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TRS Standard pair #487069127
details
property
value
status
complete
benchmark
jones2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n174.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
0.390086 seconds
cpu usage
0.536604
user time
0.386381
system time
0.150223
max virtual memory
96176.0
max residence set size
57988.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: f(empty(),l) -> l f(cons(x,k),l) -> g(k,l,cons(x,k)) g(a,b,c) -> f(a,cons(b,c)) Proof: Matrix Interpretation Processor: dim=1 interpretation: [f](x0, x1) = 6x0 + x1 + 1, [g](x0, x1, x2) = 7x0 + x1 + 2x2 + 2, [empty] = 0, [cons](x0, x1) = x0 + 2x1 + 1 orientation: f(empty(),l) = l + 1 >= l = l f(cons(x,k),l) = 12k + l + 6x + 7 >= 11k + l + 2x + 4 = g(k,l,cons(x,k)) g(a,b,c) = 7a + b + 2c + 2 >= 6a + b + 2c + 2 = f(a,cons(b,c)) problem: g(a,b,c) -> f(a,cons(b,c)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [f](x0, x1) = [0 0 0]x0 + [0 0 1]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [1 0 0] [1] [g](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [1 0 0]x2 + [0] [0 0 0] [0 0 0] [0 0 0] [0], [1 0 0] [1 0 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [1 0 0] orientation: [1 0 0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1 0 0] g(a,b,c) = [0 0 0]a + [0 0 0]b + [1 0 0]c + [0] >= [0 0 0]a + [0 0 0]b + [1 0 0]c = f(a,cons(b,c)) [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] problem: Qed
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