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SRS Standard pair #487084688
details
property
value
status
complete
benchmark
size-12-alpha-3-num-480.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
Waldmann_07_size12
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
46.1828 seconds
cpu usage
180.474
user time
177.021
system time
3.45337
max virtual memory
1.1452492E7
max residence set size
102032.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: a(a(x1)) -> a(b(b(c(x1)))) c(a(x1)) -> x1 c(b(x1)) -> a(c(x1)) Proof: DP Processor: DPs: a#(a(x1)) -> c#(x1) a#(a(x1)) -> a#(b(b(c(x1)))) c#(b(x1)) -> c#(x1) c#(b(x1)) -> a#(c(x1)) TRS: a(a(x1)) -> a(b(b(c(x1)))) c(a(x1)) -> x1 c(b(x1)) -> a(c(x1)) TDG Processor: DPs: a#(a(x1)) -> c#(x1) a#(a(x1)) -> a#(b(b(c(x1)))) c#(b(x1)) -> c#(x1) c#(b(x1)) -> a#(c(x1)) TRS: a(a(x1)) -> a(b(b(c(x1)))) c(a(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)) -> a#(b(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(b(c(x1)))) -> a#(a(x1)) -> a#(b(b(c(x1)))) a#(a(x1)) -> a#(b(b(c(x1)))) -> a#(a(x1)) -> c#(x1) EDG Processor: DPs: a#(a(x1)) -> c#(x1) a#(a(x1)) -> a#(b(b(c(x1)))) c#(b(x1)) -> c#(x1) c#(b(x1)) -> a#(c(x1)) TRS: a(a(x1)) -> a(b(b(c(x1)))) c(a(x1)) -> x1 c(b(x1)) -> a(c(x1)) graph: c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) c#(b(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1)) c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> c#(x1) c#(b(x1)) -> a#(c(x1)) -> a#(a(x1)) -> a#(b(b(c(x1)))) a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> c#(x1) a#(a(x1)) -> c#(x1) -> c#(b(x1)) -> a#(c(x1)) SCC Processor: #sccs: 1 #rules: 3 #arcs: 6/16 DPs: c#(b(x1)) -> c#(x1) c#(b(x1)) -> a#(c(x1)) a#(a(x1)) -> c#(x1) TRS: a(a(x1)) -> a(b(b(c(x1)))) c(a(x1)) -> x1 c(b(x1)) -> a(c(x1)) Arctic Interpretation Processor: dimension: 2 usable rules: a(a(x1)) -> a(b(b(c(x1)))) c(a(x1)) -> x1 c(b(x1)) -> a(c(x1)) interpretation: [c#](x0) = [0 3]x0 + [0], [-& 0 ] [0] [c](x0) = [0 -&]x0 + [0], [a#](x0) = [3 2]x0 + [0], [-& 0 ] [0] [a](x0) = [0 2 ]x0 + [3], [2 0] [3] [b](x0) = [0 0]x0 + [0] orientation: c#(b(x1)) = [3 3]x1 + [3] >= [0 3]x1 + [0] = c#(x1) c#(b(x1)) = [3 3]x1 + [3] >= [2 3]x1 + [3] = a#(c(x1)) a#(a(x1)) = [2 4]x1 + [5] >= [0 3]x1 + [0] = c#(x1) [0 2] [3] [0 2] [3] a(a(x1)) = [2 4]x1 + [5] >= [2 4]x1 + [5] = a(b(b(c(x1)))) [0 2 ] [3] c(a(x1)) = [-& 0 ]x1 + [0] >= x1 = x1 [0 0] [0] [0 -&] [0] c(b(x1)) = [2 0]x1 + [3] >= [2 0 ]x1 + [3] = a(c(x1))
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