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SRS Standard pair #487084766
details
property
value
status
complete
benchmark
size-12-alpha-3-num-456.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n144.star.cs.uiowa.edu
space
Waldmann_07_size12
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
44.4106 seconds
cpu usage
173.824
user time
170.703
system time
3.12099
max virtual memory
1.1834088E7
max residence set size
101932.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: a(x1) -> b(c(x1)) b(b(x1)) -> x1 b(c(c(x1))) -> c(c(a(b(x1)))) Proof: String Reversal Processor: a(x1) -> c(b(x1)) b(b(x1)) -> x1 c(c(b(x1))) -> b(a(c(c(x1)))) DP Processor: DPs: a#(x1) -> b#(x1) a#(x1) -> c#(b(x1)) c#(c(b(x1))) -> c#(x1) c#(c(b(x1))) -> c#(c(x1)) c#(c(b(x1))) -> a#(c(c(x1))) c#(c(b(x1))) -> b#(a(c(c(x1)))) TRS: a(x1) -> c(b(x1)) b(b(x1)) -> x1 c(c(b(x1))) -> b(a(c(c(x1)))) TDG Processor: DPs: a#(x1) -> b#(x1) a#(x1) -> c#(b(x1)) c#(c(b(x1))) -> c#(x1) c#(c(b(x1))) -> c#(c(x1)) c#(c(b(x1))) -> a#(c(c(x1))) c#(c(b(x1))) -> b#(a(c(c(x1)))) TRS: a(x1) -> c(b(x1)) b(b(x1)) -> x1 c(c(b(x1))) -> b(a(c(c(x1)))) graph: c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> b#(a(c(c(x1)))) c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> a#(c(c(x1))) c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(c(x1)) c#(c(b(x1))) -> c#(c(x1)) -> c#(c(b(x1))) -> c#(x1) c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> b#(a(c(c(x1)))) c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> a#(c(c(x1))) c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(c(x1)) c#(c(b(x1))) -> c#(x1) -> c#(c(b(x1))) -> c#(x1) c#(c(b(x1))) -> a#(c(c(x1))) -> a#(x1) -> c#(b(x1)) c#(c(b(x1))) -> a#(c(c(x1))) -> a#(x1) -> b#(x1) a#(x1) -> c#(b(x1)) -> c#(c(b(x1))) -> b#(a(c(c(x1)))) a#(x1) -> c#(b(x1)) -> c#(c(b(x1))) -> a#(c(c(x1))) a#(x1) -> c#(b(x1)) -> c#(c(b(x1))) -> c#(c(x1)) a#(x1) -> c#(b(x1)) -> c#(c(b(x1))) -> c#(x1) SCC Processor: #sccs: 1 #rules: 4 #arcs: 14/36 DPs: c#(c(b(x1))) -> c#(c(x1)) c#(c(b(x1))) -> c#(x1) c#(c(b(x1))) -> a#(c(c(x1))) a#(x1) -> c#(b(x1)) TRS: a(x1) -> c(b(x1)) b(b(x1)) -> x1 c(c(b(x1))) -> b(a(c(c(x1)))) Arctic Interpretation Processor: dimension: 2 usable rules: a(x1) -> c(b(x1)) b(b(x1)) -> x1 c(c(b(x1))) -> b(a(c(c(x1)))) interpretation: [-& 0 ] [0] [c](x0) = [0 -&]x0 + [1], [a#](x0) = [2 3]x0 + [3], [c#](x0) = [2 0]x0 + [0], [0 1 ] [2] [a](x0) = [-& 0 ]x0 + [1], [-& 0 ] [0] [b](x0) = [0 1 ]x0 + [2] orientation: c#(c(b(x1))) = [2 3]x1 + [4] >= [0 2]x1 + [2] = c#(c(x1)) c#(c(b(x1))) = [2 3]x1 + [4] >= [2 0]x1 + [0] = c#(x1) c#(c(b(x1))) = [2 3]x1 + [4] >= [2 3]x1 + [4] = a#(c(c(x1))) a#(x1) = [2 3]x1 + [3] >= [0 2]x1 + [2] = c#(b(x1)) [0 1 ] [2] [0 1 ] [2] a(x1) = [-& 0 ]x1 + [1] >= [-& 0 ]x1 + [1] = c(b(x1)) [0 1] [2] b(b(x1)) = [1 2]x1 + [3] >= x1 = x1 [-& 0 ] [1] [-& 0 ] [1] c(c(b(x1))) = [0 1 ]x1 + [2] >= [0 1 ]x1 + [2] = b(a(c(c(x1))))
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