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TRS Standard pair #487068872
details
property
value
status
complete
benchmark
rta1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n182.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
0.88155 seconds
cpu usage
2.27149
user time
1.74055
system time
0.530943
max virtual memory
1658308.0
max residence set size
69444.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: plus(s(s(x)),y) -> s(plus(x,s(y))) plus(x,s(s(y))) -> s(plus(s(x),y)) plus(s(0()),y) -> s(y) plus(0(),y) -> y ack(0(),y) -> s(y) ack(s(x),0()) -> ack(x,s(0())) ack(s(x),s(y)) -> ack(x,plus(y,ack(s(x),y))) Proof: DP Processor: DPs: plus#(s(s(x)),y) -> plus#(x,s(y)) plus#(x,s(s(y))) -> plus#(s(x),y) ack#(s(x),0()) -> ack#(x,s(0())) ack#(s(x),s(y)) -> ack#(s(x),y) ack#(s(x),s(y)) -> plus#(y,ack(s(x),y)) ack#(s(x),s(y)) -> ack#(x,plus(y,ack(s(x),y))) TRS: plus(s(s(x)),y) -> s(plus(x,s(y))) plus(x,s(s(y))) -> s(plus(s(x),y)) plus(s(0()),y) -> s(y) plus(0(),y) -> y ack(0(),y) -> s(y) ack(s(x),0()) -> ack(x,s(0())) ack(s(x),s(y)) -> ack(x,plus(y,ack(s(x),y))) TDG Processor: DPs: plus#(s(s(x)),y) -> plus#(x,s(y)) plus#(x,s(s(y))) -> plus#(s(x),y) ack#(s(x),0()) -> ack#(x,s(0())) ack#(s(x),s(y)) -> ack#(s(x),y) ack#(s(x),s(y)) -> plus#(y,ack(s(x),y)) ack#(s(x),s(y)) -> ack#(x,plus(y,ack(s(x),y))) TRS: plus(s(s(x)),y) -> s(plus(x,s(y))) plus(x,s(s(y))) -> s(plus(s(x),y)) plus(s(0()),y) -> s(y) plus(0(),y) -> y ack(0(),y) -> s(y) ack(s(x),0()) -> ack(x,s(0())) ack(s(x),s(y)) -> ack(x,plus(y,ack(s(x),y))) graph: ack#(s(x),0()) -> ack#(x,s(0())) -> ack#(s(x),s(y)) -> ack#(x,plus(y,ack(s(x),y))) ack#(s(x),0()) -> ack#(x,s(0())) -> ack#(s(x),s(y)) -> plus#(y,ack(s(x),y)) ack#(s(x),0()) -> ack#(x,s(0())) -> ack#(s(x),s(y)) -> ack#(s(x),y) ack#(s(x),0()) -> ack#(x,s(0())) -> ack#(s(x),0()) -> ack#(x,s(0())) ack#(s(x),s(y)) -> ack#(s(x),y) -> ack#(s(x),s(y)) -> ack#(x,plus(y,ack(s(x),y))) ack#(s(x),s(y)) -> ack#(s(x),y) -> ack#(s(x),s(y)) -> plus#(y,ack(s(x),y)) ack#(s(x),s(y)) -> ack#(s(x),y) -> ack#(s(x),s(y)) -> ack#(s(x),y) ack#(s(x),s(y)) -> ack#(s(x),y) -> ack#(s(x),0()) -> ack#(x,s(0())) ack#(s(x),s(y)) -> ack#(x,plus(y,ack(s(x),y))) -> ack#(s(x),s(y)) -> ack#(x,plus(y,ack(s(x),y))) ack#(s(x),s(y)) -> ack#(x,plus(y,ack(s(x),y))) -> ack#(s(x),s(y)) -> plus#(y,ack(s(x),y)) ack#(s(x),s(y)) -> ack#(x,plus(y,ack(s(x),y))) -> ack#(s(x),s(y)) -> ack#(s(x),y) ack#(s(x),s(y)) -> ack#(x,plus(y,ack(s(x),y))) -> ack#(s(x),0()) -> ack#(x,s(0())) ack#(s(x),s(y)) -> plus#(y,ack(s(x),y)) -> plus#(x,s(s(y))) -> plus#(s(x),y) ack#(s(x),s(y)) -> plus#(y,ack(s(x),y)) -> plus#(s(s(x)),y) -> plus#(x,s(y)) plus#(s(s(x)),y) -> plus#(x,s(y)) -> plus#(x,s(s(y))) -> plus#(s(x),y) plus#(s(s(x)),y) -> plus#(x,s(y)) -> plus#(s(s(x)),y) -> plus#(x,s(y)) plus#(x,s(s(y))) -> plus#(s(x),y) -> plus#(x,s(s(y))) -> plus#(s(x),y) plus#(x,s(s(y))) -> plus#(s(x),y) -> plus#(s(s(x)),y) -> plus#(x,s(y)) SCC Processor: #sccs: 2 #rules: 5 #arcs: 18/36 DPs: ack#(s(x),0()) -> ack#(x,s(0())) ack#(s(x),s(y)) -> ack#(s(x),y) ack#(s(x),s(y)) -> ack#(x,plus(y,ack(s(x),y))) TRS: plus(s(s(x)),y) -> s(plus(x,s(y))) plus(x,s(s(y))) -> s(plus(s(x),y)) plus(s(0()),y) -> s(y) plus(0(),y) -> y ack(0(),y) -> s(y) ack(s(x),0()) -> ack(x,s(0())) ack(s(x),s(y)) -> ack(x,plus(y,ack(s(x),y))) Subterm Criterion Processor: simple projection: pi(ack#) = 0 problem:
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