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TRS Standard pair #487068607
details
property
value
status
complete
benchmark
z04.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n073.star.cs.uiowa.edu
space
Zantema_05
run statistics
property
value
solver
ttt2-1.20
configuration
ttt2
runtime (wallclock)
0.428632 seconds
cpu usage
0.674004
user time
0.50256
system time
0.171444
max virtual memory
96176.0
max residence set size
59536.0
stage attributes
key
value
starexec-result
YES
output
YES Problem: a(f(),a(f(),x)) -> a(x,x) a(h(),x) -> a(f(),a(g(),a(f(),x))) Proof: Extended Uncurrying Processor: application symbol: a symbol table: g ==> g0/0 g1/1 h ==> h0/0 h1/1 f ==> f0/0 f1/1 uncurry-rules: a(f0(),x1) -> f1(x1) a(h0(),x3) -> h1(x3) a(g0(),x5) -> g1(x5) eta-rules: problem: f1(f1(x)) -> a(x,x) h1(x) -> f1(g1(f1(x))) a(f0(),x1) -> f1(x1) a(h0(),x3) -> h1(x3) a(g0(),x5) -> g1(x5) Matrix Interpretation Processor: dim=3 interpretation: [1] [f0] = [0] [1], [1] [g0] = [0] [1], [1 0 1] [1 1 1] [a](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [1 0 0] [1 1 1] , [1 0 1] [f1](x0) = [0 0 0]x0 [1 1 1] , [1 0 1] [h1](x0) = [0 0 0]x0 [1 1 1] , [1 1 0] [g1](x0) = [0 0 0]x0 [0 1 0] , [0] [h0] = [0] [1] orientation: [2 1 2] [2 1 2] f1(f1(x)) = [0 0 0]x >= [0 0 0]x = a(x,x) [2 1 2] [2 1 1] [1 0 1] [1 0 1] h1(x) = [0 0 0]x >= [0 0 0]x = f1(g1(f1(x))) [1 1 1] [1 0 1] [1 1 1] [2] [1 0 1] a(f0(),x1) = [0 0 0]x1 + [0] >= [0 0 0]x1 = f1(x1) [1 1 1] [1] [1 1 1] [1 1 1] [1] [1 0 1] a(h0(),x3) = [0 0 0]x3 + [0] >= [0 0 0]x3 = h1(x3) [1 1 1] [0] [1 1 1] [1 1 1] [2] [1 1 0] a(g0(),x5) = [0 0 0]x5 + [0] >= [0 0 0]x5 = g1(x5) [1 1 1] [1] [0 1 0] problem: f1(f1(x)) -> a(x,x) h1(x) -> f1(g1(f1(x))) Matrix Interpretation Processor: dim=1 interpretation: [a](x0, x1) = x0 + 2x1, [f1](x0) = 2x0 + 1, [h1](x0) = 4x0 + 5, [g1](x0) = x0 + 1 orientation: f1(f1(x)) = 4x + 3 >= 3x = a(x,x) h1(x) = 4x + 5 >= 4x + 5 = f1(g1(f1(x))) problem: h1(x) -> f1(g1(f1(x))) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [f1](x0) = [0 0 0]x0
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