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SRS Standard pair #487083620
details
property
value
status
complete
benchmark
size-12-alpha-3-num-494.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)
42.7626 seconds
cpu usage
167.502
user time
164.893
system time
2.60916
max virtual memory
1.1290896E7
max residence set size
102024.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: a(a(x1)) -> b(x1) b(c(x1)) -> a(x1) c(b(x1)) -> a(b(c(c(x1)))) Proof: DP Processor: DPs: a#(a(x1)) -> b#(x1) b#(c(x1)) -> a#(x1) c#(b(x1)) -> c#(x1) c#(b(x1)) -> c#(c(x1)) c#(b(x1)) -> b#(c(c(x1))) c#(b(x1)) -> a#(b(c(c(x1)))) TRS: a(a(x1)) -> b(x1) b(c(x1)) -> a(x1) c(b(x1)) -> a(b(c(c(x1)))) TDG Processor: DPs: a#(a(x1)) -> b#(x1) b#(c(x1)) -> a#(x1) c#(b(x1)) -> c#(x1) c#(b(x1)) -> c#(c(x1)) c#(b(x1)) -> b#(c(c(x1))) c#(b(x1)) -> a#(b(c(c(x1)))) TRS: a(a(x1)) -> b(x1) b(c(x1)) -> a(x1) c(b(x1)) -> a(b(c(c(x1)))) graph: c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> a#(b(c(c(x1)))) c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> b#(c(c(x1))) c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> c#(c(x1)) c#(b(x1)) -> c#(c(x1)) -> c#(b(x1)) -> c#(x1) c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(b(c(c(x1)))) c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> b#(c(c(x1))) c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(c(x1)) c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) c#(b(x1)) -> b#(c(c(x1))) -> b#(c(x1)) -> a#(x1) c#(b(x1)) -> a#(b(c(c(x1)))) -> a#(a(x1)) -> b#(x1) b#(c(x1)) -> a#(x1) -> a#(a(x1)) -> b#(x1) a#(a(x1)) -> b#(x1) -> b#(c(x1)) -> a#(x1) SCC Processor: #sccs: 2 #rules: 4 #arcs: 12/36 DPs: c#(b(x1)) -> c#(c(x1)) c#(b(x1)) -> c#(x1) TRS: a(a(x1)) -> b(x1) b(c(x1)) -> a(x1) c(b(x1)) -> a(b(c(c(x1)))) Arctic Interpretation Processor: dimension: 2 usable rules: a(a(x1)) -> b(x1) b(c(x1)) -> a(x1) c(b(x1)) -> a(b(c(c(x1)))) interpretation: [-& 0 ] [0] [b](x0) = [1 1 ]x0 + [1], [c#](x0) = [-& 0 ]x0 + [0], [-& 0 ] [0] [a](x0) = [1 0 ]x0 + [1], [0 0 ] [-&] [c](x0) = [-& 0 ]x0 + [0 ] orientation: c#(b(x1)) = [1 1]x1 + [1] >= [-& 0 ]x1 + [0] = c#(c(x1)) c#(b(x1)) = [1 1]x1 + [1] >= [-& 0 ]x1 + [0] = c#(x1) [1 0] [1] [-& 0 ] [0] a(a(x1)) = [1 1]x1 + [1] >= [1 1 ]x1 + [1] = b(x1) [-& 0 ] [0] [-& 0 ] [0] b(c(x1)) = [1 1 ]x1 + [1] >= [1 0 ]x1 + [1] = a(x1) [1 1] [1] [1 1] [1] c(b(x1)) = [1 1]x1 + [1] >= [1 1]x1 + [1] = a(b(c(c(x1)))) problem: DPs: TRS: a(a(x1)) -> b(x1) b(c(x1)) -> a(x1) c(b(x1)) -> a(b(c(c(x1)))) Qed DPs: b#(c(x1)) -> a#(x1) a#(a(x1)) -> b#(x1) TRS: a(a(x1)) -> b(x1)
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