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TRS Standard pair #487069077
details
property
value
status
complete
benchmark
gcd.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n177.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
1.32885 seconds
cpu usage
3.95382
user time
3.11576
system time
0.838058
max virtual memory
5665704.0
max residence set size
69280.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: min(x,0()) -> 0() min(0(),y) -> 0() min(s(x),s(y)) -> s(min(x,y)) max(x,0()) -> x max(0(),y) -> y max(s(x),s(y)) -> s(max(x,y)) -(x,0()) -> x -(s(x),s(y)) -> -(x,y) gcd(s(x),0()) -> s(x) gcd(0(),s(x)) -> s(x) gcd(s(x),s(y)) -> gcd(-(max(x,y),min(x,y)),s(min(x,y))) Proof: DP Processor: DPs: min#(s(x),s(y)) -> min#(x,y) max#(s(x),s(y)) -> max#(x,y) -#(s(x),s(y)) -> -#(x,y) gcd#(s(x),s(y)) -> min#(x,y) gcd#(s(x),s(y)) -> max#(x,y) gcd#(s(x),s(y)) -> -#(max(x,y),min(x,y)) gcd#(s(x),s(y)) -> gcd#(-(max(x,y),min(x,y)),s(min(x,y))) TRS: min(x,0()) -> 0() min(0(),y) -> 0() min(s(x),s(y)) -> s(min(x,y)) max(x,0()) -> x max(0(),y) -> y max(s(x),s(y)) -> s(max(x,y)) -(x,0()) -> x -(s(x),s(y)) -> -(x,y) gcd(s(x),0()) -> s(x) gcd(0(),s(x)) -> s(x) gcd(s(x),s(y)) -> gcd(-(max(x,y),min(x,y)),s(min(x,y))) TDG Processor: DPs: min#(s(x),s(y)) -> min#(x,y) max#(s(x),s(y)) -> max#(x,y) -#(s(x),s(y)) -> -#(x,y) gcd#(s(x),s(y)) -> min#(x,y) gcd#(s(x),s(y)) -> max#(x,y) gcd#(s(x),s(y)) -> -#(max(x,y),min(x,y)) gcd#(s(x),s(y)) -> gcd#(-(max(x,y),min(x,y)),s(min(x,y))) TRS: min(x,0()) -> 0() min(0(),y) -> 0() min(s(x),s(y)) -> s(min(x,y)) max(x,0()) -> x max(0(),y) -> y max(s(x),s(y)) -> s(max(x,y)) -(x,0()) -> x -(s(x),s(y)) -> -(x,y) gcd(s(x),0()) -> s(x) gcd(0(),s(x)) -> s(x) gcd(s(x),s(y)) -> gcd(-(max(x,y),min(x,y)),s(min(x,y))) graph: gcd#(s(x),s(y)) -> gcd#(-(max(x,y),min(x,y)),s(min(x,y))) -> gcd#(s(x),s(y)) -> gcd#(-(max(x,y),min(x,y)),s(min(x,y))) gcd#(s(x),s(y)) -> gcd#(-(max(x,y),min(x,y)),s(min(x,y))) -> gcd#(s(x),s(y)) -> -#(max(x,y),min(x,y)) gcd#(s(x),s(y)) -> gcd#(-(max(x,y),min(x,y)),s(min(x,y))) -> gcd#(s(x),s(y)) -> max#(x,y) gcd#(s(x),s(y)) -> gcd#(-(max(x,y),min(x,y)),s(min(x,y))) -> gcd#(s(x),s(y)) -> min#(x,y) gcd#(s(x),s(y)) -> -#(max(x,y),min(x,y)) -> -#(s(x),s(y)) -> -#(x,y) gcd#(s(x),s(y)) -> max#(x,y) -> max#(s(x),s(y)) -> max#(x,y) gcd#(s(x),s(y)) -> min#(x,y) -> min#(s(x),s(y)) -> min#(x,y) -#(s(x),s(y)) -> -#(x,y) -> -#(s(x),s(y)) -> -#(x,y) max#(s(x),s(y)) -> max#(x,y) -> max#(s(x),s(y)) -> max#(x,y) min#(s(x),s(y)) -> min#(x,y) -> min#(s(x),s(y)) -> min#(x,y) SCC Processor: #sccs: 4 #rules: 4 #arcs: 10/49 DPs: gcd#(s(x),s(y)) -> gcd#(-(max(x,y),min(x,y)),s(min(x,y))) TRS: min(x,0()) -> 0() min(0(),y) -> 0() min(s(x),s(y)) -> s(min(x,y)) max(x,0()) -> x max(0(),y) -> y max(s(x),s(y)) -> s(max(x,y)) -(x,0()) -> x -(s(x),s(y)) -> -(x,y) gcd(s(x),0()) -> s(x) gcd(0(),s(x)) -> s(x) gcd(s(x),s(y)) -> gcd(-(max(x,y),min(x,y)),s(min(x,y))) Usable Rule Processor: DPs: gcd#(s(x),s(y)) -> gcd#(-(max(x,y),min(x,y)),s(min(x,y))) TRS: min(x,0()) -> 0() min(0(),y) -> 0() min(s(x),s(y)) -> s(min(x,y)) max(x,0()) -> x
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