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SRS Standard pair #487085174
details
property
value
status
complete
benchmark
size-12-alpha-3-num-294.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n149.star.cs.uiowa.edu
space
Waldmann_07_size12
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
43.4117 seconds
cpu usage
170.015
user time
167.029
system time
2.98602
max virtual memory
1.1251908E7
max residence set size
137680.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: a(x1) -> x1 a(b(b(x1))) -> b(b(a(b(c(a(x1)))))) b(c(x1)) -> x1 Proof: DP Processor: DPs: a#(b(b(x1))) -> a#(x1) a#(b(b(x1))) -> b#(c(a(x1))) a#(b(b(x1))) -> a#(b(c(a(x1)))) a#(b(b(x1))) -> b#(a(b(c(a(x1))))) a#(b(b(x1))) -> b#(b(a(b(c(a(x1)))))) TRS: a(x1) -> x1 a(b(b(x1))) -> b(b(a(b(c(a(x1)))))) b(c(x1)) -> x1 TDG Processor: DPs: a#(b(b(x1))) -> a#(x1) a#(b(b(x1))) -> b#(c(a(x1))) a#(b(b(x1))) -> a#(b(c(a(x1)))) a#(b(b(x1))) -> b#(a(b(c(a(x1))))) a#(b(b(x1))) -> b#(b(a(b(c(a(x1)))))) TRS: a(x1) -> x1 a(b(b(x1))) -> b(b(a(b(c(a(x1)))))) b(c(x1)) -> x1 graph: a#(b(b(x1))) -> a#(b(c(a(x1)))) -> a#(b(b(x1))) -> b#(b(a(b(c(a(x1)))))) a#(b(b(x1))) -> a#(b(c(a(x1)))) -> a#(b(b(x1))) -> b#(a(b(c(a(x1))))) a#(b(b(x1))) -> a#(b(c(a(x1)))) -> a#(b(b(x1))) -> a#(b(c(a(x1)))) a#(b(b(x1))) -> a#(b(c(a(x1)))) -> a#(b(b(x1))) -> b#(c(a(x1))) a#(b(b(x1))) -> a#(b(c(a(x1)))) -> a#(b(b(x1))) -> a#(x1) a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> b#(b(a(b(c(a(x1)))))) a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> b#(a(b(c(a(x1))))) a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> a#(b(c(a(x1)))) a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> b#(c(a(x1))) a#(b(b(x1))) -> a#(x1) -> a#(b(b(x1))) -> a#(x1) SCC Processor: #sccs: 1 #rules: 2 #arcs: 10/25 DPs: a#(b(b(x1))) -> a#(b(c(a(x1)))) a#(b(b(x1))) -> a#(x1) TRS: a(x1) -> x1 a(b(b(x1))) -> b(b(a(b(c(a(x1)))))) b(c(x1)) -> x1 Arctic Interpretation Processor: dimension: 2 usable rules: a(x1) -> x1 a(b(b(x1))) -> b(b(a(b(c(a(x1)))))) b(c(x1)) -> x1 interpretation: [0 0] [2] [b](x0) = [1 0]x0 + [0], [a#](x0) = [-& 2 ]x0 + [0], [0 0] [0 ] [a](x0) = [0 0]x0 + [-&], [-& -&] [0] [c](x0) = [0 0 ]x0 + [0] orientation: a#(b(b(x1))) = [3 3]x1 + [5] >= [2 2]x1 + [3] = a#(b(c(a(x1)))) a#(b(b(x1))) = [3 3]x1 + [5] >= [-& 2 ]x1 + [0] = a#(x1) [0 0] [0 ] a(x1) = [0 0]x1 + [-&] >= x1 = x1 [1 1] [3] [1 1] [3] a(b(b(x1))) = [1 1]x1 + [3] >= [1 1]x1 + [3] = b(b(a(b(c(a(x1)))))) [0 0] [2] b(c(x1)) = [0 0]x1 + [1] >= x1 = x1 problem: DPs: TRS: a(x1) -> x1 a(b(b(x1))) -> b(b(a(b(c(a(x1)))))) b(c(x1)) -> x1 Qed
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