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SRS Standard pair #487084862
details
property
value
status
complete
benchmark
size-12-alpha-3-num-82.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n137.star.cs.uiowa.edu
space
Waldmann_07_size12
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
44.6483 seconds
cpu usage
174.617
user time
171.796
system time
2.82062
max virtual memory
1.1828588E7
max residence set size
102004.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: a(x1) -> x1 a(a(x1)) -> b(a(b(c(x1)))) b(x1) -> x1 c(b(x1)) -> a(c(x1)) Proof: DP Processor: DPs: a#(a(x1)) -> c#(x1) a#(a(x1)) -> b#(c(x1)) a#(a(x1)) -> a#(b(c(x1))) a#(a(x1)) -> b#(a(b(c(x1)))) c#(b(x1)) -> c#(x1) c#(b(x1)) -> a#(c(x1)) TRS: a(x1) -> x1 a(a(x1)) -> b(a(b(c(x1)))) b(x1) -> x1 c(b(x1)) -> a(c(x1)) TDG Processor: DPs: a#(a(x1)) -> c#(x1) a#(a(x1)) -> b#(c(x1)) a#(a(x1)) -> a#(b(c(x1))) a#(a(x1)) -> b#(a(b(c(x1)))) c#(b(x1)) -> c#(x1) c#(b(x1)) -> a#(c(x1)) TRS: a(x1) -> x1 a(a(x1)) -> b(a(b(c(x1)))) b(x1) -> x1 c(b(x1)) -> a(c(x1)) graph: c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1)) c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(a(b(c(x1)))) c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(c(x1))) c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> b#(c(x1)) c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1) a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1)) a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(a(b(c(x1)))) a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> a#(b(c(x1))) a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> b#(c(x1)) a#(a(x1)) -> a#(b(c(x1))) -> a#(a(x1)) -> c#(x1) SCC Processor: #sccs: 1 #rules: 4 #arcs: 12/36 DPs: c#(b(x1)) -> c#(x1) c#(b(x1)) -> a#(c(x1)) a#(a(x1)) -> c#(x1) a#(a(x1)) -> a#(b(c(x1))) TRS: a(x1) -> x1 a(a(x1)) -> b(a(b(c(x1)))) b(x1) -> x1 c(b(x1)) -> a(c(x1)) Arctic Interpretation Processor: dimension: 2 usable rules: a(x1) -> x1 a(a(x1)) -> b(a(b(c(x1)))) b(x1) -> x1 c(b(x1)) -> a(c(x1)) interpretation: [c#](x0) = [1 0]x0 + [0], [0 -&] [0] [c](x0) = [1 -&]x0 + [1], [a#](x0) = [0 0]x0 + [0], [0 0] [0] [a](x0) = [2 1]x0 + [2], [1 -&] [1] [b](x0) = [0 0 ]x0 + [0] orientation: c#(b(x1)) = [2 0]x1 + [2] >= [1 0]x1 + [0] = c#(x1) c#(b(x1)) = [2 0]x1 + [2] >= [1 -&]x1 + [1] = a#(c(x1)) a#(a(x1)) = [2 1]x1 + [2] >= [1 0]x1 + [0] = c#(x1) a#(a(x1)) = [2 1]x1 + [2] >= [1 -&]x1 + [1] = a#(b(c(x1))) [0 0] [0] a(x1) = [2 1]x1 + [2] >= x1 = x1 [2 1] [2] [2 -&] [2] a(a(x1)) = [3 2]x1 + [3] >= [3 -&]x1 + [3] = b(a(b(c(x1)))) [1 -&] [1] b(x1) = [0 0 ]x1 + [0] >= x1 = x1
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