) le(0(),Y) -> true() Arctic Interpretation Processor: dimension: 1 usable rules: minus(0(),Y) -> 0() minus(s(X),Y) -> ifMinus(le(s(X),Y),s(X),Y) ifMinus(true(),s(X),Y) -> 0()
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