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TRS Standard pair #487072702
details
property
value
status
complete
benchmark
gen-9.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n189.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
1.85701 seconds
cpu usage
6.12265
user time
4.89341
system time
1.22924
max virtual memory
5439872.0
max residence set size
92660.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: c(c(z,y,a()),a(),a()) -> b(z,y) f(c(x,y,z)) -> c(z,f(b(y,z)),a()) b(z,b(c(a(),y,a()),f(f(x)))) -> c(c(y,a(),z),z,x) Proof: DP Processor: DPs: c#(c(z,y,a()),a(),a()) -> b#(z,y) f#(c(x,y,z)) -> b#(y,z) f#(c(x,y,z)) -> f#(b(y,z)) f#(c(x,y,z)) -> c#(z,f(b(y,z)),a()) b#(z,b(c(a(),y,a()),f(f(x)))) -> c#(y,a(),z) b#(z,b(c(a(),y,a()),f(f(x)))) -> c#(c(y,a(),z),z,x) TRS: c(c(z,y,a()),a(),a()) -> b(z,y) f(c(x,y,z)) -> c(z,f(b(y,z)),a()) b(z,b(c(a(),y,a()),f(f(x)))) -> c(c(y,a(),z),z,x) TDG Processor: DPs: c#(c(z,y,a()),a(),a()) -> b#(z,y) f#(c(x,y,z)) -> b#(y,z) f#(c(x,y,z)) -> f#(b(y,z)) f#(c(x,y,z)) -> c#(z,f(b(y,z)),a()) b#(z,b(c(a(),y,a()),f(f(x)))) -> c#(y,a(),z) b#(z,b(c(a(),y,a()),f(f(x)))) -> c#(c(y,a(),z),z,x) TRS: c(c(z,y,a()),a(),a()) -> b(z,y) f(c(x,y,z)) -> c(z,f(b(y,z)),a()) b(z,b(c(a(),y,a()),f(f(x)))) -> c(c(y,a(),z),z,x) graph: f#(c(x,y,z)) -> f#(b(y,z)) -> f#(c(x,y,z)) -> c#(z,f(b(y,z)),a()) f#(c(x,y,z)) -> f#(b(y,z)) -> f#(c(x,y,z)) -> f#(b(y,z)) f#(c(x,y,z)) -> f#(b(y,z)) -> f#(c(x,y,z)) -> b#(y,z) f#(c(x,y,z)) -> b#(y,z) -> b#(z,b(c(a(),y,a()),f(f(x)))) -> c#(c(y,a(),z),z,x) f#(c(x,y,z)) -> b#(y,z) -> b#(z,b(c(a(),y,a()),f(f(x)))) -> c#(y,a(),z) f#(c(x,y,z)) -> c#(z,f(b(y,z)),a()) -> c#(c(z,y,a()),a(),a()) -> b#(z,y) b#(z,b(c(a(),y,a()),f(f(x)))) -> c#(c(y,a(),z),z,x) -> c#(c(z,y,a()),a(),a()) -> b#(z,y) b#(z,b(c(a(),y,a()),f(f(x)))) -> c#(y,a(),z) -> c#(c(z,y,a()),a(),a()) -> b#(z,y) c#(c(z,y,a()),a(),a()) -> b#(z,y) -> b#(z,b(c(a(),y,a()),f(f(x)))) -> c#(c(y,a(),z),z,x) c#(c(z,y,a()),a(),a()) -> b#(z,y) -> b#(z,b(c(a(),y,a()),f(f(x)))) -> c#(y,a(),z) SCC Processor: #sccs: 2 #rules: 4 #arcs: 10/36 DPs: f#(c(x,y,z)) -> f#(b(y,z)) TRS: c(c(z,y,a()),a(),a()) -> b(z,y) f(c(x,y,z)) -> c(z,f(b(y,z)),a()) b(z,b(c(a(),y,a()),f(f(x)))) -> c(c(y,a(),z),z,x) Usable Rule Processor: DPs: f#(c(x,y,z)) -> f#(b(y,z)) TRS: b(z,b(c(a(),y,a()),f(f(x)))) -> c(c(y,a(),z),z,x) c(c(z,y,a()),a(),a()) -> b(z,y) Matrix Interpretation Processor: dim=3 usable rules: b(z,b(c(a(),y,a()),f(f(x)))) -> c(c(y,a(),z),z,x) c(c(z,y,a()),a(),a()) -> b(z,y) interpretation: [1 0 1] [1 0 1] [0 0 0] [1] [c](x0, x1, x2) = [1 0 0]x0 + [1 0 0]x1 + [1 0 0]x2 + [1] [0 0 0] [0 0 0] [0 0 0] [0], [1 1 1] [1] [f](x0) = [0 0 0]x0 + [1] [0 0 0] [1], [1] [a] = [0] [1], [f#](x0) = [0 1 0]x0 + [1], [1 0 1] [1 0 0] [b](x0, x1) = [1 0 0]x0 + [1 0 0]x1 [0 0 0] [0 0 0] orientation: f#(c(x,y,z)) = [1 0 0]x + [1 0 0]y + [1 0 0]z + [2] >= [1 0 0]y + [1 0 0]z + [1] = f#(b(y,z)) [1 1 1] [1 0 1] [1 0 1] [7] [0 0 0] [1 0 1] [1 0 1] [4] b(z,b(c(a(),y,a()),f(f(x)))) = [1 1 1]x + [1 0 1]y + [1 0 0]z + [7] >= [1 0 0]x + [1 0 1]y + [1 0 0]z + [4] = c(c(y,a(),z),z,x) [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 1] [4] [1 0 0] [1 0 1] c(c(z,y,a()),a(),a()) = [1 0 1]y + [1 0 1]z + [4] >= [1 0 0]y + [1 0 0]z = b(z,y) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] problem: DPs:
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