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TRS Standard pair #516968129
details
property
value
status
complete
benchmark
t004.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n128.star.cs.uiowa.edu
space
HirokawaMiddeldorp_04
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
1.13248991966 seconds
cpu usage
2.979971874
max memory
7.27126016E8
stage attributes
key
value
output-size
1925
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem: f(s(x)) -> s(f(f(p(s(x))))) f(0()) -> 0() p(s(x)) -> x Proof: DP Processor: DPs: f#(s(x)) -> p#(s(x)) f#(s(x)) -> f#(p(s(x))) f#(s(x)) -> f#(f(p(s(x)))) TRS: f(s(x)) -> s(f(f(p(s(x))))) f(0()) -> 0() p(s(x)) -> x TDG Processor: DPs: f#(s(x)) -> p#(s(x)) f#(s(x)) -> f#(p(s(x))) f#(s(x)) -> f#(f(p(s(x)))) TRS: f(s(x)) -> s(f(f(p(s(x))))) f(0()) -> 0() p(s(x)) -> x graph: f#(s(x)) -> f#(p(s(x))) -> f#(s(x)) -> f#(f(p(s(x)))) f#(s(x)) -> f#(p(s(x))) -> f#(s(x)) -> f#(p(s(x))) f#(s(x)) -> f#(p(s(x))) -> f#(s(x)) -> p#(s(x)) f#(s(x)) -> f#(f(p(s(x)))) -> f#(s(x)) -> f#(f(p(s(x)))) f#(s(x)) -> f#(f(p(s(x)))) -> f#(s(x)) -> f#(p(s(x))) f#(s(x)) -> f#(f(p(s(x)))) -> f#(s(x)) -> p#(s(x)) SCC Processor: #sccs: 1 #rules: 2 #arcs: 6/9 DPs: f#(s(x)) -> f#(p(s(x))) f#(s(x)) -> f#(f(p(s(x)))) TRS: f(s(x)) -> s(f(f(p(s(x))))) f(0()) -> 0() p(s(x)) -> x Arctic Interpretation Processor: dimension: 1 usable rules: f(s(x)) -> s(f(f(p(s(x))))) f(0()) -> 0() p(s(x)) -> x interpretation: [f#](x0) = x0 + 0, [f](x0) = x0 + 0, [0] = 2, [s](x0) = 1x0 + 1, [p](x0) = -1x0 + 0 orientation: f#(s(x)) = 1x + 1 >= x + 0 = f#(p(s(x))) f#(s(x)) = 1x + 1 >= x + 0 = f#(f(p(s(x)))) f(s(x)) = 1x + 1 >= 1x + 1 = s(f(f(p(s(x))))) f(0()) = 2 >= 2 = 0() p(s(x)) = x + 0 >= x = x problem: DPs: TRS: f(s(x)) -> s(f(f(p(s(x))))) f(0()) -> 0() p(s(x)) -> x Qed
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