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TRS Equational pair #487092763
details
property
value
status
complete
benchmark
AC26.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)
0.0717469 seconds
cpu usage
0.048829
user time
0.029024
system time
0.019805
max virtual memory
113188.0
max residence set size
9272.0
stage attributes
key
value
starexec-result
YES
output
YES Input TRS: AC symbols: plus times 1: plus(x,0()) -> x 2: plus(x,s(y)) -> s(plus(x,y)) 3: plus(x,plus(s(y),z)) -> plus(s(plus(x,y)),z) 4: times(x,0()) -> 0() 5: times(x,times(0(),z)) -> times(0(),z) 6: times(x,s(y)) -> plus(times(x,y),x) 7: times(x,times(s(y),z)) -> times(plus(times(x,y),x),z) Number of strict rules: 7 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #plus(x,s(y)) -> #plus(x,y) #2: #times(x,s(y)) -> #plus(times(x,y),x) #3: #times(x,s(y)) -> #times(x,y) #4: #times(x,times(y,z)) ->= #times(times(x,y),z) #5: #times(x,times(y,z)) ->= #times(x,y) #6: #times(x,times(s(y),z)) -> #times(plus(times(x,y),x),z) #7: #times(x,times(s(y),z)) -> #plus(times(x,y),x) #8: #times(x,times(s(y),z)) -> #times(x,y) #9: #plus(x,plus(s(y),z)) -> #plus(s(plus(x,y)),z) #10: #plus(x,plus(s(y),z)) -> #plus(x,y) #11: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z) #12: #plus(x,plus(y,z)) ->= #plus(x,y) Number of SCCs: 2, DPs: 10 SCC { #1 #9..12 } POLO(Sum)... succeeded. s w: x1 + 1 #plus w: x1 + x2 #times w: 0 0 w: 21277 times w: 0 plus w: x1 + x2 + 7720 USABLE RULES: { 1..3 8 } Removed DPs: #1 #10 #12 Number of SCCs: 2, DPs: 7 SCC { #9 #11 } POLO(Sum)... succeeded. s w: 40651 #plus w: x1 + x2 #times w: 0 0 w: 21277 times w: 0 plus w: x1 + x2 + 7720 USABLE RULES: { 1..3 8 } Removed DPs: #9 Number of SCCs: 2, DPs: 6 SCC { #11 } only weak rules. Number of SCCs: 1, DPs: 5 SCC { #3..6 #8 } POLO(Sum)... POLO(max)... QLPOS... succeeded. s s: [1] p: 0 #plus s: {} p: 1 #times s: {1,2} p: 2 0 s: [] p: 0 times s: {1,2} p: 2 plus s: {1,2} p: 1 USABLE RULES: { 1..9 } Removed DPs: #3 #5 #6 #8 Number of SCCs: 1, DPs: 1 SCC { #4 } only weak rules. Number of SCCs: 0, DPs: 0 Next Dependency Pairs: #13: #plus(plus(x,s(y)),_1) -> #plus(s(plus(x,y)),_1) #14: #times(times(x,s(y)),_1) -> #times(plus(times(x,y),x),_1) #15: #times(x,times(y,z)) ->= #times(times(x,y),z) #16: #times(x,times(y,z)) ->= #times(x,y) #17: #times(times(x,times(s(y),z)),_1) -> #times(times(plus(times(x,y),x),z),_1) #18: #times(times(x,times(0(),z)),_1) -> #times(times(0(),z),_1) #19: #plus(plus(x,plus(s(y),z)),_1) -> #plus(plus(s(plus(x,y)),z),_1) #20: #plus(plus(x,0()),_1) -> #plus(x,_1) #21: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z) #22: #plus(x,plus(y,z)) ->= #plus(x,y) #23: #times(times(x,0()),_1) -> #times(0(),_1) Number of SCCs: 2, DPs: 11 SCC { #14..18 #23 } POLO(Sum)... POLO(max)... QLPOS... succeeded. s s: [1] p: 0 #plus s: {} p: 1 #times s: {1,2} p: 2 0 s: [] p: 0 times s: {1,2} p: 2 plus s: {1,2} p: 1 USABLE RULES: { 1..9 } Removed DPs: #14 #16..18 #23 Number of SCCs: 2, DPs: 6 SCC { #15 } only weak rules. Number of SCCs: 1, DPs: 5 SCC { #13 #19..22 } POLO(Sum)... succeeded. s w: 24867 #plus w: x1 + x2 #times w: 0 0 w: 46824 times w: 46823
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