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SRS Standard pair #487084394
details
property
value
status
complete
benchmark
size-12-alpha-3-num-110.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n143.star.cs.uiowa.edu
space
Waldmann_07_size12
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
42.9588 seconds
cpu usage
190.844
user time
188.081
system time
2.76316
max virtual memory
1.0885848E7
max residence set size
101904.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: a(x1) -> x1 a(a(b(x1))) -> b(b(a(a(x1)))) c(b(x1)) -> c(a(x1)) Proof: String Reversal Processor: a(x1) -> x1 b(a(a(x1))) -> a(a(b(b(x1)))) b(c(x1)) -> a(c(x1)) DP Processor: DPs: b#(a(a(x1))) -> b#(x1) b#(a(a(x1))) -> b#(b(x1)) b#(a(a(x1))) -> a#(b(b(x1))) b#(a(a(x1))) -> a#(a(b(b(x1)))) b#(c(x1)) -> a#(c(x1)) TRS: a(x1) -> x1 b(a(a(x1))) -> a(a(b(b(x1)))) b(c(x1)) -> a(c(x1)) TDG Processor: DPs: b#(a(a(x1))) -> b#(x1) b#(a(a(x1))) -> b#(b(x1)) b#(a(a(x1))) -> a#(b(b(x1))) b#(a(a(x1))) -> a#(a(b(b(x1)))) b#(c(x1)) -> a#(c(x1)) TRS: a(x1) -> x1 b(a(a(x1))) -> a(a(b(b(x1)))) b(c(x1)) -> a(c(x1)) graph: b#(a(a(x1))) -> b#(b(x1)) -> b#(c(x1)) -> a#(c(x1)) b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(a(b(b(x1)))) b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> a#(b(b(x1))) b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> b#(b(x1)) b#(a(a(x1))) -> b#(b(x1)) -> b#(a(a(x1))) -> b#(x1) b#(a(a(x1))) -> b#(x1) -> b#(c(x1)) -> a#(c(x1)) b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(a(b(b(x1)))) b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> a#(b(b(x1))) b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(b(x1)) b#(a(a(x1))) -> b#(x1) -> b#(a(a(x1))) -> b#(x1) SCC Processor: #sccs: 1 #rules: 2 #arcs: 10/25 DPs: b#(a(a(x1))) -> b#(b(x1)) b#(a(a(x1))) -> b#(x1) TRS: a(x1) -> x1 b(a(a(x1))) -> a(a(b(b(x1)))) b(c(x1)) -> a(c(x1)) Arctic Interpretation Processor: dimension: 2 usable rules: a(x1) -> x1 b(a(a(x1))) -> a(a(b(b(x1)))) b(c(x1)) -> a(c(x1)) interpretation: [b#](x0) = [0 1]x0 + [0], [0 0 ] [0] [b](x0) = [-& 0 ]x0 + [0], [0 0] [3] [a](x0) = [1 0]x0 + [3], [0 2] [-&] [c](x0) = [2 3]x0 + [3 ] orientation: b#(a(a(x1))) = [2 2]x1 + [5] >= [0 1]x1 + [1] = b#(b(x1)) b#(a(a(x1))) = [2 2]x1 + [5] >= [0 1]x1 + [0] = b#(x1) [0 0] [3] a(x1) = [1 0]x1 + [3] >= x1 = x1 [1 1] [4] [1 1] [3] b(a(a(x1))) = [1 1]x1 + [4] >= [1 1]x1 + [4] = a(a(b(b(x1)))) [2 3] [3] [2 3] [3] b(c(x1)) = [2 3]x1 + [3] >= [2 3]x1 + [3] = a(c(x1)) problem: DPs: TRS: a(x1) -> x1 b(a(a(x1))) -> a(a(b(b(x1)))) b(c(x1)) -> a(c(x1)) Qed
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