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TRS Equational pair #487092736
details
property
value
status
complete
benchmark
AC12.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n145.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
NaTT v.1.6c
configuration
Default
runtime (wallclock)
0.069806 seconds
cpu usage
0.037336
user time
0.01863
system time
0.018706
max virtual memory
113188.0
max residence set size
6076.0
stage attributes
key
value
starexec-result
YES
output
YES Input TRS: AC symbols: f 1: f(g(f(h(x),x)),x) -> f(h(x),f(x,x)) 2: f(h(x),g(x)) -> f(g(h(x)),x) 3: f(g(h(x)),f(x,f(x,y))) -> f(g(f(h(x),y)),x) 4: f(g(g(x)),x) -> f(g(x),g(x)) Number of strict rules: 4 Direct POLO(bPol) ... removes: 1 3 h w: x1 f w: x1 + x2 + 1 g w: x1 + 1 Number of strict rules: 2 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #f(h(x),g(x)) -> #f(g(h(x)),x) #2: #f(x,f(y,z)) ->= #f(f(x,y),z) #3: #f(x,f(y,z)) ->= #f(x,y) #4: #f(g(g(x)),x) -> #f(g(x),g(x)) Number of SCCs: 1, DPs: 4 SCC { #1..4 } POLO(Sum)... succeeded. h w: x1 + 1 f w: x1 + x2 + 1 #f w: x1 + x2 g w: x1 + 20653 USABLE RULES: { 2 4 5 } Removed DPs: #3 Number of SCCs: 1, DPs: 3 SCC { #1 #2 #4 } POLO(Sum)... succeeded. h w: x1 + 20654 f w: x1 + x2 + 1 #f w: x1 + x2 g w: 0 USABLE RULES: { 2 4 5 } Removed DPs: #1 Number of SCCs: 1, DPs: 2 SCC { #2 #4 } POLO(Sum)... POLO(max)... succeeded. h w: 0 f w: max(x1, x2) #f w: max(x1, x2) g w: x1 + 1 USABLE RULES: { 2 4 5 } Removed DPs: #4 Number of SCCs: 1, DPs: 1 SCC { #2 } only weak rules. Number of SCCs: 0, DPs: 0 Next Dependency Pairs: #5: #f(f(h(x),g(x)),_1) -> #f(f(g(h(x)),x),_1) #6: #f(x,f(y,z)) ->= #f(f(x,y),z) #7: #f(x,f(y,z)) ->= #f(x,y) #8: #f(f(g(g(x)),x),_1) -> #f(f(g(x),g(x)),_1) Number of SCCs: 1, DPs: 4 SCC { #5..8 } POLO(Sum)... succeeded. h w: x1 + 1 f w: x1 + x2 + 1 #f w: x1 + x2 g w: x1 + 1424 USABLE RULES: { 2 4 5 } Removed DPs: #7 Number of SCCs: 1, DPs: 3 SCC { #5 #6 #8 } POLO(Sum)... succeeded. h w: x1 + 1 f w: x1 + x2 + 29283 #f w: x1 + x2 g w: 0 USABLE RULES: { 2 4 5 } Removed DPs: #5 Number of SCCs: 1, DPs: 2 SCC { #6 #8 } POLO(Sum)... POLO(max)... QLPOS... succeeded. h s: [] p: 1 f s: {1,2} p: 2 #f s: {1,2} p: 2 g s: 1 USABLE RULES: { 2 4 5 } Removed DPs: #8 Number of SCCs: 1, DPs: 1 SCC { #6 } only weak rules. Number of SCCs: 0, DPs: 0
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