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TRS Equational pair #487092718
details
property
value
status
complete
benchmark
AC03.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n142.star.cs.uiowa.edu
space
AProVE_AC_04
run statistics
property
value
solver
NaTT v.1.6c
configuration
Default
runtime (wallclock)
0.052326 seconds
cpu usage
0.03274
user time
0.022382
system time
0.010358
max virtual memory
113188.0
max residence set size
6564.0
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: times(x,0()) -> 0() 4: times(x,s(y)) -> plus(x,times(x,y)) 5: power(x,0()) -> s(0()) 6: power(x,s(y)) -> times(x,power(x,y)) Number of strict rules: 6 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #plus(x,s(y)) -> #plus(x,y) #2: #power(x,s(y)) -> #times(x,power(x,y)) #3: #power(x,s(y)) -> #power(x,y) #4: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z) #5: #plus(x,plus(y,z)) ->= #plus(x,y) #6: #times(x,times(y,z)) ->= #times(times(x,y),z) #7: #times(x,times(y,z)) ->= #times(x,y) #8: #times(x,s(y)) -> #plus(x,times(x,y)) #9: #times(x,s(y)) -> #times(x,y) Number of SCCs: 3, DPs: 7 SCC { #3 } POLO(Sum)... succeeded. s w: x1 + 1 #power w: x2 #plus w: 0 #times w: 0 0 w: 0 times w: 0 power w: 0 plus w: 0 USABLE RULES: { } Removed DPs: #3 Number of SCCs: 2, DPs: 6 SCC { #6 #7 #9 } POLO(Sum)... POLO(max)... QLPOS... succeeded. s s: [1] p: 0 #power s: [1,2] p: 0 #plus s: {} p: 1 #times s: {1,2} p: 2 0 s: [] p: 0 times s: {1,2} p: 2 power s: 2 plus s: {1,2} p: 1 USABLE RULES: { 1..4 7 8 } Removed DPs: #7 #9 Number of SCCs: 2, DPs: 4 SCC { #6 } only weak rules. Number of SCCs: 1, DPs: 3 SCC { #1 #4 #5 } POLO(Sum)... succeeded. s w: x1 + 1 #power w: 0 #plus w: x1 + x2 #times w: 0 0 w: 16575 times w: x1 + x2 + 23676 power w: 0 plus w: x1 + x2 + 2 USABLE RULES: { 1 2 7 } Removed DPs: #1 #5 Number of SCCs: 1, DPs: 1 SCC { #4 } only weak rules. Number of SCCs: 0, DPs: 0 Next Dependency Pairs: #10: #plus(plus(x,s(y)),_1) -> #plus(s(plus(x,y)),_1) #11: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z) #12: #plus(x,plus(y,z)) ->= #plus(x,y) #13: #times(times(x,0()),_1) -> #times(0(),_1) #14: #plus(plus(x,0()),_1) -> #plus(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,s(y)),_1) -> #times(plus(x,times(x,y)),_1) Number of SCCs: 2, DPs: 8 SCC { #13 #15..17 } POLO(Sum)... POLO(max)... QLPOS... succeeded. s s: [1] p: 0 #power s: [1,2] p: 0 #plus s: {} p: 1 #times s: {1,2} p: 2 0 s: [] p: 0 times s: {1,2} p: 2 power s: 2 plus s: {1,2} p: 1 USABLE RULES: { 1..4 7 8 } Removed DPs: #13 #16 #17 Number of SCCs: 2, DPs: 5 SCC { #15 } only weak rules. Number of SCCs: 1, DPs: 4 SCC { #10..12 #14 } POLO(Sum)... succeeded. s w: 1 #power w: 0 #plus w: x1 + x2 #times w: 0
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